relating mechanical properties of dry and …
TRANSCRIPT
The Pennsylvania State University
The Graduate School
College of Engineering
RELATING MECHANICAL PROPERTIES OF DRY AND
GRANULATED PHARMACEUTICAL POWDER
FORMULATIONS WITH TABLET QUALITY
PARAMETERS
A Dissertation in
Agricultural and Biological Engineering
by
Anuranjan Pandeya
© 2009 Anuranjan Pandeya
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Doctor of Philosophy
August 2009
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The dissertation of Anuranjan Pandeya was reviewed and approved* by the following: Virendra M. Puri Graduate Officer for the Department of Agricultural and Biological Engineering Distinguished Professor of Agricultural and Biological Engineering Dissertation Adviser Chair of Committee Jeffrey M. Catchmark Associate Professor of Agricultural and Biological Engineering Mian C. Wang Professor of Civil Engineering Durland L. Shumway Assistant Professor of Statistics *Signatures are on file in the Graduate School.
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Abstract
Mechanical properties of powders are very important to understand various unit
operations such as storage, flow, granulation, compaction, and mixing. Pharmaceutical
tablets are formed by compressing powder formulations consisting of ingredients such as
filler, binder, lubricant, disintegrant, and active pharmaceutical ingredient (API). These
powder formulations are sometimes granulated to improve flow and compression
property as well as to prevent segregation of ingredients specially the API. Tablet quality
is important for industries involved in compaction such as pharmaceutical, food, ceramic,
and cosmetic. The important tablet’s mechanical quality parameters include hardness,
strength, and friability. These are important with respect to tablets’ handling,
performance during operations such as packaging and transportation. If the tablet quality
can be predicted based upon the fundamental mechanical property of the powder prior to
its manufacture, powder industries will save significant amount of time and money.
Binder plays an important role in the tablet quality; therefore, there is a definite need to
understand and evaluate its effect. Therefore, the goal of the research was to predict the
tablet quality based on the mechanical behavior of the powder formulations prior to
manufacturing of the tablet with an emphasis on the effect of binder.
The formulations used for the research were composed of Avicel (filler),
Methocel (binder), Magnesium stearate (lubricant), Ac-Di-Sol (disintegrant), and
Acetaminophen (active pharmaceutical ingredient). Three different levels of methocel
(binder): 0 (none), 5, and 10%, were used in powder formulation. The proportion of other
four ingredients were maintained at same level, i.e., Avicel: Acetaminophen: Ac-Di-Sol:
Magnesium stearate:: 0.90:0.05:0.03:0.02. Hydrostatic triaxial compression (HTC) and
conventional triaxial compression (CTC) tests were conducted using a cubical triaxial
tester (CTT) for both dry blended and wet granulated formulations at different binder
contents. Modified Cam-clay constitutive equation parameters such as bulk modulus,
shear modulus, compression index, spring-back index, shear modulus, and failure
strength were determined using data obtained from HTC and CTC tests. Tablets at binder
contents of 5 and 10% and without binder were formed at 70 and 90 MPa. Diametral
strength, axial penetration strength, indentation hardness, and friability tests were
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conducted to quantify the tablets’ quality parameters. Relationships between the
mechanical properties of dry blended and granulated pharmaceutical powder
formulations and tablet quality parameters were developed.
For dry blended formulations, at 10 MPa/min loading rate, the bulk modulus
increased with increase in the isotropic pressure and binder content in all cases. At 20
MPa/min, the bulk modulus was maximum at 0% binder followed by those at 10 and 5%
binder content. Increase in bulk modulus with increase in the binder content was also
observed for granulated formulations at both loading rates of 10 and 20 MPa/min.
In case of dry formulations, the compression index value increased with pressure;
whereas, for granulated formulations, at 10 MPa/min loading rate, the compression index
values at 10% binder content increased with pressure. At 5% binder, the compression
index decreased and then increased. At 20 MPa/min loading rate, the compression index
decreased and then increased for both binder contents.
In all cases, the spring-back index value increased with pressure. In case of dry
blended formulations at 10 MPa/min loading rate, the spring-back index value decreased
with binder content. At 20 MPa/min, the spring-back index value for dry powder
formulations was lowest at 0% binder content followed by 10 and 5% binder contents. In
case of granulated formulations, at both loading rates, the spring back index for 10%
binder content was higher than for 5% binder content.
The shear modulus increased with increase in the confining pressure in all cases
including dry and granulated formulations. In case of 20 MPa/min loading rate also, the
shear modulus increased with increase in the confining pressure in all cases.
Various tablet quality parameters such as diametral strength, axial penetration
strength, indentation hardness, and friability were evaluated. Diametral strength, axial
penetration strength, and indentation hardness, values were higher at 90 MPa than at 70
MPa compression pressure for all binder contents. These parameters increased upto 5%
binder content; thereafter, very little or no change was observed when binder content
increased from 5 to 10%. This shows that increase in binder after 5% only had marginal
effect on tablet quality parameters. Furthermore, binder content of around 5% appears to
be optimum for tablet formation for ingredient and proportions used in this study. In case
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of granulated formulations, the values increased slightly when binder changed from 5 to
10%. Friability of tablets was higher for tablets formed at 70 MPa compared to those
formed at 90 MPa compression pressure for all binder contents for both dry and
granulated formulations. The friability decreased with binder content upto 5%; thereafter,
it increased when binder content increased from 5 to 10% for dry blended formulation. In
case of granulated formulations, the friability decreased when binder content increased
from 5 to 10%. The friability for granulated formulations was less than for dry blended
formulations.
Statistical relations were developed between tablets’ quality parameters and the
powder mechanical properties at different binder contents and loading conditions. The
regression equations between each tablet quality and powder property having r2 value
more than 0.8 were selected for prediction. For dry formulations, spring-back index and
compression index were found most suitable for predicting diametral strength,
indentation hardness, and friability. In case of axial penetration strength, compression
index, spring-back index, and shear modulus at higher loading rate had good relation (r2 >
0.8) for tablets formed at 90 MPa. For tablets formed using granulated formulations,
compression index, spring-back index, and bulk modulus were found most suitable for
predicting diametral strength, axial penetration strength, indentation hardness, and
friability. An elastic energy-based approach was successfully used to explain the
relationship of tablet quality parameters with spring-back index.
Bulk modulus values increased and spring-back index values decreased with
binder content for dry formulations at 10 MPa/min loading rate. Bulk modulus increased
with binder content at 10 MPa/min while decreased at 20 MPa/min loading rate for
granulated formulations. Spring-back index increased with binder content for granulated
formulations. All tablet quality parameters changed upto 5% binder content; thereafter,
only marginal effect was observed. For granulated formulations, tablet quality parameters
were only marginally different from each other at 5% and 10% binder contents.
In summary, the mechanical properties of dry and granulated pharmaceutical
powder formulations at different loading conditions and binder contents were determined.
Tablets were formed using the same formulations and quality parameters were quantified.
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Statistical relationships were successfully developed between powder property
and tablet quality. Based on the results it can be stated that the powders’ fundamental
mechanical properties can be used to predict the quality of the tablet.
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TABLE OF CONTENTS LIST OF FIGURES....................................................................................................... xiii LIST OF TABLES…..................................................................................................... xx ACKNOWLEDGEMENTS......................................................................................... xxiv 1. CHAPTER – INTRODUCTION ............................................................................1 2. CHAPTER – LITERATURE REVIEW…….......................................................... 4 2.1. General Theory and Concept ……..........................................................................4 2.1.1 Powder Characteristics……................................................................................4 2.1.2 Mechanical Behavior (Stress-Strain Behavior) of Materials...............................5 2.1.3 General Statement of Constitutive Law.............................................................. 5 2.1.4 Steps in Developing a Constitutive Law............................................................. 6 2.2 Constitutive Models................................................................................................. 7 2.2.1 Linear Elastic Model (First-Order Cauchy Elastic Model) ................................ 7 2.2.2 Critical State Model............................................................................................ 7 2.2.3 Cam-clay Model................................................................................................. 8 2.2.4 Modified Cam-clay Model.................................................................................. 10 2.2.5 Model Parameters............................................................................................... 11 2.3 Densification Process.............................................................................................. 11 2.3.1 Rearrangement of Particles................................................................................. 11 2.3.2 Elastic Deformation of Particles......................................................................... 12 2.3.3 Plastic Deformation of Particles......................................................................... 12 2.3.4 Bulk Compression............................................................................................... 12 2.4 Creep Behavior…………………………………………………………………… 12 2.5 Constitutive Model Parameters………………………………………………….... 13 2.6 Instruments for Constitutive Model Parameters Determination………………….. 13 2.6.1 Uniaxial Testers……………………………………………………………….. 13 2.6.2 Two-Dimensional Testers……………………………………………………... 14 2.6.3 Triaxial Testers………………………………………………………………... 14 2.6.3.1 Conventional Triaxial Tester………………………………………………. 14 2.6.3.2 Cubical Triaxial Tester (CTT)……………………………………………... 14 2.7 Hydrostatic Triaxial Compression (HTC) Test…………………………………… 15 2.8 Conventional Triaxial Compression (CTC) Test…………………………………. 16 2.9 Determination of the Constitutive Model Parameters……………………………. 16 2.10 Tablet Quality………………………………………………………………….... 18 2.11 Factors Affecting Compression and Tablet Quality…………………………...... 19 2.11.1 Particle Size Distribution and Grading………………………………………. 19 2.11.2 Particle Shape………………………………………………………………... 19 2.11.3 Bulk and Tap Density………………………………………………………... 19 2.11.4 Moisture Content ……………………………………………………………. 19 2.11.5 Binders……………………………………………………………………….. 19
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2.11.6 Plasticizers…………………………………………………………………… 20 2.11.7 Lubricants……………………………………………………………………. 20 2.12 Tablet Quality Parameters………………………………………………………. 20 2.13 Effect of Compression Rate on Tablet Quality…………………………………. 20 2.14 Effect of Deposition Method on Tablet Quality………………………………… 21 2.15 Effect of Powder Constituent on Tablet Quality………………………………… 21 2.16 Determination of Tablet Quality………………………………………………… 22 2.16.1 Tensile Strength……………………………………………………………… 22 2.16.2 Hardness……………………………………………………………………… 22 2.16.3 Friability……………………………………………………………………… 23 2.17 Granulation……………………………………………………………………… 23 2.17.1 Purpose of Granulation………………………………………………………. 23 2.17.2 Methods of Granulation……………………………………………………… 24 2.17.2.1 Dry Method……………………………………………………………….. 24 2.17.2.2 Wet Method………………………………………………………………. 24 2.17.3 Granulation Process………………………………………………………….. 24 2.17.3.1 Wetting, Nucleation, and Binder Distribution…………………………… 25 2.17.3.2 Consolidation and Growth…………………………………………………25 2.17.3.3 Attrition and Breakage……………………………………………………. 25 2.17.4 Wet Granulators……………………………………………………………… 25 2.17.4.1 Shear Granulator………………………………………………………….. 26 2.17.4.2 High-Speed Mixer/Granulators…………………………………………… 26 2.17.4.3 Fluidized Bed Granulators…………………………………………………26 2.17.4.4 Spray Driers………………………………………………………………. 27 2.17.5 Effect of Process Parameters on Granulation…………………………………27 2.18 State of the Art Related to Mechanical Properties and Tablet Quality………….. 28 3. CHAPTER – GOAL AND OBJECTIVES……………………………………….. 30 3.1 Goal……………………………………………………………………………….. 30 3.2 Objectives………………………………………………………………………… 30 4. CHAPTER – METHODOLOGY…………………………………………………. 31 4.1 Materials…………………………………………………………………………. 31 4.1.1 Avicel………………………………………………………………………….. 31 4.1.2 Acetaminophen……………………………………………………………….. 32 4.1.3 Ac-Di-Sol……………………………………………………………………... 33 4.1.4 Magnesium Stearate…………………………………………………………... 34 4.1.5 Methocel (hydroxy propyl methyl cellulose)………………………………….. 34 4.1.6 Granules with 5% Binder……………………………………………………… 35 4.1.7 Granules with 10% Binder……………………………………………………. 36 4.2 Laboratory Description…………………………………………………………… 36 4.3 Experimental Designs…………………………………………………………….. 36 4.3.1 HTC and CTC Tests…..………………………………………………………. 36
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4.3.2 Formation of the Tablets………………………………………………………. 38 4.4 Blending and Granulation……………………………………………………….... 39 4.5 Compression Tests…………………………………………………………………40 4.5.1 Cubical Triaxial Tester…………………………………………………………40 4.6 Description of Technique for Determination of Different Parameters of Modified Cam-clay Model……………………………………………………………………40 4.6.1 Determination of Bulk modulus ….………………………………………….... 41 4.6.2 Determination of Failure Stress……………………………………………….. 42 4.6.2.1 Increase in the Strain Difference……………………………………………43 4.6.2.2 Decrease in Slope of Strain Difference vs. Stress Difference Curve……… 43 4.6.2.3 Critical State Concept……………………………………………………… 44 4.6.2.4 15% Axial Strain Value……………………………………………………. 44 4.6.3 Determination of Shear Modulus …..…………………………………………. 45 4.6.4 Determination of Compression Index………………………………………….46 4.6.5 Determination of Spring-back Index………………………………………….. 46 4.6.6 Determination of Slope of Critical State Line (CSL) ………………………… 47 4.7 Formation of the Tablets………………………………………………………….. 48 4.7.1 Die and Punch Assembly……………………………………………………… 48 4.7.1.1 Design of Die………………………………………………………………. 48 4.7.1.1.1 Calculations Based on Strength………………………………………… 52 4.7.1.1.2 Calculations Based on Elongation……………………………………… 52 4.7.1.2 Design of Upper and Lower Punch………………………………………… 53 4.7.1.2.1 Calculation for Upper Punch…………………………………………... 53 4.7.1.2.2 Calculation for Lower Punch………………………………………….. 54 4.7.2 Description of Process for Tablet Formation…………………………………. 54 4.8 Determination of Tablet Quality Parameters…………………………………….. 54 4.8.1 Diametral Strength Test.………………………………………………………. 54 4.8.2 Axial Penetration Strength Test……..……………………………………….... 55 4.8.3 Indentation Hardness test.…………………………………………………….. 55 4.8.4 Friability Test………………………………………………………………….. 56 4.9 Statistical Analysis………………………………………………………………... 57 4.9.1 Analysis of Variance (ANOVA)………………………………………………. 57 4.9.2 Analysis of Covariance (ANCOVA)………………………………………….. 57 4.9.3 Development of Regression Equation to Predict tablet Quality parameters ….. 57 5. CHAPTER – DRY POWDER FORMULATION TEST RESULTS……………. 58 5.1 HTC Test Results…………………………………………………………………. 58 5.1.1 HTC Test Profile………………………………………………………………. 58 5.1.2 Bulk Modulus…………………………………………………………………..62 5.1.2.1 Loading Rate of 10 MPa/min………………………………………………. 62 5.1.2.2 Loading Rate of 20 MPa/min………………………………………………. 64 5.1.2.3 Loading Rate Comparison…………………………………………………. 65
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5.1.2.4 Analysis of Covariance……………………………………………………. 67 5.1.3 Compression Index……………………………………………………………. 67 5.1.3.1 Loading Rate of 10 MPa/min………………………………………………. 68 5.1.3.2 Loading Rate of 20 MPa/min………………………………………………. 69 5.1.3.3 Loading Rate Comparison…………………………………………………. 70 5.1.3.4 Analysis of Variance….……………………………………………………. 71 5.1.4 Spring-back Index…………………………………………………………….. 74 5.1.4.1 Loading Rate of 10 MPa/min………………………………………………. 74 5.1.4.2 Loading Rate of 20 MPa/min……………………………………………… 76 5.1.4.3 Loading Rate Comparison…………………………………………………. 77 5.1.4.4 Analysis of Covariance……………………………….……………………. 79 5.2 CTC Test Results………………………………………….……………………… 81 5.2.1 CTC Test Profile………………………………………….…………………… 81 5.2.2 Shear Modulus………………………………………………………………… 88 5.2.2.1 Loading Rate of 10 MPa/min ……………………………………………... 88 5.2.2.2 Loading Rate of 20 MPa/min …………….................................................. 90 5.2.2.3 Loading Rate Comparison…………………………………………………. 92 5.2.2.4 Analysis of Variance….……………………………………………………. 95 5.2.3 Failure Stress and Critical State Line…………………………………………..96 5.2.3.1 Loading Rate of 10 MPa/min……………..……………………………….. 96 5.2.3.2 Loading Rate of 20 MPa/min…………..………………………………….. 98 5.2.3.3 Loading Rate comparison………………………………………………….. 99 5.2.3.4 Analysis of Variance….……………………………………………………. 101 5.3 Summary………………………………..………………………………………… 102 6. CHAPTER – GRANULATED POWDER FORMULATION TEST RESULTS.. 103 6.1 HTC Test Results…………………………………………………………………. 103 6.1.1 HTC Test Profile………………………………………………………………. 103 6.1.2 Bulk Modulus…………………………………………………………………. 106 6.1.2.1 Loading Rate of 10 MPa/min………………………………………..……... 106 6.1.2.2 Loading Rate of 20 MPa/min………………………………………..……... 107 6.1.2.3 Loading Rate Comparison ………………………………………………… 109 6.1.2.4 Analysis of Covariance……………………………….……………………. 110 6.1.3 Compression Index……………………………………………………………. 110 6.1.3.1 Loading Rate of 10 MPa/min…………………….……………………..….. 110 6.1.3.2 Loading Rate of 20 MPa/min…….…………………………………..…….. 111 6.1.3.3 Loading Rate Comparison…………………………………………………. 112 6.1.3.4 Analysis of Variance….……………………………………………………. 114 6.1.4 Spring-back Index……………………………………………………………... 114 6.1.4.1 Loading Rate of 10 MPa/min………………………………………..…….. 115 6.1.4.2 Loading rate of 20 MPa/min…………………………………….…………. 116 6.1.4.3 Loading Rate Comparison……………………………………….………… 117 6.1.4.4 Analysis of Covariance……………………………….……………………. 118
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6.2 CTC Test Results…………………………………………………………………. 120 6.2.1 CTC Test Profile………………………………………………………………. 120 6.2.2 Shear Modulus………………………………………………………………… 127 6.2.2.1 Loading Rate of 10 MPa/min ……………................................................... 127 6.2.2.2 Loading Rate of 20 MPa/min ……………………………………………... 128 6.2.2.3 Loading Rate Comparison…………………………………………………. 129 6.2.2.4 Analysis of Variance….……………………………………………………. 130 6.2.3 Failure Stress and Critical State Line…………………………………………. 131 6.2.3.1 Loading Rate of 10 MPa/min……………………………..……………….. 131 6.2.3.2 Loading Rate of 20 MPa/min……………………..……………………….. 132 6.2.3.3 Loading Rate Comparison ………………………………………………… 133 6.2.3.4 Analysis of Variance….……………………………………………………. 134 6.3 Comparison between Dry vs. Granulated formulation…………………………… 135 6.3.1 Bulk Modulus………………………………………………………………… 135 6.3.2 Compression Index…………………………………………………………… 136 6.3.3 Spring-back Index…………………………………………………………….. 137 6.3.4 Shear Modulus…………………………………………………………..……. 138 6.3.5 Failure Stress…………………………………………………………………. 139 6.4 Summary………………………………………………………………………….. 140 7. CHAPTER – TABLET QUALITY PARAMETERS AND RELATIONSHIP
DEVELOPMENT FOR DRY POWDER FORMULATIONS 141 7.1 Tablet Quality…………………………………………………………………….. 141 7.1.1 Diametral Strength Test……………………………………………………….. 141 7.1.2 Axial Penetration Strength Test……………………………………………….. 142 7.1.3 Indentation Hardness Test……………………………………………………... 143 7.1.4 Friability Test………………………………………………………………….. 144 7.1.5 Summary of Tablet Quality Tests……………………………………………... 145 7.2 Relationship between Tablet Quality parameters and Powder Properties…...….... 145 7.2.1 Equations for Predicting Diametral Strength...................................................... 146 7.2.2 Equations for Predicting Axial Penetration Strength………………………….. 149 7.2.3 Equations for Predicting Indentation Hardness……..………………………… 152 7.2.4 Equations for Predicting Friability…………………..……………………........ 155 7.2.5 Elastic Energy Explanation of Tablet Quality Relationship with Powder Spring-back Index............................................................................................... 157 7.3 Summary…………..…………………………………………………………….... 161 8. CHAPTER – TABLET QUALITY PARAMETERS AND RELATIONSHIP
DEVELOPMENT FOR GRANULATED POWDER FORMULATIONS……... 162 8.1 Tablet Quality…………………………………………………………………….. 162 8.1.1 Diametral Strength Test……………………………………………………….. 162 8.1.2 Axial Penetration Strength Test……………………………………………….. 163 8.1.3 Indentation Hardness Test……………………………………………………... 164
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8.1.4 Friability Test………………………………………………………………….. 165 8.1.5 Summary of Tablet Quality Tests…………………....………………………... 166 8.2 Relationship between Tablet Quality Parameters and Powder Properties..….…… 167 8.2.1 Equations for Predicting Diametral Strength………...………………………... 167 8.2.2 Equations for Predicting Axial Penetration Strength…….……………………. 170 8.2.3 Equations for Predicting Indentation Hardness……….…..…………………... 172 8.2.4 Equations for Predicting Friability……………..……………….……………... 175 8.2.5 Elastic Energy Explanation of Tablet Quality Relationship with Powder Spring-back Index……………………………………………………………... 177 8.2.6 Summary of Relations…………….……………………………………………182 8.3 Comparison between Dry vs. Granulated Formulations …….…………..................182 8.3.1 Diametral Strength ………………………………………………………….... 182 8.3.2 Axial Penetration Strength …..……………………………….……………….. 182 8.3.3 Indentation Hardness………………………………………………………….. 183 8.3.4 Friability …………………………………………………………………….... 183 8.4 Summary…………..………………………………………………..……………... 184 9. CHAPTER – SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK …………………………..………………………………. 185 9.1 Powder Property…………………………………………………………………...185 9.2 Tablet Quality…………………………………………………………………….. 189 9.3 Relationship between Tablet Quality Parameters and Powder Properties............... 190 9.4 Effect of Binder…………………………………………………………………… 191 9.5 Recommendations for Future Work………………………………………………. 192 REFERENCES……………………………………………………………………..….. 193 APPENDIX A Tablet Quality Parameters vs. Powder Property for Dry Formulations.. 197 APPENDIX B Regression Equations to Predict Tablet Quality Parameters Using Powder Property for Dry Formulations…….…………………... 221 APPENDIX C Tablet Quality Parameters vs. Powder Property for Granulated Formulations………………………………………………. 229 APPENDIX D Regression Equations to Predict Tablet Quality Parameters Using Powder Property for Granulated Formulations………………… 245 APPENDIX E Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) for Dry Powder Formulations……………………………. 253 APPENDIX F Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) for Granulated Powder Formulations…………………….. 273
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LIST OF FIGURES Figure 2.1 Yield loci based upon Cam-clay model……………..……………………… 8 Figure 2.2 Hydrostatic triaxial compression (HTC) test………………………………. 16 Figure 2.3 Conventional triaxial compression (CTC) test……………………………... 16 Figure 4.1 Micrograph of Avicel PH 102 …………………………………………........32 Figure 4.2 Particle size distribution of Avicel PH 102 …………………………………32 Figure 4.3 Micrograph of Acetaminophen at 400x magnification.………..……………33 Figure 4.4 Micrograph of Acetaminophen at 150x magnification ..……………………33 Figure 4.5 Micrograph of Ac-di-sol……………………………………………………. 33 Figure 4.6 Particle size distribution of Ac-di-sol………………………………………. 33 Figure 4.7 Micrograph of Magnesium stearate at 400x magnification ……………....... 34 Figure 4.8 Micrograph of Magnesium stearate at 600x magnification ………………... 34 Figure 4.9 Micrograph of Methocel……………………………………………………. 34 Figure 4.10 Particle size distribution of Methocel…………………………………….. 34 Figure 4.11 Micrograph of granules (5% Binder)……………………………………... 35 Figure 4.12 Particle size distribution of granules (5% Binder)………………………... 35 Figure 4.13 Micrograph of granules (10% Binder)……………………………………. 36 Figure 4.14 Particle size distribution of granules (10% Binder)………………………. 36 Figure 4.15 Powder mixer……………………………………………………………... 40 Figure 4.16 High shear mixer granulator……………………………………………… 40 Figure 4.17 Determination of bulk modulus (K) using HTC test plot with pressure on y-axis………………………………………………….... 42 Figure 4.18 Determination of bulk modulus (K) using HTC test plot with pressure on x-axis…………………………………………………… 42 Figure 4.19 Typical stress difference vs. strain difference plot for determination of failure point.…………………………………………….. 43 Figure 4.20 Stress-strain behavior of dense and loose soils………………………….. 44 Figure 4.21 Typical axial stress vs. stress difference plot for determination of failure... 45 Figure 4.22 Typical stress difference vs. strain difference plot for determining shear modulus………………………..……………………… 46 Figure 4.23 ln(pressure) vs. void ratio plot for determination of compression and spring-back index……………………………………..……………… 47 Figure 4.24 Determining slope of critical state line from mean pressure (p) vs. stress difference at failure(q) plot………………………………….….. 47 Figure 4.25 (a) SolidWorks® drawing of die-punch assembly (b) Photograph of die-punch assembly components…………………………….…….. 48 Figure 4.26 Forces acting on a hollow cylindrical die…………………………………. 49 Figure 4.27 Diametral Strength Test…………………………………………………… 55 Figure 4.28 Axial Penetration Strength Test…………………………………………... 55 Figure 4.29 Indentation Hardness Test………………………………………………… 56 Figure 4.30 Friabilator used in tablet dedusting tests (a) Drawing (b) Photograph …… 56
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Figure 5.1 Typical HTC response for binder content of 0% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min……………………………………. 59 Figure 5.2 Typical HTC response for binder content of 5% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min……………………………………. 60 Figure 5.3 Typical HTC response for binder content of 10% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min……………………………... 61 Figure 5.4 Bulk modulus of dry blended powder formulations at 10 MPa/min loading rate and three binder contents…………………………………….. 63 Figure 5.5 Bulk modulus of dry blended powder formulations at 20 MPa/min loading rate and three binder contents…………………………………….. 64 Figure 5.6 Bulk modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content…………………………. 66 Figure 5.7 Bulk modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content….……………………… 66 Figure 5.8 Bulk modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 10% binder content…………………………67 Figure 5.9 Compression index of dry blended powder formulations at 10 MPa/min loading rate and three binder contents………………………. 68 Figure 5.10 Compression index of dry blended powder formulations at 20 MPa/min loading rate and three binder contents………………………. 69 Figure 5.11 Compression index of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content………………… 70 Figure 5.12 Compression index of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content………………….71 Figure 5.13 Compression index of dry blended powder formulations at 10 and 20 MPa/min loading rates and 10% binder content……………….. 71 Figure 5.14 Mean compression index vs. (a) pressure at different binder contents (b) binder content at different loading rates and (c) pressure at different loading rates……………………………………... 73 Figure 5.15 Spring-back index of dry blended powder formulations at 10 MPa/min loading rate and three binder contents………………………. 75 Figure 5.16 Spring-back index of dry blended powder formulations at 20 MPa/min loading rate and three binder contents………………………. 75 Figure 5.17 Spring-back index of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content………………… 78 Figure 5.18 Spring-back index of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content………………….78 Figure 5.19 Spring-back index of dry blended powder formulations at 10 and 20 MPa/min loading rates and 10% binder content……………….. 79 Figure 5.20 Mean spring-back index vs. binder content at different loading rates……. 80 Figure 5.21 Typical CTC response at 1 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%................ 82
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Figure 5.22 Typical CTC response at 1 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%................ 83 Figure 5.23 Typical CTC response at 2 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%................ 84 Figure 5.24 Typical CTC response at 2 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%................ 85 Figure 5.25 Typical CTC response at 3 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%............... 86 Figure 5.26 Typical CTC response at 3 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%................ 87 Figure 5.27 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 1 MPa stress difference at three binder contents............... 89 Figure 5.28 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 2 MPa stress difference at three binder contents……….. 90 Figure 5.29 Shear modulus of dry blended powder formulations at 20 MPa/min loading rate and 1 MPa stress difference at three binder contents……….. 91 Figure 5.30 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 2 MPa stress difference at three binder contents………... 92 Figure 5.31 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content at a stress difference of 1 MPa…….. 93 Figure 5.32 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content at a stress difference of 1 MPa…….. 93 Figure 5.33 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content at a stress difference of 1 MPa……...94 Figure 5.34 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content at a stress difference of 2 MPa.......... 94 Figure 5.35 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content at a stress difference of 2 MPa.......... 95 Figure 5.36 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 10% binder content at a stress difference of 2 MPa…….95 Figure 5.37 Mean shear modulus of dry blended powder formulations at different pressures and loading rates at a stress difference of 1 MPa……... 96 Figure 5.38 Failure stress and Fixed Yield Surface of dry blended powder formulations at 10 MPa/min loading rate at different binder contents…………………. 97 Figure 5.39 Failure stress and Fixed Yield Surface of dry blended powder formulations at 20 MPa/min loading rate at different binder contents……. 98 Figure 5.40 Failure stress and Fixed Yield Surface of dry blended powder formulations at 10 and 20 MPa/min loading rates at 0% binder content….. 100 Figure 5.41 Failure stress and Fixed Yield Surface of dry blended powder formulations at 10 and 20 MPa/min loading rates at 5% binder content….100 Figure 5.42 Failure stress and Fixed Yield Surface of dry blended powder formulations at 10 and 20 MPa/min loading rates at 10% binder content... 101 Figure 5.43 Mean failure stress value at different pressures and loading rates………... 102
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Figure 6.1 Typical HTC response of granulated powder formulation for binder content of 5% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min........ 104 Figure 6.2 Typical HTC response of granulated powder formulation for binder content of 10% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min...... 105 Figure 6.3 Bulk modulus of granulated powder formulations at 10 MPa/min loading rate and two binder contents………………………………………. 107 Figure 6.4 Bulk modulus of granulated powder formulations at 20 MPa/min loading rate and two binder contents……………………………..………... 108 Figure 6.5 Bulk modulus of granulated powder formulations at 10 and 20 MPa/min loading rates and 5% binder content.…………………..…………………... 109 Figure 6.6 Bulk modulus of granulated powder formulations at 10 and 20 MPa/min loading rates and 10% binder content…………………………………….... 110 Figure 6.7 Compression index of granulated powder formulations at 10 MPa/min loading rate and two binder contents……………………………….……… 111 Figure 6.8 Compression index of granulated powder formulations at 20 MPa/min loading rate and two binder contents……………………………….……… 112 Figure 6.9 Compression index of granulated powder formulations at 10 and 20 MPa/min loading rates and 5% binder content……………………………... 113 Figure 6.10 Compression index of granulated powder formulations at 10 and 20 MPa/min loading rates and 10% binder content………………….………... 114 Figure 6.11 Spring-back index of granulated powder formulations at 10 MPa/min loading rate and two binder contents……………………………………... 115 Figure 6.12 Spring-back index of granulated powder formulations at 20 MPa/min loading rate and two binder contents……………………………………... 116 Figure 6.13 Spring-back index of granulated powder formulations at 10 and 20 MPa/min loading rates and 5% binder content………………………… 117 Figure 6.14 Spring-back index of granulated powder formulations at 10 and 20 MPa/min loading rates and 10% binder content…………….…………. 118 Figure 6.15 Mean spring-back index vs. binder content at different loading rates……. 119 Figure 6.16 Typical CTC response at 1 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 5% and (b) 10% ………………….. 121 Figure 6.17 Typical CTC response at 1 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 5% and (b) 10%............................... 122 Figure 6.18 Typical CTC response at 2 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 5% and (b) 10%.............................. 123 Figure 6.19 Typical CTC response at 2 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 5% and (b) 10%............................. 124 Figure 6.20 Typical CTC response at 3 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 5% and (b) 10%.............................. 125 Figure 6.21 Typical CTC response at 3 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 5% and (b) 10%.............................. 126 Figure 6.22 Shear modulus of granulated powder formulations at 10 MPa/min loading rate and 1 MPa stress difference at two binder contents………..... 128
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Figure 6.23 Shear modulus of granulated powder formulations at 20 MPa/min loading rate and 1 MPa stress difference at two binder contents…………. 129 Figure 6.24 Shear modulus of granulated powder formulations at 10 and 20 MPa/min loading rates and 5% binder content at a stress difference of 1 MPa ......... 129 Figure 6.25 Shear modulus of granulated powder formulations at 10 and 20 MPa/min loading rates and 10% binder content at a stress difference of 1 MPa........ 130 Figure 6.26 Mean shear modulus of granulated powder formulations at different loading rates and binder contents…………………………………………. 131 Figure 6.27 Mean failure stress vs. pressure at different binder contents……………… 134 Figure 6.28 Mean failure stress vs. pressure at different loading rates ……………….. 135 Figure 7.1 Diametral strength of tablets using dry formulation at different binder contents…………..………………………………………………… 142 Figure 7.2 Axial penetration strength of tablets using dry formulation at different binder contents………………………………………………… 143 Figure 7.3. Indentation hardness of tablets using dry formulation at different binder contents……………………………………………………………... 144 Figure 7.4. Friability of tablets using dry formulation at different binder contents........ 145 Figure 7.5 Relation between diametral strength and spring-back index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations………………………………………..………………. 148 Figure 7.6 Relation between diametral strength and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations…………………………………………………………148 Figure 7.7 Relation between axial penetration strength and spring-back index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations ……………………………………………. 151 Figure 7.8 Relation between axial penetration strength and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations……………………………………………. 151 Figure 7.9 Relation between indentation hardness and spring-back index (determined at 10 MPa/min loading rate) at different loading conditions for dry formulations…………………………………………….. 154 Figure 7.10 Relation between indentation hardness and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations…………………………………………… 154 Figure 7.11 Relation between friability and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations……………………………………………………….. 156 Figure 7.12 Relation between friability and spring-back index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations …………………………..……………… 157 Figure 7.13 Force vs. displacement (loading-unloading before failure) plot for tablets formed at 90 MPa using dry formulation in (a) diametral
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strength test (b) axial penetration test, and (c) indentation hardness test mode……………………………………….......................................... 159 Figure 7.14 Plot between elastic energy and spring-back index vs. (a) diametral strength, (b) axial penetration strength, and (c) indentation hardness for tablets formed at 90 MPa using dry powder formulations...................... 160 Figure 8.1 Diametral strength of tablets using granulated powder formulations at different binder contents…………….…………………………………... 163 Figure 8.2 Axial penetration strength of tablets using granulated powder formulations at different binder contents.………………………………….. 164 Figure 8.3 Indentation hardness of tablets using granulated powder formulations at different binder contents….…………………………………………….. 165 Figure 8.4 Friability of tablets using granulated powder formulations at different binder contents…………………………………………………… 166 Figure 8.5 Relation between diametral strength and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations………………………………...……………….169 Figure 8.6 Relation between diametral strength and compression index (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations ………………………………..……….………169 Figure 8.7 Relation between axial penetration strength and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations ………………………………..…………….…171 Figure 8.8 Relation between axial penetration strength and compression index (determined at 20 MPa/min loading rate) at different loading conditions for granulated formulations ……………………………………. 172 Figure 8.9 Relation between indentation hardness and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations…………………………………………………174 Figure 8.10 Relation between indentation hardness and spring-back index (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations ………………………………………..………174 Figure 8.11 Relation between friability and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations ………………………….…………………… 176 Figure 8.12 Relation between friability and compression index (determined at 20 MPa/min loading rate) at different loading conditions for granulated formulations ……………………………..……………….. 177 Figure 8.13 Force vs. displacement (loading-unloading before failure) plot for tablets formed at 90 MPa using granulated formulation in (a) diametral strength test, (b) axial penetration test, and (c) indentation hardness test modes……………………………………….178 Figure 8.14 Plot between elastic energy and spring-back index vs. (a) diametral strength, (b) axial penetration strength, and (c) indentation hardness
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for tablets formed at 90 MPa using granulated powder formulations……. 179 Figure 8.15 Impact response curves for (a) elastic body, and (b) inelastic body……… 181 Figure 8.16 Force-deformation response curves for (a) elastic body, and (b) inelastic body…………………………………………………………...181
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LIST OF TABLES Table 2.1 Significance of powder's compression parameters…………………………...11 Table 4.1 Formulation of pharmaceutical powder for dry blend and wet granulation….31 Table 4.2 Properties of formulation ingredients…………………………………….......32 Table 4.3 Experimental design for HTC tests………………………………………...... 38 Table 4.4 Experimental design for CTC tests………………………………………...... 38 Table 5.1 Bulk modulus of dry blended powder formulations at 10 MPa/min loading rate…………………………………………………...... 63 Table 5.2 Regression equation for predicting bulk modulus at 10 MPa/min……...........64 Table 5.3 Bulk modulus of dry blended powder formulations at 20 MPa/min loading rate…………….……………………………………………………..65 Table 5.4 Regression equation for predicting bulk modulus at 20 MPa/min……...........65 Table 5.5 Compression index of dry blended powder formulations at 10 MPa/min loading rate………………………………………….…………. 69 Table 5.6 Compression index of dry blended powder formulations at 20 MPa/min loading rate…………………………………………………….. 70 Table 5.7 Spring-back index of dry blended powder formulations at 10 MPa/min loading rate………………………………………………………76 Table 5.8 Regression equation for predicting spring-back index at 10 MPa/min……………………………………………………………………76 Table 5.9 Spring-back index of dry blended powder formulations at 20 MPa/min loading rate………………………………………………………77 Table 5.10 Regression equation for predicting spring-back index at 20 MPa/min…………………………………………………………………..77 Table 5.11 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 1 MPa stress difference……………………………………89 Table 5.12 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 2 MPa stress difference……………………………........... 90 Table 5.13 Shear modulus of dry blended powder formulations at 20 MPa/min loading rate and 1 MPa stress difference……………………………........... 91 Table 5.14 Shear modulus of dry blended powder formulations at 20 MPa/min loading rate and 2 MPa stress difference……………………………………92 Table 5.15 Failure stress value of dry blended powder formulations at 10 MPa/min loading rate…………………………………………………… 97 Table 5.16 Critical state line equation at 10 MPa/min loading rate……………………. 98 Table 5.17 Failure stress value of dry blended powder formulations at 20 MPa/min loading rate…………………………………………………… 99 Table 5.18 Critical state line equation at 20 MPa/min loading rate……………………. 99 Table 6.1 Bulk modulus of dry blended powder formulations at 10 MPa/min loading rate……………………………………………………... 107 Table 6.2 Regression equation for predicting bulk modulus at 10 MPa/min………….. 107
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Table 6.3 Bulk modulus of dry blended powder formulations at 20 MPa/min loading rate…………………………………………………...... 108 Table 6.4 Regression equation for predicting bulk modulus at 20 MPa/min………...... 109 Table 6.5 Compression index of granulated powder formulations at 10 MPa/min loading rate…………………………………………………...... 111 Table 6.6 Compression index of granulated powder formulations at 20 MPa/min loading rate…………………………………………………...... 112 Table 6.7 Spring-back index of granulated powder formulations at 10 MPa/min loading rate…………………………………………………...... 116 Table 6.8 Spring-back index of granulated powder formulations at 20 MPa/min loading rate…………………………………………………...... 117 Table 6.9. Shear modulus of granulated powder formulations at 10 MPa/min loading rate and 1 MPa stress difference…………………………………… 127 Table 6.10 Shear modulus of granulated powder formulations at 10 MPa/min loading rate and 1 MPa stress difference……………………………........... 128 Table 6.11 Failure stress value of granulated powder formulations at 10 MPa/min loading rate…………………………………………………… 132 Table 6.12 Failure stress value of granulated powder formulations at 20 MPa/min loading rate …………………………………………………… 132 Table 6.13 Failure stress of granulated powder formulations at 10 and 20 MPa/min loading rates for 5% binder…………………………………… 133 Table 6.14 Failure of granulated powder formulations at 10 and 20 MPa/min loading rates for 10% binder………………………………...... 133 Table 6.15 Bulk modulus of dry and granulated powder formulations at 10 MPa/min loading rate…………………………… ……………………... 136 Table 6.16 Bulk modulus of dry and granulated powder formulations at 20 MPa/min loading rate……….…………………………………………... 136 Table 6.17 Compression index of dry and granulated powder formulations at 10 MPa/min loading rate……….………………………………………... 137 Table 6.18 Compression index of dry and granulated powder formulations at 20 MPa/min loading rate………………………………………………… 137 Table 6.19 Spring-back index of dry and granulated powder formulations at 10 MPa/min loading rate…………………………………….…………... 138 Table 6.20 Spring-back index of dry and granulated powder formulations at 20 MPa/min loading rate…………………………………………………. 138 Table 6.21 Shear modulus of dry and granulated powder formulations at 10 MPa/min loading rate and 1 MPa stress difference……………………... 139 Table 6.22 Shear modulus of dry and granulated powder formulations at 20 MPa/min loading rate…………………………………………………… 139 Table 6.23 Failure stress values of dry blended powder formulations at 10 MPa/min loading rate…………………………………………………… 140 Table 6.24 Failure stress values of dry blended powder formulations at 20 MPa/min loading rate…………………………………………………… 140
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Table 7.1 Diametral strength of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents………... 141 Table 7.2 Axial penetration strength of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents……... 142 Table 7.3 Indentation hardness of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents………... 143 Table 7.4 Friability (%) of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents………... 144 Table 7.5 r2 values for equations to predict diametral strength of tablet formed at 70 MPa on the basis of powders’ mechanical properties for dry formulations……………………………………….………………… 146 Table 7.6 r2 values for equations to predict diametral strength of tablet formed at 90 MPa on the basis of powders’ mechanical properties for dry formulations ………………………………………………………… 147 Table 7.7 r2 values for equations to predict axial penetration strength of tablet formed at 70 MPa on the basis of powders’ mechanical properties for dry formulations …………………………………………….. 149 Table 7.8 r2 values for equations to predict axial penetration strength of tablet formed at 90 MPa on the basis of powders’ mechanical properties for dry formulations ……………………………………………... 150 Table 7.9 r2 values for equations to predict indentation hardness of tablet formed at 70 MPa on the basis of powders’ mechanical properties for dry formulations ……………………………………………... 152 Table 7.10 r2 values for equations to predict indentation hardness of tablet formed at 90 MPa on the basis of powders’ mechanical properties for dry formulations ……............................................................. 153 Table 7.11 r2 values for equations to predict friability of tablet formed at 70 MPa on the basis of powder’s mechanical properties for dry formulations…………………………………………….. 155 Table 7.12 r2 values for equations to predict friability of tablet formed at 90 MPa on the basis of powders’ mechanical properties for dry formulations……………………………………………. 155 Table 8.1 Diametral strength of tablets made from granulated powder formulations at 70 and 90 MPa compression pressure and different binder contents........... 162 Table 8.2 Axial compressive strength of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents........... 163 Table 8.3 Indentation hardness of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents……….. 164 Table 8.4 Friability of tablets made from dry powder formulations at 70 and 90 MPa compression pressure and different binder contents……………….. 165 Table 8.5 r2 values for equations to predict diametral strength of tablet formed at 70 MPa on the basis of granulated powders’ mechanical properties……... 167
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Table 8.6 r2 values for equations to predict diametral strength of tablet formed at 90 MPa on the basis of granulated powders’ mechanical properties……... 168 Table 8.7 r2 values for equations to predict axial penetration strength of tablet formed at 70 MPa on the basis of granulated powders’ mechanical properties………………………………………………………... 170 Table 8.8 r2 values for equations to predict axial penetration strength of tablet formed at 90 MPa on the basis of granulated powders’ mechanical properties………………………………………………………... 170 Table 8.9 r2 values for equations to predict indentation hardness of tablet formed at 70 MPa on the basis of granulated powders’ mechanical properties……... 172 Table 8.10 r2 values for equations to predict indentation hardness of tablet formed at 90 MPa on the basis of granulated powders’ mechanical properties…………………………………………… 173 Table 8.11 r2-values for equations to predict friability of tablet formed at 70 MPa on the basis of granulated powders’ mechanical properties……..... 175 Table 8.12 r2 values for equations to predict friability of tablet formed at 90 MPa on the basis of granulated powders’ mechanical properties……………………………………………………… 175 Table 8.13 Diametral strength of tablets made from dry and granulated powder formulations at 70 and 90 MPa compression pressure and different binder contents……………………………………………………………... 182 Table 8.14 Axial penetration strength of tablets made from dry and granulated powder formulations at 70 and 90 MPa compression pressure and different binder contents……………………………………... 183 Table 8.15 Indentation hardness of tablets made from dry and granulated powder formulations at 70 and 90 MPa compression pressure and different binder contents............................................................ 183 Table 8.16 Friability of tablets made from dry and granulated powder formulations at 70 and 90 MPa compression pressure and different binder contents…….. 184
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Acknowledgements
I would like to take the opportunity to thank everyone who directly or indirectly
supported me to accomplish my Ph.D. research and write thesis. Thanks to my advisor,
Dr. Virendra M. Puri for his invaluable guidance throughout my Ph.D. program of study.
It has been great honor for me to pursue Ph.D. under the guidance of Dr. Puri. I am
grateful to my Ph.D. advisory committee members Dr. Jeffrey M. Catchmark, Dr. Mian
C. Wang, and Dr. Durland L. Shumway for their great support and guidance. Special
thank goes to Dr. Hojae Yi for his help throughout my research.
I am thankful to Dr. Roy E. Young, Head of the Department of Agricultural and
Biological Engineering, for providing me the resources. Thanks to Mr. Randall G. Bock
and Dr. Roderick S. Thomas for their technical support to keep the experimental set-up
running and in design and fabrication of research devices. I would also like to thanks all
the office staff for their support. Thanks are also due to Dr. Ghassan Chehab for allowing
to use his lab for forming the tablets.
I am also thankful to all my colleagues and supervisors at various work places
including R. T. Exports Ltd, Indian Agricultural Research Institute, and Scientific and
Digital Systems.
I am extremely thankful to my parents, wife Laxmi, and daughter for their
continuous unconditional support and encouragement. I am also thankful to my entire
relative and friends those have positive influence in my life.
I would like to dedicate my thesis to my late mother.
Chapter 1 - Introduction
Processing and handling of powders play a major role in the production of
materials; it constitutes a large and high value industry. Industries that produce, handle
and process powdered materials include agriculture, chemical, cosmetic, construction,
electronic, feed, food, mineral, and pharmaceutical. According to Feda (1982), powders
can be defined phenomenologically or structurally. Phenomenologically, powders are
materials that exhibit dilatancy and contractancy and are sensitive to hydrostatic stress.
Structurally, powders are substances composed of mutually contacting solid particles, or
structural units, within liquid and/or gaseous phases.
Particulate material production and related services contribute one trillion dollars
annually to the U.S. economy alone. More than 60% of U.S. manufactured goods are
associated with particle science and technology. In pharmaceutical manufacturing, 80%
of all medicines are produced in solid dosage form, i.e., tablet or capsule (Muzzio et al.,
2003).
Understanding the mechanical behavior of materials in powdered form is very
important for different unit operations such as storage, flow, granulation, compaction,
and mixing. In industry, bulk materials are usually stored in bins, compacted as medicine
or pellets, and packaged as products for consumption. The knowledge of mechanical
behavior of powder helps in determining, among others, flow properties and
compactibility. Of these, powder compression is a very important unit operation for
making various industrial products. Products manufactured using powder compaction
include pharmaceutical tablets, cosmetic powder compacts, graphite electrodes, ceramic
components, automotive parts, cutting tools, and feed pellets.
The process of making tablets is known as compaction. Tablets are produced by
applying external pressure using punches onto the powder contained in a die. Usually,
pressure is applied along the vertical direction; whereas, the die into which the powder is
pressed gives it a lateral constraint. This is a very rapid process and is used for mass
2
production in many powder industries. Tablet formation by applying compressive forces
involves complex mechanisms during densification.
Pharmaceutical tablets are formed using powder ingredients such as filler, binder,
lubricant, disintegrant, and active pharmaceutical ingredient (API). Tablets are formed
either by dry blending the above ingredients or wet granulation of the powder mix
followed by compaction. Each ingredient has its own role in tablet formation. Binder
helps in granule formation and gives strength to the tablets. Lubricant helps in reducing
friction, i.e., for both die wall-particle and inter-particle. The function of disintegrant is to
control the release of the API into the body. Granulation is the process in which primary
powder particles are made to adhere to form larger, multi-particle entities called granules.
The purpose of granulation is to improve compression and flow properties and prevent
segregation of the constituents of the powder formulation.
Powders are studied from two viewpoints: physical characteristics and mechanical
behavior. Physical characteristics involve particle attributes such as chemical
composition, shape, size distribution, and particle density. Mechanical behavior is
basically the force-deformation or stress-strain behavior of the powder in bulk. The study
of mechanical behavior of powder is important with respect to its handling and
processing. Many constitutive models are available to describe the stress-strain behavior
of a powder (Tripodi et al., 1992). Using a stress-strain test, the constitutive parameters of
these models can be determined. A cubical triaxial tester with a flexible pressure
application membrane can be used to perform a true 3D stress-strain test.
Tablet quality is important for industries involved in compaction such as
pharmaceutical, food, ceramic, and cosmetic. The important tablet or compact quality
parameters include hardness, strength, friability, and rebound. In case of pharmaceutical
tablets, dissolution is also one of the key quality parameters, which predicts the rate of
drug release into the body. Hardness is defined as resistance to penetration and strength is
resistance to bending and breaking. Hardness and strength of a tablet are important with
respect to handling and end use of the tablet. A tablet should be hard enough so that it
3
does not break during handling while it should not be so hard that it does not dissolve at
the desired rate when consumed. Rebound is the expansion of a tablet after release of
compression forces. Some rebound is desired at initial time as rebound helps in releasing
the tablet from the punch after compaction; however, there should be limited rebound
after removal from die. Friability is measure of the tablet’s resistance to attrition and
fragmentation to subsequent process condition and transportation. Hardness and strength
can be related with bulk and shear modulus of elasticity; whereas, rebound can be related
with spring-back index. Spring-back index is a parameter of the modified Cam-clay
Model (Desai and Siriwardane, 1984).
Many researchers have studied the process of powder compression with the aim to
improve tablet quality. Work has been done to predict the relationship between tablet
quality and mechanical property of a powder mixture. If the quality of a tablet can be
predicted prior to its manufacture, powder industries will save significant amount of time
and money. Furthermore, time to launch a new product will be considerably shortened.
Mittal (1999) and Mittal and Puri (1999a and b) found that there were certain compact or
tablet quality parameters that related very well (r2 > 0.90) with the powder’s material
parameters. However, the effect of each individual component on tablet quality was and
since has not been studied. Binder plays an important role in tablet quality; therefore,
there is a definite need to understand and evaluate its effect.
The goal of the study was to enable prediction of the tablet quality based on the
mechanical behavior of the powder formulation prior to manufacturing of the tablet with
an emphasis on the effect of binder. Towards that end, select mechanical properties
formulations that related with tablet quality parameters were identified and relations
developed and explained.
4
Chapter 2 - Literature Review
Study of a powder’s mechanical behavior (such as stress-strain response) and
tablet quality is very important for profitability of an industry and acceptance by end
user. Numerous constitutive models have been proposed by several researchers to predict
the load-response of particulate materials. Many quality-related tablet parameters have
been studied also by several academic and industrial researchers. In this chapter, some of
the key research findings that are relevant to these studies are discussed and critically
analyzed in order to determine areas of knowledge gap. This chapter has three sections:
general theory and concept, constitutive model determination, and tablet quality.
2.1. General Theory and Concept
Behavior of bulk material can be explained by the fundamental laws of physics.
The subject of continuum mechanics is based upon the foregoing governing laws. These
laws are not explicitly dependent on the material constituents; however, material
constituents are known to play an important role in the behavior of a bulk material. The
response of material can be explained by the study of (a) external excitation, and (b) the
internal constitution of materials.
2.1.1 Powder Characteristics
There are two types of properties that characterize powders (Mittal, 1999).
1. Primary properties: A particle is defined as the smallest unit of a powder that cannot be
readily subdivided. The characteristics of these particles determine the primary properties
of the powder system. Particle size, shape, surface area, chemical composition, density,
and porosity are key primary properties.
2. Secondary properties: The properties of a powder system as a whole constitute these
properties. Particle size distribution, cohesion, angle of internal friction, bulk porosity,
bulk density, moisture content, and specific surface area of bulk are key secondary
properties.
5
2.1.2 Mechanical Behavior (Stress-Strain Behavior) of Materials
When a body is subjected to external forces, it undergoes deformation. With the
removal of an external force, the body may tend to return to its original state. If a body
fully returns to its original state, it is known as an elastic material while, if the material
does not return to its original state, it is known as inelastic material.
Strain
Strain is defined as the unit change of size and/or shape. The concept of strain
can be generalized for three-dimensional (3D) bodies. In the case of 3D, the strain is
given by a 3*3 matrix denoted by εij (where, i = x, y, z; j = x, y, z; alternately i, j = 1, 2,
3).
Stress
Stress is defined as the unit intensity at a point, i.e., force per unit area. For 3D,
the stress is given by a 3*3 matrix denoted by σij (where, i = x, y, z; j = x, y, z; alternately
i, j = 1, 2, 3).
2.1.3 General Statement of Constitutive Law
A constitutive equation is a mathematical model that can permit reproduction of
the observed response of the continuous media. A general mathematical form, f, for
constitutive law can be expressed as (Desai and Siriwardane, 1984):
0),,,( =••
εεσσf (2.1)
where σ denotes stress, ε denotes infinitesimal strain, and the overdot denotes rate of
change with respect to time.
Due to their non linearity and multi-valued nature, most useful constitutive laws
for particulate materials are obtained by using the incremental form. The incremental
forms are applicable also to powders and particulate matters; herein powder, particulate
materials, granular materials and bulk solids are used interchangeably. The incremental
form of the equation can be expressed as:
[ ] εσ dDd = (2.2)
or in inverse form it can be expressed as:
[ ] σε dCd = (2.3)
6
where [ ]D and [ ]C are constitutive matrices. Examples of [ ]D and [ ]C are given below.
[ ]
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+−−
−+−
−−+
=
GG
G
GKGKGK
GKGKGK
GKGKGK
D
200000020000002000
0003
43
23
2
0003
23
43
2
0003
23
23
4
(2.4)
[ ]
⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
+−−
−+−
−−+
=
G
G
G
KGGKGK
GKKGGK
GKGKKG
C
2100000
0210000
0021000
00091
31
61
91
61
91
00061
91
91
31
61
91
00061
91
61
91
91
31
(2.5)
where, K and G are bulk modulus and shear modulus of elasticity, respectively.
2.1.4 Steps in Developing a Constitutive Law
Developing a constitutive law requires various steps, which involve mathematical
formulation and laboratory tests. These steps can be summarized as:
1. Mathematical formulation based on fundamental laws of physics and
experimental observations.
2. Identification of significant parameters.
3. Determination of parameters from laboratory test and verification.
4. Successful prediction of a majority of observed data from which the parameters
were determined and of other test data under different stress paths.
7
5. Satisfactory comparisons between predictions from a solution scheme in which
the constitutive law is introduced.
2.2 Constitutive Models
Various constitutive models are available to govern the behavior of powder. The
commonly used linear elastic model and critical state models are discussed below.
2.2.1 Linear Elastic Model (First-Order Cauchy Elastic Model)
For linear elastic behavior, the equation can be written as (Desai and Siriwardane, 1984):
ijijijij I εαδαδασ 2110 )( ++= (2.6)
where σij (i= 1, 2, and 3; j = 1, 2, and 3) is stress component, I1 is first invariant of strain,
α1 and α2 are material constant, (α0)δij is initial (isotropic) stress. δij is known as
Kronecker delta; j represents the three principal directions and i represents three planes
of orientation.
δij = 1 when i = j and δij = 0 when i ≠ j.
In the absence of initial stress, the equation becomes:
ijijij I εαδασ 211 += (2.7)
where, α1 and α2 can be related to bulk modulus (K) and shear modulus (G) of elasticity
as:
1α = 32GK − and 2α = 2G (2.8)
2.2.2 Critical State Model
The key variables that are used in the critical state model are deviatoric stress (q),
which represents instability in the system, mean stress (p) which represents stability in
the system, and voids ratio (e) which represents the pore volume inclusive of shapes.
Critical state theory has been used successfully to describe failure observed in
particulate materials (such as sands, soils, and grains) during triaxial tests. According to
the critical state theory, when a loose soil sample is sheared, it passes through progressive
states of yielding before reaching a state of collapse. That is, the stress path passes
through several yield surfaces (hardening caps), causing plastic deformations. The
yielding continues to occur until the material reaches a critical voids ratio (or critical
8
density), after which the voids ratio remains constant during subsequent deformations.
Therefore, the material reaches a state where further deformation proceeds with no
change in volume, i.e., is in the critical state, additional load may change the shape of a
given mass, but not its volume (Desai and Siriwardane, 1984).
2.2.3 Cam-clay Model
The Cam-clay Model was the first to use the critical state theory to describe yield
criterion and hardening of particulate materials. The advantage of this model is that it is
simple, relatively easy to use with well defined meaning of material parameters.
Additionally, a small number of parameters can be determined from standard triaxial
tests.
Equation for Moving Yield Surface
According to the normality condition of the flow rule, the incremental plastic
strain vector is normal to the yield surface at any stress point (Figure 2.1). The
incremental plastic strain vector AB is normal to a given yield surface. This can be
mathematically expressed by Equation 2.9.
Figure 2.1 Yield loci based upon Cam-clay model (Desai and Siriwardane, 1984)
p0 p0 p0 p vp,ε
tan-11/ψ
M
Fixed yield surface or critical state line
Critical Point
Moving yield surface (cap)
A
d spε
d vpε
B
q sp,ε
9
ψε
ε 1=−=
dpdq
dd
pv
ps (2.9)
where, psdε is shear strain and
pvdε is volumetric plastic strain.
The stress ratio (η) is defined as:
η η= =qp
or q p (2.10)
On differentiating Equation 2.10 the following is obtained:
dq = p dη + η dp (2.11)
By substituting Equation 2.11 into Equation 2.9 and rearranging, one gets
dpp
d+
+=
ηη ψ
0 (2.12)
Equation 2.12 defines a yield surface. Original Cam-clay model assumed isotropic
hardening. Therefore, the successive yield surfaces (hardening caps) are geometrically
similar, and ψ is a function of η only. Therefore, any yield curve passing through a
known point can be obtained by integrating Equation 2.12.
Work Hypothesis for Original Cam-Clay Model
In the original Cam-clay model, the following work hypothesis was assumed
based on the energy dissipated while undergoing deformation on the state boundary
surface:
sps
pv MpdqdpddW εεε =+= (2.13)
where, M = slope of critical state line.
ηηεε
−=
−=
−=
MpMpp
qMpp
pv
ps 1
dd
= ψ1
=−dpdq (2.14)
Therefore, M – η = ψ (2.15)
Integrating Equation 2.12 one gets,
00
=+
+ ∫∫η
ψηηd
pdpp
po
Substituting M – η = ψ, one gets,
10
pMq
MMdndn
==−+
=+ ∫∫
ηηηψη
ηη
00
Therefore, pMq
epp −
=0
or, pMq
eppf−
−= 0 = 0 (2.16)
where po is the initial state of stress and considered as the hardening parameter.
Equation 2.16 is the original Cam-clay model.
2.2.4 Modified Cam-clay Model
In the Modified Cam-clay, the work hypothesis used was different from the
original Cam-clay model. The improved work hypothesis was used because it represented
more accurately the particle en masse response to force. The work hypothesis for
modified Cam-clay was assumed to be:
222 )d()(d ps
pv MpdW εε += (2.17)
Plastic work done on a test specimen per unit volume can also be written as:
dW =p dεvp +q dεs
p (2.18)
From Equations 2.17 and 2.18 the following is obtained (Desai and Siriwardane, 1984):
dd M
sp
vp
εε
ηη
=−
22 2 (2.19)
Therefore
ηηψ
2
22 −=
Mcm (2.20)
where subscript cm denotes modified Cam-clay model.
By substituting Equation 2.20 into Equation 2.12 and integrating, one obtains:
2 12 20 0
ηη
ηη
Md
pdp
p
p
+= −∫∫ (2.21)
Upon integration, the following function for the modified Cam-clay yield surface
is obtained:
f(p,q;p0,M) = M2p2 - M2p0p + q2 = 0 (2.22)
11
where p0 = a strain-hardening parameter representing the value of p at the intersection of
the yield cap with the p-axis.
Equation 2.22 gives an elliptical moving yield surface similar to that shown in Figure 2.1.
2.2.5 Model Parameters
Six parameters are needed to implement the original and modified Cam-clay
models, namely, G, K, λ, κ, p0 and M, which are listed in Table 2.1. In addition, the
significance of each parameter is included.
Table 2.1 Significance of powder's compression parameters (Mittal, 2003).
Parameter Symbol Type Significance
Shear
Modulus
G Elastic Measure of material's rigidity during shear testing
Bulk Modulus K Elastic Measure of material's resistance to volumetric
deformation
Compression
Index
λ Elasto-
plastic
Quantifies compressibility of powder at given
isotropic pressure
Spring-back
Index
κ Elasto-
plastic
Quantifies powder's ability to swell/relax after
release of pressure
Failure stress σf Failure Ultimate value at which a given powder fails during
shear loading
Slope of CSL M Determines the slope of the critical state line (CSL)
or fixed yield surface which is based on different
failure stress values
Hardening
parameter
po Gives the initial state of stress
2.3 Densification Process
Generally, the densification process proceeds in four stages (German, 1994),
namely, 1) rearrangement of particles, 2) elastic deformation of particles, 3) plastic
deformation, and 4) bulk compression.
2.3.1 Rearrangement of Particles: At the beginning of a compression cycle, the powder
has a density equal to the bulk density. For this loose powder, there is an excess of
12
void space, very low strength, and low coordination number. As pressure is applied,
initially the rearrangement of the particles with filling of large pores takes place,
thereby achieving a higher coordination number. Liu and Delo (2001) also studied the
motion of particle toward each other, including particle rearrangement and particle
deformation during compaction. They found that process of particle sliding and
rearrangement has a critical influence on densification in practice, especially during the
first stage of compaction.
2.3.2 Elastic Deformation of Particles: With increase in pressure, better packing is
achieved leading to decrease in porosity with the formation of new particle contacts.
The point contacts undergo elastic deformation, and a residual elastic energy is stored
in the tablet.
2.3.3 Plastic Deformation of Particles: As the pressure is further increased, contact
enlargement through plastic deformation takes place: thereby leading to higher packing
density. Thus, the pressure causes localized deformation at the contacts, giving work
(strain) hardening and allowing to form new contacts as the gaps between particles
collapse. The inter-particle contact zones take on a flattened appearance with a circular
profile. During deformation, cold welding at the inter-particle contacts contributes to
the development of strength in the tablet.
2.3.4 Bulk Compression: At very high compression pressures, usually in excess of 1
GPa, massive deformation occurs, leaving only small pores. Continual pressurization
beyond that level is of little benefit. The material response is similar to that of a near-
dense solid.
2.4 Creep Behavior
Creep is time-dependent strain occurring under applied stress. Creep behavior,
which is generally neglected during constitutive formulations, is important in powder
compaction. Knowledge of creep behavior of material will help in deciding the loading
rate of compaction. Abyaneh et. al. (2001) studied time-dependent creep behavior of
13
particulate matter. In this paper, creep behavior due to sudden increase in load during the
short period was reported. This load-induced deformation resulted in a rapid rise in local
temperature at the contact zones. During creep, this excess temperature dissipates and
causes a progressive increase in the viscosity of the contact zones resulting in a
decreasing creep rate with time.
2.5 Constitutive Model Parameters
The application of a continuum model depends on the determination of the
material parameters associated with the constitutive equation. Tripodi et al. (1992)
reviewed various constitutive models for cohesive powders. They identified two
constitutive equations as candidate models for application to cohesive powders; an elasto-
viscoplastic model based on the critical state theory, and an endochronic model. The
parameters for constitutive models are determined using experimental stress-strain (or
force-deformation) data.
2.6 Instruments for Constitutive Model Parameters Determination
Many test devices based on different principles have been used to determine the
stress-strain behavior of particulate materials. A widely used approach to classify these
test devices is based on the control of a number of independent variables. Based on this
approach, the test devices can be categorized as one-dimensional, such as uniaxial
compression tester; two-dimensional, such as a shear tester; and three-dimensional such
as a cubical triaxial tester. These testers are reviewed and discussed in the following
sections.
2.6.1 Uniaxial Testers
A uniaxial compaction tester was developed primarily for compression testing of
soils. The common one-dimensional tester is the consolidometer or oedometer in which
the cylindrical sample is confined in a metallic ring and loaded vertically. Fixed ring and
floating ring oedometers are the two primary oedometers (Feda, 1982). In a fixed ring
oedometer, the friction gradually reduces to zero at the bottom, whereas, in the case of a
14
floating ring, the plane of zero friction is at the center as the sample is loaded from both
sides.
2.6.2 Two-Dimensional Testers
Two-dimensional testers are used for measuring the shear, flow, and compaction
properties of bulk solids. Powder is filled into a shear cell and normal load is applied. The
axial load is applied until the specimen fails. Many two-dimensional shear testers have
been developed. Jenike (1964) was a pioneer in development of the shear tester; in
particular, the translational shear tester. Ladipo and Puri (1997) developed a computer-
controlled yield locus tester.
2.6.3 Triaxial Testers
Triaxial testers can be classified as conventional and cubical triaxial testers.
2.6.3.1 Conventional Triaxial Tester
A conventional triaxial tester uses cylindrical shaped specimen, and stress is
applied using hydraulic or pneumatic pressure. Two of the three principal stresses are
always the same in a conventional triaxial tester. So, effectively, it is a two-dimensional
tester. Tripodi et al. (1994) used a conventional triaxial tester to test powders related to its
mechanical properties.
2.6.3.2 Cubical Triaxial Tester (CTT)
Kjellmann (1936) first proposed the concept of a cubical triaxial tester (CTT).
However, because of its mechanical complexity, Kjellmann’s tester had limited success.
Since then, extensive research has been carried out in the area of cubical triaxial testing
by several researchers. The three basic categories of cubical triaxial testers are:
1. All-rigid boundary type,
2. All-flexible boundary type, and
3. Mixed (rigid and flexible) boundary type.
Out of these three, the all-flexible boundary type CTT is most commonly used
and is discussed in this section.
Kamath and Puri (1997) and Li and Puri (1997) developed the all-flexible cubical
triaxial tester for low and medium pressures, respectively. These CTTs were capable of
15
applying pressure on six sides of a cubical sample (powder). The pressure is applied
through flexible rubber membranes by pressurized nitrogen gas. The powder sample is
contained in a cube-shaped Sample Holding Membrane (SHM) (made out of silicone
rubber), which has dimensions of 50.8×50.8×50.8 mm. The SHM is placed in the cubical
cavity of the CTT and pressure is applied to the six surfaces of SHM via flexible rubber
membranes. Due to the application of pressure, change in the dimensions of the powder
sample takes place. The change in the dimensions can be analyzed using linear motion
potentiometers that are in constant contact with pressure application membranes.
The CTT developed by Li and Puri (1997) had certain limitations. The tester was
designed for 42 MPa, however, it was not able to apply a pressure more than 24.5 MPa.
By 2002, due to aging, the pressure limit reduced to 17.7 MPa. The safe limit for pressure
was 14 MPa. Mittal (2003) redesigned the CTT to enhance its testing regime with
reconsideration of the safety of the operator of the tester. A flexible Kevlar shield was
designed to enclose the tester and to avoid injury to the operator in case of failure. A
safety Kevlar shield was also developed for secure housing of the high pressure gas tank.
Hydrostatic triaxial compression (HTC) and conventional triaxial compression (CTC)
tests can be conducted using CTT to determine the various constitutive parameters. The
HTC and CTC tests are described below.
2.7 Hydrostatic Triaxial Compression (HTC) Test
In HTC tests, the test sample is subjected to an isotropic loading and the stress
state is the same in all three principal directions such that σ1 = σ2 = σ3 , where, σ1, σ2 and
σ3 are the major, intermediate, and minor principal stresses, respectively (Figure 2.2). The
pressures are then increased uniformly according to the pre-determined stress paths.
16
Figure 2.2: Hydrostatic triaxial compression (HTC) test.
2.8 Conventional Triaxial Compression (CTC) Test
In CTC tests, equal pressure is maintained initially on the six faces of the cubical
specimen until a pre-determined pressure value (known as the confining pressure, σ0) is
reached such that σ0 = σ1 = σ2 = σ3 (Figure 2.3). After the confining pressure is reached,
four sides of the CTT (i.e., right and left, and front and back faces) are maintained at the
confining pressure value, whereas, the pressure is increased on the top and bottom faces
until failure.
Figure 2.3: Conventional triaxial compression (CTC) test.
2.9 Determination of the Constitutive Model Parameters
Many researchers have used the CTT in determining constitutive model
parameters. The work done by the researchers are discussed below.
Li and Puri (1996) studied the anisotropy in cohesive and cohesionless powder.
They studied the effect of particle shape and deposition method on the anisotropy.
Δσ1
Δσ2
Δσ3
Δσ1 = Δσ2 = Δσ3
σ0 = σ1 = σ2 = σ3 σ1’ > σ2’ = σ3’
σ1
σ2
σ3
σ1
σ2
σ3
Application of initial confining pressure Maintenance of horizontal pressure while increasing vertical pressure
17
Hydrostatic triaxial compression (HTC) and conventional triaxial compression (CTC)
tests were conducted on four powders. Two of the powders were cohesive: wheat flour
(irregular shaped particle) and potato starch (rounded) and two were cohesionless
powder: glass beads (spherical) and milled glass fiber (cylinder). Li and Puri (1996) used
two different sample filling methods, tapping and plunging, to fill cubical sample holder.
They reported that particle shape, deposition method and cohesion affected the
anisotropy. Anisotropy decreased with roundness of the particle.
Kamath and Puri (1997) used the CTT for measuring the parameters for wheat
flour. They used a modified Cam-clay model to predict the mechanical behavior. CTT
was used to load the sample along isotropic, deviatoric, and mean effective stress path.
Li and Puri (2003) used flexible membrane CTT to measure the true three-
dimensional response of powders. In their study, compression behavior and strength of a
microcrystalline cellulose powder, a spray-dried alumina powder, and a fluid-bed-
granulated silicon nitride based powder were measured. To characterize the mechanical
behaviour, three types of triaxial stress paths, that is, HTC, CTC, and the constant mean
pressure triaxial compression (CMPTC) tests were performed. They found that bulk
modulus value increased with an increase in isostatic pressure. The shear modulus and
failure stress value increased with an increase in confining pressure. The shear modulus
value and failure stress determined from the CTC test were consistently greater than
those from the CMPTC test at the same constant mean pressures.
Mittal and Puri (2005) studied the rate-dependent mechanical behavior of a dry
industrial powder using a cubical triaxial tester within the context of a new elasto-
viscoplastic model (PSU-EVP model). The compression and shear properties of the
powder were quantified at different compression levels. Test results showed that the
compression and shear responses of the powder were nonlinear, consistent, and
reproducible. The model parameters were determined using HTC and CTC tests.
Sinka et al. (2001) investigated compaction behavior of steel powders, hard
metals, and ceramic powders using a high pressure triaxial testing facility. Results from
isostatic compaction, simulated closed die compaction, and compaction along different
radial loading paths in stress space are reported for six commercial powders. The
18
experimental data are compared and considerations regarding the constitutive modeling
of the compaction response of the different classes of materials are presented.
Tripodi et al. (1994) and Tripodi (1994) used a triaxial tester to determine the
constitutive parameters for the modified Cam-clay model for wheat flour. They
developed a comprehensive finite element model to predict the stress distribution in
powder and strain developed in the cylinder wall.
Yi et al. (2001) studied the bulk mechanical behavior of angular sand, round sand
and their binary mixtures. In the study, the effect of individual sand component on the
behavior of the mixture was not discussed. The effect of varying the percent of both
components on the property of the mixture was not studied. The study of the effect of
component on the mixture is needed. Mittal et al. (2001) studied the effect of moisture on
mechanical behavior root zone sand. Yi et al. (2002) studied the effects of organic and
moisture content on mechanical behavior of root zone sand.
2.10 Tablet Quality
In the previous sections the various constitutive models, their associated
parameters, and determination of these parameters were discussed. The main application
of these models and their parameters with respect to compaction is to learn the
compaction behavior and tablet quality. The tablet quality is important for its handling
and end use. The work done by various researchers to evaluate the tablet quality is
discussed below.
Shu et al. (2002) manufactured tablets from 30% (w/w) co-ground mixture of D-
mannitol and crospovidone (mixed ratio 9:1) mixed with 65.5% (w/w) of non-ground
mannitol, 4% (w/w) of crospovidone, and 0.5% (w/w) of magnesium stearate. They
reported that adding a coground mixture of D-mannitol and crospovidone was useful in
enhancing hardness of the tablets, which could not be achieved by addition of their
individually ground mixtures. However, the components that had the dominant effect on
hardness were not studied.
19
2.11 Factor Affecting Compression and Tablet Quality
2.11.1 Particle Size Distribution and Grading
The highest density for a loose powder is obtained when the voids among the
largest particles are filled just with smaller particles, and these voids are in turn filled
with still smaller particles, and so on. This is known as particle size grading. Particle
size grading along with particle size distribution are helpful in obtaining a good particle
packing, which in turn improves the quality of the tablet. However, a very broad particle
size distribution may also promote the undesirable phenomenon of size segregation.
2.11.2 Particle Shape
It is desirable to obtain spherical-shaped granules for better flow and compression
characteristics. Nearly spherical-shaped granules can be obtained by subjecting the
powder to various granulation techniques such as spray drying, fluid bed granulation, and
high-shear granulation.
2.11.3 Bulk and Tap Density
Bulk density is the density of the loose powder in the die. It is desirable to obtain
as high a bulk density as possible. Tap density is the density of a loose powder which is
obtained after a powder is subjected to pre-decided number of tappings or to vibration
conditions (ASTM B527, 2006). The tap density is usually higher than the bulk density as
tapping and/or vibration leads to particle rearrangement, thereby reducing the voids in
microstructure.
2.11.4 Moisture Content
Water is the most common liquid used in agglomeration and the amount added
must be maintained within a narrow range because granule growth is very sensitive to the
amount of liquid in the system. The moisture content favorable for granulation has been
found to be dependent upon the spread of the particle size distribution (Stanley-Wood,
1990).
2.11.5 Binders
In order to induce size enlargement, organic chemicals known as binders are
incorporated into particle assemblies. Binders in the form of either matrix, film, or
chemical types contribute significantly to the bond strength. These immobile liquid
binders affect the type of granule produced not only in the mechanism of agglomeration
20
but also by their distribution within the agglomerate. In wet massed agglomerates the
binder tends to be evenly distributed throughout the granule while with spray-dried
material the surface shell shows a high concentration of binder (Stanley-Wood, 1990).
Carneim (2000) studied granulated ceramic powder system with systematically varied
binder content and binder plasticity. α-alumina was used as the inorganic component and
polyvinyl alcohol as the base binder system. Carneim found that green strength increased
and achievable green density decreased with increasing binder content.
2.11.6 Plasticizers
A plasticizer is added to modify the viscoelastic properties of a condensed binder-
phase film on the particles. Generally, powder systems containing a binder are
commonly molded above the glass transition temperature of the binder. The presence of
the small “plasticizing” molecules softens and increases the flexibility of the binder but
also reduces its strength. The plasticizer effectively reduces the glass transition
temperature of the binder (Reed, 1995).
2.11.7 Lubricants
A lubricant is a surfactant that is strongly adsorbed and especially effective in
reducing the coefficient of friction between the powder and the die wall. Effective
boundary lubricants must have high adhesion strength but low shear strength (Reed,
1995).
2.12 Tablet Quality Parameters
Mittal (1999) listed some of the key parameters that can be used to test the quality of
the tablet. These parameters are: (1) Radial strength; (2) Axial compressive strength; (3)
Isotropy ratio; (4) Work of failure; (5) Indentation hardness.
2.13 Effect of Compression Rate on Tablet Quality
Compression rate influences the mechanical behavior of powder and quality of a
tablet. Mittal and Puri (2005) studied the effect of compression speed on mechanical
behavior of a dry industrial powder. They observed that failure stress decreased with
increasing compression rate, in general, and the compression rate does have substantial
effect on the compressibility and shear behavior of powders. Tye et al. (2005) examined
21
the effects of tableting speed on the compressibility (relationship between compression
pressure and solid fraction or porosity), tabletability (relationship between tensile
strength and compression pressure), and compactibility (relationship between tensile
strength and solid fraction) of four common direct compression excipients and a placebo
formulation. The tabletability and compressibility of some of these materials were
observed to be speed-dependent; whereas, the compactibility of all materials tested was
essentially independent of tableting speed.
The tensile strength at different compaction pressures at different dwell times has
also been studied by Tye et al. (2005). The tensile strength increased with the increase in
compaction pressure. The dwell time also affected the tensile strength. In general, tensile
strength was higher at high dwell time.
2.14 Effect of Deposition Method on Tablet Quality
Deposition method of powder into the die can affect the quality of pressed tablets.
Work has been done to see the effect of deposition method on tablet quality. Mittal and
Puri (1999a) and Mittal (1999) studied the influence of different deposition methods on
the mechanical properties and tablet quality. Some of the quality parameters had good
correlation with deposition method and mechanical behavior.
2.15 Effect of Powder Constituent on Tablet Quality
The tablet is comprised of a number of components that contribute to its quality.
Some studies on the tablet of binary mixtures have been conducted. Wu et al. (2005)
studied the tensile strength of tablets of single-component powders and the binary
mixture of these powders. They used microcrystalline cellulose (MCC),
hydroxypropylmethyl cellulose (HPMC), and starch as constituent powders. The mixture
of MCC and HPMC at three different ratios (50:50, 90:10, and 10:90) and mixture of
MCC and starch at three different ratios (50:50, 80:20, and 20:80) were used to form the
tablet. The tensile strength of tablets was found to be proportional to the porosity or
relative density. A predictive model for tensile strength, based upon the Ryshkewitch-
Duckworth equation was developed. The model was validated with experimental data for
various binary mixtures.
22
Alebiowu and Itiola (2003) studied the effect of starch on the properties of
paracetamol tablet formulation. They used native starch as binder from different sources
such as corn, sorghum and plantain. The tensile strength was found to be different for
different starch and increased with relative density.
Kuentz and Leuenberger (2000) analyzed the tensile strengths of tablets formed
from binary mixtures of well and poorly compacted substances. Mixture of Avicel PH101
and paracetamol at different ratios (the amount of Avicel varied from 30 to 100%) were
chosen as a model system. They proposed two laws based upon the theory of percolation;
one for the tensile strength as a function of relative density of the mixture and the other
for relationship between strength and compaction pressure.
2.16 Determination of Tablet Quality
The important quality metrics used in industries for tablets are tensile strength,
axial strength, indentation hardness, and friability.
2.16.1 Tensile strength
Tensile strength can be determined from diametrical compression test using a
universal testing machine. Wu et al. (2005) determined the tensile strength using an
Instron universal testing machine to measure the maximal diametrical crushing force (F).
The tensile strength (σt) was calculated as follows:
tdF
t πσ 2
= (2.23)
where d and t are the diameter and thickness of the tablet, respectively.
2.16.2 Hardness
Hardness may be defined as the resistance of a solid to local permanent
deformation (Tabor, 1951). Leuenberger and Rohera (1986) discussed hardness tests in
their review paper. According to them hardness is related primarily to the plasticity
assesses a number of fundamental material properties and is usually measured by
indentation test. They divided the hardness testing technique into two groups: 1) hardness
determination by static impression method; and 2) hardness determination by dynamic
23
method. The first method i.e. hardness determination using static methods are most
widely used. The Brinell hardness number (BHN) is expressed as the ratio of the load to
the diameter of the indentation and can be calculated as:
hDF
dDDDFBHN
ππ
2)(
222
=−−
= (2.24)
where, F = Indentation Force,
D = diameter of indenter,
d = diameter of indent,
h = depth of indentation.
2.16.3 Friability
It is the measure of the tablet’s resistance to subsequent process condition and
transportation. Friability is measured using a rotating drum known a friabilator. Riippi et
al. (1998) performed the friability test on erythromycin acistrate tablets using a friabilator
for 100 rotations. Ameye et al. (2002) performed the friability test on tablets formed
using granulated powder formulation. They used Pharma Test-type friabilator at 25 rpm
for 4 min (100 rotations). Dedusted tablets were reweighed and percentage loss in weight
was measured as friability.
2.17 Granulation
Granulation is the process in which powder particles are made to adhere by some
physical means to form large object called granules. In case of pharmaceutical granules,
generally the size range between 0.2 and 4.0 mm, depending on their subsequent use. In
the majority of cases granulation is done during the production of tablets or capsules.
Generally, granules are an intermediate product that have a typical size range between 0.2
and 0.5 mm; however, larger granules are used as a dosage form in their own right.
2.17.1 Purpose of Granulation
Granulation is considered to be a very costly unit operation. Even though granulation
is done prior to tablet formation for the following benefits:
• To prevent segregation of the constituents of the powder mixture
24
• To improve the flowability
• To improve the compaction characteristics of the mixture
• To reduce the dust during handling of the powder which can be hazardous to the
person directly in contact with the powder
• To prevent caking due to moisture absorption in case of hygroscopic powder
2.17.2 Methods of Granulation
The granulation method can be broadly classified as dry and wet method.
2.17.2.1 Dry Method
In this methods powder particles are aggregated using high pressure. This is done by
two different methods.
1. A large tablet (known as a ‘slug’) is produced in a heavy-duty tabletting press
2. The powder is compressed and passed between two rollers to form a sheet. This
method is known as roller compaction.
In both cases these large aggregates are broken into small granules using a mill.
These granules are usually sieved to get the desired size for tablet formation.
2.17.2.2 Wet Method
Wet granulation is done using a granulation fluid or liquid. Some of the
commonly used liquids are water, ethanol, and isopropanol. Generally a binder is used to
ensure particle adhesion. Binders are either mixed with the dry powder or the solvent.
The liquid added is mixed thoroughly with the dry powder by some mechanical means.
The granules formed are dried and sometimes sieved to get the desired size fractions.
2.17.3 Granulation Process
Granulation is a complex process with several physical phenomena occurring. These
phenomena can be divided into three groups of processes (Litster and Ennis, 2004):
25
2.17.3.1 Wetting, Nucleation, and Binder Distribution
This is the first stage of granulation, in which the addition and distribution of
binder to form nuclei granules takes place. The liquid binder is usually sprayed onto the
moving powder bed. Ideally each drop should penetrate into the powder bed making
particle to form a single granule nucleus. Sometimes large wet agglomerates are formed
at the surface. These agglomerates are usually broken by the high shear force of the
rotating blades.
2.17.3.2 Consolidation and Growth
The granule nuclei formed in the first stage consolidate through collisions with
other granules and granulator blade. The extent of consolidation depends on the intensity
of agitation and resistance of the granules to deform. Granules made from fine powders
deform less and consolidate slowly while granules from coarse powders have more
consolidation. The granulation consolidation controls the granule porosity.
Granule growth occurs by coalescence of two granules. The granules collide and
stick to each other to form a large granule. For successful coalescence (a) the energy of
impact must be absorbed to avoid rebound; and (b) a strong bond must be formed
between the colliding granules. The presence of liquid is also a very important factor for
granule growth.
2.17.3.3 Attrition and Breakage
The breakage of the granules can occur in two ways (a) breakage of wet granules
in the granulator (b) attrition or fracture of granules in the drier or subsequent handling.
The granules formed through the process of nucleation and growth are finally dried. The
attrition of granules results in the formation of dusts, which could lead to a hazardous
situation to be avoided.
2.17.4 Wet Granulators
Wet granulators are commonly used in the pharmaceutical industries for forming
the granules. Various wet granulators are discussed in the following sections.
26
2.17.4.1 Shear Granulator
The mixed powders are fed into the bowl of the planetary mixer and granulating
liquid is added as the paddle of the mixer agitates the powders. The planetary action of
the blade when mixing is similar to that of a household mixer. The moist mass has then to
be transferred to a granulator, such as an oscillating granulator. The rotor bars of the
granulator oscillate and force the moist mass through the sieve screen, the size of which
determines the granule size. The mass should be sufficiently moist to form discrete
granules when sieved. If excess liquid is added, strings of material will be formed and if
the mix is too dry the mass will be sieved to powder and granules will not be formed. The
granules can be collected on trays and transferred to a drying oven (Aulton, 2002).
2.17.4.2 High-speed Mixer/Granulators
This type of granulator is used extensively in pharmaceutics. The machines have a
stainless steel mixing bowl containing a three-bladed main impeller, which revolves in
the horizontal plane, and a three-bladed auxiliary chopper (breaker blade) which revolves
either in the vertical or the horizontal plane. The unmixed dry powders are placed in the
bowl and mixed by the rotating impeller for a few minutes. Granulating liquid is then
added via a port in the lid of the granulator while the impeller is turning. The granulating
fluid is mixed into the powders by the impeller. The chopper is usually switched on when
the moist mass is formed, as its function is to break up the wet mass to produce a bed of
granular material. Once a satisfactory granule has been produced, the granular product is
discharged, passing through a wire mesh which breaks up any large aggregates, into the
bowl of a fluidized-bed drier (Aulton, 2002).
2.17.4.3 Fluidized Bed Granulators
Fluidized-bed granulators have a similar design and operation to fluidized-bed
driers, i.e. the powder particles are fluidized in a stream of air, but in addition granulation
fluid is sprayed from a nozzle on to the bed of powders. Granulating fluid is pumped
from a reservoir through a spray nozzle positioned over the bed of particles (Aulton,
2002).
27
2.17.4.4 Spray Driers
In this method granular product is made from a solution or a suspension of the
powder particles. The powder solution is sprayed through a nozzle into a chamber. The
spherical granules are dried using hot air (Aulton, 2002; Parikh, 1997).
2.17.5 Effect of Process Parameters on Granulation
The properties of granules depends upon various parameters such as binder
content, time of granulation, amount of liquid addition and particle size distribution of
powder. Walker et al. (2006) studied the effect of process parameters such as binder
content and binder viscosity on granulation time and particle size distribution. They
reported that after initial nucleation the granulation mechanism was dependent upon
binder content and binder viscosity. Binder viscosity had a significant affect on the
granule growth mechanism. Granulation with a binder viscosity of 500 MPa.s resulted in
granule growth by coalescence, however, an increase in binder viscosity resulted in less
coalescence and a lower granule growth rate.
Saleh et al. (2005) studied the mechanism of wet granulation and effect of
physico-chemical properties and operating conditions on the growth mechanisms.
Experimental data showed that as the liquid content increases, the granulation process
proceeds through three distinct growth regimes whatever the nature of the powder, the
binder liquid or the operating conditions used. The first stage is nucleation of primary
particles (regime 0). In first regime new agglomerates are not created and there is a
balance between attrition (creating fines) and fines consuming growth mechanisms
(agglomeration, layering). In the second regime, granules growth takes place by layering
of the fine agglomerates onto the surface of the other species. The phenomena that
govern the transition between the first and the second regime are the densification of the
granules and the binder transport to the granule surface. Third and final regime starts
when the fine agglomerates are entirely exhausted and granulation mechanism is a
preferential coalescence mechanism of small and coarse granules.
Alkan and Yuksel (1986) studied the formulation of lactose, starch and
polyvinylpyrrolidone (PVP) to see the effect of binder (PVP) on final granule size, size
distribution and friability in a fluidized bed granulator. The mean granule size increased
28
with increase in the binder. The increase in the size was more significant upto 6% binder.
The granule friability decreased with increase in binder content. They reported that there
is a critical binder level at which the formation of the primary granules come to an end.
After this critical binder content, the granule growth occurs by agglomeration of primary
granules. The physical properties of granules formed before and after this critical binder
are different.
2.18 State of the Art Related to Mechanical Properties and Tablet Quality
The review of literature presented in the previous sections gives the overview of
the work done by various researchers in the area of mechanical properties of powder and
tablet quality. From the review of literature it can be stated that many researchers have
worked in these areas.
Some work has been reported on the study of mechanical behavior of powder or
particulate mixture. Yi et al. (2001) studied the bulk mechanical behavior of binary
mixtures of angular and round sand; however, the effect of individual sand on the
behavior of the mixture has not been studied. The effect of varying the percent of
components on the properties of the mixture were not evaluated. Shu et al. (2002)
manufactured tablets from a mixture of D-mannitol and crospovidone with non-ground
mannitol, crospovidone, and magnesium stearate. They reported that adding a coground
mixture of D-mannitol and crospovidone is useful in enhancing hardness of the tablets,
which could not be achieved by addition of their individually ground mixtures. However,
the components that had the dominant effect on the hardness were not studied. Mittal and
Puri (1999 a, b) and Mittal (1999) studied the correlation between different deposition
methods, mechanical properties, and quality of tablets; however they did not study the
powder mixture and effect of the constituents on tablet quality. Wu et al. (2005) studied
the tensile strength of tablets of single-component powders and binary mixture of these
powders. No systematic study on the fundamental mechanical properties of granulated
powder has been reported. Binder plays an important role in granulation and tablet
formation. Effect of binder on the mechanical properties of powder mixture (dry blend
and granulated) has not been studied.
29
From the review of literature one can conclude that a detailed systematic study of
true mechanical behavior of granulated powders is missing. Very few studies have been
reported for mechanical properties of dry mixture and there is a need to study the
mechanical properties of dry blended and granulated powder formulation with an
emphasis on effect of binder. Also, a mathematical relationship needs to established
between mechanical properties and tablet quality parameters.
30
Chapter 3 - Goal and Objectives 3.1 Goal
From the review of literature it was noted that research has been conducted to
determine the mechanical properties of powders, but the effect of constituents on the
overall mechanical behavior of powder mixture has not been systematically studied.
Therefore, the goal of the research was to establish a relationship between the mechanical
properties of pharmaceutical powder formulation (dry blended and wet granulated) with
an emphasis on effect of binder and tablet quality parameters.
3.2 Objectives The specific objectives formulated to achieve the goals were: Objective 1.
To measure the mechanical behavior of dry and granulated pharmaceutical powder
formulations at varying binder contents using the cubical triaxial tester over a range of
loading conditions.
Objective 2.
To determine the fundamental elastic, elastoplastic, and rate-dependent properties and
binder content effect by analyzing the data from Objective 1.
Objective 3. To design and fabricate a die and punch assembly and form tablets using dry and
granulated pharmaceutical powder formulations and to determine the quality parameters
of tablets.
Objective 4.
To develop and explain relationships between the fundamental mechanical properties of
dry and granulated formulations and the tablet quality parameters, and recommend
powder formulation properties that are best predictors of quality parameters.
31
Chapter 4 - Methodology
This chapter presents the methods of research to accomplish the various
objectives listed in Chapter 3. As mentioned previously, the goal of the proposed research
was to develop a mathematical relationship between the mechanical behavior of powder
mixtures with emphasis on binder content and tablet quality parameters. This chapter
describes the various tests conducted to determine the mechanical properties and
scientific techniques used to determine various parameters. The method for
determination of various tablet quality parameters is also given. Finally, methods to
develop relation between the mechanical behavior of powder mixture with emphasis on
binder content and tablet quality and development of the models are explained.
4.1 Materials
Herein, research was conducted using pharmaceutical powder formulations. The
formulations are composed of Avicel (filler), Methocel (binder), Magnesium stearate
(lubricant), Ac-Di-Sol (disintegrant), and Acetaminophen (active pharmaceutical
ingredient). The composition of the formulations are given in Table 4.1. Three different
levels of methocel (binder): 0(no binder), 5, and 10%, were used for preparing the
formulations. The proportion of other four ingredients were maintained at same level, i.e.,
Avicel: Acetaminophen: Ac-Di-Sol: Magnesium stearate:: 0.90:0.05:0.03:0.02. The
amount of binder and other ingredients were based upon the actual tablet formulation
being used in industry (Singh, et al., 2008; FMC, 2008).
Table 4.1 Formulation of pharmaceutical powder for dry blend and wet granulation
A. Methocel (Binder) 0 5 10 B. Other ingredients 100 95 90
B1. Avicel 90 85.5 81 B2. Acetaminophen 5 4.75 4.5 B3. Ac-Di-Sol 3 2.85 2.7 B4. Magnesium stearate 2 1.9 1.8
4.1.1 Avicel
Avicel PH 102, i.e., micro crystalline cellulose (FMC Biopolymers, Philadelphia,
PA) was used as filler agent in the tablet formulation. Avicel has median particle (d50) of
32
78 μm (Table 4.2) that are elongated and needle-like in shape (Figure 4.1). The particle
size distribution is shown in Figure 4.2. Avicel is a commonly used filler in
pharmaceutical tablets for its excellent compaction quality in dry as well as granulated
form. In addition, Avicel is chemically neutral.
Figure 4.1 Micrograph of Avicel PH 102
Table 4.2 Properties of formulation ingredients Parameters
Ingredients Bulk density (g/cc)
Particle density* (g/cc)
Median (d50) particle size† (μm)
Avicel PH 102 0.41 1.61 78 Methocel 0.42 1.33 108 Acetaminophen 0.25 1.36 15 Ac-Di-Sol 0.46 1.66 60 Magnesium stearate 0.26 1.13 10 * Measured using Micromeretics Multivolume Helium Pycnometer 1305 (Boynton Beach, FL) † Measured using the Malvern Instruments Mastersizer (Westborough, MA)
4.1.2 Acetaminophen (para-acetylaminophenol, C8H9NO2)
Acetaminophen, also known as Paracetamol, is an active pharmaceutical ingredient
(API), which is widely-used as analgesic and antipyretine. Acetaminophen has median
particle 15 μm (Table 4.2) that are elongated and needle-shaped with sharp edge (Figures
4.3 and 4.4).
Figure 4.2 Particle size distribution of Avicel PH 102
0
20
40
60
80
100
120
0.01 0.1 1 10 100 1000
Particle s ize (m icrom eters)
Cum
ulat
ive
% le
ss th
and50=78µm
33
4.1.3 Ac-Di-Sol
Ac-Di-Sol (FMC Biopolymers, Philadelphia, PA) is a cross caramellose sodium,
which is an internally cross-linked sodium carboxymethyl-celluose. The cross linkings
serve to greatly reduce water solubility, allowing the material to swell and absorb many
times its weight of water. Due to its swelling property, Ac-Di-Sol is a very commonly
used disintegrant and dissolution aid in pharmaceutical tablets and capsules. Ac-Di-Sol
has median particle size (d50) of 60 μm (Table 4.2) that are fibrous-shaped (Figure 4.5).
The particle size distribution is shown in Figure 4.6.
Figure 4.5 Micrograph of Ac-Di-Sol
Figure 4.6 Particle size distribution of Ac-Di-Sol
Figure 4.4 Micrograph of Acetaminophen at 150x Magnification
0
20
40
60
80
100
120
0.01 0.1 1 10 100 1000
s ize, m icrom eters
cum
ulat
ive
% le
ss th
an
d50=60 µm
Figure 4.3 Micrograph of Acetaminophen at 400x Magnification
34
4.1.4 Magnesium Stearate
Magnesium stearate (C36H70MgO4), magnesium salt of stearic acid, is one of the
most widely used lubricant in tablet compaction. Magnesium stearate has median particle
size of 10 μm (Table 4.2) that are nearly round-shaped (Figures 4.7 and 4.8).
4.1.5 Methocel (hydroxy propyl methyl cellulose)
Methocel, also known as, hydroxy propyl methyl cellulose or HPMC is a widely
used binder in pharmaceutical industry in dry as well as wet state. Methocel has median
particle size (d50) of 108 μm (Table 4.2) that are elongated in shape (Figure 4.9). The
particle size distribution is shown in Figure 4.10.
Figure 4.8 Particle size distribution of Magnesium stearate at 600x Magnification
Figure 4.10 Particle size distribution of Methocel
0
20
40
60
80
100
120
1 10 100 1000
particle size (micrometers)
cum
ulat
ive
% le
ss th
an
D50=108 µm
Figure 4.7 Particle size distribution of Magnesium stearate at 400x Magnification
Figure 4.9 Micrograph of Methocel
35
4.1.6 Granules with 5% Binder
Granules were formed at 5% as per the formulation given in Table 4.1 (Section
4.1). These granules had median particle size (d50) of 200 μm that were near angular in
shape (Figure 4.11). The particle size distribution is shown in Figure 4.12.
Figure 4.12 Particle size distribution of granules (5% binder)
0
20
40
60
80
100
120
10 100 1000
Particle size, micrometersC
umul
ativ
e %
less
than
d50=200 µm
Figure 4.11 Micrograph of granules (5% binder)
36
4.1.7 Granules with 10% Binder
Granules were formed also at 10% as per the formulation given in Table 4.1
(Section 4.1). These granules formed had median particle (d50) of 300 μm that were
angular shaped (Figure 4.13). The particle size distribution is shown in Figure 4.14.
4.2 Laboratory Description
Mechanical properties of dry blend and granulated powder formulations were
determined using a medium pressure cubical triaxial tester. A die and punch assembly
was designed and fabricated to form tablets using a hydraulic press. Powder ingredients
were dry-blended using Manual Mini-Inversina (Bioengineering AG, Switzerland). High
shear mixer/granulator (Model HSM-100LSK, Ross Mixing, Port St. Lucia, FL) was used
for granulating the powder mixture.
4.3 Experimental Design
Pharmaceutical formulation described in section 4.1 and summarized in Table 4.1
were used for the study. The details of the different experiments conducted are given in
the following sections.
4.3.1 HTC and CTC Tests
HTC and CTC tests were conducted on dry and wet granulated powder
formulations. These tests were conducted at two binder contents of 5 and 10% and one
Figure 4.14 Particle size distribution of granules (10% binder)
0
20
40
60
80
100
120
1 10 100 1000
Particle size, micrometersC
umul
ativ
e %
less
than
d50=300 µm
Figure 4.13 Micrograph of granules
(10% binder)
37
without binder. To evaluate the effect of loading rate, tests were conducted at two
different loading rates of 10 and 20 MPa/min. These loading rates were selected on the
basis of study conducted by Mittal (2003) to evaluate the capability of CTT to handle
maximum loading rate. Mittal reported that meaningful data is obtained only upto a
loading rate of 20 MPa/min. HTC tests were conducted upto 10 MPa pressure level. This
pressure was selected on the basis of safe limit of CTT (Section 2.6.3.2). The stress path
used for the HTC test was 0.0 – 2.5 – 0.3 – 5.0 – 0.3 – 10.0 – 0.3 – 10.0 – 0 to utilize the
entire regime of the tester. First, pressure up to 2.5 MPa was applied. After reaching 2.5
MPa, the pressure was reduced to 0.3 MPa (not 0 MPa) to ensure positive contact
between pressure application membrane and the sample. Second, the pressure was
increased from 0.3 MPa to 5.0 MPa and again reduced to 0.3 MPa and so on at the same
unloading rate as the loading rate.
CTC tests were performed at three confining pressures of 1.0, 2.0, and 3.0 MPa
based on initial trials conducted to evaluate the capability of the membranes to handle the
pressure. When the initial tests were conducted at 4.0 MPa confining pressure, the
membranes could not withstand the excessive pressure resulting in compromising
membranes’ integrity, i.e., developed a pinhole or rip or were ruptured. After reaching the
confining pressure, stress difference upto 2 MPa was applied. The stress path used for the
CTC test for dry formulation at 2 and 3 MPa confining pressure was 0.0 – 1.0 – 0.0 – 2.0
– 0.0 – 2.0 – 0.0 MPa, i.e., first, stress difference up to 1.0 MPa was applied. After
reaching 1.0 MPa stress difference, the pressure was reduced to 0.0 MPa. Second, the
stress difference was increased from 0.0 MPa to 2.0 MPa and again reduced to 0.0 MPa
and so on at the same unloading rate as the loading rate. The stress path for dry
formulation at 1 MPa confining pressure was 0.0 – 1.0 – 0.0 – 1.0 – 0.0 MPa. The stress
path for granulated formulation at all confining pressure were 0.0 – 1.0 – 0.0 – 1.0 – 0.0
MPa. Three replications for each test were carried out based on the tests conducted by
earlier researchers (Li, 1995 and 1999; Kamath 1996; Huang , 2000; Mittal 2003). The
experimental design for HTC and CTC is given in Tables 4.3 and 4.4, respectively.
38
Table 4.3 Experimental design for HTC tests
Binder content (%) Stress path (MPa)
Formulation type Loading rate 0 5 10
10 MPa/min 3* 3 3 Dry blend 20 MPa/min 3 3 3 10 MPa/min 3 3 3
0.0 – 2.5 – 0.3 – 5.0 – 0.3 – 10.0 – 0.3 – 10.0 - 0 Wet granulated
20 MPa/min 3 3 3 *Number of replicates
Table 4.4 Experimental design for CTC tests
Binder content (%)
Formulation type
Loading rate
(MPa/min)
CP* (MPa)
Stress path (MPa)
0 5 10 1 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3** 3 3 2 0.0 – 1.0 – 0.0 – 2.0 – 0.0 – 2.0 –
0.03 3 3
10
3 0.0 – 1.0 – 0.0 – 2.0 – 0.0 – 2.0 – 0.0
3 3 3
1 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3 2 0.0 – 1.0 – 0.0 – 2.0 – 0.0 – 2.0 –
0.03 3 3
Dry blend
20
3 0.0 – 1.0 – 0.0 – 2.0 – 0.0 – 2.0 – 0.0
3 3 3
1 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3 2 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3
10
3 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3 1 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3 2 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3
Wet granulated
20
3 0.0 – 1.0 – 0.0 – 1.0 – 0.0 3 3 3 *CP - Confining pressure **Number of replicates
4.3.2 Formation of the Tablets
Tablets at binder contents of 5 and 10% and without binder were formed at
pressures of 70 and 90 MPa; commonly used pressures in industrial applications. The
load was applied at a rate of 1 MPa/s. Three replications of each sample were prepared.
All quality parameters (discussed in Section 4.8) were determined for each tablet.
39
4.4 Blending and Granulation
All the powder constituents were weighed using a balance (Acculab, readability
± 0.001 g) as per the proportion mentioned in Table 4.1. The powders were blended using
manual Mini-Inversina (Bioengineering AG, Switzerland) capable of giving 360° motion
to powder (Figure 4.15). For determining the mixing time, colored powder was used.
After various trials it was observed that the after five minutes the colored particles were
uniformly distributed. Based on these trials, the mixing was performed at 80 rpm for 5
minutes.
The granulation was done using a high shear mixer (Model HSM-100LSK, Ross
Mixing, Port St. Lucia, FL) shown in Figure 4.16. The granulation was done in batch size
of 10 g, which was determined as the optimum load size based on vendor’s information
and several initial in-house trials. Prior to granulation, ingredients of powder formulation
were weighed and placed in a beaker (50 ml) which was then attached to the high shear
mixer. The mixer blade was rotated at about 3,500 rpm for 10 s to condition and
uniformly mix the formulation. After conditioning, 4.8 g water was sprayed (6 sprays)
using a hand operated batch-type sprayer and the mixer was operated for 10 s to
uniformly distribute the water. The water sprayed powder was removed and the lumps
formed were broken manually. Delumped mix was again transferred into the beaker and
the high shear mixer was again operated for 20 s to complete the process of granulation.
The granulated formulation having moisture content of 30% (wet basis) was dried in an
oven at temperature of 50°C for approximately 3 h to reach the desired moisture of 2-3%.
The dried granules were sieved using US standard sieve No. 16 (opening size 1,180 µm)
and sieve No. 100 (opening size 100 µm) using 4 2 series to get the desired size range
(i.e., 100 µm<dparticle<1,180 µm). The granule size range was established to keep the
particle size distribution range broad while minimizing segregation (Duffy and Puri, 2002
and 2003). The broad particle size allows the fines to fill the void spaces, which results in
better particle packing. These granules were stored in air sealed plastic bags (double
bagged) to prevent moisture absorption from ambient.
40
Figure 4.15. Powder mixer Figure 4.16. High shear mixer granulator
4.5 Compression Tests
HTC and CTC tests were conducted using a CTT to determine the mechanical
properties of the powders’ formulations. The HTC and CTC test data were stored in a
computer through LabView software (National Instruments, version 8.2, Austin, TX) and
analyzed further to determine the parameters.
4.5.1 Cubical Triaxial Tester
The flexible boundary medium pressure cubical triaxial tester (CTT) originally
developed by Li and Puri (1997) and upgraded by Mittal (2003) was used for
compression tests. Change in the dimensions of the original cubical sample (50 mm x 50
mm x 50 mm) were measured using six linear motion potentiometers (LMPs); one along
each face. By using a reliable data acquisition system, real-time data of the pressure and
the displacement experienced by the powder sample were collected. These data were
analyzed to obtain the material parameters of the powder formulations under different
pressures.
4.6 Description of Technique for Determination of Different Parameters of Modified
Cam-clay Model
Data obtained from the HTC and CTC tests were analyzed to determine the
parameters of the constitutive model. As mentioned in the Section 2.2.5, the determined
41
parameters were bulk modulus, failure stress, shear strength, compression index, spring-
back index, and slope of the critical state line.
4.6.1 Determination of Bulk Modulus
Bulk modulus (K) was determined by using the HTC test results. In this research,
method used to determine the bulk modulus was different from that used by earlier
researchers. Previously, K was determined by performing a linear regression on the entire
unloading and reloading curve of a plot having stress or pressure on x-axis and strain on
y-axis (Figure 4.17). The CTT is a stress or pressure controlled-type instrument in which
the pressure is applied through pressurized nitrogen gas and change in dimension is
measured as a response. Hence, in this these tests, the stress was an independent
parameter and strain was dependent parameter. For statistical analysis, the independent
parameters should be on x-axis and dependent parameter should be on y-axis. Hence, for
determination of bulk modulus, plot was made with stress on x-axis and strain on y-axis
(Figure 4.18).
To determine the bulk modulus at a given mean pressure, using the new method, a
linear regression was performed on the entire unloading and reloading curve (Figure
4.18) with stress as independent variable and strain as dependent variable. The lowest
point of the loop was fixed at the intersection of x and y-axes (0, 0). The slope of the
linear regression line gave the inverse of the bulk modulus (K) at the pressure at which
the sample was unloaded. In this way, the bulk modulus values at different pressures
were determined.
42
0
2
4
6
8
10
12
0.00 0.05 0.10 0.15 0.20 0.25 0.30Volumetric Strain
Pre
ssur
e, M
Pa
Figure 4.17 Determination of bulk modulus (K) using HTC test plot with pressure on y-axis
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 2 4 6 8 10 12
Pressure, MPa
Volu
met
ric s
trai
n
Figure 4.18 Determination of bulk modulus (K) using HTC test plot with pressure
on x-axis
4.6.2 Determination of Failure Stress
The failure stress can be determined by CTC test results. Failure is the point at which
the material (in this study various powder formulations) loses its functionality. There are
different ways to determine the failure value as follows:
1. Increase in the strain difference,
Slope = Bulk modulus
Slope= 1/Bulk modulus
43
2. Change in slope of strain difference vs. stress difference curve,
3. Critical state concept,
4. 15% axial strain value.
4.6.2.1 Increase in the Strain Difference
With the increase in stress, the strain increases. With the approach to the failure
state, the change in the strain becomes considerably high as compared to the previous
value even with a slight increase in stress (Figure 4.19). This point can be taken as the
failure stress point.
4.6.2.2 Decrease in Slope of Strain Difference vs. Stress Difference Curve
By definition, the slope of the stress difference vs. strain difference curve is zero
at the failure point. The slopes of line between each consecutive point are determined.
The point at which slope is minimum is the failure point. The magnitude of slope is
sensitive to the units of stress and strain. Therefore, both the variables should be
normalized for determining the slope.
Figure 4.19 Typical stress difference vs. strain difference plot for determination of
failure point
0
20
40
60
80
100
120
0.0 0.3 0.6 0.9Strain Difference
Stre
ss D
iffer
ence
(kPa
)
Failure point
44
4.6.2.3 Critical State Concept
The critical state concept (Desai and Siriverdane, 1984) states that a bulk material
reaches a critical volume, after which additional loading does not produce any change in
volume. The point at which the volume stops changing with load is termed as critical
void ratio or density. This point can be taken as the point of failure as shown in Figure
4.20.
Figure 4.20 Stress-strain behavior of dense and loose soils (Desai and Siriwardane,
1984)
4.6.2.4 15% Axial Strain Value
As per ASTM standard D 2850-87 (ASTM, 1995), the failure stress value is the
stress in the specimen corresponding to the minimum principal stress difference
(deviatoric stress) attained or principal stress difference (deviatoric stress) at 15% axial
strain, whichever is obtained first during the performance of a test. In a CTC tests, the
deformation in all three principal directions are measured. The axial strain is calculated
from deformation in the vertical direction, i.e., direction of applied stress increments
(Figure 4.21).
Loose
Dense
Axial strain
Volumetric Strain
Failure point
45
0
0.5
1
1.5
2
2.5
0.00 0.05 0.10 0.15 0.20 0.25
Axial strain
Stre
ss d
iffer
ence
, MPa
Figure 4.21 Typical axial stress vs. stress difference plot for determination of failure
4.6.3 Determination of Shear Modulus (G)
The shear modulus was determined by using the CTC test results for different
confining pressures. To determine the shear modulus at a given stress difference, a linear
regression was performed on the entire unloading and reloading curve (Figure 4.22) with
stress difference as independent variable and strain difference as dependent variable. The
lowest point of the loop was fixed at the intersection of x and y-axes (0, 0). The slope of
the linear regression line gives the inverse of the twice of the shear modulus (G) at the
pressure at which the sample was unloaded. In this way, the shear modulus at different
pressures were determined (Figure 4.22).
Failure point
46
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
4.6.4 Determination of Compression Index
Compression index (λ) was calculated from the HTC test data. An example is
shown in Figure 4.23. The graph of ln(pressure) vs. void ratio was plotted. The slope of
the consolidation line was used to estimate the compression index.
4.6.5 Determination of Spring-back Index
Spring-back index (к) was calculated from the HTC test data from the same graph
as for the compression index. The slope of the unloading-reloading line was used to
estimate the spring-back index (Figure 4.23).
Figure 4.22 Typical stress difference vs. strain difference plot for determining shear modulus
Slope= 1/(2*shear modulus)
47
1.7
1.9
2.1
2.3
2.5
2.7
2.9
2.0 2.5 3.0 3.5 4.0 4.5 5.0
ln(Pressure)
Void
ratio
Figure 4.23 ln(pressure) vs. void ratio plot for determination of compression and
spring-back index 4.6.6 Determination of Slope of Critical State Line (CSL) (M)
This was determined by plotting the CTC test results in the q-p plane, where p is
the mean pressure and q is the deviatoric stress or the stress difference at failure (Figure
4.24). The slope of best fit line passing through the origin was used to determine the
slope, M.
0
0.5
1
1.5
2
2.5
0 1 2 3 4
Mean pressure, MPa
Failu
re s
tress
, MP
a
Figure 4.24 Determining slope of critical state line from mean pressure (p) vs. stress
difference at failure(q) plot
Slope = Compression index
Slope = Spring-back index
48
4.7 Formation of the Tablets
The die and punch assembly was designed and fabricated to form tablets. A
material testing system (MTS 810, Eden Prairie, MN) fitted with a load cell of 100 kN ( ±
0.1 kN) and capable of applying load at varying speed was used to apply the pressure on
the powder through the punch. The tablets were formed using dry and granulated
formulations at different binder contents of 0, 5, and 10% and compaction pressures of 70
and 90 MPa. These tablets were formed at a loading rate of 1 MPa/s.
4.7.1 Die and Punch Assembly
The die and punch assembly consisted of a cylindrical die, one upper punch, and a
lower punch (Figure 4.25). These components were designed and fabricated as part of the
research. For completeness, the design of die, upper punch, and lower punch is given in
the following sections.
Figure 4.25 (a) SolidWorks® drawing of die-punch assembly (b) Photograph of die-
punch assembly components – (1) Die (2) Lower punch (3) Upper punch (4) Die plate
4.7.1.1 Design of Die
The die was designed to form the tablet of 10 mm diameter. The schematic of the
die-punch assembly and components are shown in Figure 4.25 (a) and (b). Figure 4.26(a)
is the cross sectional view of the die where,
1 2
3
4
4
1
2
3
49
a = internal diameter of the die
b= external diameter of the die
pi = pressure on internal surfaces due to the lateral component of force action on the
powder
po = pressure on external surfaces
Top and bottom surfaces are assumed to be free from load.
Body and loading are symmetric about the axis, hence shear stresses in the
tangential axis directions are not present, and only normal stresses σt (tangential
direction) and σr (radial direction) act on the element.
Consider the stress acting on the semi-circular element of thickness dr at a radial
distance r from the center of the die (Figure 4.26). The thickness in the direction
perpendicular to the paper is taken as unity. The vertical component of inward radial
stress across the diameter of the element is 2σrr and for the outward component of the
stress is 2(σr + dσr) (r + dr)
(b) (a)
Figure 4.26 Forces acting on a hollow cylindrical die
The equilibrium equation for this element is:
2σrr + 2σtdr = 2(σr + dσr) (r + dr) (4.1)
σr + dr
σt
σt1
σr
b
a
pi
po
rdr
50
Expanding and neglecting the higher order terms gives:
rr
t drdr σσσ += (4.2)
The strain or unit deformation oε in the direction perpendicular to the paper can be given as (Timoshenko and Goodier, 1951):
EErt
oμσμσε −−= (4.3)
where, µ = Poisson’s ratio, E = modulus of elasticity
or, μ
εσσ Eort −=+ (4.4)
Substituting Equation (4.4) into Equation (4.2)
122 Cdr
dr rr =+ σσ
(4.5)
where, 12CEo =−
με
or, 12 22 rCr
drdr r
r =+ σσ (4.6)
or, 12 2)( rCr
drd
r =σ (4.7)
Integrating Equation (4.7),
22
12 CrCr r +=σ (4.8)
or, 22
1 rCCr +=σ (4.9)
From Equations (4.4) and (4.9), the following is obtained:
22
1 rCCt −=σ (4.10)
At inner boundary, r = a= die inner radius, the radial stress σr becomes equal to -pi. Here, the pressure is taken as negative because the normal stress for tension is taken as positive. From Equation (4.10)
51
22
1 rCCpi +=− (4.11)
At outer boundary, r = b, the radial stress σr becomes equal to –po.
22
1 rCCpo +=− (4.12)
Solving Equations (4.11) and (4.12) one gets:
22
22
1 abpbpa
C oi
−−
=
22
22
2)(
abppba
C oi
−−−
=
Substituting C1 and C2 into Equations (4.9) and (4.10), gives:
)()(
222
22
22
22
abrppba
abpbpa oioi
r −−
−−−
=σ (4.13)
)()(
222
22
22
22
abrppba
abpbpa oioi
t −−
+−−
=σ (4.14)
For tablet die, the outer pressure po = 0 Hence,
)1( 2
2
22
2
rb
abpa i
r −−
=σ (4.15)
)1( 2
2
22
2
rb
abpa i
t +−
=σ (4.16)
The stresses are maximum at the inner surface where r = a and σr = -pi
⎥⎦
⎤⎢⎣
⎡−+
= 2
2
)/(1)/(1
babaptσ where p= pi (4.17)
The tangential elongation at inner surface is given as:
)(1rtt E
μσσε −= (4.18)
The total increase in the length of the inner edge of the die will be 2πaεt . Therefore, increase in the radius uh is given as uh = 2πaεt/2π = aεt (4.19)
52
⎥⎦
⎤⎢⎣
⎡+
−+
= μ2
2
)/(1)/(1
baba
Eapuh (4.20)
4.7.1.1.1 Calculations Based on Strength Properties of steel (Stainless steel 316 grade) (AZOM, 2008) Allowable stress, σ = 515 MPa
Modulus of elasticity, E = 193 GPa
Poisson’s ratio, µ= 0.3
Taking Factor of Safety (FOS) = 4 (considering that the material strength will reduce
with aging), allowable stress = 515/4 ≈ 129 MPa
Maximum vertical pressure to be applied = 100 MPa Horizontal force acting on the wall, pl
ppl μμ−
=1
= 0.43*100 = 43 MPa
⎥⎦
⎤⎢⎣
⎡
−+
=2
2
max )/(1)/(1
babaptσ (4.21)
maxtσ = 129 MPa
p = 43 MPa
2/1/ =ba
a = 5 mm (inner radius of the die) based on the size of the tablet to be formed
Therefore, b = 7.1 mm
Thickness = 2.1 mm
4.7.1.1.2 Calculations Based on Elongation
⎥⎦
⎤⎢⎣
⎡+
−+
= μ2
2
)/(1)/(1
baba
Eapuh (4.22)
Taking allowable strain 0.2%, FOS = 4
53
Actual allowable strain = 0.2/4 =0.05% = ε
Inner radius (a) = 5 mm Hence, uh = 5*.05/100 =0.0025
⎥⎦
⎤⎢⎣
⎡+
−+
= 3.0)/(1)/(1
10*1935*430025.0 2
2
3 baba
Solving, a/b = 0.56 Hence, b = 8.92 mm Thickness = 3.92 mm
Based on the calculations the thickness of the die wall used was 5 mm.
4.7.1.2 Design of Upper and Lower Punch
The upper punch was designed using Euler’s Equation which gives the maximum
axial load that a long, slender, ideal column can carry without buckling. The Euler’s
Equation is written as (Wikipedia):
2
2
)(KlEIF π
= (4.23)
where F = maximum or critical force, E = modulus of elasticity, I = area moment of inertia = πD4/64 D = diameter of punch, l = unsupported length of column, K = column effective length factor, whose value depends on the conditions of end
support of the column, as follows. For both ends pinned (hinged, free to rotate), K = 1.0.
4.7.1.2.1 Calculation for Upper Punch
E = 1.93 x 1011 N/m2, D = 10 mm, I = area moment of inertia = 5 x 10-10 m4 l = 60 mm,
K = 1.0. F = 244 kN
Hence, punch with 10 mm diameter can be safely be used for making the tablets.
54
4.7.1.2.2 Calculation for Lower Punch
E = 1.93 x 1011 N/m2, D = 4 mm, I = area moment of inertia = 12.5 x 10-12 m4 l = 55 mm, K = 1.0. F = 4 kN
4.7.2 Description of Process for Tablet Formation
Cylindrical-shaped tablets of 10 mm diameter were formed using the die-punch.
The amount of powder filled into the die was 0.3 g (±0.001 g). The average height of
tablets formed using dry formulations were 3.35 mm and 3.26 mm at compression
pressures of 70 and 90 MPa, respectively. These heights for granulated powder
formulations were 3.77 and 3.43 mm. The punch, attached to the cross-head, was moved
down into the die and powder was compressed at 1 MPa/s to different loading conditions
discussed in Section 4.3.2. During compression, the compaction pressure on the punch
was recorded.
4.8 Determination of Tablet Quality Parameters
Diametral strength test, axial compressive strength test, indentation hardness test
and friability tests were conducted to evaluate the tablet properties. These quality
parameters were determined for all the tablets formed at different binder contents of 0%,
5%, and 10% at compression pressures of 70 and 90 MPa (Section 4.7). Three
replications were done for diametral strength, axial compressive strength, and indentation
hardness tests. These parameters were determined using universal testing machine
(Instron 4444, Canton, MA). Friability test was conducted using 5 tablets and the result
was average of these five tablets.
4.8.1 Diametral Strength Test
Diametral strength test, also known as Brazilian test, was done for characterizing
the mechanical strength of the tablet. The force was applied diametrically on the tablet
and the crushing force (Fx) is measured. The diametral strength, DS was calculated as:
DS = 2 Fx/(π D h) (4.24)
where D and h are diameter and height, respectively, of the tablet.
55
For conducting the diametral test, the cross-head speed of UTM was set at 12.52
mm/min (Figure 4.27). The peak force at which the tablet failed was measured as
crushing force.
4.8.2 Axial Penetration Strength Test
Axial penetration strength was also conducted using UTM at a cross head speed
of 12.52 mm/min (Figure 4.28). In the test, the tablet was compressed axially using a
cylindrical probe of 3 mm diameter. The pressure at which the specimen fails was taken
as strength in compression.
Figure 4.27 Diametral Strength Test Figure 4.28 Axial Penetration Strength Test
4.8.3 Indentation Hardness Test
Hardness is a surface property that does not reflect the strength or stiffness of the
tablet. However, the Brinell Hardness has been used to measure the properties over the
surfaces of the tablet and has been related with their overall strength. The Brinell
Hardness Number (BHN) is calculated from either the depth of penetration or diameter of
indentation, using:
BHN = Fi / (П Di hi) (4.25)
where Fi is the load applied, Di is the diameter of the indenting sphere and hi is
the depth of penetration.
The indentation hardness test was conducted using UTM. The load was applied at
a slow speed of 0.15 mm/min (quasi-static) using a spherical probe of 10 mm diameter
(Figure 4.29). The indentation depth was 0.3 mm. The peak force to make the indent was
measured and the indentation hardness was calculated using Equation (4.25).
56
Figure 4.29 Indentation Hardness Test
4.8.4 Friability Test
Friability is the measure of the tablet’s resistance of dedusting to subsequent
process condition and transportation. This test was conducted using a friabilator, which
was fabricated in the Engineering Machine Shop of Department of Agricultural and
Biological Engineering. Drawing and photograph of the friabilator are given in Figure
4.30. For this test, known weight (wo) of tablets to be dedusted were placed in the
friabilator. The friabilator was rotated at a speed of 26 rpm. Diameter of the drum was
140 mm, wherein tablets were moved up by the baffle and dropped from a height of 140
mm to simulate impact loading. On average, tablets were subjected to free fall for 100
times. The speed of rotation was set low to prevent the tablet from sticking to the surface
of the cylinder due to centrifugal force. The tablets were then reweighed (w) and the
friability, f, was calculated from:
f ( %) = 100 [ 1- (w/wo) ] (4.26)
Figure 4.30 Friabilator used in tablet dedusting tests (a) Drawing (b) Photograph
76 mm
140
mm
57
4.9 Statistical Analysis
Statistical analysis were performed to compare the values and develop regression
equations.
4.9.1 Analysis of Variance (ANOVA)
Analysis of variance was performed using Minitab (Version 15.1.0.0, Minitab
Inc., State college, PA) to compare the mean values of various parameters at different
treatment combinations of pressure, binder content, and loading rate. The mean
comparison were done at confidence level of 95%. The difference between two values are
significant or not was determined based on the p-value, i.e., if the p>0.05, the difference
was considered not significant.
4.9.2 Analysis of Covariance (ANCOVA)
Analysis of covariance was performed using Minitab to analyze the effect of
binder content and loading rate on the slope of the regression line. The ANCOVA was
performed in case of bulk modulus and spring-back index where these value had a linear
relation with pressure. The difference between the slopes are significant or not was
determined based on the p-value, if the p>0.05, the difference was considered not
significant.
4.9.3 Development of Regression Equation to Predict tablet Quality parameters
Regression equations were developed between tablets’ quality parameters at
different binder contents and loading conditions and powder mechanical properties.
Tablet quality parameters included diametral strength, axial penetration strength,
indentation hardness, and friability. Powder properties included bulk modulus,
compression index, spring-back index, shear modulus, and failure strength. Linear
regression were performed between each powder property and tablet quality using MS
Excel. Regression equations having r2 value more than 0.8 were considered good. Energy
principle-based explanation for powder property corrections with tablet quality
parameters is included.
58
Chapter 5 – Dry Powder Formulation Test Results
The hydrostatic triaxial compression (HTC) and conventional triaxial
compression (CTC) tests were conducted on dry blended powder formulations at
different binder contents. In this chapter, the HTC and CTC test results including the
various associated modified Cam-clay model parameters are discussed. The parameters
that were determined from HTC tests are bulk modulus, compression index, and spring-
back index; whereas those from CTC tests are shear modulus, failure stress difference,
and slope of the critical state line (CSL).
5.1 HTC Test Results
In HTC tests, the dry blended formulation samples at binder content of 0, 5, and
10% were unloaded and reloaded at three different isostatic pressures of 2.5, 5.0, and
10.0 MPa, as explained in the preceding chapter. These tests were carried out at loading
rates of 10 and 20 MPa/min.
5.1.1 HTC Test Profile
Typical HTC test profiles of dry blended formulations at 10 and 20 MPa/min
loading rates for 0, 5, and 10% binder are shown in Figures 5.1, 5.2, and 5.3,
respectively. It was observed that powders had limited recovery during unloading
demonstrating predominantly plastic responses. The volumetric compression increased
with increase in binder. Binder being a plastic and soft material, contributed towards the
increased compressibility of powder formulations. Also, the volumetric compression was
higher in case of loading rate of 10 MPa/min compared to 20 MPa/min. At low loading
rate, the powder mass had more time to respond hence it compressed more compared to
high loading rate.
59
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 2 4 6 8 10 12Pressure, MPa
Volu
met
ric s
train
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 2 4 6 8 10 12Pressure, MPa
Volu
met
ric s
train
(b)
Figure 5.1 Typical HTC response for binder content of 0% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min
60
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 2 4 6 8 10 12
Pressure, MPa
Vol
umet
ric s
train
(a)
(b)
Figure 5.2 Typical HTC response for binder content of 5% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min
61
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 2 4 6 8 10 12
Pressure, MPa
Volu
met
ric s
trai
n
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 2 4 6 8 10 12
Pressure, MPa
Vol
umet
ric
stra
in
(b)
Figure 5.3 Typical HTC response for binder content of 10% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min
62
5.1.2 Bulk Modulus
The bulk modulus, an elastic parameter, is the measure of the resistance of the
material to volumetric change. Bulk modulus (K) was determined from HTC tests as
described in Section 4.6.1. The method used to determine the bulk modulus was different
from that used by earlier researchers. Previously it was determined by plotting stress or
pressure on y-axis and volumetric strain on x-axis. The CTT is a stress or pressure
controlled type instrument in which the pressure is applied through pressurized nitrogen
gas and change in dimension is measured as a response. Hence, in these tests, stress was
the independent variable and strain the dependent variable. For statistical analysis, the
independent variable should be on x-axis and dependent variable should be on y-axis.
Hence, for determination of bulk modulus, plot was made with stress on x-axis and strain
on y-axis. However, for comparison purposes the bulk modulus values were determined
using both methods.
The bulk modulus determined using both the methods, discussed above, were
very close to each other. For example, the average bulk modulus value for formulation
having 5% binder content using stress as dependent variable were 108, 137, and 210 MPa
at 2.5, 5.0, and 10.0 MPa unloading stress, respectively. These values were 116,143, and
216 MPa, respectively, using stress as independent variable. The average difference
between the two methods was 4.7% ranging from 2.1 to 10.1%. For analysis purpose,
results obtained using stress as independent variable were used.
The bulk modulus increased with increase in the isotropic pressure in all cases.
With increase in pressure, the interparticle porosity decreased. Therefore, the powder’s
structure became more stable which resulted in increase in resistance to further
volumetric change. Increase in bulk modulus with pressure has also been reported by
earlier researchers (Li,1999; Mittal and Puri, 1999a; Huang and Puri, 2000; Mittal and
Puri, 2003).
5.1.2.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate, (1) the bulk modulus increased with increase in the
binder content (Figure 5.4), and (2) the average bulk modulus values at 2.5 MPa
unloading pressure were 102, 116, and 136 MPa at 0, 5 and 10% binder content,
63
respectively. The arrow on the figure indicates increase in bulk modulus with increase in
binder content. The error bar is based on the standard deviation. These values increased
to 139 (36%), 143 (23%), 170 (25%) MPa at 5.0 MPa and 215 (111%), 216 (86%) and
251 (85%) at 10.0 MPa unloading pressure. The numbers in parentheses show percent
change in values from 2.5 MPa pressure values. The average bulk modulus values at 10
MPa/min loading rate are given in Table 5.1. At low loading rate (10 MPa/min), the
binder had sufficient time to spread and make contact with other ingredients. Hence, with
increase in binder content, the material had less recovery; as a result, the bulk modulus
increased. The regression equations for bulk modulus vs. pressure at 10 MPa/min for
various binder contents are given in Table 5.2.
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12Pressure, MPa
Bulk
mod
ulus
, MP
a
10% binder5% binder0% binder
Figure 5.4 Bulk modulus of dry blended powder formulations at 10 MPa/min
loading rate and three binder contents
Table 5.1 Bulk modulus of dry blended powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 0 5 10
2.5 102 MPa (5.8) 116 MPa (2.1) 136 MPa (15.2)
5.0 139 MPa (6.3) 143 MPa (1.8) 170 MPa (16.9)
10.0 215 MPa (7.1) 216 MPa (4.6) 251 MPa (19.9)
* Standard deviation value in parenthesis
Increasing binder
64
Table 5.2 Regression equation for predicting bulk modulus at 10 MPa/min (bulk modulus and pressure in MPa)
Binder, % Regression equation r2
0 Bulk Modulus = 15*Pressure + 64.0 0.98
5 Bulk Modulus = 13*Pressure + 79.9 0.98
10 Bulk Modulus = 15*Pressure + 95.9 0.91
5.1.2.2 Loading Rate of 20 MPa/min At 20 MPa/min, (1) the bulk modulus was maximum at 0% binder followed by
those at 10 and 5% binder contents (Figure 5.5) and (2) the average bulk modulus at 2.5
MPa unloading pressure were 163, 127, 145 MPa at 0, 5 and 10% binder content,
respectively. These values increased to 207 (27%), 172 (35%), and 196 (35%) MPa at 5
MPa and 314 (92%), 256 (101%) and 280 (93%) at 10.0 MPa unloading pressure. The
average bulk modulus values at 20 MPa/min loading rate are given in Table 5.3. At high
loading rate the binder particles get deformed much more compared to 10 MPa/min
loading rate to create sufficient void space to be filled by the ingredients which resulted
in more recovery and, hence, bulk modulus was less in the presence of binder at higher
loading rate. The regression equations for bulk modulus values vs. pressure at 20
MPa/min for various binder contents are given in Table 5.4.
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12Pressure, MPa
Bul
k m
odul
us, M
Pa
10% binder5%binder
0% binder
Figure 5.5 Bulk modulus of dry blended powder formulations at 20 MPa/min
loading rate and three binder contents
65
Table 5.3 Bulk modulus of dry blended powder formulations at 20 MPa/min loading rate*
Binder content, %
Pressure, MPa 0 5 10
2.5 163 MPa (19.4) 127 MPa (14.6) 145 MPa (29.9) 5.0 207 MPa (9.5) 172 MPa (24.3) 196 MPa (38.0) 10.0 314 MPa (25.6) 256 MPa (32.0) 280 MPa (54.0)
* Standard deviation value in parenthesis
Table 5.4 Regression equation for predicting bulk modulus at 20 MPa/min (bulk
modulus and pressure in MPa)
Binder, % Regression equation r2
0 Bulk Modulus = 20*Pressure + 110.0 0.93
5 Bulk Modulus = 17*Pressure + 84.8 0.87
10 Bulk Modulus = 17*Pressure + 103.1 0.72
5.1.2.3 Loading Rate Comparison
The bulk modulus at 20 MPa/min loading rate was higher than at 10 MPa/min
loading rate in all cases, which indicated that the mechanical behavior of powder
formulations is rate-dependent. The bulk modulus at 10 and 20 MPa/min loading rates for
0, 5, and 10% binder contents are given in Figures 5.6, 5.7, and 5.8, respectively. The
arrow on the figure indicates increase in bulk modulus with increase in loading rate. At
higher loading rate, the powder did not have sufficient time to respond to applied stress,
i.e., the residual stress during loading continued the process of compression during
unloading leading to less recovery and higher bulk modulus values.
66
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12Pressure, MPa
Bul
k m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.6 Bulk modulus of dry blended powder formulations at 10 and 20 MPa/min
loading rates and 0% binder content
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12Pressure, MPa
Bulk
mod
ulus
, MPa
10 MPa/min
20 MPa/min
Figure 5.7 Bulk modulus of dry blended powder formulations at 10 and 20 MPa/min
loading rates and 5% binder content
Increasing loading rate
67
0
50
100
150
200
250
300
350
400
0 2 4 6 8 10 12Pressure, MPa
Bul
k m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.8 Bulk modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 10% binder content
5.1.2.4 Analysis of Covariance (ANCOVA)
The relationship of bulk modulus with pressure was analyzed at different levels of
binder content and loading rate. Based on the ANCOVA table (Appendix E) neither
binder content nor loading rate had significant effect (p>0.05) on bulk modulus value. In
addition, slopes of the regression lines did not differ significantly (p>0.05). Bulk modulus
did increase as a linear function of pressure.
5.1.3 Compression Index
The compression index, an elastoplastic parameter, is the measure of
compressibility of the material using void ratio as the dependent variable. In all cases, the
compression index value increased with pressure (Figures 5.9 and 5.10). Similar trend
was observed by Li (1999) for micro-crystalline cellulose (MCC). Mittal and Puri
(1999a) also observed similar trend for MCC upto 9 MPa pressure. In the present
research, the formulation contained 80 to 90% MCC, which appears to dominate the
results.
68
5.1.3.1 Loading Rate of 10 MPa/min At 10 MPa/min loading rate, the average compression index values for 0% binder
were 0.460, 0.577 (25.4%, percent change with respect to 2.5 MPa) and 0.787 (71.0%) at
2.5, 5.0 and 10 MPa unloading pressures, respectively (Figure 5.9). These values were
0.283, 0.579 (104.5%), and 0.699 (146.9%) for 5% binder content and 0.250, 0.537
(114.8%) and 0.726 (190.4%) for 10% binder content. The compression index value at 10
MPa/min loading rate and different binder contents are given in Table 5.5. Based on the
values, the material became more compressible with increase in pressure. The powder
formulations contained irregular shaped ingredients such as MCC (81-90%), methocel,
and acetaminophen which have needle-like shape (Figures 4.1, 4.9, and 4.3, respectively).
Due to irregular shapes, the particle rearrangement continued throughout the pressure
loading regime of 10 MPa. The compression index was higher for powder formulation
without binder compared to powder formulations having 5 and 10% binder at 2.5 MPa
pressure, which means that powders with binder were more resistant to void ratio change
due presence of binder. The compression index in case of 5 and 10% binder were very
close, which indicated that increasing the binder from 5 to 10% had a limited effect.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12
Pressure, MPa
Com
pres
sion
inde
x
10% binder
5% binder
0% binder
Figure 5.9 Compression index of dry blended powder formulations at 10 MPa/min
loading rate and three binder contents
69
Table 5.5 Compression index of dry blended powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 0 5 10
2.5 0.460 (0.002) 0.283 (0.014) 0.250 (0.007) 5.0 0.577 (0.007) 0.579 (0.063) 0.537 (0.037) 10.0 0.787 (0.028) 0.699 (0.045) 0.726 (0.007) * Standard deviation value in parenthesis
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12
Pressure, MPa
Com
pres
sion
inde
x
10% binder
5% binder
0% binder
Figure 5.10 Compression index of dry blended powder formulations at 20 MPa/min
loading rate and three binder contents
5.1.3.2 Loading Rate of 20 MPa/min At 20 MPa/min loading rate, as in the case of 10 MPa/min, compression index
increased with increase in the pressure. The average compression index values for 0%
binder were 0.345, 0.485 (40.5%) and 0.632 (83.1%) at 2.5, 5.0 and 10 MPa unloading
pressure, respectively (Figure 5.10). These values were 0.279, 0.530 (89.9%), and 0.695
(149.1%) for 5% binder and 0.280, 0.500 (78.5%) and 0.651 (132.5%), respectively, for
10% binder. The compression index values at 20 MPa/min loading rate and different
binder contents are given in Table 5.6.
70
Table 5.6 Compression index of dry blended powder formulations at 20 MPa/min loading rate*
Binder content, %
Pressure, MPa 0 5 10
2.5 0.345 (0.014) 0.279 (0.027) 0.280 (0.034) 5.0 0.485 (0.013) 0.530 (0.022) 0.500 (0.013) 10.0 0.632 (0.023) 0.695 (0.056) 0.651 (0.029)
* Standard deviation value in parenthesis
5.1.3.3 Loading Rate Comparison
In general, the compression index values were higher at 10 MPa/min compared to
those at 20 MPa/min loading rate (Figures 5.11, 5.12 and 5.13). The arrow on the figure
indicates decrease in bulk modulus with increase in loading rate. This difference was
more in case of 0% binder content. A 10 MPa/min the the powder had more time to
respond to the applied load, and hence was more compressible, resulting in higher
compression index. Similar trend has been observed by Huang and Puri (2000) for MCC
at pressure upto 3 MPa.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10 MPa/min
20 MPa/min
Figure 5.11 Compression index of dry blended powder formulations at 10 and 20
MPa/min loading rates and 0% binder content
71
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10 MPa/min20 MPa/min
Figure 5.12 Compression index of dry blended powder formulations at 10 and 20
MPa/min loading rates and 5% binder content
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10 MPa/min20 MPa/min
Figure 5.13 Compression index of dry blended powder formulations at 10 and 20
MPa/min loading rates and 10% binder content
5.1.2.4 Analysis of Variance (ANOVA)
Compression index was analyzed for interaction at different level of binder
contents, pressure, and loading rates. Tukey comparison was performed between the
72
mean values of compression index using Minitab (Version 15.1.0.0, Minitab Inc., State
College, PA) to evaluate the effect of pressure, binder content and loading rate. Based on
the ANOVA table (Appendix E) pressure, binder content, and loading rate together did
not have significant effect (p>0.05) on compression index value. However, treatment
combinations of binder content and pressure, binder content and loading rate, and
pressure and loading rate were significant (p<0.05). These values were significantly
different (1) Treatment combination of binder content and pressure. Mean values at two
loading rates – 2.5 MPa pressure of 0% binder vs. 5% and 10% binder (Figure 5.14a). (2)
Treatment combination of binder content and loading rate. Mean values at three pressures
– 0% binder vs. 5% and 10% binder for 10 MPa/min loading rates; 10 vs. 20 MPa/min
loading rates at 0% binder (Figure 5.14b). (3) Treatment combination of pressure and
loading rate. Mean values at three binder contents - 10 vs. 20 MPa/min loading rates at 5
and 10 MPa pressures (Figure 5.14c).
73
0.00.10.20.30.40.50.60.70.80.91.0
0 2 4 6 8 10 12
Pressure, MPa
Mea
n co
mpr
essi
on in
dex
0% binder5% binder10% binder
0.00.10.20.30.40.5
0.60.70.80.91.0
0 2 4 6 8 10
Binder content, %
Mea
n co
mpr
essi
on in
dex
10 MPa/min20 MPa/min
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12
Pressure, %
Mea
n co
mpr
essi
on in
dex
10 MPa/min20 MPa/min
Figure 5.14 Mean compression index vs. (a) pressure at different binder contents (b) binder content at different loading rates and (c) pressure at different loading rates
74
5.1.4 Spring-back Index
Spring-back index, an elastic parameter, is the measure of elastic recovery of the
material’s void ratio after the applied pressure has been released. In all cases, the spring-
back index value increased with pressure (Figure 5.15 and 5.16). With increase in
pressure, the powder formulation particles became more stable and gained strength which
resulted in the solid-like behavior of powder formulation, i.e. greater elastic response as
reflected in spring-back index values. Similar trends were observed by Li (1999) for
MCC, Alumina, and Silcon Nitride. Mittal and Puri (1999a) reported similar result for
Silicon Nitride.
5.1.4.1 Loading Rate of 10 MPa/min At 10 MPa/min loading rate, the spring-back index values decreased with binder
content (Figure 5.15). The arrow on the figure indicates decrease in spring-back index
with increase in binder content. Binder material being soft and more plastic, reduced the
elastic recovery of the powder hence the spring-back index declined with increase in
binder content. The average spring-back index values for 0% binder were 0.090, 0.096
(6.7%) and 0.109 (21.4%) at 2.5, 5.0 and 10 MPa unloading pressure, respectively. These
values were 0.064, 0.083 (29.7%), and 0.096 (50.0%) respectively for 5% binder and
0.066, 0.080 (21.7%) and 0.094 (43.5%), respectively for 10% binder. The average
spring-back index values vs. pressure at 10 MPa/min loading rate are given in Table 5.7.
The regression equations for spring-back index values at 10 MPa/min for various binder
contents are given in Table 5.8.
75
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12
Pressure, MPa
Spri
ng-b
ack
inde
x
10% binder5% binder0% binder
Figure 5.15 Spring-back index of dry blended powder formulations at 10 MPa/min
loading rate and three binder contents
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12
Pressure, MPa
Spri
ng-b
ack
inde
x
10% binder
5% binder
0% binder
Figure 5.16 Spring-back index of dry blended powder formulations at 20 MPa/min
loading rate and three binder contents
Increasing binder
76
Table 5.7 Spring-back index of dry blended powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 0 5 10
2.5 0.0897 (0.0067) 0.0642 (0.0018) 0.0657 (0.0036) 5.0 0.0957 (0.0016) 0.0833 (0.0031) 0.800 (0.0061) 10.0 0.1089 (0.0066) 0.0963 (0.0025) 0.0943 (0.0075)
* Standard deviation in parenthesis.
Table 5.8 Regression equation for predicting spring-back index at 10 MPa/min
Binder, % Regression equation r2
0 Spring-back Index = 0.003*Pressure + 0.0830 0.85
5 Spring-back Index = 0.004*Pressure + 0.0577 0.89
10 Spring-back Index = 0.004*Pressure + 0.0586 0.81
5.1.4.2 Loading Rate of 20 MPa/min At 20 MPa/min the spring-back index values were the lowest at 0% binder
followed by 10 and 5% binder content (Figure 5.16). The average spring-back index
values for 0% binder were 0.050, 0.057 (15.5%) and 0.070 (41.41%) at 2.5, 5.0 and 10
MPa unloading pressure, respectively. These values were 0.065, 0.075 (14.5%), and
0.081 (24.3%), respectively for 5% binder and 0.059, 0.068 (14.6%), and 0.079,
respectively for 10% (33.0%) binder. The average spring-back index values at 20
MPa/min loading rate are given in Table 5.9. The regression equations for spring-back
index values vs. pressure at 20 MPa/min for various binder contents are given in Table
5.10. With addition of the binder, the recovery was more (as explained in Bulk modulus
Section 5.1.2) which resulted in less spring-back index at higher loading rates.
77
Table 5.9 Spring-back index of dry blended powder formulations at 20 MPa/min loading rate*
Binder content, %
Pressure, MPa 0 5 10
2.5 0.0495 (0.0036) 0.0654 (0.0133) 0.0593 (0.0172) 5.0 0.0572 (0.0036) 0.0749 (0.0093) 0.0680 (0.0134) 10.0 0.0700 (0.0027) 0.0813 (0.0093) 0.0789 (0.0139)
* Standard deviation in parenthesis.
Table 5.10 Regression equation for predicting spring-back index at 20 MPa/min
Binder, % Regression equation r2
0 Spring-back Index = 0.003*Pressure + 0.0431 0.90
5 Spring-back Index = 0.002*Pressure + 0.0622 0.32
10 Spring-back Index = 0.003*Pressure + 0.0538 0.29
5.1.4.3 Loading Rate Comparison
The spring-back index values were higher at 10 MPa/min loading rate as
compared to 20 MPa/min loading rate. This difference was maximum in case of 0%
binder. The spring-back index values at 10 and 20 MPa/min loading rates for 0, 5, and
10% binder contents are given in Figures 5.17, 5.18 and 5.19, respectively. The arrow on
the figure indicates decrease in spring-back index with increase in loading rate. At 10
MPa/min loading rate, the powder particle had more time to respond to the applied force
and gained more strength compared to 20 MPa/min loading rate which resulted in
increased solid-like behavior and, consequently, greater elastic recovery response.
78
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spr
ing-
back
inde
x
10 MPa/min20 MPa/min
Figure 5.17 Spring-back index of dry blended powder formulations at 10 and 20
MPa/min loading rates and 0% binder content
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spr
ing-
back
inde
x
10 MPa/min20 MPa/min
Figure 5.18 Spring-back index of dry blended powder formulations at 10 and 20
MPa/min loading rates and 5% binder content
Increasing loading rate
79
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spr
ing-
back
inde
x
10 MPa/min20 MPa/min
Figure 5.19 Spring-back index of dry blended powder formulations at 10 and 20
MPa/min loading rates and 10% binder content
5.1.4.4 Analysis of Covariance (ANCOVA)
The relationship of spring-back index with pressure was analyzed at different
levels of binder content and loading rate. Based on the ANCOVA table (Appendix E),
neither binder content nor loading rate had significant effect (p>0.05) on slopes of the
regression lines, i.e., slopes did not differ significantly. Therefore, it was a case of
common slope model and Tukey mean comparisons were performed. The binder*loading
rate interaction was significant (p<0.05). Mean values of spring-back index at different
pressure were compared at different binder contents and loading rates. These values were
significantly different (p<0.05) – 0% binder vs. 5% and 10% binder for 10 MPa/min
loading rate; 0% binder vs. 5% binder for 20 MPa/min loading rate; 10 vs. 20 MPa/min
loading rates at 0% binder (Figure 5.20).
80
0.000.01
0.020.03
0.040.050.06
0.070.08
0.090.10
0 2 4 6 8 10
Binder content, %
Mea
n sp
ring
-bac
k in
dex
10 MPa/min
20 MPa/min
Figure 5.20 Mean spring-back index vs. binder content at different loading rates
81
5.2 CTC Test Results
In CTC tests, the dry blended samples at binder contents of 0, 5, and 10% were
unloaded and reloaded at three different confining pressures of 1.0, 2.0, and 3.0 MPa.
These tests were carried out at loading rates of 10 and 20 MPa/min.
5.2.1 CTC Test Profile
Considering the operational safety of CTT, all CTC tests were conducted at a
stress difference of upto 2 MPa. Higher stress difference induced instability in the tester
causing membranes to fail. Typical CTC test profiles for dry blended formulations at 10
and 20 MPa/min loading rates for 0, 5, and 10% binder and confining pressures of 1, 2,
and 3 MPa are shown in Figures 5.21 to 5.26. From these CTC profiles, as the confining
pressure increased, the strain difference decreased. Effect of binder on the strain
difference values was not very prominent. The strain difference at 20 MPa/min loading
rate was more than at 10 MPa/min loading rate in case of 1 MPa confining pressure.
82
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(b)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(c)
Figure 5.21 Typical CTC response at 1 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%
83
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.04
0.08
0.12
0.16
0.20
0 0.5 1 1.5 2 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(b)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(c)
Figure 5.22 Typical CTC response at 1 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%
84
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(b)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5
Stress difference, MPa
Stra
in d
iffer
ence
(c)
Figure 5.23 Typical CTC response at 2 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%
85
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(b)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(c)
Figure 5.24 Typical CTC response at 2 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%
86
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Str
ain
diffe
renc
e
(b)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(c)
Figure 5.25 Typical CTC response at 3 MPa confining pressure and 10 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%
87
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(b)
0.00
0.04
0.08
0.12
0.16
0.20
0.0 0.5 1.0 1.5 2.0 2.5Stress difference, MPa
Stra
in d
iffer
ence
(c)
Figure 5.26 Typical CTC response at 3 MPa confining pressure and 20 MPa/min loading rate for binder contents of (a) 0%, (b) 5%, and (c) 10%
88
5.2.2 Shear Modulus
The shear modulus (G) is the measure of resistance of the material to deformation
in shear loading. Shear modulus was determined from CTC tests as described Section
4.6.3. The method used to determine the shear modulus was different from that used by
previous researchers as mentioned in the 5.1.2 Bulk Modulus section with stress on x-
axis and strain on y-axis.
At confining pressure of 2.0 and 3.0 MPa, the shear modulus was determined at
stress differences of 1.0 and 2.0 MPa at both 10 and 20 MPa/min loading rates. However,
at 1.0 MPa confining pressure, the shear modulus was determined only at a stress
difference of 1.0 MPa. Higher stress difference was not considered safe for operating the
cubical triaxial tester, i.e., due to the possibility of catastrophic failure of CTT
components.
5.2.2.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate and stress difference of 1 MPa, the average shear
modulus values at 1.0 MPa confining pressure were 13, 18, and 18 MPa at 0, 5 and 10%
binder content, respectively. These values increased to 31 (72%, percent change from the
1.0 MPa confining pressure value), 30 (66%), 30 (25%) MPa at 2.0 MPa and 36 (176%),
37 (105%) and 33 (83%) at 3.0 MPa confining pressures (Figure 5.27). The average shear
modulus values at 10 MPa/min loading rate and 1 MPa stress difference are given in
Table 5.11.
The average shear modulus values at a stress difference of 2 MPa and 2.0 MPa
confining pressure were 25, 26, and 26 MPa at 0, 5, and 10% binder content,
respectively. These values at 3.0 MPa confining pressure were 37 (48%, percent change
from 2 MPa confining pressure), 35 (35%), and 34 (30%) MPa, respectively (Figure
5.28). The average shear modulus values at 10 MPa/min loading rate and 2 MPa stress
difference are given in Table 5.12.
The shear modulus increased with increase in the confining pressure in all cases.
With increase in confining pressure, the strength of the sample increased, and hence, the
resistance to deform increased as a result the shear modulus increased. Increase in shear
modulus with pressure has also been reported by earlier researchers. (Li, 1999; Mittal and
89
Puri, 1999a; Huang and Puri, 2000; Mittal and Puri, 2003). No clear trend of the effect of
binder on shear modulus values was observed unlike bulk modulus. Binder in dry form
spread and filled the void spaces. In case of HTC tests, the hydrostatic pressure
compressed the sample from all directions and binder under pressure spread and filled the
void spaces. In case of CTC tests, the pressure is applied differently in the form of
deviatoric stress; as a result binder could not spread and fill the void spaces.
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
Shea
r m
odul
us, M
Pa
0% binder5% binder10% binder
Figure 5.27 Shear modulus of dry blended powder formulations at 10 MPa/min
loading rate and 1 MPa stress difference at three binder contents
Table 5.11 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 1 MPa stress difference*
Binder content, %
Confining pressure, MPa 0 5 10
1.0 13 MPa (1.3) 18 (1.9) 18 MPa (1.3)
2.0 31 MPa (2.8) 30 (2.8) 30 MPa (0.9)
3.0 36 MPa (2.7) 37 (3.0) 33 MPa (2.0)
* Standard deviation in parenthesis
90
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
Shea
r mod
ulus
, MPa
0% binder5% binder10% binder
Figure 5.28 Shear modulus of dry blended powder formulations at 10 MPa/min
loading rate and 2 MPa stress difference at three binder contents
Table 5.12 Shear modulus of dry blended powder formulations at 10 MPa/min loading rate and 2 MPa stress difference*
Binder content, %
Confining pressure, MPa 0 5 10
2.0 25 MPa (1.0) 26 MPa (2.6) 26 MPa (0.6)
3.0 37 MPa (3.7) 35 MPa (2.9) 34 MPa (0.8)
* Standard deviation in parenthesis
5.2.2.2 Loading Rate of 20 MPa/min At 20 MPa/min loading rate and stress difference of 1 MPa the average shear
modulus values at 1.0 MPa confining pressure were 26, 28, and 28 MPa at 0, 5 and 10%
binder content, respectively. These values increased to 35 (35%), 32 (14%), 30 (7%) MPa
at 2.0 MPa and 37 (42%), 36 (29%) and 35 (25%) at 3.0 MPa confining pressures (Figure
5.29). The average shear modulus values at 20 MPa/min loading rate and 1 MPa stress
difference are given in Table 5.13.
The average shear modulus values at a stress difference of 2 MPa and 2.0 MPa
confining pressure were 28, 25, and 24 MPa at 0, 5 and 10% binder content, respectively.
These values at 3.0 MPa confining pressure were 30, 32, and 34 MPa, respectively
91
(Figure 5.30). The average shear modulus values at 20 MPa/min loading rate and 2 MPa
stress difference are given in Table 5.14.
Similar to the case of 10 MPa/min loading rate, the shear modulus increased with
increase in the confining pressure in all cases. Also, no clear trend of the effect of binder
on shear modulus values was observed.
05
101520253035404550
0 1 2 3 4Confining pressure, MPa
Shea
r m
odul
us, M
Pa
0% binder5% binder10% binder
Figure 5.29 Shear modulus of dry blended powder formulations at 20 MPa/min
loading rate and 1 MPa stress difference at three binder contents
Table 5.13 Shear modulus of dry blended powder formulations at 20 MPa/min loading rate and 1 MPa stress difference
Binder content, %
Confining pressure, MPa 0 5 10
1.0 26 MPa (3.6)* 28 MPa (5.7) 28 MPa (4.0)
2.0 31 MPa (2.8) 30 MPa (2.0) 30 MPa (2.2)
3.0 36 MPa (5.0) 37 MPa (7.9) 33 MPa (3.0)
* Standard deviation
92
05
1015202530354045
0 1 2 3 4Confining pressure, MPa
She
ar m
odul
us, M
Pa
0% binder5% binder10% binder
Figure 5.30 Shear modulus of dry blended powder formulations at 20 MPa/min
loading rate and 2 MPa stress difference at three binder contents
Table 5.14 Shear modulus of dry blended powder formulations at 20 MPa/min loading rate and 2 MPa stress difference*
Binder content, %
Confining pressure, MPa 0 5 10
2.0 28 MPa (2.5) 25 MPa (1.5) 24 MPa (0.9)
3.0 30 MPa (1.7) 32 MPa (7.6) 34 MPa (6.0)
* Standard deviation in parenthesis
5.2.2.3 Loading Rate Comparison
The shear modulus values at 10 and 20 MPa/min loading rate were different,
which indicated that the formulations were rate-dependent. However, no clear trend of
the effect of loading rate was observed. Other researchers also observed variation in shear
modulus values with loading rates. Huang and Puri (2000) observed decrease in shear
modulus value with strain rate. Mittal (2003) also observed decrease in shear modulus
with compression rate. The shear modulus at 10 and 20 MPa/min loading rates and 1
MPa stress difference at confining pressures of 1, 2, and 3 MPa for 0, 5, and 10% binder
contents are given in Figures 5.31, 5.32 and 5.33, respectively. The arrow on the figure
indicates increase in shear modulus with increase in loading rate. In general, the shear
modulus increased with loading rate at 1 MPa stress difference. The shear modulus at 2
93
MPa stress difference are shown in Figures 5.34, 5.35, and 5.36. The shear modulus
values at 2 MPa stress difference were only marginally different at the two loading rates.
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
She
ar m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.31 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content at a stress difference of 1 MPa
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
She
ar m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.32 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content at a stress difference of 1 MPa
Increasing loading rate
94
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
She
ar m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.33 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content at a stress difference of 1 MPa
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
Shea
r m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.34 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 0% binder content at a stress difference of 2 MPa
95
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
Shea
r mod
ulus
, MP
a
10 MPa/min
20 MPa/min
Figure 5.35 Shear modulus of dry blended powder formulations at 10 and 20 MPa/min loading rates and 5% binder content at a stress difference of 2 MPa
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4Confining pressure, MPa
She
ar m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 5.36 Shear modulus of dry blended powder formulations at 10 and 20
MPa/min loading rates and 10% binder content at a stress difference of 2 MPa
5.2.2.4 Analysis of Variance (ANOVA)
Tukey comparison was performed between the mean values of shear modulus
using Minitab to evaluate the effect of pressure, binder content, and loading rate. Based
on the ANOVA table (Appendix E), pressure, binder content, and loading rate together
did not have significant effect (p>0.05) on shear modulus values. However, treatment
combination of pressure and loading rate was significant (p<0.05). These values were
significantly different (p<0.05) for 1 MPa stress difference – 1 MPa vs. 2 MPa confining
pressure for 10 and 20 MPa/min loading rates; 1 MPa vs. 3 MPa confining pressure for
96
10 and 20 MPa/min loading rates; 10 vs. 20 MPa/min loading rates at 1 MPa confining
pressure (Figure 5.37). For 2 MPa stress difference, no combination of binder, pressure
and loading rate had any significant effect (p>0.05).
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4
Pressure, MPa
Mea
n sh
ear
mod
ulus
, MP
a
10 MPa/min
20 MPa/min
Figure 5.37 Mean shear modulus of dry blended powder formulations at different
pressures and loading rates at a stress difference of 1 MPa 5.2.3 Failure Stress and Critical State Line
The stress difference value at failure (failure stress) was determined at strain
difference value of 14%. In some cases of 3 MPa confining pressure, the 15% strain
difference value was not reached hence for uniformity, the stress value at 14% strain
difference value was taken as the failure point. The failure stress value increased with
confining pressure in all cases. The modified Cam-clay model (see Section 4.6.6 in
Chapter 4) assumes that the critical state line (fixed yield surface), a plot between mean
pressure and failure stress, is a straight line passing through the origin. However, in
present case the line was not linear. Therefore, using Mittal and Puri’s (2005)
mathematical formulation, the critical state line equation was obtained using a power law
representation passing through the origin.
5.2.3.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate, the average stress difference values at failure point
for 1.0 MPa confining pressure were 0.95, 1.01, and 1.02 MPa at 0, 5, and 10% binder
97
content, respectively. These values increased to 1.81 (103%, percent change from 1 MPa
value), 1.71 (80%), 1.69 (72%) MPa at 2.0 MPa and 1.97 (111%), 1.99 (92%) and 1.88
(76%) at 3.0 MPa confining pressures (Figure 5.38). The average failure stress values at
10 MPa/min loading rate and at different confining pressures are given in Table 5.15. The
equations of critical state line at different binder contents are given in Table 5.16.
Increase in failure stress value with confining pressure are also reported by other
researchers (Li, 1999; Huang, 2000; and Mittal, 2003).
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4Mean pressure, MPa
Failu
re s
tres
s, M
Pa
0% binder5% binder10% binder
Figure 5.38 Failure stress and fixed yield surface of dry blended powder
formulations at 10 MPa/min loading rate at different binder contents
Table 5.15 Failure stress values of dry blended powder formulations at 10 MPa/min loading rate *
Binder content, %
0 5 10
Confining pressure,
MPa Mean
Pressure, MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
1.0 1.3 0.95 (0.04) 1.3 1.01 (0.02) 1.3 1.02 (0.02) 2.0 2.6 1.81 (0.19) 2.6 1.71 (0.12) 2.6 1.69 (0.12) 3.0 3.7 1.97 (0.04) 3.6 1.99 (0.07) 3.6 1.88 (0.17)
* Standard deviation in parenthesis
98
Table 5.16 Critical state line equation at 10 MPa/min loading rate Binder Content, % Critical State Line Equation r2
0 Failure Stress = 0.870*(Mean Pressure)0.634 0.96 5 Failure Stress = 0.846*(Mean Pressure)0.685 0.98 10 Failure Stress = 0.796*(Mean Pressure)0.751 0.95
5.2.3.2 Loading Rate of 20 MPa/min
At 20 MPa/min loading rate, the average failure stress values at 1.0 MPa
confining pressure were 1.33, 1.42, and 1.38 MPa at 0, 5 and 10% binder content,
respectively. These values increased to 1.84 (38%, percent change from 1 MPa value),
1.82 (29%), 1.83 (32%) MPa at 2.0 MPa and 1.90 (43%), 1.95 (38%) and 1.99 (44%) at
3.0 MPa confining pressures (Figure 5.39). The average failure stress values at 20
MPa/min loading rate and at different confining pressures are given in Table 5.17. The
equation of critical state line at different binder contents are given in Table 5.18.
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4Mean pressure, MPa
Failu
re s
tress
, MPa
0% binder5% binder10% binder
Figure 5.39 Failure stress and Fixed Yield Surface of dry blended powder
formulations at 20 MPa/min loading rate at different binder contents
99
Table 5.17 Failure of dry blended powder formulations at 10 MPa/min loading rate* Binder content, %
0 5 10
Confining pressure,
MPa Mean
Pressure, MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
1.0 1.4 1.33 (0.14) 1.5 1.42
(0.09) 1.5 1.38 (0.12)
2.0 2.6 1.84 (0.70) 2.6 1.82
(0.01) 2.6 1.83 (0.06)
3.0 3.6 1.90 (0.04) 3.6 1.95
(0.06) 3.6 1.99 (0.12)
* Standard deviation in parenthesis
Table 5.18 Critical state line equation at 20 MPa/min loading rate
Binder Content Critical State Line Equation r2 0 Failure Stress = 1.119*(Mean Pressure)0.416 0.93 5 Failure Stress = 1.216*(Mean Pressure)0.359 0.96 10 Failure Stress = 1.211*(Mean Pressure)0.370 0.98
5.2.3.3 Loading Rate Comparison
The failure stress values at 10 and 20 MPa/min loading rate were different at
confining pressure of 1 MPa. At 2 and 3 MPa confining pressures, these values were very
close. Mittal (2003) also reported that failure stress values at different loading rates were
very close. The failure stress at 10 and 20 MPa/min loading rates for 0, 5, and 10% binder
contents are given in Figures 5.40, 5.41, and 5.42, respectively
100
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4Mean pressure, MPa
Failu
re s
tres
s, M
Pa
10 MPa/min
20 MPa/min
Figure 5.40 Failure stress and Fixed Yield Surface of dry blended powder
formulations at 10 and 20 MPa/min loading rates at 0% binder content
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4Mean pressure, MPa
Failu
re s
tress
, MPa
10 MPa/min
20 MPa/min
Figure 5.41 Failure stress and Fixed Yield Surface of dry blended powder
formulations at 10 and 20 MPa/min loading rates at 5% binder content
101
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4Mean pressure, MPa
Failu
re s
tres
s, M
Pa
10 MPa/min
20 MPa/min
Figure 5.42 Failure stress and Fixed Yield Surface of dry blended powder formulations at 10 and 20 MPa/min loading rates at 10% binder content
5.2.2.4 Analysis of Variance (ANOVA)
Tukey comparison was performed between the mean values of failure stress to
evaluate the effect of pressure, binder content and loading rate. Based on the ANOVA
table (Appendix E), pressure, binder content, and loading rate together did not have
significant effect (p>0.05) on failure stress values. However, treatment combination of
pressure and loading rate was significant (p<0.05). Mean values of failure stress at
different binder contents were compared at different pressures and loading rates. These
values were significantly different (p<0.05) for 1 MPa stress difference – All values with
change in confining pressure; 10 vs. 20 MPa/min loading rates at 1 MPa confining
pressure (Figure 5.43).
102
0.0
0.5
1.0
1.5
2.0
2.5
0 1 2 3 4
Pressure, MPa
Mea
n Fa
ilure
str
ess,
MP
a
10 MPa/min20 MPa/min
Figure 5.43 Mean failure stress value at different pressures and loading rates
5.3 Summary
HTC and CTC tests were conducted on dry powder formulations at different
loading conditions and binder contents. Fundamental mechanical properties such as bulk
modulus, compression index, and spring-back index were determined using the HTC
tests. Shear modulus and failure stress were determined using the CTC tests. Bulk
modulus, compression index, and spring-back index increased with pressure. Shear
modulus and failure stress increased with confining pressure. Bulk modulus increased
with binder content at 10 MPa/min loading rate; furthermore, bulk modulus increased
with loading rate. Spring-back index decreased with binder content at 10 MPa/min.
Spring-back and compression index values were higher at 10 MPa/min compared to 20
MPa/min.
103
Chapter 6 – Granulated Powder Formulation Test Results
The hydrostatic triaxial compression (HTC) and conventional triaxial
compression (CTC) tests were conducted for granulated powder formulation at binder
contents of 5 and 10%; analogous to dry powder formulations. In this chapter, the HTC
and CTC test results of granulated formulations including the various property values,
similar to those given in Chapter 5, are presented.
6.1 HTC Test Results
In HTC tests, the granulated powder formulation samples at binder contents of 5
and 10% were unloaded and reloaded at three different isostatic pressures of 2.5, 5.0, and
10.0 MPa. These tests were carried out at loading rates of 10 and 20 MPa/min.
6.1.1 HTC Test Profile
In HTC tests, as in the case of dry powder formulations, the granules formed at
binder content of 5 and 10% were unloaded and reloaded at three different isostatic
pressures of 2.5, 5.0, and 10.0 MPa. The tests were done at loading rates of 10 and 20
MPa/min. Typical HTC test profiles for granulated formulation at 10 and 20 MPa/min
loading rates are shown in Figures 6.1 and 6.2, respectively. In this case also, the granules
had limited recovery during unloading which infers plastic nature of granulated powder
formulations. The volumetric compression decreased with increase in binder. With
increase in binder, the granules at 10% binder content became stronger and difficult to
compress; as a result, less compressible compared to granules having 5% binder content.
Also, the volumetric compression was higher in case of loading rate of 10 MPa/min
compared to 20 MPa/min loading rate in case of 5% binder content. At low loading rate,
the powder mass had more time to respond hence it compressed more compared to high
loading rate.
104
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12Pressure, MPa
Volu
met
ric
stra
in
(a)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12Pressure, MPa
Volu
met
ric s
trai
n
(b)
Figure 6.1 Typical HTC response of granulated powder formulation for binder content of 5% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min
105
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12
Pressure, MPa
Volu
met
ric
stra
in
(a)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12
Pressure, MPa
Vol
umet
ric s
train
(b)
Figure 6.2 Typical HTC response of granulated powder formulation for binder content of 10% at loading rates of (a) 10 MPa/min and (b) 20 MPa/min
106
6.1.2 Bulk Modulus
As in the case of dry powder formulations, the bulk modulus values were
determined for the granulated powder formulations using the two methods discussed in
Section 5.1.2.
The methods were (1) stress on y-axis, and (2) stress on x-axis. Both methods
produced values that were sufficiently close to each other as in the case of dry powder
formulations. For example, the average bulk modulus value for formulation having 5%
binder content using the first method were 149, 234, and 381 MPa at 2.5, 5.0, and 10.0
MPa unloading pressure, respectively. These values were 167, 256, and 420 MPa using
the second method. The average difference between the two methods was 9.7%; ranging
from 1 to 23%. For analysis purpose, similar to the case of dry powder formulation,
results obtained using the second method (pressure on x-axis) is used.
The bulk modulus values increased with the increase in pressure in all cases
(Figures 6.3 and 6.4). Similar trends of bulk modulus have been reported by other
researchers (Li, 1999; Mittal and Puri, 1999; Huang and Puri, 2000). A small increase (2
to 4%) in bulk modulus with increase in the binder content was also observed at loading
rate of 10 MPa/min.
6.1.2.1 Loading Rate of 10 MPa/min
At loading rate of 10 MPa/min, the average bulk modulus values for 5% binder
were 167, 256 (53.3%, percent increase from 2.5 MPa value), and 420 (151.5%) MPa at
unloading pressures of 2.5, 5.0 and 10.0 MPa, respectively; these values were 171, 267
(56.1%), and 439 (156.7%) MPa for 10% binder content, respectively (Figure 6.3). The
arrow on the figure indicates increase in bulk modulus with increase in binder content.
With increase in binder, the contact between the particles improved; as a result, the
material had less recovery or became more plastic and hence the bulk modulus increased.
The average bulk modulus values at 10 MPa/min loading rate are given in Table 6.1. The
regression equations for bulk modulus values vs. pressure (i.e., hydrostatic stress) at 10
MPa/min loading rate are given in Table 6.2.
107
0
100
200
300
400
500
600
0 2 4 6 8 10 12Pressure, MPa
Bul
k m
odul
us, M
Pa
10% binder5% binder
Figure 6.3 Bulk modulus of granulated powder formulations at 10 MPa/min loading
rate and two binder contents
Table 6.1 Bulk modulus of dry blended powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 5 10
2.5 167 MPa (23.7) 171 MPa (8.6)
5.0 256 MPa (30.2) 267 MPa (25.8)
10.0 420 MPa (76.2) 439 MPa (18.7)
*Standard deviation value in parenthesis
Table 6.2 Regression equation for predicting bulk modulus at 10 MPa/min (bulk modulus and pressure in MPa)
Binder, % Regression equation r2
5 Bulk Modulus = 34*Pressure + 85 0.87
10 Bulk Modulus = 34*Pressure + 95 0.96
6.1.2.2 Loading Rate of 20 MPa/min
At loading rate of 20 MPa/min, the average bulk modulus values for 5% binder
were 172, 192 (11.6%, percent increase from 2.5 MPa value), and 358 (108.1%) MPa at
unloading pressure of 2.5, 5.0 and 10.0 MPa, respectively; these values were 154, 178
(15.6%), and 285 (85.0%) MPa for 10% binder content, respectively (Figure 6.4). The
Increasing binder
108
arrow on the figure indicates decrease in bulk modulus with increase in binder content.
Granules with 10% binder were large sized and stronger compared to granules with 5%
binder. At higher loading rate, material did not have enough time to respond (i.e. the
pressure applied on the surface of the sample could not reach the center of sample) and
granules with 10% binder being large-sized and stronger compared to granules having
5% binder did not attain stable state and had larger recovery, which resulted in low bulk
modulus. The average bulk modulus values at 20 MPa/min loading rate are given in
Table 6.3. The regression equations for bulk modulus vs. pressure at 20 MPa/min loading
rate is given in Table 6.4.
0
100
200
300
400
500
600
0 2 4 6 8 10 12Pressure, MPa
Bulk
mod
ulus
, MPa
10% binder5% binder
Figure 6.4 Bulk modulus of granulated powder formulations at 20 MPa/min loading
rate and two binder contents
Table 6.3 Bulk modulus of dry blended powder formulations at 20 MPa/min loading rate
Binder content, %
Pressure, MPa 5 10
2.5 172 MPa (3.6) 154 MPa (10.7)
5.0 192 MPa (0.2) 178 MPa (7.4)
10.0 358 MPa (29.3) 285 MPa (22.9)
*Standard deviation value in parenthesis
Increasing binder
109
Table 6.4 Regression equation for predicting bulk modulus at 20 MPa/min (bulk modulus and pressure in MPa)
Binder, % Regression equation r2
5 Bulk Modulus = 27*Pressure + 81 0.91
10 Bulk Modulus = 18*Pressure + 100 0.92
6.1.2.3 Loading Rate Comparison
The bulk modulus at 10 MPa/min loading rate was higher than at 20 MPa/min
loading rate in all cases, which indicated that the mechanical behavior of granulated
formulation is rate-dependent. The bulk modulus at 10 and 20 MPa/min loading rates for
5% are given in Figure 6.5 and for 10% binder in Figure 6.6. The arrow on the figure
indicates decrease in bulk modulus with increase in loading rate. At higher loading rate
the granules did not get enough time to respond (i.e. the pressure applied on the surface
of the sample could not reach the center); whereas, at low loading rate (10 MPa/min) the
granules had more time to respond to the applied pressure due to which at lower loading
rate the sample attained the a new equilibrium condition resulting in less recovery and
high bulk modulus.
0
100
200
300
400
500
600
0 2 4 6 8 10 12Pressure, MPa
Bulk
mod
ulus
, MP
a
10 MPa/min
20 MPa/min
Figure 6.5 Bulk modulus of granulated powder formulations at 10 and 20 MPa/min
loading rates and 5% binder content
Increasing loading rate
110
0
100
200
300
400
500
600
0 2 4 6 8 10 12Pressure, MPa
Bul
k m
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 6.6 Bulk modulus of granulated powder formulations at 10 and 20 MPa/min
loading rates and 10% binder content
6.1.2.4 Analysis of Covariance (ANCOVA)
The relationship of bulk modulus with pressure was analyzed at different levels of
binder content and loading rate. Based on the ANCOVA table (Appendix F), binder
content did not have significant effect (p>0.05) on bulk modulus value and slopes of the
regression lines did not differ at both binder contents significantly (p>0.05) while loading
rate had significant effect on the slope of regression lines (p<0.05).
6.1.3 Compression Index
As in the case of dry powder formulations, the compression index values were
determined for the granulated powder formulations using the methods discussed in
Section 4.6.4. Compression index is an indication of the compressibility of powder
formulations.
6.1.3.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate, for 5% binder content the compression index
decreased and then slightly increased (Figure 6.7). The compression index values at 5%
binder were 0.847, 0.764 (-9.8%, percent change from 2.5 MPa value), and 0.830 (-2.0%)
at unloading pressure of 2.5, 5.0 and 10 MPa, respectively. The compression index values
111
at 10% binder content were 0.768, 0.813 (5.8%), and 0.853 (11.0%) at unloading pressure
of 2.5, 5.0 and 10 MPa, respectively (Table 6.5). Initially, the inter-granular structure had
some resistance to deformation which made it less compressible. As the granules started
to (i) deform, (ii) overcome inter-granular friction, and (iii) subsequently fragment, the
formulation became more compressible.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10% binder
5% binder
Figure 6.7 Compression index of granulated powder formulations at 10 MPa/min
loading rate and two binder contents
Table 6.5 Compression index of granulated powder formulations at 10 MPa/min loading rate
Binder content, %
Pressure, MPa 5 10
2.5 0.847 (0.043) 0.768 (0.051)
5.0 0.764 (0.005) 0.813 (0.046)
10.0 0.830 (0.025) 0.853 (0.060)
*Standard deviation value in parenthesis
6.1.3.2 Loading Rate of 20 MPa/min
At 20 MPa/min loading rate, the compression index decreased and then increased
for both binder contents. The compression index values at 5% binder content were 0.899,
0.809 (-10.0%, percent change from 2.5 MPa value), and 0.872 (-3.0%) at unloading
112
pressure of 2.5, 5.0 and 10 MPa, respectively (Figure 6.8 and Table 6.6). These values
were 0.839, 0.765 (-8.8%), and 0.807 (-3.8%), respectively, at 10% binder.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10% binder
5% binder
Figure 6.8 Compression index of granulated powder formulations at 20 MPa/min
loading rate and two binder contents
Table 6.6 Compression index of granulated powder formulations at 20 MPa/min loading rate*
Binder content, %
Pressure, MPa 5 10
2.5 0.899 (0.034) 0.839 (0.095)
5.0 0.809 (0.029) 0.765 (0.012)
10.0 0.872 (0.045) 0.807 (0.018)
*Standard deviation value in parenthesis
6.1.3.3 Loading Rate Comparison
The compression index value at 20 MPa/min was higher than at 10 MPa/min for
the granules having 5% binder (Figure 6.9). The granules at 5% binder content had
dominant plastic behavior at higher loading rate and did not have enough time for the
elastic recovery; as a result, were more compressible. Mittal (2000) also reported similar
Increasing binder
113
trend for MZF and Alumina. However, in case of granules having 10% binder the
compression index values were higher at 10 MPa/min loading rate at unloading pressures
of 5 and 10 MPa (Figure 6.10). At 20 MPa/min loading rate, the granular assembly: (1)
did not have sufficient time to respond to applied loads (2) granules at 10% binder were
large sized compared with 5% (Figure 4.11 and 4.13) and (3) was stronger compared to
granules having 5% binder, did not deform as much and/or fragment. Therefore, the 10%
binder content granular assemblies were less compressible resulting in low compression
index.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10 MPa/min
20 MPa/min
Figure 6.9 Compression index of granulated powder formulations at 10 and 20
MPa/min loading rates and 5% binder content
Increasing loading rate
114
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10 12Pressure, MPa
Com
pres
sion
inde
x
10 MPa/min
20 MPa/min
Figure 6.10 Compression index of granulated powder formulations at 10 and 20
MPa/min loading rates and 10% binder content
6.1.3.4 Analysis of Variance (ANOVA)
Tukey comparison was performed between the mean values of compression index
to evaluate the effect of pressure, binder content, and loading rate. Based on the ANOVA
table (Appendix F), only pressure had significant effect (p<0.05) on compression index
value. No treatment combinations of pressure, binder, and loading rate were significant
(p<0.05). These mean values were significantly different (p<0.05) – 2.5 MPa vs. 5.0 MPa
and 5.0 MPa vs. 10.0 MPa.
6.1.4 Spring-back Index
The spring-back index increased with unloading pressure in all cases. These
results were consistent with earlier findings (Li, 1999 and Mittal and Puri ,1999a and b)
as discussed in Section 5.1.4. At both loading rates, the spring-back index for 10% binder
content was higher than for 5% binder content (Figures 6.11 and 6.12). At 10% binder
content, the granule sizes were larger than granules formed at 5% binder. Spring-back
index is the measure of the recovery of void space. Granules having 10% binder were not
only larger but stronger compared to 5% binder; hence, had more resistance to plastic
deformation resulting in more elastic recovery, i.e., higher spring-back index.
115
6.1.4.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate, the spring-back index values for 5% binder content
were 0.036, 0.043 (38.7%, percent change from 2.5 MPa), and 0.048 (54.8%) at 2.5, 5.0,
and 10.0 MPa unloading pressures, respectively. These values were 0.060, 0.060 (0.5%),
and 0.063 (4.8%) for 10% binder content (Figure 6.11). The spring-back index values at
10 MPa/min loading rate are given in Table 6.7.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spr
ing-
back
inde
x
10% binder5% binder
Figure 6.11 Spring-back index of granulated powder formulations at 10 MPa/min
loading rate and two binder contents
Increasing binder
116
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spr
ing-
back
inde
x
10% binder5% binder
Figure 6.12 Spring-back index of granulated powder formulations at 20 MPa/min
loading rate and two binder contents
Table 6.7 Spring-back index of granulated powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 5 10
2.5 0.036 (0.007) 0.060 (0.004)
5.0 0.051 (0.007) 0.060 (0.005)
10.0 0.054 (0.006) 0.063 (0.007)
*Standard deviation value in parenthesis
6.1.4.2 Loading Rate of 20 MPa/min
At 20 MPa/min the spring-back values were 0.046, 0.056 (20.3%, percent change
from 2.5 MPa), and 0.056 (21.0%) and 0.045, 0.065 (42.8%), and 0.069 (51.8%) for 5
and 10% binder content, respectively. In general, the spring-back index value increased
with loading rate (Figure 6.12). The spring-back index values at 20 MPa/min loading rate
are given in Table 6.8.
117
Table 6.8 Spring-back index of granulated powder formulations at 20 MPa/min loading rate*
Binder content, %
Pressure, MPa 5 10
2.5 0.046 (0.004) 0.045 (0.005)
5.0 0.056 (0.006) 0.065 (0.006)
10.0 0.056 (0.002) 0.069 (0.005)
*Standard deviation value in parenthesis 6.1.4.3 Loading Rate Comparison
The spring-back index values were slightly higher at 20 MPa/min loading rate as
compared to 10 MPa/min loading rate except for 10% binder case at 2.5 MPa pressure.
The spring-back index values at 10 and 20 MPa/min loading rates for 5 and 10% binder
contents are given in Figures 6.13 and 6.14, respectively. No clear effect of loading rate
was visible.
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spri
ng-b
ack
inde
x
10 MPa/min20 MPa/min
Figure 6.13 Spring-back index of granulated powder formulations at 10 and 20
MPa/min loading rates and 5% binder content
118
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 2 4 6 8 10 12Pressure, MPa
Spri
ng-b
ack
inde
x
10 MPa/min20 MPa/min
Figure 6.14 Spring-back index of granulated powder formulations at 10 and 20
MPa/min loading rates and 10% binder content
6.1.4.4 Analysis of Covariance (ANCOVA)
The relationship of spring-back index with pressure was analyzed at different
levels of binder content and loading rate. Based on the ANCOVA table (Appendix F),
binder content did not have significant effect (p>0.05) on spring-back index value and
slopes of the regression lines did not differ at both binder contents significantly (p>0.05)
while loading rate had significant effect on the slope of regression lines (p<0.05). The
combination of pressure with loading rate had significant effect (p<0.05). The treatment
combination of binder and loading rate was significant (p<0.05). Mean values of spring-
back index at different pressure were compared at different binder contents and loading
rates. These values were significantly different (p<0.05) – 5% binder vs. 10% and for 10
and 20 MPa/min loading rate; 10 vs. 20 MPa/min loading rates at 5% binder (Figure
6.15).
119
0.00
0.02
0.04
0.06
0.08
0.10
0 5 10
Binder content, %
Mea
n sp
ring
-bac
k in
dex
10 MPa/min
20 MPa/min
Figure 6.15 Mean spring-back index vs. binder content at different loading rates
120
6.2 CTC Test Results
In CTC tests, the granulated powder samples at binder contents of 5 and 10%
were unloaded and reloaded at three different confining pressures of 1.0, 2.0, and 3.0
MPa, similar to the dry powder formulations. These tests were carried out at loading rates
of 10 and 20 MPa/min.
6.2.1 CTC Test Profile
The CTC tests were conducted at a stress difference of 1 MPa. Higher stress
difference developed instability in the CTT system resulting in catastrophic membrane
and/or component failures. Hence, the tests were conducted at 1 MPa stress difference.
Typical CTC test profiles for granulated formulations at 10 and 20 MPa/min loading rates
for 5 and 10% binder and confining pressures of 1, 2, and 3 MPa are shown in Figures
6.16 to 6.21. From these CTC profiles, as the confining pressure increased, the strain
difference decreased. At confining pressures of 2 and 3 MPa, the effect of loading rate
and binder content was not apparent. However, at 1 MPa confining pressure, the strain
difference for 10% binder content granular assembly was higher than at 5% binder
content. At 10% binder, the granules being larger compared to 5% binder formed less
stable granular assembly, which was more flowable resulting in greater strain difference.
121
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Stress difference, MPa
Stra
in d
iffer
ence
(b)
Figure 6.16 Typical CTC response at 1 MPa confining pressure and 10 MPa/min
loading rate for binder contents of (a) 5% and (b) 10%
122
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2Stress difference, MPa
Stra
in d
iffer
ence
, MPa
(b)
Figure 6.17 Typical CTC response at 1 MPa confining pressure and 20 MPa/min
loading rate for binder contents of (a) 5% and (b) 10%
123
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(b)
Figure 6.18 Typical CTC response at 2 MPa confining pressure and 10 MPa/min
loading rate for binder contents of (a) 5% and (b) 10%
124
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(b)
Figure 6.19 Typical CTC response at 2 MPa confining pressure and 20 MPa/min
loading rate for binder contents of (a)5% and (b) 10%
125
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Stress difference, MPa
Stra
in d
iffer
ence
(b)
Figure 6.20 Typical CTC response at 3 MPa confining pressure and 10 MPa/min
loading rate for binder contents of (a) 5% and (b) 10%
126
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 0.2 0.4 0.6 0.8 1 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(a)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.0 0.2 0.4 0.6 0.8 1.0 1.2
Stress difference, MPa
Stra
in d
iffer
ence
(b)
Figure 6.21 Typical CTC response at 3 MPa confining pressure and 20 MPa/min
loading rate for binder contents of (a) 5% and (b) 10%
127
6.2.2 Shear Modulus
The shear modulus is measure of the resistance of a material to shear deformation.
Shear modulus was determined from CTC tests as described in Section 4.6.3. The method
used to determine the shear modulus was different from that used by earlier researcher;
similar to bulk modulus determination with stress on x-axis and strain on y-axis.
The shear modulus values were determined at stress differences of 1.0 MPa at
both 10 and 20 MPa/min loading rates. The shear modulus increased with increase in the
confining pressure in all cases. With increase in confining pressure, the strength of the
sample increased, and hence the resistance to deformation increased; consequently, the
shear modulus increased. Similar trends were obtained by earlier researchers (Li, 1999;
Mittal and Puri, 1999a; Huang and Puri, 2000).
6.2.2.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate, the average shear modulus values at 1.0 MPa
confining pressure were 24 and 12 MPa at 5 and 10% binder contents, respectively.
These values increased to 33 (37.5%, percent change in values from 1.0 MPa) and 37
(67.5%) MPa at 2.0 MPa and 55 (129%) and 74 (500%) at 3.0 MPa confining pressures
(Figure 6.22). Very low value of shear modulus was observed in case of 10% binder at
1.0 MPa confining pressure which indicated failure of the specimen. The average shear
modulus values at 10 MPa/min loading rate and 1 MPa stress difference are given in
Table 6.9. In general, the shear modulus values at 10% binder content were higher than at
5% binder.
Table 6.9 Shear modulus of granulated powder formulations at 10 MPa/min loading
rate and 1 MPa stress difference* Binder content, %
Confining pressure, MPa 5 10
1.0 24 MPa (2.3) 12 MPa (0.9)
2.0 33 MPa (5.6) 37 MPa (6.6)
3.0 55 MPa (5.4) 74 MPa (1.0)
*Standard deviation value in parenthesis
128
0102030405060708090
100
0 1 2 3 4
Confining Pressure, MPa
She
ar M
odul
us, M
Pa
5% binder
10% binder
Figure 6.22 Shear modulus of granulated powder formulations at 10 MPa/min
loading rate and 1 MPa stress difference at two binder contents
6.2.2.2 Loading Rate of 20 MPa/min At 20 MPa/min loading rate, the average shear modulus values at 1.0 MPa
confining pressure were 27 and 26 MPa at 5 and 10% binder contents, respectively.
These values increased to 30 (11%, percent change from 1 MPa value) and 39 (50%)
MPa at 2.0 MPa and 49 (45%) and 75 (188%) MPa at 3.0 MPa confining pressures
(Figure 6.23). The shear modulus value at 10% binder was higher than that at 5% binder.
The average shear modulus values at 20 MPa/min loading rate and 1 MPa stress
difference are given in Table 6.10.
Table 6.10 Shear modulus of granulated powder formulations at 20 MPa/min
loading rate and 1 MPa stress difference* Binder content, %
Confining pressure, MPa 5 10
1.0 27 MPa (1.1) 26 MPa (1.1)
2.0 30 MPa (6.0) 39 MPa (6.4)
3.0 49 MPa (5.4) 75 MPa (4.9)
*Standard deviation value in parenthesis
129
01020304050
60708090
100
0 1 2 3 4
Confining Pressure, MPa
She
ar M
odul
us, M
Pa
5% binder
10% binder
Figure 6.23 Shear modulus of granulated powder formulations at 20 MPa/min
loading rate and 1 MPa stress difference at two binder contents 6.2.2.3 Loading Rate Comparison
The shear modulus at 10 and 20 MPa/min loading rate were different, which
indicated that the granules are rate-dependent materials. However, no clear trend on the
effect of loading rate was observed. The shear modulus at 10 and 20 MPa/min loading
rates and 1 MPa stress difference at confining pressures of 1, 2, and 3 MPa for 5 and 10%
binder contents are given in Figures 6.24 and 6.25, respectively.
01020304050
60708090
100
0 1 2 3 4
Confining Pressure, MPa
She
ar M
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 6.24 Shear modulus of granulated powder formulations at 10 and 20
MPa/min loading rates and 5% binder content at a stress difference of 1 MPa
130
01020
3040506070
8090
100
0 1 2 3 4
Confining Pressure, MPa
Shea
r M
odul
us, M
Pa
10 MPa/min
20 MPa/min
Figure 6.25 Shear modulus of granulated powder formulations at 10 and 20
MPa/min loading rates and 10% binder content at a stress difference of 1 MPa
6.2.2.4 Analysis of Variance (ANOVA)
Tukey comparison was performed between the mean values of shear modulus
using Minitab to evaluate the effect of pressure, binder content, and loading rate. Based
on the ANOVA table (Appendix F), combined effect of pressure, binder content, and
loading rate were significant (p>0.05) on shear modulus values. These values were
significantly different (p<0.05) with change in binder content and loading rate– 10 vs. 20
MPa/min loading rate at 5% binder and 3 MPa confining pressure; 5% vs. 10% binder at
3 MPa confining pressure (both 10 and 20 MPa/min loading rates). Values not
significantly different (p>0.05) with change in pressure were - 1 MPa vs. 2 MPa
confining pressure at 5% binder content (both 10 and 20 MPa/min loading rates); 1 MPa
vs. 2 MPa confining pressure at 10% binder content and 20 MPa/min loading rate (Figure
6.26).
131
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5 3 3.5
Pressure, MPa
Mea
n sh
ear m
odul
us, M
Pa
5% binder, 10 MPa/min
5% binder, 20 MPa/min
10% binder, 10 MPa/min
10% binder, 20 MPa/min
Figure 6.26 Mean shear modulus of granulated powder formulations at different loading rates and binder contents
6.2.3 Failure Stress and Critical State Line
The failure stress value was determined at strain difference value of 12% for 1.0
and 2.0 MPa confining pressure. For 3 MPa confining pressure, the 7% strain difference
value was taken as failure point. At high confining pressure less strain difference was
obtained at 1 MPa stress difference. Higher stress differences developed instability and,
therefore, were not used. Mittal (2003) also used variable strain difference for failure
point. The failure stress value increased with confining pressure in all cases.
6.2.3.1 Loading Rate of 10 MPa/min
At 10 MPa/min loading rate, the average failure stress values for 1.0 MPa
confining pressure were 0.93 and 0.78 MPa at 5 and 10% binder contents, respectively.
These values increased to 1.12 (20%, percent change in values from 1.0 MPa confining
pressure value) and 1.19 (52%) MPa at 2.0 MPa. The 7% strain difference (taken as
failure point) were reached at 1.0 and 1.12 MPa stress difference at 3.0 MPa confining
pressures. The average failure stress values at 10 MPa/min loading rate and at different
confining pressure are given in Table 6.11.
132
Table 6.11 Failure stress of granulated powder formulations at 10 MPa/min loading rate * Binder content, %
5 10
Confining pressure,
MPa Mean
Pressure, MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
1.0 1.3 0.93 (0.02) 1.3 0.78 (0.11) 2.0 2.4 1.12 (0.05) 2.4 1.19 (0.18) 3.0 3.3 1.00** (0.00) 3.4 1.12** (0.00)
*Standard deviation value in parenthesis ** Strain difference of 7%
6.2.3.2 Loading Rate of 20 MPa/min
At 20 MPa/min loading rate, the average failure stress values for 1.0 MPa
confining pressure were 1.09 and 0.94 MPa at 5 and 10% binder contents, respectively.
These values were 1.09 (0%, percent change in values from 1.0 MPa confining pressure
value) and 1.01 (7%) MPa at 2.0 MPa. The 7% strain difference was reached at 1.04 and
1.06 MPa stress difference at 3.0 MPa confining pressures. The average failure stress
values at 10 MPa/min loading rate and at different confining pressure are given in Table
6.12.
Table 6.12 Failure of granulated powder formulations at 20 MPa/min loading rate*
Binder content, %
5 10
Confining pressure,
MPa Mean Pressure,
MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
1.0 1.4 1.09 (0.02) 1.3 0.94 (0.14) 2.0 2.4 1.09 (0.19) 2.4 1.01 (0.07) 3.0 3.3 1.04** (0.04) 3.4 1.06** (0.1)
*Standard deviation value in parenthesis ** Strain difference of 7%
133
6.2.3.3 Loading Rate Comparison
The failure stress values at 10 and 20 MPa/min loading rate were very close at
confining pressure of 1, 2, and 3 MPa. Mittal (2003) also reported that failure stress
values at different loading rates were very close. The failure stress at 10 and 20 MPa/min
loading rates for 5 and 10% binder contents are given in Tables 6.13 and 6.14,
respectively.
Table 6.13 Failure stress of granulated powder formulations at 10 and 20 MPa/min loading rates for 5% binder *
Binder content, %
10 20
Confining pressure,
MPa Mean Pressure,
MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
1.0 1.3 0.93 (0.02) 1.4 1.09 (0.02) 2.0 2.4 1.12 (0.05) 2.4 1.09 (0.19) 3.0 3.3 1.00** (0.00) 3.3 1.04** (0.04)
*Standard deviation value in parenthesis ** Strain difference of 7%
Table 6.14 Failure of granulated powder formulations at 10 and 20 MPa/min loading rates for 10% binder *
Binder content, %
5 10
Confining pressure,
MPa Mean Pressure,
MPa
Failure Stress, MPa
Mean Pressure,
MPa
Failure Stress, MPa
1.0 1.3 0.93 (0.02) 1.3 0.94 (0.14) 2.0 2.4 1.12 (0.05) 2.4 1.01 (0.07) 3.0 3.3 1.00** (0.00) 3.4 1.06** (0.1)
*Standard deviation value in parenthesis ** Strain difference of 7%
134
6.2.3.4 Analysis of Variance (ANOVA)
Tukey comparison was performed between the mean values of failure stress to
evaluate the effect of pressure, binder content and loading rate. Based on the ANCOVA
table (Appendix F), pressure, binder content, and loading rate together did not have
significant effect (p>0.05) on failure stress values. However, treatment combinations of
binder and pressure and pressure and loading rate were significant (p<0.05). These values
were significantly different (p<0.05) for (1) treatment combination of binder content and
pressure. Mean values at two loading rates – 1 MPa vs. 2 MPa and 1 MPa vs. 3 MPa
confining pressure for 10% binder (Figure 6.27). (2) treatment combination of pressure
and loading rate. Mean values at three binder contents - 1 MPa vs. 2 MPa and 1 MPa vs.
3 MPa confining pressure at10 MPa/min; 10 vs. 20 MPa/min loading rates at 1 MPa
confining pressure (Figure 6.28).
0.0
0.5
1.0
1.5
0 1 2 3 4
Pressure, MPa
Mea
n fa
ilure
stre
ss, M
Pa
5% binder
10% binder
Figure 6.27 Mean failure stress vs. pressure at different binder contents
135
0.0
0.5
1.0
1.5
0 1 2 3 4
Pressure, MPa
Mea
n fa
ilure
stre
ss, M
Pa
10 MPa/min
20 MPa/min
Figure 6.28 Mean failure stress vs. pressure at different loading rates
6.3 Comparison between Dry vs. Granulated Formulation In Chapter 5 and Section 6.1 to 6.3 of Chapter 6, mechanical properties of dry and
granulated formulations at different binder contents have been discussed. The mechanical
properties in case of granulated formulations were different from those of dry
formulations. This was due to change in the property of powder formulations during
granulation. In the following sections the comparison between each mechanical
properties of dry and granulated formulation are presented.
6.3.1 Bulk Modulus
Bulk modulus values for dry blended and granulated powder formulations at 5
and 10% binder contents for 10 and 20 MPa/min loading rates are given in Tables 6.13
and 6.14, respectively. At 10 MPa/min loading rate and 5% binder content, the bulk
modulus after granulation increased by 44% (116 to 167 MPa), 79% and 94% at 2.5, 5.0
and 10.0 MPa pressure, respectively. These values were 26%, 57%, and 75% at 10%
binder content, respectively. At 20 MPa/min loading rate and 5% binder content, the bulk
modulus after granulation increased by 35% (127 to 172 MPa), 12% and 40% at 2.5, 5.0
and 10.0 MPa pressure, respectively. These values were 6%, -2%, and 10% at 10%
binder content, respectively. In general, bulk modulus increased with granulation. The
136
granules were more plastic resulting in less elastic recovery and hence had high bulk
modulus.
Table 6.15 Bulk modulus of dry and granulated powder formulations at 10
MPa/min loading rate* Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
2.5 116 MPa (2.1) 167 MPa (23.7) 136 MPa (15.2) 171 MPa (8.6)
5.0 143 MPa (1.8) 256 MPa (30.2) 170 MPa (16.9) 267 MPa (25.8)
10.0 216 MPa (4.6) 420 MPa (76.2) 251 MPa (19.9) 439 MPa (18.7)
* Standard deviation value in parenthesis
Table 6.16 Bulk modulus of dry and granulated powder formulations at 20
MPa/min loading rate* Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
2.5 127 MPa (14.6) 172 MPa (3.6) 145 MPa (29.9) 154 MPa (10.7)
5.0 172 MPa (24.3) 192 MPa (0.2) 196 MPa (38.0) 178 MPa (7.4)
10.0 256 MPa (32.0) 358 MPa (29.3) 280 MPa (54.0) 285 MPa (22.9)
* Standard deviation value in parenthesis
6.3.2 Compression Index
Compression index values for dry blended and granulated powder formulations at
5 and 10% binder contents for 10 and 20 MPa/min loading rates are given in Table 6.17
and 6.18, respectively. At 10 MPa/min loading rate and 5% binder content, the
compression index after granulation increased by 200%, 40% and 19% at 2.5, 5.0 and
10.0 MPa pressure, respectively. These values were 207%, 51%, and 17% at 10% binder
content, respectively. At 20 MPa/min loading rate and 5% binder content, the
compression index after granulation increased by 222%, 53% and 25% at 2.5, 5.0 and
137
10.0 MPa pressure, respectively. These values were 200%, 53%, and 24% at 10% binder
content, respectively. The compression index increased with granulation in all cases.
Table 6.17 Compression index of dry and granulated powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
2.5 0.283 (0.014) 0.847 (0.043) 0.250 (0.007) 0.768 (0.051) 5.0 0.579 (0.063) 0.764 (0.005) 0.537 (0.037) 0.813 (0.046) 10.0 0.699 (0.045) 0.830 (0.025) 0.726 (0.007) 0.853 (0.060)
* Standard deviation value in parenthesis
Table 6.18 Compression index of dry and granulated powder formulations at 20
MPa/min loading rate* Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
2.5 0.279 (0.027) 0.899 (0.034) 0.280 (0.034) 0.839 (0.095)
5.0 0.530 (0.022) 0.809 (0.029) 0.500 (0.013) 0.765 (0.012)
10.0 0.695 (0.056) 0.872 (0.045) 0.651 (0.029) 0.807 (0.018)
* Standard deviation value in parenthesis
6.3.3 Spring-back Index
Spring-back index values for dry blended and granulated powder formulations at
5 and 10% binder contents for 10 and 20 MPa/min loading rates are given in Table 6.19
and 6.20, respectively. At 10 MPa/min loading rate and 5% binder content, the spring-
back index after granulation decreased by 90%, 94%, and 94% at 2.5, 5.0, and 10.0 MPa
pressure, respectively. These values were 90%, 92%, and 93% at 10% binder content,
respectively. At 20 MPa/min loading rate and 5% binder content, the spring-back index
after granulation increased by 93%, 93%, and 93% at 2.5, 5.0, and 10.0 MPa pressure,
respectively. These values were 92%, 90%, and 91% at 10% binder content, respectively.
The spring-back index decreased with granulation in all cases.
138
Table 6.19 Spring-back index of dry and granulated powder formulations at 10 MPa/min loading rate*
Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
2.5 0.0642 (0.0018) 0.036 (0.007) 0.0657 (0.0036) 0.060 (0.004)
5.0 0.0833 (0.0031) 0.051 (0.007) 0.800 (0.0061) 0.060 (0.005)
10.0 0.0963 (0.0025) 0.054 (0.006) 0.0943 (0.0075) 0.063 (0.007)
* Standard deviation value in parenthesis
Table 6.20 Spring-back index of dry and granulated powder formulations at 20
MPa/min loading rate* Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
2.5 0.0654 (0.0133) 0.046 (0.004) 0.0593 (0.0172) 0.045 (0.005) 5.0 0.0749 (0.0093) 0.056 (0.006) 0.0680 (0.0134) 0.065 (0.006) 10.0 0.0813 (0.0093) 0.056 (0.002) 0.0789 (0.0139) 0.069 (0.005)
* Standard deviation value in parenthesis
6.3.4 Shear Modulus
Shear modulus values for dry blended and granulated powder formulations at 5
and 10% binder contents for 10 and 20 MPa/min loading rates are given in Table 6.21
and 6.22, respectively. At 10 MPa/min loading rate and 5% binder content, the shear
modulus after granulation increased by 33%, 10%, and 32% at 1, 2, and 3 MPa confining
pressure, respectively. These values were -33%, 23%, and 124% at 10% binder content,
respectively. At 20 MPa/min loading rate and 5% binder content, the shear modulus after
granulation increased by -4%, 0%, and 32% at 1, 2, and 3 MPa confining MPa pressure,
respectively. These values were -7%, 30%, and 127% at 10% binder content,
respectively. In general, the shear modulus increased with granulation.
139
Table 6.21 Shear modulus of dry and granulated powder formulations at 10 MPa/min loading rate and 1 MPa stress difference*
Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
1.0 18 MPa (1.9) 24 MPa (2.3) 18 MPa (1.3) 12 MPa (0.9)
2.0 30 MPa (2.8) 33 MPa (5.6) 30 MPa (0.9) 37 MPa (6.6)
3.0 37 MPa (3.0) 55 MPa (5.4) 33 MPa (2.0) 74 MPa (1.0)
* Standard deviation value in parenthesis
Table 6.22 Shear modulus of dry and granulated powder formulations at 20
MPa/min loading rate* Binder content, %
Pressure, MPa 5 10
Dry Granulated Dry Granulated
1.0 28 MPa (5.7) 27 MPa (1.1) 28 MPa (4.0) 26 MPa (1.1)
2.0 30 MPa (2.0) 30 MPa (6.0) 30 MPa (2.2) 39 MPa (6.4)
3.0 37 MPa (7.9) 49 MPa (5.4) 33 MPa (3.0) 75 MPa (4.9)
* Standard deviation value in parenthesis
6.3.5 Failure Stress Failure stress values for dry blended and granulated powder formulations
at 5 and 10% binder contents for 10 and 20 MPa/min loading rates are given in Table
6.23 and 6.24, respectively. At 10 MPa/min loading rate and 5% binder content, the
failure stress value after granulation decreased by 8%, 35%, and 50% at 1, 2, and 3 MPa
confining pressure, respectively. These values were 23%, 30%, and 40% at 10% binder
content, respectively. At 20 MPa/min loading rate and 5% binder content, the failure
stress after granulation decreased by 23%, 40%, and 47% at 1, 2, and 3 MPa confining
pressure, respectively. These values were 32%, 45%, and 47% at 10% binder content,
respectively. In general, the failure stress decreased with granulation.
140
Table 6.23 Failure stress values of dry blended powder formulations at 10 MPa/min loading rate *
Failure Stress, MPa
5% binder content 10% binder content
Confining pressure,
MPa Dry
formulations Granulated
formulations Dry
formulations Granulated
formulations 1.0 1.01 (0.02) 0.93 (0.02) 1.02 (0.02) 0.78 (0.11) 2.0 1.71 (0.12) 1.12 (0.05) 1.69 (0.12) 1.19 (0.18) 3.0 1.99 (0.07) 1.00** (0.00) 1.88 (0.17) 1.12** (0.00) * Standard deviation in parenthesis, ** Strain difference of 7%
Table 6.24 Failure stress values of dry blended powder formulations at 20 MPa/min
loading rate * Failure Stress, MPa
5% binder content 10% binder content
Confining pressure,
MPa Dry
formulations Granulated
formulations Dry
formulations Granulated
formulations 1.0 1.42 (0.09) 1.09 (0.02) 1.38 (0.12) 0.94 (0.14) 2.0 1.82 (0.01) 1.09 (0.19) 1.83 (0.06) 1.01 (0.07) 3.0 1.95 (0.06) 1.04** (0.04) 1.99 (0.12) 1.06** (0.1) * Standard deviation in parenthesis, ** Strain difference of 7%
6.4 Summary HTC and CTC tests were conducted on granulated powder formulations at
different loading conditions and binder contents similar to dry powder formulations. Bulk
modulus, compression index, spring-back index, shear modulus, and failure stress were
determined. Bulk modulus, compression index, and spring-back index increased with
pressure. Shear modulus and failure stress increased with confining pressure. Bulk
modulus increased with binder content at 10 MPa/min while decreased at 20 MPa/min
loading rate. Bulk modulus increased with loading rate. Spring-back index increased with
binder content. Compression index values at 20 MPa/min were higher than at 10
MPa/min for the granules having 5% binder. However, for 10% binder content, the
compression index values were higher at 10 MPa/min for pressures of 5 and 10 MPa.
Spring-back and compression index values were higher at 10 MPa/min compared to 20
MPa/min.
141
Chapter 7 - Tablet Quality Parameters and Relationship Development for
Dry Powder Formulations
The tablets were formed using a die-punch set at different loading conditions and
binder content. Tablet quality parameters were evaluated and relationships were
developed between tablet quality parameters and dry powder formulation properties.
7.1 Tablet Quality
As discussed in Chapter 4, the tablets were formed at different binder contents at
two pressing stresses of 70 and 90 MPa. For each tablet, 300 mg (± 1 mg) powder was
used. Various quality parameters such as diametral strength, axial penetration strength,
indentation hardness, and friability were evaluated. Each parameter is discussed in the
following sections. An overall discussion of results for these tablets is presented in
Section 7.1.5.
7.1.1 Diametral Strength Test
As expected, the average diametral strength values were higher at 90 MPa than at
70 MPa compression pressure at all binder contents. The diametral strength at different
binder contents of 0, 5, and 10% is shown in Figure 7.1 and given in Table 7.1. The
arrow on the figure indicates increase in diametral strength with increase in pressure. The
average diametral strength values at 70 MPa were 0.19, 0.35, and 0.33 MPa at 0, 5, and
10% binder, respectively. These values at 90 MPa compression pressure were 0.32 (69%,
increase over 70 MPa value), 0.38 (12%), and 0.38 MPa (15%). The diametral strength
increased with binder content upto 5%; thereafter, it decreased slightly when binder
content increased from 5 to 10%.
Table 7.1 Diametral strength of tablets made from dry powder formulations at 70 and 90 MPa compression pressures and different binder contents*
Compression pressure Binder content, %
70 MPa 90 MPa
0 0.19 MPa (0.021) 0.32 MPa (0.005)
5 0.35 MPa (0.008) 0.38 MPa (0.008)
10 0.33 MPa (0.030) 0.38 MPa (0.029)
*Standard deviation in parenthesis
142
0.0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12
Binder content, %
Diam
etra
l str
engt
h, M
Pa
70 MPa90 MPa
Figure 7.1 Diametral strength of tablets using dry formulations at different binder
contents
7.1.2 Axial Penetration Test
The axial penetration strength values were higher at 90 MPa than at 70 MPa
compression pressure at all binder contents. The axial penetration strength at different
binder contents of 0, 5, and 10% is shown in Figure 7.2 and given in Table 7.2. The
average axial penetration strength values at 70 MPa were 30.8, 32.9, and 29.8 MPa at 0,
5, and 10% binder, respectively. These values at 90 MPa compression pressure were 32.0
(4%, increase over 70 MPa value), 36.5 (11%), and 34.3 MPa (15%). The axial
penetration strength increased with binder content upto 5%; thereafter, it decreased when
binder content increased from 5 to 10% similar to the diametral strength.
Table 7.2 Axial penetration strength of tablets made from dry powder formulations
at 70 and 90 MPa compression pressures and different binder contents* Compression pressure Binder content, %
70 MPa 90 MPa
0 30.8 MPa (2.4) 32.0 MPa (1.2)
5 32.9 MPa (2.2) 36.5 MPa (1.3)
10 29.8 MPa (1.6) 34.3 MPa (0.7)
*Standard deviation in parenthesis
Increasing compression pressure
143
0
5
10
15
20
25
30
35
40
0 2 4 6 8 10 12
Binder content, %
Axia
l stre
ngth
, MPa
70 MPa
90 MPa
Figure 7.2 Axial penetration strength of tablets using dry formulations at different
binder contents
7.1.3 Indentation Hardness Test
The indentation hardness values were higher at 90 MPa than at 70 MPa
compression pressure at all binder contents. These values at different binder contents of
0, 5, and 10% are shown in Figure 7.3 and given in Table 7.3. The average indentation
hardness values at 70 MPa were 1.15, 1.28, and 1.27 MPa at 0, 5, and 10% binder,
respectively. These values at 90 MPa compression pressure were 1.25 (9%, increase over
70 MPa value), 1.38 (8%), and 1.40 MPa (10%). The indentation hardness also increased
with binder content upto 5%; thereafter, it did not change when binder content increased
from 5 to 10%.
Table 7.3 Indentation hardness of tablets made from dry powder formulations at 70
and 90 MPa compression pressure and different binder contents* Compression pressure Binder content, %
70 MPa 90 MPa
0 1.15 MPa (0.06) 1.25 MPa (0.07)
5 1.28 MPa (0.07) 1.38 MPa (0.11)
10 1.27 MPa (0.09) 1.40 MPa (0.07)
*Standard deviation in parenthesis
144
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
0 2 4 6 8 10 12
Binder content, %
Inde
ntat
ion
hard
ness
, MPa
70 MPa
90 MPa
Figure 7.3 Indentation hardness of tablets using dry formulations at different
binder contents 7.1.4 Friability Test
Friability values were higher for tablets formed at 70 MPa compared to those
formed at 90 MPa compression pressure at all binder contents. The friability at different
binder contents of 0, 5, and 10% is shown in Figure 7.4 and given in Table 7.4. The
friability at 70 MPa were 1.62, 1.31, and 1.48% at 0, 5, and 10% binder, respectively.
These values at 90 MPa compression pressure were 0.92 (43%, decrease over 70 MPa
value), 0.79 (40%), and 0.75% (49%). The friability decreased with binder content upto
5%; thereafter, it increased with binder content from 5 to 10%.
Table 7.4 Friability (%) of tablets made from dry powder formulations at 70 and 90
MPa compression pressures and different binder contents Compression pressure Binder content, %
70 MPa 90 MPa
0 1.62% 0.92%
5 1.31% 0.75%
10 1.48% 0.79%
145
0.00.20.40.60.81.01.21.41.61.8
0 2 4 6 8 10 12Binder content, %
Fria
bilit
y, %
70 MPa
90 MPa
Figure 7.4 Friability of tablets using dry formulations at different binder contents
7.1.5 Summary of Tablet Quality Tests
In sections 7.1.1 to Section 7.1.4 it was mentioned that all tablet quality
parameters changed upto 5% binder content. This shows that increase in binder after 5%
only had marginal effect on tablet quality parameters. Furthermore, binder content of
around 5% appears to be optimum for tablet formation using ingredients and proportions
studied in this research. Dry binder improves the strength of the tablets by spreading and
filling into the void spaces. It is hypothesized that the void filling saturation was reached
at 5% binder content due to which the strength value do not change much thereafter.
7.2 Relationship between Tablet Quality Parameters and Powder Properties
Statistical regression relations were developed between tablets’ quality parameters
at different binder contents and loading conditions vs. powder formulations’ mechanical
properties. Tablet qualities included diametral strength, axial penetration strength,
indentation hardness, and friability. Powder properties included bulk modulus,
compression index, spring-back index, shear modulus, and failure stress. The regression
equations between each tablet quality parameter and powder property were developed;
however, equations having r2 > 0.8 were considered acceptable for tablet quality
predictions.
Increasing compression pressure
146
7.2.1 Equations for Predicting Diametral Strength
The r2 values for equations to predict diametral strength of tablets formed at 70
MPa based upon the powder’s mechanical properties such as bulk modulus, compression
index, spring-back index, shear modulus and failure strength are given in Table 7.5.
These values for tablets formed at 90 MPa are given in Table 7.6. Based on the criterion
r2 value > 0.8, compression index, spring-back index, and shear modulus were found
most suitable for predicting the diametral strength. All of the six spring-back index values
at three different pressures and two loading rates related with diametral strength of tablets
formed at 70 and 90 MPa (r2 > 0.8). Five values of compression index (except at 10
MPa/min loading rate and 5 MPa pressure) and five shear modulus values (except at 10
MPa/min loading rate and 3 MPa confining pressure) related with diametral strength of
tablets formed at 70 and 90 MPa with r2 > 0.8.
Table 7.5 r2 values for equations to predict diametral strength of tablet formed at 70
MPa on the basis of powders’ mechanical properties for dry formulations* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.51 0.27 0.28 0.82 0.64 0.89 Compression Index 0.97 0.00 0.91 0.99 0.92 0.82 Spring-back Index 0.99 0.88 0.99 0.91 0.91 0.99
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.98 0.99 0.00 0.99 0.83 0.82 Shear Modulus 2 MPa SD** *** 0.63 0.97 *** 0.91 0.66 Failure stress 0.96 0.96 0.07 0.98 0.33 0.73 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
147
Table 7.6 r2 values for equations to predict diametral strength of tablet formed at 90 MPa on the basis of powders’ mechanical properties for dry formulations*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.5 0.24 0.27 0.83 0.64 0.897 Compression Index 0.96 0 0.90 0.99 0.93 0.83 Spring-back Index 0.99 0.87 0.99 0.92 0.91 0.99
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.98 0.98 0.00 0.99 0.83 0.99 Shear Modulus 2 MPa SD** *** 0.62 0.97 *** 0.91 0.65 Failure stress 0.95 0.96 0.07 0.97 0.33 0.73 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
The plots between diametral strength and various powder properties are given in
Appendix A. As examples, plots between diametral strength and spring-back index
(determined at 20 MPa/min loading rate), and diametral strength and compression index
(determined at 20 MPa/min loading rate), at different loading conditions are shown in
Figures 7.5 and 7.6, respectively. The regression equations are given in Appendix B. As
examples, two regression equations are given below:
DS70 = 14.115 SI10, 20 - 0.7946, r2 = 0.99 (7.1) where, DS70 = Diametral strength at 70 MPa compaction pressure and SI10, 20 = Spring-
back index at 10 MPa pressure and 20 MPa/min loading rate
DS90 = -1.021 CI10,10 + 1.1297, r2 = 0.90 (7.2) where, DS90 = Diametral strength at 90 MPa compaction pressure and CI10, 10 =
Compression index at 10 MPa pressure and 10 MPa/min loading rate
148
0.00
0.05
0.100.15
0.20
0.25
0.300.35
0.40
0.45
0.00 0.05 0.10 0.15Spring-back index
Diam
etra
l str
engt
h, M
Pa2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back index was determined. Figure 7.5 Relation between diametral strength and spring back index (determined
at 20 MPa/min loading rate) at different loading conditions for dry formulations
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.45
0.0 0.2 0.4 0.6 0.8 1.0Compression index
Diam
etra
l str
engt
h, M
Pa
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 7.6 Relation between diametral strength and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations
*
*
149
7.2.2 Equations for Predicting Axial Penetration Strength
The r2 values for equations to predict axial penetration strength of tablet formed at
70 MPa based upon the powder’s mechanical properties are given in Table 7.7. These
values for tablets formed at 90 MPa is given in Table 7.8. From Tables 7.7 and 7.8, it is
clear that few powder properties had good relations (r2> 0.8) with the axial penetration
strength. In no case all six of the r2 values were more than 0.8. Only compression index,
spring-back index, and shear modulus (at 2 MPa stress difference) at higher loading rate
had good relation (r2 > 0.8) with axial penetration strength of tablets formed at 90 MPa.
Table 7.7 r2 values for equations to predict axial penetration strength of tablet formed at 70 MPa on the basis of powders’ mechanical properties for dry
formulations* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.2 0.46 0.42 0.45 0.65 0.35 Compression Index 0.01 0.93 0.00 0.06 0.30 0.45 Spring-back Index 0.00 0.07 0.04 0.32 0.32 0.16
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.02 0.02 0.90 0.12 0.02 0.01 Shear Modulus 2 MPa SD** *** 0.40 0.44 *** 0.6 0.45 Failure stress 0.00 0.01 0.69 0.02 0.90 0.50 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
150
Table 7.8 r2 values for equations to predict axial penetration strength of tablet formed at 90 MPa on the basis of powders’ mechanical properties for dry
formulations* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0 0.12 0.10 0.81 0.94 0.73 Compression Index 0.68 0.2 0.56 0.80 0.98 0.99 Spring-back Index 0.82 0.51 0.77 0.98 0.98 0.91
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.73 0.75 0.14 0.87 0.45 0.43 Shear Modulus 2 MPa SD** *** 0.03 0.01 *** 0.97 0.99 Failure stress 0.66 0.67 0.00 0.72 0.73 0.33 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
The plots between axial penetration strength and various powder properties are
given in Appendix A. Plots between axial penetration strength and spring-back index
(determined at 20 MPa/min loading rate), and axial penetration strength and compression
index (determined at 20 MPa/min loading rate), at different loading conditions are shown
in Figures 7.7 and 7.8, respectively. The complete list of regression equations are given in
Appendix B. Two regression equations, as examples are given below:
AS90 = 52.005 SI5, 20 – 8.6849, r2 = 0.98 (7.3) where, AS90 - Axial penetration strength at 90 MPa compaction pressure and SI5, 20 -
Spring-back index at 5 MPa pressure and 20 MPa/min loading rate
AS90 = 50.078 CI10,20 + 1.6915, r2 = 0.99 (7.4) where, AS90 = Axial penetration strength at 90 MPa compaction pressure and CI10,20 =
Compression index at 10 MPa pressure and 20 MPa/min loading rate
151
26
28
30
32
34
36
38
40
0.00 0.05 0.10 0.15Spring-back index
Axia
l str
engt
h, M
Pa 2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 7.7 Relation between axial penetration strength and spring-back index (determined at 20 MPa/min loading rate) at different loading conditions for dry
formulations
26
28
30
32
34
36
38
40
0.0 0.2 0.4 0.6 0.8 1.0Compression index
Axi
al s
tren
gth,
MP
a 2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 7.8 Relation between axial penetration strength and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry
formulations
*
*
152
7.2.3 Equations for Predicting Indentation Hardness
The r2 values for predictive equations of indentation hardness of tablets formed at
70 and 90 MPa based upon the powder’s mechanical properties are given in Tables 7.9
and 7.10, respectively. Based on these r2 values, compression index, spring-back index,
and shear modulus were found most suitable for predicting the indentation hardness. All
six of the r2 values were more than 0.8 in case of spring-back index while five r2 values
(except at 10 MPa/min loading rate and 5 MPa pressure) were more than 0.8 in case of
shear modulus.
Table 7.9 r2 values for equations to predict indentation hardness of tablets formed at 70 MPa on the basis of powders’ mechanical properties for dry formulations*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.55 0.27 031 0.79 0.61 0.87 Compression Index 0.98 0.00 0.92 0.99 0.91 0.80 Spring-back Index 0.99 0.89 0.99 0.89 0.89 0.98
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.99 0.99 0.00 0.99 0.86 0.84 Shear Modulus 2 MPa SD** *** 0.33 0.29 *** 0.67 0.80 Failure stress 0.97 0.97 0.09 0.91 0.30 0.76 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
153
Table 7.10 r2 values for equations to predict indentation hardness of tablets formed
at 90 MPa on the basis of powders’ mechanical properties for dry formulations* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.73 0.46 0.5 0.63 0.42 0.72 Compression Index 0.99 0.02 0.99 0.97 0.78 0.62 Spring-back Index 0.95 0.98 0.98 0.75 0.75 0.89
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.99 0.98 0.05 0.92 0.96 0.95 Shear Modulus 2 MPa SD** *** 0.48 0.52 *** 0.62 0.48 Failure stress 0.99 0.99 0.23 0.99 0.14 0.90 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
The plots between indentation hardness and various powder properties are given in
Appendix A. As example, plots between indentation hardness and spring-back index
(determined at 20 MPa/min loading rate), and indentation hardness and shear modulus
(determined at 20 MPa/min loading rate), at different loading conditions are shown in
Figures 7.9 and 7.10, respectively. Regression equations are given in Appendix B. Two
examples of regression equations for predicting the indentation hardness are given below:
IH70 = -8.3372 SI10,10 – 2.0623, r2 = 0.99 (7.5) where, IH70 - Indentation hardness at 70 MPa compaction pressure and SI10, 10 - Spring-
back index at 10 MPa pressure and 10 MPa/min loading rate
IH70 = 0.0523 SM2.5,10 – 0.1798, r2 = 0.99 (7.6) where, IH70 = Indentation hardness at 70 MPa compaction pressure and SM2.5,10 - Shear
modulus at 1 MPa confining pressure, 1 MPa stress difference and 10 MPa/min loading
rate
154
1.00
1.051.10
1.15
1.201.25
1.30
1.351.40
1.45
0.00 0.02 0.04 0.06 0.08 0.10 0.12Spring-back index
Inde
ntat
ion
hard
ness
, MPa
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 7.9 Relation between indentation hardness and spring back index (determined at 10 MPa/min loading rate) at different loading conditions for dry
formulations
1.001.051.101.151.201.251.301.351.401.45
0 10 20 30 40 50Shear modulus, MPa
Inde
ntat
ion
hard
ness
, MPa
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined. Figure 7.10 Relation between indentation hardness and compression index
(determined at 20 MPa/min loading rate) at different loading conditions for dry formulations
*
*
155
7.2.4 Equations for Predicting Friability
The r2 values for equations to predict friability of tablets formed at 70 MPa and 90
MPa based upon the powder’s mechanical properties are given in Tables 7.11 and 7.12,
respectively. Based on these r2 values, bulk modulus, compression index, spring-back
index, and shear modulus at higher loading rate were found suitable for predicting the
friability.
Table 7.11 r2 values for equations to predict friability of tablet formed at 70 MPa on
the basis of powders’ mechanical properties for dry formulations* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.09 0.00 0.00 0.99 0.97 0.98 Compression Index 0.62 0.26 0.49 0.74 0.95 0.99 Spring-back Index 0.76 0.49 0.70 0.97 0.97 0.86
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.66 0.69 0.20 0.82 0.38 0.36 Shear Modulus 2 MPa SD** *** 0.00 0.00 *** 0.99 0.99 Failure stress 0.59 0.60 0.04 0.65 0.79 0.26 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined Table 7.12 r2 values for equations to predict friability of tablet formed at 90 MPa on
the basis of powders’ mechanical properties for dry formulations* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.37 0.14 0.16 0.92 0.75 0.96 Compression Index 0.90 0.03 0.81 0.96 0.98 0.92 Spring-back Index 0.97 0.77 0.95 0.97 0.97 0.99
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.92 0.94 0.15 0.99 0.72 0.70 Shear Modulus 2 MPa SD** *** 0.18 0.15 *** 0.91 0.92 Failure stress 0.88 0.89 0.04 0.92 0.47 0.60 * r2 > 0.8 are highlighted, **SD = Stress difference, *** Not determined
156
Plots between friability and various powder properties are given in Appendix A.
As examples, plots between friability and compression index (determined at 20 MPa/min
loading rate), and diametral strength and spring-back index (determined at 20 MPa/min
loading rate), at different loading conditions are shown in Figures 7.11 and 7.12,
respectively. The regression equations are given in Appendix B. As examples, two
regression equations are given below:
FR70 = 14.115 SI10, 20 - 0.7946, r2 = 0.99 (7.7) where, FR70 = Friability at 70 MPa compaction pressure and SI10, 20 = Spring-back index
at 10 MPa pressure and 20 MPa/min loading rate
FR90 = -1.021 CI10,10 + 1.1297, r2 = 0.90 (7.8) where, FR90 = Friability at 90 MPa compaction pressure and CI10, 10 = Compression
index at 10 MPa pressure and 10 MPa/min loading rate
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0.0 0.2 0.4 0.6 0.8 1.0Compression index
Fria
bilty
, %
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 7.11 Relation between friability and compression index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations
*
157
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0.00 0.05 0.10 0.15Spring-back index
Fria
bilty
, %2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 7.12 Relation between friability and spring-back index (determined at 20 MPa/min loading rate) at different loading conditions for dry formulations
7.2.5 Elastic Energy Explanation of Tablet Quality Relationship with Powder
Spring-back Index
Tablet quality such as diametral strength, axial penetration strength, and
indentation hardness related very well with spring-back index. Spring-back index is the
measure of elastic recovery of the powder after the pressure is removed. The recovery
includes contributions of both the solid particles and interparticle void spaces. This
means that powder’s elastic property can be used to predict the tablet quality and powder
has a memory of tablets’ elastic behavior. To explain and prove this hypothesis, an
energy based approach was proposed. During tablet formation, force or pressure is
applied through a punch which inputs energy into the system. When the compaction force
is released, part of the energy is recovered in the form of elastic energy. The energy
balance for the tablet compaction process can be written as:
ET = EC + EE (7.9)
where,
ET = Total Energy Input
*
158
EC = Energy Used in Compression (Includes Energy utilized in movement
and rearrangement of particles, overcoming the friction between the
particle and friction between the die wall and particles)
EE = Elastic Energy Recovered
Tablet strength or hardness behavior can also be explained on the basis of energy
approach. To establish the energy based approach, tablets were loaded and unloaded
similarly as in the case of diametral strength, axial penetration strength, and indentation
hardness tests. However, during this study, the force was applied as close as practically
feasible to, but below, the failure of the tablet. To ensure the contact of the probe with the
tablets, initial force of 2.2 N was applied, before starting the test. Next, force and
displacement during both loading as well as unloading were plotted. The area under the
curve was used to estimate the energy. The loading and unloading curves for the case of
diametral strength, axial penetration strength, and indentation hardness tests are given in
Figures 7.13a, b, and c, respectively. The elastic energy was calculated by numerical
integration to obtain the area under the unloading curve, i.e., shaded area in Figures
7.13a, b, and c, respectively. The plots between the diametral strength, axial penetration
strength and indentation hardness and their respective elastic energy are given in Figures
7.14a, b, and c. Corresponding plots between these tablet qualities and spring-back index
values are also shown in Figures 7.14a, b, and c, respectively. From the figures it is clear
that with increase in the hardness or strength values, the elastic energy also increased in
all cases. This indicated that tablet’s elastic energy can be directly related to the tablet’s
physical properties, i.e., both are related.
Since friability is associated with impacts and requires a different treatment, the
energy based approach for explaining relation of friability with the spring-back index is
given in Section 8.2.5.
159
0
10
20
30
40
50
0.00 0.05 0.10 0.15 0.20
Displacement, mm
Forc
e, N
(a)
0
10
20
30
40
50
0.00 0.05 0.10 0.15 0.20
Displacement, mm
Forc
e, N
(b)
0
10
20
30
40
50
0.00 0.05 0.10 0.15 0.20
Displacement, mm
Forc
e, N
(c)
Figure 7.13 Force vs. displacement (loading-unloading before failure) plot for tablet formed at 90 MPa using dry formulation in (a) diametral strength test, (b) axial
penetration test, and (c) indentation hardness test modes
Elastic Energy Elastic Energy
Elastic Energy
Elastic Energy
160
(a)
(b)
(c)
Figure 7.14 Plot between elastic energy and spring-back index vs. (a) diametral strength, (b) axial penetration strength, and (c) indentation hardness for tablets
formed at 90 MPa using dry powder formulations
1.501.752.002.25Elastic energy, N.mm
30
34
38
0.06 0.07 0.08 0.09Spring-back index
Ind
hard
ness
, MPa
1.51.7522.25Elastic energy, N.mm
30
34
38
0.06 0.07 0.08 0.09Spring-back index
Axi
al s
tren
gth,
MPa
0.901.001.101.20
Elastic energy, N.mm
0.30
0.35
0.40
0.06 0.07 0.08 0.09Spring-back Index
Dia
str
engt
h, M
Pa
161
7.3 Summary
Tablet quality parameters were determined for dry powder formulation.
Diametral strength, axial penetration strength, and indentation hardness increased while
friability decreased with compression pressure. All tablet quality parameters changed
upto 5% binder content. This shows that increase in binder after 5% only had marginal
effect on tablet quality parameters. Relationships were developed between various tablet
quality parameters and powder mechanical properties. Based on the results in the
preceding sections, spring-back index and compression index were found most suitable
for predicting diametral strength and indentation hardness. In case of axial penetration
strength, compression index, spring-back index, and shear modulus at higher loading rate
had good r2 (> 0.8) with tablets formed at 90 MPa. Bulk modulus and shear modulus
were also found suitable for predicting the various tablet qualities. Spring-back index and
compression index are determined from the HTC test. Spring-back index, an elastic
parameter, is determined from the unloading- reloading loop of HTC, is the measure of
elastic recovery of the material’s void spaces after the applied pressure has been released.
The compression index, an elastoplastic parameter, determined from HTC test is the
measure of compressibility of the material using void ratio as the dependent variable. An
elastic energy based approach was successfully used to explain the relation of tablet
quality parameters, i.e., diametral strength, axial penetration strength, and indentation
hardness, with spring-back index. The energy based approach for friability is presented,
explained, and discussed in Section 8.2.5.
162
Chapter 8 - Tablet Quality Parameters and Relationship Development for Granulated Powder Formulations
The tablets were formed using granulated powder at different loading conditions
and binder contents. Tablet quality parameters were evaluated and relationships were
developed between tablet quality parameters and powder properties similar to dry powder
formulations.
8.1 Tablet Quality
The tablets were also formed using granulated powder formulations at binder
contents of 5 and 10% and two pressures of 70 and 90 MPa. For each tablet 300 mg (± 1
mg) powder was used. Various quality parameters similar to that of dry formulation were
evaluated. Each parameter is discussed in the following sections.
8.1.1 Diametral Strength Test
The average diametral strength values were higher at 90 MPa than at 70 MPa
compression pressure at all binder contents. The diametral strength at binder contents of 5
and 10% are shown in Figure 8.1 and given in Table 8.1. The arrow on the figure
indicates increase in diametral strength with increase in pressure. The average diametral
strength values at 70 MPa were 0.257 MPa and 0.277 MPa at 5 and 10% binder,
respectively. These values at 90 MPa compression pressure were 0.286 MPa (11%,
percent increase in diametral strength from 70 MPa) and 0.338 MPa (22%). The
diametral strength increased when binder content increased from 5% to 10%.
Table 8.1 Diametral strength of tablets made from granulated powder formulation at 70 and 90 MPa compression pressures and different binder contents*
Compression pressure Binder content, %
70 MPa 90 MPa
5 0.26 MPa (0.007) 0.29 MPa (0.007)
10 0.28 MPa (0.019) 0.34 MPa (0.018)
*Standard deviation in parenthesis
163
0.0
0.1
0.2
0.3
0.4
0.5
0 2 4 6 8 10 12Binder content, %
Diam
etra
l stre
ngth
, MPa
70 MPa90 MPa
Figure 8.1 Diametral strength of tablets using granulated powder formulations at
different binder contents
8.1.2 Axial Penetration Strength Test
The axial penetration strength values were higher at 90 MPa than at 70 MPa
compression pressure at all binder contents. The axial penetration strength at different
binder contents of 5 and 10% is shown in Figure 8.2 and given in Table 8.2. The average
axial penetration strength values at 70 MPa were 13.6 and 13.2 MPa at 5 and 10% binder,
respectively. These values at 90 MPa compression pressure were 16.1 (18%, increase in
axial penetration strength from 70 MPa) and 16.3 MPa (22%). The axial penetration
strength had almost the same value at 5 and 10% binder contents for tablets formed at 70;
as well as for tablets formed at 90 MPa.
Table 8.2 Axial penetration strength of tablets made from granulated powder formulation at 70 and 90 MPa compression pressures and different binder contents*
Compression pressure Binder content, %
70 MPa 90 MPa
5 13.6 MPa (0.7) 16.1 MPa (0.1)
10 13.2 MPa (0.3) 16.3 MPa (0.4)
*Standard deviation in parenthesis
Increasing compression pressure
164
0
2
4
6
8
10
12
14
16
18
0 2 4 6 8 10 12Binder content, %
Axi
al s
treng
th, M
Pa
70 MPa90 MPa
Figure 8.2 Axial penetration strength of tablets using granulated powder
formulations at different binder contents
8.1.3 Indentation Hardness Test
The indentation hardness values were higher at 90 MPa than at 70 MPa
compression pressure at all binder contents. The indentation hardness values at binder
contents of 5 and 10% are shown in Figure 8.3 and given in Table 8.3. The average
indentation hardness values at 70 MPa were 0.74 and 0.75 MPa at 5 and 10% binder,
respectively. These values at 90 MPa compression pressure were 0.86 (16%, percent
increase in indentation hardness from 70 MPa) and 0.91 MPa (21%). The indentation
hardness did not change with binder content.
Table 8.3 Indentation hardness of tablets made from granulated powder formulation at 70 and 90 MPa compression pressures and different binder contents*
Compression pressure Binder content, %
70 MPa 90 MPa
5 0.74 MPa (0.03) 0.86 MPa (0.03)
10 0.75 MPa (0.04) 0.91 MPa (0.03)
*Standard deviation in parenthesis
165
0.0
0.2
0.4
0.6
0.8
1.0
0 2 4 6 8 10 12Binder content, %
Inde
ntat
ion
hard
ness
, MPa
70 MPa
90 MPa
Figure 8.3 Indentation hardness of tablets using granulated powder formulations at
different binder contents 8.1.4 Friability Test
Friability of tablets were higher for tablets formed at 70 MPa compared to those
formed at 90 MPa compression pressure at all binder contents. The friability values at
binder contents of 5 and 10% are shown in Figure 8.4 and given in Table 8.4. The
friability at 70 MPa were 0.59% and 0.60% at 5 and 10% binder, respectively. These
values at 90 MPa compression pressure were 0.44% (25%, percent decrease in friability
value from 70 MPa) and 0.41% (32%). The friability value in this case was less than 1%,
which was not in case of dry formulation (Table 7.4).
Table 8.4 Friability of tablets made from granulated powder formulation at 70 and
90 MPa compression pressures and different binder contents Compression pressure Binder content, %
70 MPa 90 MPa
5 0.59% 0.44%
10 0.60% 0.41%
166
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 2 4 6 8 10 12Binder content, %
Fria
bilit
y, %
70 MPa
90 MPa
Figure 8.4 Friability of tablets using granulated powder formulations at different
binder contents 8.1.5 Summary of Tablet Quality Tests
From Sections 8.1.1 to 8.1.4, the tablet quality parameters were only marginally
different from each other at 5% and 10% binder contents. This shows that increase in
binder beyond 5% did not affect tablet quality parameters. Furthermore, for granulated
formulations prepared using ingredients proportions summarized in this study, binder
content of about 5% is hypothesized to be optimum for tablet formation similar to dry
powder formulations.
Increasing compression pressure
167
8.2 Relationship between Tablet Quality Parameters and Powder Properties Statistical regression equations were developed between tablet quality parameters
at different binder contents and loading conditions vs. powder mechanical properties as in
the case of dry formulation. The regression equations between each tablet quality and
powder property were developed; however, equations having r2 > 0.8 were selected for
prediction of tablet quality parameters.
8.2.1 Equations for Predicting Diametral Strength
The r2 values for equations to predict diametral strength of tablets formed at 70
MPa based upon the powder’s mechanical properties, i.e., bulk modulus, compression
index, spring-back index, and shear modulus are given in Table 8.5. These values for
tablets formed at 90 MPa are given in Table 8.6. Based on these r2 values, compression
index at both loading rates, bulk modulus at 10 MPa/min loading rate, and spring-back
index at 10 MPa/min loading rate were found most suitable for predicting the diametral
strength of tablets formed at 70 MPa.
Table 8.5 r2 values for equations to predict diametral strength of tablets formed at 70 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.92 0.91 0.91 0.57 0.04 0.11 Compression Index 0.83 0.99 0.98 0.90 0.89 0.80 Spring-back Index 0.59 0.82 0.86 0.99 0.30 0.13
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.05 0.66 0.40 0.21 0.03 0.77 *r2 > 0.80 are highlighted, **SD = Stress difference
168
Table 8.6 r2 values for equations to predict diametral strength of tablets formed at 90 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.09 0.11 0.10 0.95 0.46 0.87 Compression Index 0.18 0.00 0.01 0.11 0.13 0.22 Spring-back Index 0.43 0.15 0.19 0.00 0.67 0.88
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.96 0.31 0.62 0.81 0.96 0.20 *r2 > 0.80 are highlighted, **SD = Stress difference
The plots between diametral strength and various powder properties are given in
Appendix C. As examples, plots between diametral strength and bulk modulus
(determined at 10 MPa/min loading rate), and diametral strength and spring-back index
(determined at 10 MPa/min loading rate), at different loading conditions are shown in
Figures 8.5 and 8.6, respectively. In case of 90 MPa tablets, the diametral strength
increased with spring-back index, while it decreased with spring-back index for 70 MPa
tablets. At 70 MPa, the particles did not form sufficiently strong cohesive bonds
especially at 0% binder content, which resulted in low diametral strength; whereas at 90
MPa and 0% binder content, the cohesive bonds attained sufficient diametral strength.
The regression equations are given in Appendix D. As examples, two regression
equations are presented below:
DS70 = 0.0003 BM10, 10 + 0.1174, r2 = 0.91 (8.1) where, DS70 = Diametral strength at 70 MPa compaction pressure and BM10, 10 = Bulk
modulus at 10 MPa pressure and 10 MPa/min loading rate
DS70 = 0.3641 CI5,10 – 0.0193, r2 = 0.99 (8.2) where, DS90 = Diametral strength at 90 MPa compaction pressure and CI5, 10 =
Compression index at 5 MPa pressure and 10 MPa/min loading rate
169
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0 100 200 300 400 500Bulk modulus, MPa
Diam
etra
l stre
ngth
, MP
a2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 8.5 Relation between diametral strength and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0.40
0.00 0.05 0.10 0.15Spring-back index
Dia
met
ral S
tren
gth,
MPa 2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 8.6 Relation between diametral strength and spring-back index (determined at 10 MPa/min loading rate) at different loading conditions for granulated
formulations
*
*
170
8.2.2 Equations for Predicting Axial Penetration Strength
The r2 values for equations to predict axial penetration strength of tablets formed
at 70 MPa based upon the powders’ mechanical properties are given in Table 8.7. These
values for tablets formed at 90 MPa are given in Table 8.8. From Tables 8.7 and 8.8, it
can be inferred that compression index at both loading rate, bulk modulus at 10 MPa/min
loading rate, and spring-back index at 10 MPa/min loading rate were found most suitable
for predicting the axial penetration strength for tablets formed at 70 and 90 MPa.
Table 8.7 r2 values for equations to predict axial penetration strength of tablets formed at 70 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.99 0.99 0.99 0.00 0.76 0.02 Compression Index 0.95 0.97 0.89 0.98 0.98 0.93 Spring-back Index 0.78 0.95 0.97 0.96 0.14 0.29
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.17 0.46 0.60 0.39 0.00 0.59 *r2 > 0.80 are highlighted, **SD = Stress difference
Table 8.8 r2 values for equations to predict axial penetration strength of tablet formed at 90 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.99 0.99 0.99 0.00 0.78 0.01 Compression Index 0.97 0.96 0.87 0.99 0.98 0.95 Spring-back Index 0.80 0.96 0.98 0.95 0.11 0.32
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.20 0.43 0.63 0.42 0.00 0.55 *r2 > 0.80 are highlighted, **SD = Stress difference
The plots between axial penetration strength and various powder properties are
given in Appendix C. Plots between axial penetration strength and bulk modulus
(determined at 10 MPa/min loading rate), and axial penetration strength and compression
171
index (determined at 20 MPa/min loading rate), at different loading conditions are shown
in Figures 8.7 and 8.8, respectively, as examples. The complete list of regression
equations are given in Appendix D. Two regression equations, as examples, are given
below:
AS70 = -0.2579 BM2.5,10 + 57.031, r2 = 0.99 (8.3) where, AS70 - Axial penetration strength at 70 MPa compaction pressure and BM2.5, 10 –
Bulk modulus at 2.5 MPa pressure and 10 MPa/min loading rate
AS70 = 337.09 SI10,10 – 6.2082, r2 = 0.97 (8.4) where, AS70 = Axial penetration strength at 70 MPa compaction pressure and SI10,10 =
Spring-back index at 10 MPa pressure and 10 MPa/min loading rate
10
15
20
25
30
35
40
0 100 200 300 400 500Bulk modulus, MPa
Axi
al p
enet
ratio
n st
reng
th, M
Pa
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined. Figure 8.7 Relation between axial penetration strength and bulk modulus
(determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations
*
172
10
15
20
25
30
35
40
0.0 0.2 0.4 0.6 0.8 1.0Compression index
Axia
l pen
etra
tion
stre
ngth
, MPa
2.5 MPa IP, 70 MPa CP5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined. Figure 8.8 Relation between axial penetration strength and compression index
(determined at 20 MPa/min loading rate) at different loading conditions for granulated formulations
8.2.3 Equations for Predicting Indentation Hardness
The r2 values for predictive equations of indentation hardness of tablets formed at
70 and 90 MPa based upon the granulated powders’ mechanical properties are given in
Tables 8.9 and 8.10, respectively. Based on these r2-values, compression index at both
loading rates, bulk modulus at 10 MPa/min loading rate, and spring-back index at 10
MPa/min loading rate were found most suitable for predicting the indentation hardness
for tablets formed at 70 and 90 MPa.
Table 8.9 r2 values for equations to predict indentation hardness of tablets formed at 70 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.99 0.99 0.99 0.00 0.80 0.00 Compression Index 0.97 0.94 0.85 0.99 0.99 0.95 Spring-back Index 0.82 0.97 0.98 0.94 0.10 0.34
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.21 0.41 0.65 0.44 0.00 0.53 *r2 > 0.80 are highlighted, **SD = Stress difference
*
173
Table 8.10 r2 values for equations to predict indentation hardness of tablets formed at 90 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.99 0.99 0.99 0.02 0.86 0.00 Compression Index 0.99 0.90 0.79 0.99 1.00 0.98 Spring-back Index 0.88 0.99 0.99 0.89 0.42 0.05
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus1 MPa SD** 0.29 0.32 0.73 0.53 0.03 0.45 *r2 > 0.80 are highlighted, **SD = Stress difference
The plots between indentation hardness and various powder properties are given
in Appendix C. As two examples, plots between indentation hardness and bulk modulus
(determined at 10 MPa/min loading rate), and indentation hardness and spring-back index
(determined at 20 MPa/min loading rate), at different loading conditions are shown in
Figures 8.9 and 8.10, respectively. The list of regression equations are given in Appendix
D. Two examples of regression equations for predicting the indentation hardness are
given below:
IH70 = -6.5528 CI10,10 + 6.2764, r2 = 0.86 (8.5) where, IH70 - indentation hardness at 70 MPa compaction pressure and CI10, 10 –
Compression index at 10 MPa pressure and 10 MPa/min loading rate
IH70 = 7.9827 SI10,10 + 0.2799, r2 = 0.98 (8.6) where, IH70 = indentation hardness at 70 MPa compaction pressure and SI10,10 – Spring-
back index at 1 MPa confining pressure, 1 MPa stress difference and 10 MPa/min loading
rate
174
0.7
0.8
0.9
1.0
1.1
1.2
1.3
0 100 200 300 400 500 600Bulk modulus, MPa
Inde
ntat
ion
hard
ness
, MP
a2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 8.9 Relation between indentation hardness and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated
formulations
0.60.70.80.91.01.11.21.31.41.5
0.00 0.02 0.04 0.06 0.08 0.10 0.12Spring-back index
Inde
ntat
ion
hard
ness
, MP
a
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back
index was determined.
Figure 8.10 Relation between indentation hardness and spring-back index (determined at 10 MPa/min loading rate) at different loading conditions for
granulated formulations
*
*
175
8.2.4 Equations for Predicting Friability
The r2 values for equations to predict friability of tablets formed at 70 MPa and
90 MPa based upon the granulated powders’ mechanical properties are given in Tables
8.11 and 8.12, respectively. Based on these r2 values, similar to the case of axial
penetration strength and indentation hardness, compression index at both loading rate,
bulk modulus at 10 MPa/min loading rate, and spring-back index at 10 MPa/min loading
rate were found most suitable for predicting the friability for tablets formed at 70 and 90
MPa.
Table 8.11 r2 values for equations to predict friability of tablets formed at 70 MPa
on the basis of granulated powders’ mechanical properties* Loading Rate 10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.99 0.99 0.99 0.00 0.78 0.01 Compression Index 0.87 0.95 0.87 0.99 0.98 0.94 Spring-back Index 0.80 0.96 0.98 0.95 0.11 0.32
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.2 0.43 0.63 0.42 0.00 0.55 *r2 > 0.80 are highlighted, **SD = Stress difference
Table 8.12 r2 values for equations to predict friability of tablets formed at 90 MPa on the basis of granulated powders’ mechanical properties*
Loading Rate 10 MPa/min 20 MPa/min HTC test parameters
Pressure, MPa Pressure, MPa Powder properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus 0.99 0.98 0.98 0.00 0.74 0.02 Compression Index 0.94 0.97 0.90 0.98 0.97 0.92 Spring-back Index 0.76 0.93 0.96 0.97 0.15 0.27
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties 1.0 2.0 3.0 1.0 2.0 3.0 Shear Modulus 1 MPa SD** 0.15 0.48 0.58 0.37 0.00 0.61 *r2 > 0.80 are highlighted, **SD = Stress difference
The plots between friability and various powder properties are given in Appendix
C. As examples, plots between friability and bulk modulus (determined at 20 MPa/min
176
loading rate), and friability and compression index (determined at 20 MPa/min loading
rate), at different loading conditions are shown in Figures 8.11 and 8.12, respectively.
The regression equations are given in Appendix D. As examples, two regression
equations are given below:
FR90 = 24.521 SI5, 10 - 0.7526, r2 = 0.96 (8.7) where, FR70 = Diametral strength at 70 MPa compaction pressure and SI5, 10 = Spring-
back index at 5 MPa pressure and 10 MPa/min loading rate
FR90 = -4.6457 CI5,10 +4.2734, r2 = 0.95 (8.8) where, FR90 = Diametral strength at 90 MPa compaction pressure and CI50, 10 =
Compression index at 5 MPa pressure and 10 MPa/min loading rate
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0 100 200 300 400 500Bulk modulus, MPa
Fria
bilit
y, %
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back index was determined.
Figure 8.11 Relation between friability and bulk modulus (determined at 10 MPa/min loading rate) at different loading conditions for granulated formulations
*
177
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
0.0 0.2 0.4 0.6 0.8 1.0Compression index
Fria
bilit
y, %
2.5 MPa IP, 70 MPa CP
5.0 MPa IP, 70 MPa CP
10.0 MPa IP, 70 MPa CP
2.5 MPa IP, 90 MPa CP
5.0 MPa IP, 90 MPa CP
10.0 MPa IP, 90 MPa CP
*CP – Compression pressure for tablet formation, IP – Pressure at which spring-back index was determined.
Figure 8.12 Relation between friability and compression index (determined at 20 MPa/min loading rate) at different loading conditions for granulated formulations
8.2.5 Elastic Energy Explanation of Tablet Quality Relationship with Powder
Spring-back Index
Tablet quality parameters such as diametral strength, axial penetration strength,
and indentation hardness related very well with spring-back index similar to the dry
powder formulations. The loading and unloading curves for the case of diametral
strength, axial penetration strength, and indentation hardness tests are given in Figures
8.13a, b, and c, respectively. The plot between the diametral strength, axial penetration
strength, and indentation hardness and their respective elastic energy is given in Figures
8.14a, b, and c. The elastic energy, as for dry formulations, was determined numerically
by calculating the area of the shaded portions shown in Figures 8.13a, b, and c,
respectively. Corresponding plots between these tablet qualities and spring-back index
values are also shown in Figure 8.14a, b, and c, respectively. From the figures, the
hardness or strength values can be related with the elastic energy in all cases. Also, the
spring-back index is related with tablet quality. This explains the relationship of spring-
back index with tablet quality parameters.
*
178
0
10
20
30
40
50
0 0.05 0.1 0.15 0.2
Displacement, mm
Forc
e, N
(a)
0
10
20
30
40
50
0 0.05 0.1 0.15 0.2
Displacement, mm
Forc
e, N
(b)
0
10
20
30
40
50
0 0.05 0.1 0.15 0.2
Displacement, mm
Forc
e, N
(c)
Figure 8.13 Force vs. displacement (loading-unloading before failure) plot for tablets formed at 90 MPa using granulated formulations in (a) diametral strength
test, (b) axial penetration test, and (c) indentation hardness test modes
Elastic Energy
Elastic Energy
Elastic Energy
179
(a)
(b)
(c)
Figure 8.14 Plot between elastic energy and spring-back index vs. (a) diametral strength, (b) axial penetration strength, and (c) indentation hardness for tablets
formed at 90 MPa using granulated powder formulations
0.751.251.75
Elastic energy, N.mm
0.15
0.20
0.25
0.30
0.35
0.05 0.06 0.07 0.08Spring-back Index
Dia
str
engt
h, M
Pa
1.251.451.651.85Elastic energy, N.mm
05
101520253035
0.05 0.07 0.09 0.11 0.13Spring-back index
Axi
al s
tren
gth,
MPa
1.701.801.902.002.10Elastic energy, N.mm
0.6
0.70.8
0.9
1.0
1.11.2
1.3
0.05 0.07 0.09 0.11 0.13Spring-back index
Ind
hard
ness
, MPa
180
Three of the four tablet quality parameters: diametral strength, axial penetration
strength, and indentation hardness, are based on quasi-static tests, i.e., slow loading rates
(on the order of mm per minute) are used to quantify these parameters. The fourth
quality parameter, friability of tablets, simulates repeated impact loading conditions
similar to those experienced during handling and transportation. Impact loading involves
high magnitude forces that occur over a very short duration of time (Mohsenin, 1986).
Depending on the test material, the impact duration may last from microseconds to
milliseconds. Tablets being soft compared to hard materials such as steel and aluminum,
are expected to have impact durations on the order of milliseconds. For a perfectly elastic
material, the force-time response during impact is known to be a symmetric curve (Figure
8.15a); whereas, for an inelastic material, the force-time response curve is known to be
asymmetric (Figure 8.15b). In order to explain the observed strong relationships between
dry and granulated powder formulations with the friability of tablets, it is hypothesized
that the powder formulation’s elastic response at low pressures is related to tablets’
elastic energy during impact. In other words, powder retains memory of its elastic
response even after the tablet is formed.
Based on the literature (Mohsenin, 1986), the force-time impact curves (Figure
8.15) can be integrated to determine force-deformation curves (Figure 8.16). Figure
8.16a is for an elastic material, which by definition, will have full recovery, i.e., the
recovery ratio (ratio of elastic energy to total energy) is 1; whereas, for an inelastic
material, the recovery ratio will be lower than 1. In fact, lower the recovery ratio, greater
the absorbed energy; therefore, higher fragmentation is expected. As noted and
mentioned previously, the granules formed using wet granulation process are more elastic
and pliable when compared with particles comprising the dry powder mix. In addition,
tablets formed using dry powder formulations are known to be brittle (lower recovery
ratio anticipated) and those formed using granulated formulation are known to be ductile
(higher recovery ratio anticipated). Therefore, tablets formed using granulated powder
formulations will better withstand impact loads resulting in less fragmentation (i.e.,
dusting) compared with tablets formed using dry powder formulations. Consequently,
under similar loading conditions using same ingredients and proportions, the measured
friability values for tablets formed using dry powder formulations will be much higher
181
than those formed using the granulated powder formulations. Friability results for tablets
formed with dry powder formulations are given in Section 7.1.4. Comparisons of
friability with the granulated formulations results are given in Section 8.3.4.
Figure 8.15 Impact response curves for (a) elastic body, and (b) inelastic body
Figure 8.16 Force-deformation response curves for (a) elastic body, and (b) inelastic body
Time
Forc
e
(a)Time
Forc
e
Time
Forc
e
(a)Time
Forc
e(b)
TimeFo
rce
TimeFo
rce
Forc
e(b)
Deformation
Forc
e
(b)Deformation
Forc
e
(b)Deformation
Forc
e
(a)Deformation
Forc
e
(a)
182
8.2.6 Summary of Relations
Relationships were developed between various tablet quality parameters and
powder mechanical properties. Based on the results, compression index, spring-back
index, and bulk modulus were found most suitable for predicting diametral strength, axial
penetration strength, indentation hardness, and friability. Similar results were obtained
for dry powder formulations (Section 7.3).
8.3 Comparison between Dry vs. Granulated Formulations
8.3.1 Diametral Strength
Diametral strength values for dry blended and granulated powder formulations at
5 and 10% binder contents for 70 and 90 MPa compression pressures are given in Table
8.13. At 70 MPa compression pressure, the diametral strength after granulation decreased
by 25% and 16% at 5% and 10% binder contents, respectively. These values were 26%
and 11% at 90 MPa compression pressure, respectively. The strength value decreased due
to the previously noted large particle size of the granules (Figures 4.11 and 4.13).
Table 8.13 Diametral strength of tablets made from dry and granulated powder formulations at 70 and 90 MPa compression pressures and different binder
contents* Compression pressure Binder
content, % 70 MPa 90 MPa
Dry Granulated Dry Granulated
5 0.345 MPa
(0.008)
0.257 MPa
(0.007)
0.386 MPa
(0.008)
0.286 MPa
(0.007)
10 0.330 MPa
(0.030)
0.277 MPa
(0.019)
0.379 MPa
(0.029)
0.338 MPa
(0.018)
*Standard deviation in parenthesis
8.3.2 Axial Penetration Strength
Axial penetration strength values for dry blended and granulated powder
formulations at 5 and 10% binder contents for 70 and 90 MPa compression pressure is
given in Table 8.14. At 70 MPa compression pressure, the axial penetration strength after
183
granulation decreased by 59% and 56% at 5% and 10% binder content, respectively.
These values were 56% and 52% at 90 MPa compression pressure, respectively.
Table 8.14 Axial penetration strength of tablets made from dry and granulated
powder formulations at 70 and 90 MPa compression pressures and different binder contents*
Compression pressure Binder
content, % 70 MPa 90 MPa
Dry Granulated Dry Granulated
5 32.9 MPa (2.2) 13.6 MPa (0.7) 36.5 MPa (1.3) 16.1 MPa (0.1)
10 29.8 MPa (1.6) 13.2 MPa (0.3) 34.3 MPa (0.7) 16.3 MPa (0.4)
*Standard deviation in parenthesis
8.3.3 Indentation Hardness
Indentation hardness values for dry blended and granulated powder formulations
at 5 and 10% binder contents for 70 and 90 MPa compression pressure is given in Table
8.15. At 70 MPa compression pressure, the indentation hardness after granulation
decreased by 42% and 41% at 5% and 10% binder contents, respectively. These values
were 38% and 35% at 90 MPa compression pressure, respectively.
Table 8.15 Indentation hardness of tablets made from dry and granulated powder
formulations at 70 and 90 MPa compression pressures and different binder contents* Compression pressure Binder
content, % 70 MPa 90 MPa
Dry Granulated Dry Granulated
5 1.28 MPa (0.07) 0.74 MPa (0.03) 1.38 MPa (0.11) 0.86 MPa (0.03)
10 1.27 MPa (0.09) 0.75 MPa (0.04) 1.40 MPa (0.07) 0.91 MPa (0.03)
*Standard deviation in parenthesis
8.3.4 Friability
Friability values for dry blended and granulated powder formulations at 5 and
10% binder contents for 70 and 90 MPa compression pressures are given in Table 8.16.
At 70 MPa compression pressure, the friability after granulation decreased by 55% and
184
60% at 5% and 10% binder contents, respectively. These decreases were 41% and 48%
at 90 MPa compression pressure, respectively. As hypothesized and explained in Section
8.2.5, the friability values for granulated formulations were expected to be lower for
granulated formulations than dry formulations. The observed decrease in friability values
for granulated formulations were in the range of 41% to 60%. In other words, there is a
strong evidence of support for the proposed energy-based explanation for friability.
Table 8.16 Friability of tablets made from dry and granulated powder formulations
at 70 and 90 MPa compression pressures and different binder contents* Compression pressure Binder
content, % 70 MPa 90 MPa
Dry Granulated Dry Granulated
5 1.31% 0.59% 0.75% 0.44%
10 1.48% 0.60% 0.79% 0.41%
*Standard deviation in parenthesis
8.4 Summary
Tablet quality parameters were determined for granulated formulation similar to
dry powder formulation. Diametral strength, axial penetration, and indentation hardness
increased while friability decreased with compression pressure. The tablet quality
parameters were only marginally different from each other at 5% and 10% binder
contents. This shows that increase in binder beyond 5% did not affect tablet property.
Relationships were developed between various tablet quality parameters and powder
mechanical properties. Based on the results, compression index, spring-back index, and
bulk modulus were found suitable for predicting diametral strength, axial penetration
strength, indentation hardness, and friability. Comparison between the tablet quality
parameters is presented in Section 8.3. The strength and hardness values of tablets from
dry formulations were higher compared to granulated formulations. Friability values of
tablets from granulated formulations were lower compared to dry formulations.
185
Chapter 9 – Summary, Conclusions, and Recommendations for Future Work
Powder compaction is a very important unit operation for making various
industrial products. Pharmaceutical tablets are formed using powder ingredients such as
filler, binder, lubricant, disintegrant, and active pharmaceutical ingredient (API). Tablets
are formed either by dry blending the above ingredients or wet granulation of the powder
mix followed by compaction. Granulation is the process in which primary powder
particles are made to adhere to form larger, multi-particle entities called granules. In the
present research, dry blended and granulated pharmaceutical powder formulations were
used.
The formulations used for the research were composed of Avicel (filler),
Methocel (binder), Magnesium stearate (lubricant), Ac-Di-Sol (disintegrant), and
Acetaminophen (active pharmaceutical ingredient). Three different levels of methocel
(binder): 0 (none), 5, and 10%, were used in powder formulations. The proportion of
other four ingredients were maintained at the same level, i.e., Avicel: Acetaminophen:
Ac-Di-Sol: Magnesium stearate:: 0.90:0.05:0.03:0.02. Hydrostatic triaxial compression
(HTC) and conventional triaxial compression (CTC) tests were conducted using a CTT
for both dry blended and granulated formulations at different binder contents. Modified
Cam-clay constitutive equation parameters such as bulk modulus, shear modulus,
compression index, spring-back index, shear modulus, and failure strength were
determined using data obtained from HTC and CTC tests. Tablets at binder contents of 5
and 10% and without binder were formed at pressures of 70 and 90 MPa. Diametral
strength, axial penetration strength, indentation hardness, and friability tests were
conducted to evaluate the tablets’ quality. Relationships between the mechanical
properties of dry bended and granulated pharmaceutical powder formulations and tablet
quality parameters were developed and explained. In the following sections, the key
conclusions are summarized.
9.1 Powder Property
The bulk modulus, compression index, and spring-back index were determined
using the HTC test at unloading pressures of 2.5, 5.0, and 10.0 MPa. The shear modulus
186
and failure stress were determined using the CTC tests at confining pressures of 1, 2, and
3 MPa. These parameters were determined at loading rates of 10 and 20 MPa/min at 0, 5,
and 10% binder contents for dry and granulated powder formulations. Some of the key
conclusions are noted below.
Dry Powder Formulations
Bulk Modulus:
• Bulk modulus increased with increase in the isotropic pressure in all cases.
• Bulk modulus increased with binder content at 10 MPa/min loading rate.
• Bulk modulus was maximum at 0% binder followed by those at 10 and 5% binder
content at 20 MPa/min loading rate.
• Bulk modulus at 20 MPa/min loading rate was higher than at 10 MPa/min loading
rate in all cases.
• Based on the ANCOVA table (Appendix E) neither binder content nor loading
rate had significant effect (p>0.05) on bulk modulus value.
Compression Index:
• Compression index value increased with pressure in all cases, i.e., material
became more compressible with increase in pressure.
• Effect of binder on compression index was not very prominent.
• In general, the compression index values were higher at 10 MPa/min compared to
those at 20 MPa/min loading rate.
• Treatment combination of binder content and pressure, binder content and loading
rate, and pressure and loading rate had significant (p<0.05) effect on compression
index.
Spring-back Index:
• Spring-back index value increased with pressure in all cases.
• Spring-back value decreased with binder content at 10 MPa/min loading rate.
• At 20 MPa/min the spring-back index value was lowest at 0% binder followed by
10 and 5% binder contents.
• Spring-back index values were higher at 10 MPa/min as compared to 20 MPa/min
loading rate.
187
• Treatment combination of binder content and loading rate had significant
(p<0.05) effect on spring-back index values.
Shear Modulus:
• Shear modulus increased with increase in the confining pressure in all cases.
• No clear trend of the effect of binder on shear modulus values was observed.
• Treatment combination of pressure and loading rate had significant (p<0.05)
effect on shear modulus.
Failure Stress:
• The failure stress value increased with increase in the confining pressure in all
cases
• Effect of binder on failure stress values was not very prominent.
• The failure stress was different at two loading rates; however, no clear trend was
observed.
• Treatment combination of pressure and loading rate had significant (p<0.05)
effect on failure stress.
Granulated Formulation
Bulk Modulus:
• Bulk modulus increased with increase in the isotropic pressure in all cases.
• Bulk modulus values was higher for 10% binder compared to 5% binder at 10
MPa/min loading rate; while it was higher for 5% binder at 20 MPa/min loading
rate.
• Bulk modulus at 20 MPa/min was higher than at 10 MPa/min loading rate in all
cases.
• Loading rate had significant effect on the slope of regression lines (p<0.05).
Compression Index:
• In general, compression index value increased with pressure.
• Compression index increased with binder content at 10 MPa/min while it
decreased with binder at 20 MPa/min
188
• Compression index values at 20 MPa/min were higher than at 10 MPa/min for the
granules having 5% binder. However, for 10% binder content, the compression
index values were higher at 10 MPa/min for pressures of 5 and 10 MPa.
• Only pressure had significant effect (p<0.05) on compression index value. No
treatment combinations of pressure, binder, and loading rate were significant
(p<0.05).
Spring-back Index:
• Spring-back index value increased with pressure in all cases.
• Spring-back index for 10% binder content was higher than for 5% binder content.
• Spring-back index values were slightly higher at 20 MPa/min loading rate as
compared to 10 MPa/min loading rate except for 10% binder case at 2.5 MPa
pressure.
• Binder content did not have significant effect (p>0.05) on slopes of the regression
lines (p>0.05) while loading rate had significant effect on the slope of regression
lines (p<0.05). The combinations of pressure with loading rate and binder with
loading rate were significant (p<0.05).
Shear Modulus:
• Shear modulus increased with increase in the confining pressure in all cases.
• No clear trend of the effect of binder on shear modulus values was observed.
• Combined effect of pressure, binder content, and loading rate were significant
(p>0.05) on shear modulus values.
Failure Stress:
• The failure stress value increased with increase in the confining pressure in all
cases
• Effect of binder on failure stress values was not very prominent.
• Treatment combinations of binder and pressure and pressure and loading rate had
significant (p<0.05) effect on failure stress.
Comparison of Dry and Granulated Formulation Powder Property
• Volumetric compression was higher in case of granulated formulation compared
to dry formulation.
189
• Bulk modulus, compression index, shear modulus, and failure stress increased
after granulation.
• Spring-back index decreased after granulation.
9.2 Tablet Quality
The key conclusions for the measured tablet quality parameters are as follows:
Dry Formulation
Diametral Strength Test:
• Diametral strength values were higher at 90 MPa than at 70 MPa compression
pressure for all binder contents.
• Diametral strength values increased upto 5% binder content, thereafter, very little
or no change was observed when binder content increased from 5 to 10%.
Axial Penetration Strength Test:
• Axial penetration strength values were higher at 90 MPa than at 70 MPa
compression pressure for all binder contents.
• Axial penetration strength values increased upto 5% binder content, thereafter,
very little or no change was observed when binder content increased from 5 to
10%.
Indentation Hardness Test:
• Indentation hardness values were higher at 90 MPa than at 70 MPa compression
pressure for all binder contents.
• Indentation hardness values increased upto 5% binder content, thereafter, very
little or no change was observed when binder content increased from 5 to 10%.
Friability Test:
• Friability values were higher at 70 MPa than at 90 MPa compression pressure for
all binder contents.
• Friability decreased with binder content upto 5% thereafter it slightly increased
when binder content increased from 5 to 10%.
190
Granulated Formulations
Diametral Strength Test:
• Diametral strength values were higher at 90 MPa than at 70 MPa compression
pressure for all binder contents.
• Diametral strength values increased slightly with binder content.
Axial Penetration Strength Test:
• Axial penetration strength values were higher at 90 MPa than at 70 MPa
compression pressure for all binder contents.
• Axial penetration strength values increased slightly with binder content.
Indentation Hardness Test:
• Indentation hardness values were higher at 90 MPa than at 70 MPa compression
pressure for all binder contents.
• Indentation hardness values increased slightly with binder content.
Friability Test:
• Friability values were higher at 70 MPa than at 90 MPa compression pressure for
all binder contents.
• Friability decreased with binder content.
Comparison of Tablet Quality of Dry and Granulated Formulations
• Diametral strength, axial penetration strength, and indentation hardness values
were higher for tablets formed using dry formulation compared to granulated
formulation.
• Friability of tablets formed using dry formulation was higher compared to
granulated formulation.
9.3 Relationship between Tablet Quality Parameters and Powder Properties
Statistical equations were developed between tablets qualities and powder
mechanical properties at different binder contents and loading conditions. Some of the
key conclusions are noted below.
191
Dry Formulation
• Spring-back index and compression index were found most suitable for predicting
diametral strength, indentation hardness, and friability.
• In case of axial penetration strength, compression index, spring-back index, and
shear modulus at higher loading rate had good relations (r2 > 0.8) with tablets
formed at 90 MPa.
• Bulk modulus and shear modulus were also found suitable for predicting the
various tablet quality parameters.
• An elastic energy based approach was successfully used to explain the relation of
tablet quality parameters with spring-back index.
Granulated Formulation
• Compression index, spring-back index and bulk modulus were found most
suitable for predicting diametral strength, axial penetration strength, indentation
hardness and friability.
• An elastic energy based approach, similar to dry formulation, was used to explain
the relation of tablet quality parameters with spring-back index.
9.4 Effect of Binder
The overarching observations related to binder content effect are summarized
below:
• For dry formulation, during HTC tests, the volumetric compression increased with
binder content. For granulated formulations, the volumetric compression
decreased with binder content.
• Bulk modulus values increased and spring-back index values decreased with
binder content for dry formulations at 10 MPa/min loading rate.
• Bulk modulus increased with binder content at 10 MPa/min while decreased at 20
MPa/min loading rate for granulated formulations. Spring-back index increased
with binder content for granulated formulations.
• All tablet quality parameters changed upto 5% binder content; thereby, quality
parameters changed marginally for dry formulations. Binder content of around
192
5% appears to be optimum for tablet formation for ingredient and proportions
used in this study.
• For granulated formulations, tablet quality parameters were only marginally
different from each other at 5% and 10% binder contents.
• In case dry formulations, treatment combination of binder content with pressure
and loading rate had significant (p<0.05) effect on compression index. Treatment
combination of binder content and loading rate had significant (p<0.05) effect on
spring-back index values.
• In case of granulated formulations, effect of binder content together with pressure
and loading rate were significant (p>0.05) on shear modulus values. Treatment
combinations of binder with pressure had significant (p<0.05) effect on failure
stress.
9.5 Recommendations for Future Work
1. The present research was done to study the effect of binder on the mechanical
properties of powder formulations and tablet quality parameters. Effect of other
ingredient is highly recommended.
2. Mechanical properties of ingredients should be determined so that the effect of
ingredients on mechanical properties of powder formulation can be studied.
3. Mechanical properties of dry formulation for predicting the mechanical properties
of granulated formulation and also tablet quality of granulated formulation is
recommended.
4. Study on effect of sample sizes is recommended; especially, smaller sample sizes
in cubical triaxial tester
5. HTC and CTC tests should be conducted using low pressure CTT on the powder
formulation to save cost and time.
6. A generalized rate-dependent constitutive model for the powder formulations
should be developed.
7. In the present study the elastic energy approached has been used to explain the
relationship of tablet quality parameters with spring-back index. Explanation for
other relations using some fundamental concept should be done.
193
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197
APPENDIX A Tablet Quality Parameters vs. Powder Property for Dry Formulations
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.1. Plot between diametral strength and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
198
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.2. Plot between diametral strength and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
199
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure A.3. Plot between diametral strength and spring-back index determined at
(a) 10 and (b) 20 MPa/min loading rates using dry formulations
200
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure A.4. Plot between diametral strength and shear modulus determined at 1
MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry formulations
201
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure A.5. Plot between diametral strength and shear modulus determined at 2
MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry formulations
202
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure A.6. Plot between diametral strength and failure stress determined at (a) 10
and (b) 20 MPa/min loading rates using dry formulations
203
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.7. Plot between axial penetration strength and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
204
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.8. Plot between axial penetration strength and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
205
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.9. Plot between axial penetration strength and spring-back index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
206
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.10. Plot between axial penetration strength and shear modulus determined at 1 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry
formulations
207
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.11. Plot between axial penetration strength and shear modulus determined at 2 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry
formulations
208
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.12. Plot between axial penetration strength and failure stress determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
209
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.13. Plot between indentation hardness and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
210
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.14. Plot between indentation hardness and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
211
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.15. Plot between indentation hardness and spring-back index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
212
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.16. Plot between indentation hardness and shear modulud determined at 1 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry
formulations
213
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.17. Plot between indentation hardness and shear modulud determined at 2 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry
formulations
214
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.18. Plot between indentation hardness and failure stress determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
215
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.19. Plot between friability and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
216
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.20. Plot between friability and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
217
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.21. Plot between friability and spring-back index determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
218
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.22. Plot between friability and shear modulus determined at 1 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry formulations
219
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.23. Plot between friability and shear modulus determined at 2 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using dry formulations
220
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure A.24. Plot between friability and failure stress determined at (a) 10 and (b) 20 MPa/min loading rates using dry formulations
221
APPENDIX B Regression Equations to Predict Tablet Quality Parameters Using Powder Property for Dry Formulations
Table B.1. Regression equations to predict diametral strength of tablet formed at 70 MPa on the basis of powders’ mechanical
properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder
properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus
y = 0.0035x - 0.1234 R2 = 0.51
Y = 0.0024x - 0.0768 R2 = 0.25
y = 0.0023x - 0.2366 R2 = 0.28
y = -0.0042x + 0.9027 R2 = 0.82
y = -0.0038x + 1.0146 R2 = 0.64
y = -0.0028x + 1.0734 R2 = 0.89
Compression Index
y = -0.7218x + 0.5243 R2 = 0.97
y = 0.1211x + 0.2189 R2 = 0.00
y = -2.5363x + 2.1941 R2 = 0.91
y = -4.4826x + 1.5913 R2 = 0.99
y = 1.9335x - 0.6629 R2 = 0.93
y = 1.7419x - 0.8448 R2 = 0.82
Spring-back Index
y = -5.8716x + 0.7175 R2 = 0.99
y = -9.7723x + 1.1354 R2 = 0.88
y = -9.9757x + 1.2776 R2 = 0.99
y = 10.1x - 0.2978 R2 = 0.91
y = 9.097x - 0.3184 R2 = 0.91
y = 14.115x - 0.7946 R2 = 0.99
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = 0.0296x - 0.1997 R2 = 0.98
y = -0.1538x + 5.0009 R2 = 0.99
y = -0.0006x + 0.3102 R2 = 0.00
y = 0.0629x - 1.4127 R2 = 0.99
y = -0.0324x + 1.3315 R2 = 0.83
y = -0.0795x + 3.1478 R2 = 0.82
Shear Modulus 2 MPa SD
y = 0.1028x - 2.3393 R2 = 0.63
y = -0.0496x + 2.0503 R2 = 0.97
y = -0.0381x + 1.2777 R2 = 0.91
y = 0.0397x - 0.9888 R2 = 0.66
Failure stress
y = 1.9469x - 1.6465 R2 = 0.96
y = -1.3633x + 2.6538 R2 = 0.96
y = -0.426x + 1.1178 R2 = 0.07
y = 1.3611x - 1.5369 R2 = 0.98
y = 6.35x - 10.937 R2 = 0.33
y = 1.7369x - 2.9827 R2 = 0.73
222
Table B.2. Regression equations to predict diametral strength of tablet formed at 90 MPa on the basis of powders’ mechanical
properties Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = 0.0014x + 0.1976 R2 = 0.51
y = 0.001x + 0.2171 R2 = 0.24
y = 0.0009x + 0.1532 R2 = 0.27
y = -0.0017x + 0.6112 R2 = 0.83
y = -0.0015x + 0.6571 R2 = 0.65
y = -0.0011x + 0.6801 R2 = 0.89
Compression Index
y = -0.2908x + 0.4577 R2 = 0.96
y = 0.0552x + 0.3309 R2 = 0.00
y = -1.021x + 1.1297 R2 = 0.90
y = -1.8078x + 0.8881 R2 = 0.99
y = 0.7816x - 0.0219 R2 = 0.93
y = 0.7051x - 0.0961 R2 = 0.83
Spring-back Index
y = -2.3685x + 0.5357 R2 = 0.99
y = -3.9322x + 0.7034 R2 = 0.87
y = -4.0221x + 0.7615 R2 = 0.99
y = 4.0839x + 0.1256 R2 = 0.92
y = 3.6783x + 0.1173 R2 = 0.91
y = 5.6991x - 0.0747 R2 = 0.99
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = 0.0119x + 0.1659 R2 = 0.98
y = -0.062x + 2.2624 R2 = 0.98
y = -0.0001x + 0.3678 R2 = 0.00
y = 0.0254x - 0.324 R2 = 0.99
y = -0.013x + 0.7821 R2 = 0.83
y = -0.032x + 1.5124 R2 = 0.81
Shear Modulus 2 MPa SD
y = 0.0412x - 0.6918 R2 = 0.62
y = -0.02x + 1.0726 R2 = 0.97
y = -0.0153x + 0.7609 R2 = 0.91
y = 0.0159x - 0.15 R2 = 0.65
Failure stress
y = 0.7843x - 0.4169 R2 = 0.95
y = -0.5492x + 1.3156 R2 = 0.96
y = -0.1677x + 0.6891 R2 = 0.07
y = 0.5486x - 0.3731 R2 = 0.97
y = 2.5875x - 4.2115 R2 = 0.34
y = 0.6978x - 0.9515 R2 = 0.72
223
Table B.3. Regression equations to predict axial penetration strength of tablet formed at 70 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0408x + 35.984 R2 = 0.20
y = -0.0619x + 40.479 R2 = 0.46
y = -0.0524x + 43.136 R2 = 0.42
y = -0.0581x + 39.613 R2 = 0.45
y = -0.071x + 44.807 R2 = 0.65
y = -0.0324x + 40.357 R2 = 0.35
Compression Index
y = -1.6782x + 31.734 R2 = 0.01
y = 40.465x + 7.9078 R2 = 0.93
y = 0.2988x + 30.961 R2 = 0.00
y = -20.957x + 37.276 R2 = 0.06
y = 20.465x + 21.116 R2 = 0.30
y = 23.891x + 15.641 R2 = 0.45
Spring-back Index
y = -30.405x + 33.407 R2 = 0.07
y = 10.677x + 30.26 R2 = 0.00
y = -39.663x + 35.118 R2 = 0.045
y = 111.68x + 24.702 R2 = 0.32
y = 101.1x + 24.44 R2 = 0.32
y = 105.95x + 23.055 R2 = 0.16
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = 0.0952x + 29.615 R2 = 0.03
y = -0.566x + 48.53 R2 = 0.04
y = 0.6296x + 9.0087 R2 = 0.90
y = 0.4081x + 20.151 R2 = 0.12
y = 0.0771x + 28.708 R2 = 0.01
y = 0.2268x + 23.027 R2 = 0.01
Shear Modulus 2 MPa SD
y = 2816.7x + 18.765 R2 = 0.40
y = 1469x + 21.297 R2 = 0.44
y = 2267.9x + 19.128 R2 = 0.60
y = 2851x + 21.003 R2 = 0.45
Failure stress
y = 3.5461x + 27.661 R2 = 0.00
y = -2.6848x + 35.844 R2 = 0.01
y = 23.632x - 14.818 R2 = 0.69
y = 4.0579x + 25.743 R2 = 0.02
y = 194.75x - 313.09 R2 = 0.90
y = -8.9841x + 48.106 R2 = 0.05
224
Table B.4. Regression equations to predict axial penetration strength of tablet formed at 90 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = 0.0482x + 28.613 R2 = 0.14
y = 0.0136x + 32.234 R2 = 0.01
y = 0.0165x + 30.508 R2 = 0.02
y = -0.1217x + 51.933 R2 = 0.990.808
y = -0.1201x + 57.316 R2 = 0.94
y = -0.0763x + 55.895 R2 = 0.99
Compression Index
y = -15.886x + 39.464 R2 = 0.68
y = 26.439x + 19.065 R2 = 0.20
y = -52.159x + 73.461 R2 = 0.56
y = -104.89x + 64.758 R2 = 0.80
y = 52.005x + 8.6849 R2 = 0.98
y = 50.078x + 1.6915 R2 = 0.99
Spring-back Index
y = -139.15x + 44.439 R2 = 0.82
y = -195.33x + 51.202 R2 = 0.51
y = -229.31x + 57.01 R2 = 0.77
y = 274.49x + 18.339 R2 = 0.98
y = 247.53x + 17.759 R2 = 0.98
y = 353.94x + 7.1144 R2 = 0.91
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = 0.6671x + 23.27 R2 = 0.73
y = -3.5082x + 141.77 R2 = 0.75
y = 0.3598x + 21.601 R2 = 0.14
y = 1.5398x - 7.3589 R2 = 0.87
y = -0.6239x + 54.33 R2 = 0.45
y = -1.506x + 88.447 R2 = 0.43
Shear Modulus 2 MPa SD
y = -1072.9x + 39.005 R2 = 0.03
y = -405.55x + 37.004 R2 = 0.02
y = 4061.1x + 12.684 R2 = 0.97
y = 5956.7x + 12.999 R2 = 0.99
Failure stress
y = 42.272x - 7.7388 R2 = 0.66
y = -29.718x + 85.836 R2 = 0.66
y = 5.1913x + 24.169 R2 = 0.016
y = 30.487x - 6.6125 R2 = 0.72
y = 246.25x - 401.04 R2 = 0.73
y = 30.525x - 23.215 R2 = 0.33
225
Table B.5. Regression equations to predict indentation hardness of tablet formed at 70 MPa on the basis of powders’
mechanical properties Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = 0.003x + 0.8817 R2 = 0.55
y = 0.0021x + 0.9142 R2 = 0.27
y = 0.002x + 0.7757 R2 = 0.31
y = -0.0035x + 1.74 R2 = 0.79
y = -0.0031x + 1.8264 R2 = 0.61
y = -0.0023x + 1.8825 R2 = 0.87
Compression Index
y = -0.605x + 1.4333 R2 = 0.98
y = 0.0413x + 1.2119 R2 = 0.00
y = -2.1353x + 2.8399 R2 = 0.92
y = -3.7416x + 2.323 R2 = 0.99
y = 1.5968x + 0.4499 R2 = 0.91
y = 1.4304x + 0.305 R2 = 0.80
Spring-back Index
y = -4.8967x + 1.5934 R2 = 0.99
y = -8.2415x + 1.9499 R2 = 0.89
y = -8.3372x + 2.0623 R2 = 0.99
y = 8.3344x + 0.7518 R2 = 0.89
y = 7.5056x + 0.7349 R2 = 0.89
y = 11.722x + 0.3362 R2 = 0.98
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = 0.0248x + 0.827 R2 = 0.99
y = -0.1286x + 5.1761 R2 = 0.99
y = -0.0015x + 1.2871 R2 = 0.00
y = 0.0523x - 0.1798 R2 = 0.99
y = -0.0274x + 2.1173 R2 = 0.85
y = -0.0672x + 3.6546 R2 = 0.84
Shear Modulus 2 MPa SD
y = -115.96x + 1.747 R2 = 0.33
y = -54.196x + 1.6005 R2 = 0.29
y = 107.53x + 0.664 R2 = 0.66
y = 169.91x + 0.6288 R2 = 0.79
Failure stress
y = 1.6334x - 0.3878 R2 = 0.97
y = -1.1434x + 3.2196 R2 = 0.97
y = -0.394x + 2.0026 R2 = 0.09
y = 1.1396x - 0.2927 R2 = 0.98730.91
y = 5.0531x - 7.697 R2 = 0.30
y = 1.4755x - 1.5431 R2 = 0.76
226
Table B.6. Regression equations to predict indentation hardness of tablet formed at 90 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = 0.0039x + 0.884 R2 = 0.73
y = 0.0031x + 0.8768 R2 = 0.46
y = 0.0029x + 0.6878 R2 = 0.49
y = -0.0035x + 1.8527 R2 = 0.62
y = -0.0029x + 1.9015 R2 = 0.42
y = -0.0023x + 2.0121 R2 = 0.72
Compression Index
y = -0.6917x + 1.5729 R2 = 0.99
y = -0.3595x + 1.5538 R2 = 0.03
y = -2.504x + 3.2281 R2 = 0.99260.92
y = -4.1711x + 2.5591 R2 = 0.97
y = 1.6639x + 0.5282 R2 = 0.76970.78
y = 1.4345x + 0.4136 R2 = 0.62
Spring-back Index
y = -5.4286x + 1.7435 R2 = 0.95
y = -9.7603x + 2.1928 R2 = 0.98
y = -9.365x + 2.2755 R2 = 0.98
y = 8.6358x + 0.8456 R2 = 0.75
y = 7.7716x + 0.8284 R2 = 0.75
y = 12.661x + 0.3754 R2 = 0.89
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = 0.0281x + 0.8842 R2 = 0.99
y = -0.1449x + 5.7873 R2 = 0.98
y = -0.0081x + 1.6308 R2 = 0.05
y = 0.0572x - 0.1997 R2 = 0.92
y = -0.0329x + 2.4045 R2 = 0.96
y = -0.081x + 4.2623 R2 = 0.95
Shear Modulus 2 MPa SD
y = -78.284x + 1.8739 R2 = 0.48
y = -164.21x + 2.0711 R2 = 0.52
y = 170.26x + 0.7388 R2 = 0.62
y = 103.08x + 0.7989 R2 = 0.48
Failure stress
y = 1.8774x - 0.519 R2 = 0.99
y = -1.3122x + 3.6236 R2 = 0.99
y = -0.6996x + 2.7089 R2 = 0.23
y = 1.2939x - 0.3883 R2 = 0.99
y = 3.9553x - 5.6451 R2 = 0.14
y = 1.8187x - 2.0782 R2 = 0.90
227
Table B.7. Regression equations to predict friability of tablet formed at 70 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0027x + 1.7939 R2 = 0.09
y = -0.0003x + 1.5182 R2 = 0.00
y = -0.0006x + 1.6052 R2 = 0.00
y = 0.0084x + 0.2526 R2 = 0.99
y = 0.0084x - 0.1436 R2 = 0.97
y = 0.0052x - 0.0105 R2 = 0.97
Compression Index
y = 1.0427x + 1.1318 R2 = 0.62
y = -2.0844x + 2.6714 R2 = 0.26
y = 3.3695x - 1.0591 R2 = 0.49
y = 6.976x - 0.5549 R2 = 0.74
y = -3.5519x + 3.2202 R2 = 0.95
y = -3.4592x + 3.723 R2 = 0.99
Spring-back Index
y = 9.2781x + 0.7946 R2 = 0.76
y = 12.53x + 0.3865 R2 = 0.44160.49
y = 15.193x - 0.034 R2 = 0.70
y = -18.782x + 2.5628 R2 = 0.97
y = -16.941x + 2.6027 R2 = 0.97
y = -23.866x + 3.3037 R2 = 0.86
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = -0.044x + 2.1984 R2 = 0.66
y = 0.2321x - 5.6384 R2 = 0.69
y = -0.0291x + 2.4973 R2 = 0.20
y = -0.1033x + 4.2664 R2 = 0.82
y = 0.0396x + 0.1987 R2 = 0.38
y = 0.0953x - 1.9545 R2 = 0.36
Shear Modulus 2 MPa SD
y = 12.609x + 1.3875 R2 = 0.00
y = 43.265x + 1.2816 R2 = 0.00
y = -283.58x + 2.98 R2 = 0.99
y = -411.55x + 2.9423 R2 = 0.99
Failure stress
y = -2.7659x + 4.2214 R2 = 0.59
y = 1.9463x - 1.9044 R2 = 0.60
y = -0.5546x + 2.552 R2 = 0.04
y = -2.0087x + 4.1663 R2 = 0.65
y = -17.726x + 32.807 R2 = 0.79
y = -1.8904x + 5.0326 R2 = 0.26
228
Table B.8. Regression equations to predict friability of tablet formed at 90 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0032x + 1.2011 R2 = 0.37
y = -0.002x + 1.1154 R2 = 0.13
y = -0.0019x + 1.2558 R2 = 0.16
y = 0.0048x + 0.1248 R2 = 0.91
y = 0.0045x - 0.0334 R2 = 0.76
y = 0.0031x - 0.0555 R2 = 0.96
Compression Index
y = 0.7497x + 0.5771 R2 = 0.90
y = -0.4667x + 1.0905 R2 = 0.03
y = 2.5818x - 1.1176 R2 = 0.81
y = 4.7452x - 0.557 R2 = 0.96
y = -2.1437x + 1.8769 R2 = 0.98
y = -1.9776x + 2.1087 R2 = 0.91
Spring-back Index
y = 6.2407x + 0.3661 R2 = 0.97
y = 9.8666x - 0.033 R2 = 0.77
y = 10.501x - 0.2191 R2 = 0.95
y = -11.239x + 1.4745 R2 = 0.97
y = -10.127x + 1.4977 R2 = 0.97
y = -15.281x + 1.9946 R2 = 0.99
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus 1 MPa SD
y = -0.031x + 1.3329 R2 = 0.92
y = 0.1615x - 4.1266 R2 = 0.94
y = -0.0047x + 0.9881 R2 = 0.01
y = -0.0676x + 2.6491 R2 = 0.99
y = 0.0324x - 0.2197 R2 = 0.71
y = 0.0791x - 2.0221 R2 = 0.69
Shear Modulus 2 MPa SD
y = 50.479x + 0.4822 R2 = 0.15
y = 111.37x + 0.3309 R2 = 0.18
y = -235.04x + 1.6615 R2 = 0.81
y = -153.52x + 1.6382 R2 = 0.91
Failure stress
y = -2.0139x + 2.8236 R2 = 0.88
y = 1.4118x - 1.6275 R2 = 0.88
y = 0.2336x + 0.3674 R2 = 0.02
y = -1.4213x + 2.7282 R2 = 0.92
y = -8.1225x + 15.181 R2 = 0.47
y = -1.6936x + 4.0116 R2 = 0.60
229
APPEDIX C Tablet Quality Parameters vs. Powder Property for Granulated Formulations
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.1. Plot between diametral strength and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
230
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure C.2. Plot between diametral strength and compression index determined at
(a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
231
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure C.3. Plot between diametral strength and spring-back index determined at
(a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
232
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus was determined.
Figure C.4. Plot between diametral strength and shear modulus determined at 1
MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
233
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.5. Plot between axial penetration strength and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
234
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.6. Plot between axial penetration strength and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder
formulations
235
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.7. Plot between axial penetration strength and spring-back index determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder
formulations
236
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.8. Plot between axial penetration strength and shear modulus determined at 1 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using
granulated powder formulations
237
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.9. Plot between indentation hardness and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
238
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.10. Plot between indentation hardness and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
239
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.11. Plot between indentation hardness and spring-back index determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
240
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.12. Plot between indentation hardness and shear modulus determined at 1 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using granulated
powder formulations
241
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.13. Plot between friability and bulk modulus determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
242
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.14. Plot between friability and compression index determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
243
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.15. Plot between friability and spring-back index determined at (a) 10 and (b) 20 MPa/min loading rates using granulated powder formulations
244
CP – Compression pressure for tablet formation, IP – Pressure at which bulk modulus
was determined.
Figure C.16. Plot between friability and shear modulus determined at 1 MPa stress difference and (a) 10 and (b) 20 MPa/min loading rates using granulated powder
formulations
245
Appendix D Regression Equations to Predict Tablet Quality Parameters Using Powder Property for Granulated Formulations
Table D.1. Regression equations to predict diametral strength of tablet formed at 70 MPa on the basis of powders’ mechanical
properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder
properties 2.5 5.0 10.0 2.5 5.0 10.0 Bulk Modulus
y = 0.0011x + 0.0774 R² = 0.9234
y = 0.0006x + 0.1081R² = 0.9086
y = 0.0003x + 0.1174R² = 0.9127
y = -0.0023x + 0.689 R² = 0.5674
y = 0.001x + 0.0745 R² = 0.0379
y = 0.0004x + 0.1102R² = 0.1127
Compression Index
y = 0.2023x + 0.1021 R² = 0.8343
y = 0.3641x - 0.0193 R² = 0.9992
y = 1.3482x - 0.8679 R² = 0.9828
y = 0.1333x + 0.1509R² = 0.9015
y = 0.2164x + 0.0963R² = 0.8904
y = 0.2933x + 0.0186R² = 0.8025
Spring-back Index
y = -1.2992x + 0.3225 R² = 0.5943
y = -1.7439x + 0.3623R² = 0.8267
y = -1.4385x + 0.3505R² = 0.8671
y = -20.392x + 1.2001R² = 0.9996
y = 5.1583x - 0.0632 R² = 0.3014
y = -2.097x + 0.3781 R² = 0.1312
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = 0.0013x + 0.2193 R² = 0.0514
y = 0.0115x - 0.1474 R² = 0.6645
y = 0.0011x + 0.1756R² = 0.4043
y = 0.034x - 0.6394 R² = 0.2096
y = 0.0018x + 0.1788R² = 0.0286
y = 0.0021x + 0.1299R² = 0.7776
246
Table D.2. Regression equations to predict diametral strength of tablet formed at 90 MPa on the basis of powders’ mechanical
properties Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0002x + 0.3463 R² = 0.0917
y = -0.0001x + 0.3429R² = 0.1078
y = -7E-05x + 0.3404R² = 0.1033
y = 0.0031x - 0.1816 R² = 0.951
y = 0.0012x + 0.0771R² = 0.4596
y = 0.0007x + 0.0986R² = 0.8695
Compression Index
y = -0.0567x + 0.3547 R² = 0.1865
y = -0.0121x + 0.3243R² = 0.0032
y = 0.0838x + 0.2466R² = 0.0108
y = -0.0283x + 0.3349R² = 0.1153
y = -0.0485x + 0.3482R² = 0.1272
y = -0.0909x + 0.3848R² = 0.2197
Spring-back Index
y = 0.6569x + 0.2749 R² = 0.4326
y = 0.3569x + 0.2886R² = 0.152
y = 0.5011x + 0.281 R² = 0.1944
y = 0.5577x + 0.2894R² = 0.0021
y = 4.5685x + 0.0452R² = 0.6733
y = 3.2304x + 0.1059R² = 0.8866
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa
Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.0034x + 0.3736 R² = 0.96
y = 0.0047x + 0.1579R² = 0.31
y = -0.0008x + 0.3644R² = 0.6223
y = -0.0396x + 1.3436R² = 0.8121
y = 0.0063x + 0.0984R² = 0.9617
y = 0.0006x + 0.2819R² = 0.2002
247
Table D.3. Regression equations to predict axial penetration strength of tablet formed at 70 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.2579x + 57.031 R² = 0.9939
y = -0.1402x + 50.153R² = 0.989
y = -0.0803x + 47.949R² = 0.9905
y = 0.0072x + 18.038R² = 4E-05
y = 0.5944x - 95.107 R² = 0.7569
y = -0.0381x + 31.362R² = 0.0195
Compression Index
y = -47.883x + 52.33 R² = 0.9536
y = -79.448x + 76.238R² = 0.9703
y = -284.56x + 253.47R² = 0.8928
y = -30.886x + 40.324R² = 0.9864
y = -50.314x + 53.095R² = 0.9818
y = -70.095x + 72.616R² = 0.9347
Spring-back Index
y = 329.57x - 1.1937 R² = 0.7799
y = 413.81x - 9.3316 R² = 0.9493
y = 337.09x - 6.2082 R² = 0.971
y = 4440.9x - 189.43 R² = 0.9668
y = -769.86x + 64.768R² = 0.1369
y = 694.83x - 25.876 R² = 0.2938
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.5392x + 28.468 R² = 0.1744
y = -2.1396x + 91.385R² = 0.4655
y = -0.3056x + 37.215R² = 0.6051
y = -10.298x + 286.51R² = 0.3932
y = 0.0776x + 16.54 R² = 0.001
y = -0.4033x + 40.86 R² = 0.5916
248
Table D.4. Regression equations to predict axial penetration strength of tablet formed at 90 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.2356x + 56.018 R² = 0.9981
y = -0.1282x + 49.761R² = 0.995
y = -0.0734x + 47.739R² = 0.9959
y = 0.0429x + 14.474R² = 0.0016
y = 0.5521x - 84.717 R² = 0.7855
y = -0.0263x + 29.861R² = 0.0112
Compression Index
y = -43.96x + 51.87 R² = 0.9669
y = -71.962x + 73.119R² = 0.9577
y = -256.23x + 232.4 R² = 0.8708
y = -28.256x + 40.78 R² = 0.9931
y = -46.059x + 52.484R² = 0.9898
y = -64.447x + 70.567R² = 0.9505
Spring-back Index
y = 305.75x + 2.5346 R² = 0.8075
y = 380.04x - 4.7488 R² = 0.9632
y = 308.97x - 1.834 R² = 0.9814
y = 4021x - 167.45 R² = 0.9535
y = -641.42x + 59.421R² = 0.1143
y = 666.62x - 21.792 R² = 0.3253
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.5278x + 30.525 R² = 0.201
y = -1.8784x + 84.826R² = 0.4316
y = -0.2861x + 38.322R² = 0.6382
y = -9.7815x + 275.35R² = 0.4267
y = 0.1452x + 16.46 R² = 0.0044
y = -0.3571x + 40.632R² = 0.5579
249
Table D.5. Regression equations to predict indentation hardness of tablet formed at 70 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0061x + 1.773 R2 = 0.9994
y = -0.0033x + 1.612 R2 = 0.9974
y = -0.0019x + 1.5597 R2 = 0.998
y = 0.0016x + 0.6147 R2 = 0.0036
y = 0.0144x - 1.882 R2 = 0.8013
y = -0.0006x + 1.0587 R2 = 0.0075
Compression Index
y = -1.1368x + 1.6681 R2 = 0.9735
y = -1.8467x + 2.2074 R2 = 0.9495
y = -6.5528x + 6.2764 R2 = 0.8575
y = -0.7293x + 1.3804 R2 = 0.996
y = -1.1892x + 1.6827 R2 = 0.9933
y = -1.668x + 2.1527 R2 = 0.9586
Spring-back Index
y = 7.9532x + 0.3895 R2 = 0.8226
y = 9.8299x + 0.2038 R2 = 0.9702
y = 7.9827x + 0.2799 R2 = 0.9863
y = 103.17x - 3.9651 R2 = 0.945
y = -15.633x + 1.807 R2 = 0.1023
y = 17.658x - 0.264 R2 = 0.3436
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.0141x + 1.1244 R2 = 0.2169
y = -0.0473x + 2.4781 R2 = 0.4124
y = -0.0075x + 1.3226 R2 = 0.6567
y = -0.2577x + 7.5714 R2 = 0.446
y = 0.0048x + 0.7152 R2 = 0.0074
y = -0.009x + 1.3672 R2 = 0.5385
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Table D.6. Regression equations to predict indentation hardness of tablet formed at 90 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0055x + 1.8142 R2 = 0.9959
y = -0.003x + 1.6707 R2 = 0.9986
y = -0.0017x + 1.6231 R2 = 0.998
y = 0.0037x + 0.4146 R2 = 0.0218
y = 0.0135x - 1.584 R2 = 0.8668
y = 1E-05x + 1.0078 R2 = 3E-06
Compression Index
y = -1.0373x + 1.7285 R2 = 0.9944
y = -1.6267x + 2.1788 R2 = 0.904
y = -5.6796x + 5.6868 R2 = 0.7904
y = -0.6595x + 1.4619 R2 = 0.9994
y = -1.0771x + 1.7365 R2 = 1
y = -1.5276x + 2.175 R2 = 0.9865
Spring-back Index
y = 7.4466x + 0.5501 R2 = 0.8848
y = 8.9771x + 0.3919 R2 = 0.9928
y = 7.2537x + 0.4641 R2 = 0.9992
y = 90.787x - 3.2543 R2 = 0.8979
y = 17.826x - 0.1456 R2 = 0.4296
y = -10.364x + 1.6245 R2 = 0.0551
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.0148x + 1.2659 R2 = 0.2938
y = -0.038x + 2.2946 R2 = 0.3271
y = -0.0072x + 1.4329 R2 = 0.7379
y = -0.2547x + 7.6213 R2 = 0.5343
y = 0.0088x + 0.7067 R2 = 0.0301
y = -0.0075x + 1.4118 R2 = 0.4502
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Table D.7. Regression equations to predict friability of tablet formed at 70 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0152x + 3.1687 R² = 0.9979
y = -0.0083x + 2.7648R² = 0.9948
y = -0.0047x + 2.6343R² = 0.9958
y = 0.0027x + 0.5026R² = 0.0015
y = 0.0356x - 5.9093 R² = 0.7844
y = -0.0017x + 1.4875R² = 0.0115
Compression Index
y = 0.5396x + 0.9358 R² = 0.8708
y = -4.6457x + 4.2734R² = 0.9582
y = -16.545x + 14.559R² = 0.8717
y = -1.8234x + 2.1852R² = 0.9929
y = -2.9722x + 2.9404R² = 0.9895
y = -4.1581x + 4.1068R² = 0.9499
Spring-back Index
y = 19.72x - 0.2822 R² = 0.8064
y = 24.521x - 0.7526 R² = 0.9627
y = 19.937x - 0.5646 R² = 0.981
y = 259.59x - 11.257 R² = 0.9541
y = -41.551x + 3.3976R² = 0.1152
y = 42.94x - 1.8476 R² = 0.324
CTC test parameters Confining Pressure, MPa Confining Pressure, MPa
Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.034x + 1.5219 R² = 0.2
y = -0.1214x + 5.0343R² = 0.4329
y = -0.0184x + 2.0256R² = 0.6369
y = -0.6303x + 17.299R² = 0.4254
y = 0.0092x + 0.6223R² = 0.0042
y = -0.0231x + 2.1773R² = 0.5592
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Table D.8. Regression equations to predict friability of tablet formed at 90 MPa on the basis of powders’ mechanical properties
Loading Rate
10 MPa/min 20 MPa/min
HTC test parameters Pressure, MPa Pressure, MPa Powder properties
2.5 5.0 10.0 2.5 5.0 10.0
Bulk Modulus
y = -0.0073x + 1.6698 R² = 0.9903
y = -0.004x + 1.4738 R² = 0.9843
y = -0.0023x + 1.4114R² = 0.9861
y = -0.0005x + 0.6731R² = 0.0002
y = 0.0167x - 2.6211 R² = 0.7391
y = -0.0012x + 0.9912R² = 0.0256
Compression Index
y = -1.3568x + 1.5334 R² = 0.9446
y = -2.2696x + 2.2241R² = 0.9769
y = -8.1574x + 7.3105R² = 0.9052
y = -0.877x + 1.1945 R² = 0.9812
y = -1.4281x + 1.5568R² = 0.9759
y = -1.9844x + 2.1069R² = 0.9242
Spring-back Index
y = 9.2785x + 0.0205 R² = 0.7626
y = 11.723x - 0.2136 R² = 0.9399
y = 9.561x - 0.126 R² = 0.9637
y = 126.89x - 5.3666 R² = 0.9738
y = -23.045x + 1.9587R² = 0.1514
y = 19.147x - 0.6475 R² = 0.2752
CTC test parameter Confining Pressure, MPa Confining Pressure, MPa Powder properties
1.0 2.0 3.0 1.0 2.0 3.0
Shear Modulus
y = -0.0147x + 0.8467 R² = 0.1591
y = -0.0622x + 2.6946R² = 0.486
y = -0.0086x + 1.099 R² = 0.5849
y = -0.2856x + 8.0091R² = 0.3732
y = 0.0008x + 0.5674R² = 0.0001
y = -0.0117x + 1.2217R² = 0.6117
Appendix E: Analysis of variance (ANOVA) and analysis of covariance (ANCOVA) for dry powder formulations E 1. Bulk Modulus General Linear Model: BM versus Binder, Loading rate Factor Type Levels Values Binder fixed 3 0, 5, 10 Loadingrate fixed 2 10, 20 Analysis of Variance for BM, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Pressure 1 145570 145570 145570 322.87 0.000 Binder 2 5838 771 385 0.85 0.433 Loadingrate 1 23225 1307 1307 2.90 0.096 Binder*Loadingrate 2 8291 952 476 1.06 0.357 Binder*Pressure 2 328 328 164 0.36 0.697 Loadingrate*Pressure 1 1638 1638 1638 3.63 0.064 Binder*Loadingrate*Pressure 2 189 189 95 0.21 0.811 Error 42 18936 18936 451 Total 53 204015 S = 21.2335 R-Sq = 90.72% R-Sq(adj) = 88.29% Term Coef SE Coef T P Constant 88.897 6.130 14.50 0.000 Pressure 16.6516 0.9267 17.97 0.000 Pressure*Binder 0 0.993 1.311 0.76 0.453 5 -0.942 1.311 -0.72 0.476 Pressure*Loadingrate 10 -1.7662 0.9267 -1.91 0.064 Pressure*Binder*Loadingrate 0 10 -0.837 1.311 -0.64 0.527 5 10 0.292 1.311 0.22 0.825 Unusual Observations for BM Obs BM Fit SE Fit Residual St Resid 50 236.900 192.226 7.326 44.674 2.24 R 52 239.200 281.336 11.813 -42.136 -2.39 R 53 341.200 281.336 11.813 59.864 3.39 R R denotes an observation with a large standardized residual.
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E 2. Compression Index General Linear Model: CI versus Binder, Pressure, Loading rate Factor Type Levels Values Binder fixed 3 0, 5, 10 Pressure fixed 3 2.5, 5.0, 10.0 Loadingrate fixed 2 10, 20 Analysis of Variance for CI, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Binder 2 0.016245 0.016245 0.008123 7.11 0.003 Pressure 2 1.395237 1.395237 0.697619 610.22 0.000 Loadingrate 1 0.072529 0.072529 0.072529 63.44 0.000 Binder*Pressure 4 0.053314 0.053314 0.013329 11.66 0.000 Binder*Loadingrate 2 0.042971 0.042971 0.021486 18.79 0.000 Pressure*Loadingrate 2 0.010049 0.010049 0.005025 4.40 0.020 Binder*Pressure*Loadingrate 4 0.006856 0.006856 0.001714 1.50 0.223 Error 36 0.041156 0.041156 0.001143 Total 53 1.638358 S = 0.0338115 R-Sq = 97.49% R-Sq(adj) = 96.30% Unusual Observations for CI Obs CI Fit SE Fit Residual St Resid 28 0.247017 0.312422 0.019521 -0.065405 -2.37 R 31 0.370624 0.446573 0.019521 -0.075948 -2.75 R 44 0.637316 0.694834 0.019521 -0.057518 -2.08 R R denotes an observation with a large standardized residual. Least Squares Means for CI Binder*Pressure Mean SE Mean 0 2.5 0.3860 0.01380 0 5.0 0.5117 0.01380 0 10.0 0.6968 0.01380 5 2.5 0.2748 0.01380 5 5.0 0.5710 0.01380 5 10.0 0.7176 0.01380 10 2.5 0.2651 0.01380 10 5.0 0.5182 0.01380 10 10.0 0.6886 0.01380 Binder*Loadingrate 0 10 0.6079 0.01127 0 20 0.4551 0.01127 5 10 0.5410 0.01127 5 20 0.5012 0.01127 10 10 0.5043 0.01127 10 20 0.4769 0.01127 Pressure*Loadingrate 2.5 10 0.3267 0.01127 2.5 20 0.2906 0.01127 5.0 10 0.5752 0.01127 5.0 20 0.4921 0.01127 10.0 10 0.7513 0.01127 10.0 20 0.6506 0.01127
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Tukey 95.0% Simultaneous Confidence Intervals Response Variable CI All Pairwise Comparisons among Levels of Binder*Pressure Binder = 0 Pressure = 2.5 subtracted from: Binder Pressure Lower Center Upper 0 5.0 0.0614 0.1257 0.19001 0 10.0 0.2464 0.3107 0.37507 5 2.5 -0.1756 -0.1113 -0.04693 5 5.0 0.1207 0.1850 0.24933 5 10.0 0.2672 0.3315 0.39586 10 2.5 -0.1852 -0.1209 -0.05658 10 5.0 0.0679 0.1322 0.19652 10 10.0 0.2382 0.3025 0.36685 Binder Pressure -------+---------+---------+--------- 0 5.0 (-*-) 0 10.0 (-*--) 5 2.5 (-*-) 5 5.0 (-*-) 5 10.0 (-*-) 10 2.5 (-*-) 10 5.0 (-*--) 10 10.0 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 0 Pressure = 5.0 subtracted from: Binder Pressure Lower Center Upper 0 10.0 0.1207 0.1851 0.2494 5 2.5 -0.3013 -0.2369 -0.1726 5 5.0 -0.0050 0.0593 0.1236 5 10.0 0.1415 0.2059 0.2702 10 2.5 -0.3109 -0.2466 -0.1823 10 5.0 -0.0578 0.0065 0.0708 10 10.0 0.1125 0.1768 0.2412 Binder Pressure -------+---------+---------+--------- 0 10.0 (-*-) 5 2.5 (-*-) 5 5.0 (-*-) 5 10.0 (-*-) 10 2.5 (-*-) 10 5.0 (-*-) 10 10.0 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 0 Pressure = 10.0 subtracted from: Binder Pressure Lower Center Upper 5 2.5 -0.4863 -0.4220 -0.3577 5 5.0 -0.1901 -0.1257 -0.0614 5 10.0 -0.0435 0.0208 0.0851 10 2.5 -0.4960 -0.4316 -0.3673 10 5.0 -0.2429 -0.1786 -0.1142 10 10.0 -0.0725 -0.0082 0.0561
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Binder Pressure -------+---------+---------+--------- 5 2.5 (-*-) 5 5.0 (-*-) 5 10.0 (-*-) 10 2.5 (--*-) 10 5.0 (-*-) 10 10.0 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 5 Pressure = 2.5 subtracted from: Binder Pressure Lower Center Upper 5 5.0 0.23194 0.296265 0.36059 5 10.0 0.37847 0.442790 0.50711 10 2.5 -0.07397 -0.009643 0.05468 10 5.0 0.17913 0.243454 0.30778 10 10.0 0.34946 0.413783 0.47811 Binder Pressure -------+---------+---------+--------- 5 5.0 (-*-) 5 10.0 (-*-) 10 2.5 (-*-) 10 5.0 (-*-) 10 10.0 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 5 Pressure = 5.0 subtracted from: Binder Pressure Lower Center Upper 5 10.0 0.0822 0.1465 0.2108 10 2.5 -0.3702 -0.3059 -0.2416 10 5.0 -0.1171 -0.0528 0.0115 10 10.0 0.0532 0.1175 0.1818 Binder Pressure -------+---------+---------+--------- 5 10.0 (-*-) 10 2.5 (-*-) 10 5.0 (-*-) 10 10.0 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 5 Pressure = 10.0 subtracted from: Binder Pressure Lower Center Upper 10 2.5 -0.5168 -0.4524 -0.3881 10 5.0 -0.2637 -0.1993 -0.1350 10 10.0 -0.0933 -0.0290 0.0353 Binder Pressure -------+---------+---------+--------- 10 2.5 (-*-) 10 5.0 (-*-) 10 10.0 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 10 Pressure = 2.5 subtracted from: Binder Pressure Lower Center Upper -------+---------+---------+---------
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10 5.0 0.1888 0.2531 0.3174 (-*--) 10 10.0 0.3591 0.4234 0.4877 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Binder = 10 Pressure = 5.0 subtracted from: Binder Pressure Lower Center Upper -------+---------+---------+--------- 10 10.0 0.1060 0.1703 0.2347 (-*-) -------+---------+---------+--------- -0.30 0.00 0.30 Tukey Simultaneous Tests Response Variable CI All Pairwise Comparisons among Levels of Binder*Pressure Binder = 0 Pressure = 2.5 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 0 5.0 0.1257 0.01952 6.438 0.0000 0 10.0 0.3107 0.01952 15.919 0.0000 5 2.5 -0.1113 0.01952 -5.699 0.0001 5 5.0 0.1850 0.01952 9.477 0.0000 5 10.0 0.3315 0.01952 16.983 0.0000 10 2.5 -0.1209 0.01952 -6.193 0.0000 10 5.0 0.1322 0.01952 6.772 0.0000 10 10.0 0.3025 0.01952 15.497 0.0000 Binder = 0 Pressure = 5.0 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 0 10.0 0.1851 0.01952 9.48 0.0000 5 2.5 -0.2369 0.01952 -12.14 0.0000 5 5.0 0.0593 0.01952 3.04 0.0907 5 10.0 0.2059 0.01952 10.55 0.0000 10 2.5 -0.2466 0.01952 -12.63 0.0000 10 5.0 0.0065 0.01952 0.33 1.0000 10 10.0 0.1768 0.01952 9.06 0.0000 Binder = 0 Pressure = 10.0 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 5 2.5 -0.4220 0.01952 -21.62 0.0000 5 5.0 -0.1257 0.01952 -6.44 0.0000 5 10.0 0.0208 0.01952 1.06 0.9757 10 2.5 -0.4316 0.01952 -22.11 0.0000 10 5.0 -0.1786 0.01952 -9.15 0.0000 10 10.0 -0.0082 0.01952 -0.42 1.0000 Binder = 5 Pressure = 2.5 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 5 5.0 0.296265 0.01952 15.1767 0.0000 5 10.0 0.442790 0.01952 22.6827 0.0000
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10 2.5 -0.009643 0.01952 -0.4940 0.9999 10 5.0 0.243454 0.01952 12.4714 0.0000 10 10.0 0.413783 0.01952 21.1967 0.0000 Binder = 5 Pressure = 5.0 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 5 10.0 0.1465 0.01952 7.51 0.0000 10 2.5 -0.3059 0.01952 -15.67 0.0000 10 5.0 -0.0528 0.01952 -2.71 0.1819 10 10.0 0.1175 0.01952 6.02 0.0000 Binder = 5 Pressure = 10.0 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 10 2.5 -0.4524 0.01952 -23.18 0.0000 10 5.0 -0.1993 0.01952 -10.21 0.0000 10 10.0 -0.0290 0.01952 -1.49 0.8546 Binder = 10 Pressure = 2.5 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 10 5.0 0.2531 0.01952 12.97 0.0000 10 10.0 0.4234 0.01952 21.69 0.0000 Binder = 10 Pressure = 5.0 subtracted from: Difference SE of Adjusted Binder Pressure of Means Difference T-Value P-Value 10 10.0 0.1703 0.01952 8.725 0.0000 Tukey 95.0% Simultaneous Confidence Intervals Response Variable CI All Pairwise Comparisons among Levels of Binder*Loadingrate Binder = 0 Loadingrate = 10 subtracted from: Binder Loadingrate Lower Center Upper 0 20 -0.2007 -0.1528 -0.1049 5 10 -0.1148 -0.0669 -0.0190 5 20 -0.1545 -0.1066 -0.0587 10 10 -0.1515 -0.1036 -0.0557 10 20 -0.1788 -0.1309 -0.0830 Binder Loadingrate +---------+---------+---------+------ 0 20 (----*----) 5 10 (---*----) 5 20 (---*----) 10 10 (----*---) 10 20 (----*----) +---------+---------+---------+------ -0.20 -0.10 -0.00 0.10 Binder = 0 Loadingrate = 20 subtracted from:
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Binder Loadingrate Lower Center Upper 5 10 0.03798 0.08588 0.13378 5 20 -0.00178 0.04612 0.09402 10 10 0.00130 0.04920 0.09710 10 20 -0.02607 0.02183 0.06973 Binder Loadingrate +---------+---------+---------+------ 5 10 (----*---) 5 20 (----*---) 10 10 (----*----) 10 20 (----*----) +---------+---------+---------+------ -0.20 -0.10 -0.00 0.10 Binder = 5 Loadingrate = 10 subtracted from: Binder Loadingrate Lower Center Upper 5 20 -0.0877 -0.03975 0.00814 10 10 -0.0846 -0.03668 0.01122 10 20 -0.1120 -0.06405 -0.01615 Binder Loadingrate +---------+---------+---------+------ 5 20 (----*----) 10 10 (---*----) 10 20 (----*---) +---------+---------+---------+------ -0.20 -0.10 -0.00 0.10 Binder = 5 Loadingrate = 20 subtracted from: Binder Loadingrate Lower Center Upper 10 10 -0.04482 0.00308 0.05098 10 20 -0.07220 -0.02430 0.02360 Binder Loadingrate +---------+---------+---------+------ 10 10 (---*----) 10 20 (----*---) +---------+---------+---------+------ -0.20 -0.10 -0.00 0.10 Binder = 10 Loadingrate = 10 subtracted from: Binder Loadingrate Lower Center Upper 10 20 -0.07527 -0.02737 0.02053 Binder Loadingrate +---------+---------+---------+------ 10 20 (----*----) +---------+---------+---------+------ -0.20 -0.10 -0.00 0.10 Tukey Simultaneous Tests Response Variable CI All Pairwise Comparisons among Levels of Binder*Loadingrate Binder = 0 Loadingrate = 10 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 0 20 -0.1528 0.01594 -9.584 0.0000 5 10 -0.0669 0.01594 -4.196 0.0022
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5 20 -0.1066 0.01594 -6.691 0.0000 10 10 -0.1036 0.01594 -6.498 0.0000 10 20 -0.1309 0.01594 -8.215 0.0000 Binder = 0 Loadingrate = 20 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 5 10 0.08588 0.01594 5.388 0.0001 5 20 0.04612 0.01594 2.894 0.0652 10 10 0.04920 0.01594 3.087 0.0415 10 20 0.02183 0.01594 1.369 0.7445 Binder = 5 Loadingrate = 10 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 5 20 -0.03975 0.01594 -2.494 0.1528 10 10 -0.03668 0.01594 -2.301 0.2200 10 20 -0.06405 0.01594 -4.019 0.0036 Binder = 5 Loadingrate = 20 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 10 10 0.00308 0.01594 0.193 1.0000 10 20 -0.02430 0.01594 -1.524 0.6514 Binder = 10 Loadingrate = 10 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 10 20 -0.02737 0.01594 -1.717 0.5298 Tukey 95.0% Simultaneous Confidence Intervals Response Variable CI All Pairwise Comparisons among Levels of Pressure*Loadingrate Pressure = 2.5 Loadingrate = 10 subtracted from: Pressure Loadingrate Lower Center Upper 2.5 20 -0.08395 -0.03605 0.01185 5.0 10 0.20068 0.24858 0.29648 5.0 20 0.11749 0.16539 0.21329 10.0 10 0.37672 0.42462 0.47252 10.0 20 0.27607 0.32397 0.37187 Pressure Loadingrate -------+---------+---------+--------- 2.5 20 (-*--) 5.0 10 (-*--) 5.0 20 (-*--) 10.0 10 (-*--) 10.0 20 (-*--) -------+---------+---------+--------- 0.00 0.20 0.40 Pressure = 2.5 Loadingrate = 20 subtracted from: Pressure Loadingrate Lower Center Upper
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5.0 10 0.2367 0.2846 0.3325 5.0 20 0.1535 0.2014 0.2493 10.0 10 0.4128 0.4607 0.5086 10.0 20 0.3121 0.3600 0.4079 Pressure Loadingrate -------+---------+---------+--------- 5.0 10 (-*--) 5.0 20 (-*-) 10.0 10 (-*-) 10.0 20 (-*-) -------+---------+---------+--------- 0.00 0.20 0.40 Pressure = 5.0 Loadingrate = 10 subtracted from: Pressure Loadingrate Lower Center Upper 5.0 20 -0.1311 -0.08319 -0.03529 10.0 10 0.1281 0.17604 0.22394 10.0 20 0.0275 0.07539 0.12329 Pressure Loadingrate -------+---------+---------+--------- 5.0 20 (--*-) 10.0 10 (--*-) 10.0 20 (--*-) -------+---------+---------+--------- 0.00 0.20 0.40 Pressure = 5.0 Loadingrate = 20 subtracted from: Pressure Loadingrate Lower Center Upper 10.0 10 0.2113 0.2592 0.3071 10.0 20 0.1107 0.1586 0.2065 Pressure Loadingrate -------+---------+---------+--------- 10.0 10 (-*-) 10.0 20 (-*-) -------+---------+---------+--------- 0.00 0.20 0.40 Pressure = 10.0 Loadingrate = 10 subtracted from: Pressure Loadingrate Lower Center Upper 10.0 20 -0.1486 -0.1007 -0.05275 Pressure Loadingrate -------+---------+---------+--------- 10.0 20 (-*-) -------+---------+---------+--------- 0.00 0.20 0.40 Tukey Simultaneous Tests Response Variable CI All Pairwise Comparisons among Levels of Pressure*Loadingrate Pressure = 2.5 Loadingrate = 10 subtracted from: Difference SE of Adjusted Pressure Loadingrate of Means Difference T-Value P-Value 2.5 20 -0.03605 0.01594 -2.262 0.2360 5.0 10 0.24858 0.01594 15.596 0.0000 5.0 20 0.16539 0.01594 10.377 0.0000
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10.0 10 0.42462 0.01594 26.641 0.0000 10.0 20 0.32397 0.01594 20.326 0.0000 Pressure = 2.5 Loadingrate = 20 subtracted from: Difference SE of Adjusted Pressure Loadingrate of Means Difference T-Value P-Value 5.0 10 0.2846 0.01594 17.86 0.0000 5.0 20 0.2014 0.01594 12.64 0.0000 10.0 10 0.4607 0.01594 28.90 0.0000 10.0 20 0.3600 0.01594 22.59 0.0000 Pressure = 5.0 Loadingrate = 10 subtracted from: Difference SE of Adjusted Pressure Loadingrate of Means Difference T-Value P-Value 5.0 20 -0.08319 0.01594 -5.219 0.0001 10.0 10 0.17604 0.01594 11.045 0.0000 10.0 20 0.07539 0.01594 4.730 0.0005 Pressure = 5.0 Loadingrate = 20 subtracted from: Difference SE of Adjusted Pressure Loadingrate of Means Difference T-Value P-Value 10.0 10 0.2592 0.01594 16.264 0.0000 10.0 20 0.1586 0.01594 9.949 0.0000 Pressure = 10.0 Loadingrate = 10 subtracted from: Difference SE of Adjusted Pressure Loadingrate of Means Difference T-Value P-Value 10.0 20 -0.1007 0.01594 -6.315 0.0000
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E 3. Spring-back Index General Linear Model: sprbck versus binder, loading Factor Type Levels Values binder fixed 3 0, 5, 10 loading fixed 2 10, 20 Analysis of Variance for sprbck, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P pressure 1 0.0043272 0.0043272 0.0043272 66.48 0.000 binder 2 0.0001510 0.0000961 0.0000481 0.74 0.484 loading 1 0.0048666 0.0005663 0.0005663 8.70 0.005 binder*loading 2 0.0026967 0.0010595 0.0005297 8.14 0.001 binder*pressure 2 0.0000221 0.0000221 0.0000110 0.17 0.845 loading*pressure 1 0.0001062 0.0001062 0.0001062 1.63 0.208 binder*loading*pressure 2 0.0000866 0.0000866 0.0000433 0.67 0.520 Error 42 0.0027337 0.0027337 0.0000651 Total 53 0.0149899 S = 0.00806771 R-Sq = 81.76% R-Sq(adj) = 76.99% Term Coef SE Coef T P Constant 0.059917 0.002329 25.73 0.000 pressure 0.002871 0.000352 8.15 0.000 pressure*binder 0 -0.000259 0.000498 -0.52 0.606 5 0.000016 0.000498 0.03 0.975 pressure*loading 10 0.000450 0.000352 1.28 0.208 pressure*binder*loading 0 10 -0.000542 0.000498 -1.09 0.283 5 10 0.000435 0.000498 0.87 0.387 Unusual Observations for sprbck Obs sprbck Fit SE Fit Residual St Resid 37 0.051356 0.067190 0.003937 -0.015834 -2.25 R 48 0.040406 0.060224 0.003937 -0.019817 -2.81 R 54 0.063017 0.079404 0.004488 -0.016387 -2.44 R R denotes an observation with a large standardized residual. Means for Covariates Covariate Mean StDev pressure 5.833 3.147 Least Squares Means for sprbck binder*loading Mean SE Mean 0 10 0.09772 0.002689 0 20 0.05890 0.002689 5 10 0.08076 0.002689 5 20 0.07386 0.002689 10 10 0.07999 0.002689 10 20 0.06875 0.002689
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Tukey 95.0% Simultaneous Confidence Intervals Response Variable sprbck All Pairwise Comparisons among Levels of binder*loading binder = 0 loading = 10 subtracted from: binder loading Lower Center Upper 0 20 -0.05016 -0.03882 -0.02747 5 10 -0.02831 -0.01696 -0.00561 5 20 -0.03521 -0.02386 -0.01251 10 10 -0.02907 -0.01773 -0.00638 10 20 -0.04032 -0.02897 -0.01762 binder loading +---------+---------+---------+------ 0 20 (---*----) 5 10 (---*----) 5 20 (---*----) 10 10 (----*---) 10 20 (---*----) +---------+---------+---------+------ -0.050 -0.025 -0.000 0.025 binder = 0 loading = 20 subtracted from: binder loading Lower Center Upper 5 10 0.010510 0.021859 0.03321 5 20 0.003611 0.014959 0.02631 10 10 0.009742 0.021091 0.03244 10 20 -0.001502 0.009847 0.02120 binder loading +---------+---------+---------+------ 5 10 (----*---) 5 20 (----*----) 10 10 (---*----) 10 20 (----*---) +---------+---------+---------+------ -0.050 -0.025 -0.000 0.025 binder = 5 loading = 10 subtracted from: binder loading Lower Center Upper 5 20 -0.01825 -0.00690 0.004449 10 10 -0.01212 -0.00077 0.010581 10 20 -0.02336 -0.01201 -0.000663 binder loading +---------+---------+---------+------ 5 20 (---*----) 10 10 (----*---) 10 20 (---*----) +---------+---------+---------+------ -0.050 -0.025 -0.000 0.025 binder = 5 loading = 20 subtracted from: binder loading Lower Center Upper 10 10 -0.00522 0.006132 0.017480 10 20 -0.01646 -0.005113 0.006236 binder loading +---------+---------+---------+------ 10 10 (---*----)
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10 20 (----*---) +---------+---------+---------+------ -0.050 -0.025 -0.000 0.025 binder = 10 loading = 10 subtracted from: binder loading Lower Center Upper 10 20 -0.02259 -0.01124 0.000104 binder loading +---------+---------+---------+------ 10 20 (----*---) +---------+---------+---------+------ -0.050 -0.025 -0.000 0.025 Tukey Simultaneous Tests Response Variable sprbck All Pairwise Comparisons among Levels of binder*loading binder = 0 loading = 10 subtracted from: Difference SE of Adjusted binder loading of Means Difference T-Value P-Value 0 20 -0.03882 0.003803 -10.21 0.0000 5 10 -0.01696 0.003803 -4.46 0.0008 5 20 -0.02386 0.003803 -6.27 0.0000 10 10 -0.01773 0.003803 -4.66 0.0004 10 20 -0.02897 0.003803 -7.62 0.0000 binder = 0 loading = 20 subtracted from: Difference SE of Adjusted binder loading of Means Difference T-Value P-Value 5 10 0.021859 0.003803 5.747 0.0000 5 20 0.014959 0.003803 3.933 0.0039 10 10 0.021091 0.003803 5.546 0.0000 10 20 0.009847 0.003803 2.589 0.1226 binder = 5 loading = 10 subtracted from: Difference SE of Adjusted binder loading of Means Difference T-Value P-Value 5 20 -0.00690 0.003803 -1.814 0.4681 10 10 -0.00077 0.003803 -0.202 1.0000 10 20 -0.01201 0.003803 -3.158 0.0326 binder = 5 loading = 20 subtracted from: Difference SE of Adjusted binder loading of Means Difference T-Value P-Value 10 10 0.006132 0.003803 1.612 0.5953 10 20 -0.005113 0.003803 -1.344 0.7589 binder = 10 loading = 10 subtracted from: Difference SE of Adjusted binder loading of Means Difference T-Value P-Value 10 20 -0.01124 0.003803 -2.957 0.0536
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E 4. Shear Modulus (1 MPa stress difference) General Linear Model: SM1 versus binder, pressure, loading Factor Type Levels Values binder fixed 3 0, 5, 10 pressure fixed 3 1, 2, 3 loading fixed 2 10, 20 Analysis of Variance for response, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P binder 2 12.81 12.81 6.40 0.53 0.591 pressure 2 1805.21 1805.21 902.61 75.17 0.000 loading 1 251.12 251.12 251.12 20.91 0.000 binder*pressure 4 86.67 86.67 21.67 1.80 0.149 binder*loading 2 17.78 17.78 8.89 0.74 0.484 pressure*loading 2 263.91 263.91 131.96 10.99 0.000 binder*pressure*loading 4 16.08 16.08 4.02 0.33 0.853 Error 36 432.29 432.29 12.01 Total 53 2885.88 S = 3.46527 R-Sq = 85.02% R-Sq(adj) = 77.95% Unusual Observations for response Obs response Fit SE Fit Residual St Resid 32 22.2500 28.0000 2.0007 -5.7500 -2.03 R 33 33.7000 28.0000 2.0007 5.7000 2.01 R 49 44.9000 35.7833 2.0007 9.1167 3.22 R R denotes an observation with a large standardized residual. Tukey 95.0% Simultaneous Confidence Intervals Response Variable response All Pairwise Comparisons among Levels of pressure*loading pressure = 1 loading = 10 subtracted from: pressure loading Lower Center Upper -----+---------+---------+---------+- 1 20 5.635 10.54 15.45 (-----*-----) 2 10 9.096 14.01 18.91 (------*-----) 2 20 10.741 15.65 20.56 (------*-----) 3 10 13.819 18.73 23.64 (-----*------) 3 20 14.569 19.48 24.39 (-----*-----) -----+---------+---------+---------+- 0.0 8.0 16.0 24.0 pressure = 1 loading = 20 subtracted from: pressure loading Lower Center Upper 2 10 -1.448 3.461 8.370 2 20 0.196 5.106 10.015 3 10 3.274 8.183 13.092 3 20 4.024 8.933 13.842
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pressure loading -----+---------+---------+---------+- 2 10 (-----*-----) 2 20 (-----*------) 3 10 (-----*-----) 3 20 (-----*-----) -----+---------+---------+---------+- 0.0 8.0 16.0 24.0 pressure = 2 loading = 10 subtracted from: pressure loading Lower Center Upper 2 20 -3.265 1.644 6.554 3 10 -0.187 4.722 9.631 3 20 0.563 5.472 10.381 pressure loading -----+---------+---------+---------+- 2 20 (-----*-----) 3 10 (-----*-----) 3 20 (-----*-----) -----+---------+---------+---------+- 0.0 8.0 16.0 24.0 pressure = 2 loading = 20 subtracted from: pressure loading Lower Center Upper -----+---------+---------+---------+- 3 10 -1.831 3.078 7.987 (-----*-----) 3 20 -1.081 3.828 8.737 (-----*-----) -----+---------+---------+---------+- 0.0 8.0 16.0 24.0 pressure = 3 loading = 10 subtracted from: pressure loading Lower Center Upper -----+---------+---------+---------+- 3 20 -4.159 0.7500 5.659 (-----*-----) -----+---------+---------+---------+- 0.0 8.0 16.0 24.0 Tukey Simultaneous Tests Response Variable response All Pairwise Comparisons among Levels of pressure*loading pressure = 1 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 1 20 10.54 1.634 6.455 0.0000 2 10 14.01 1.634 8.574 0.0000 2 20 15.65 1.634 9.580 0.0000 3 10 18.73 1.634 11.465 0.0000 3 20 19.48 1.634 11.924 0.0000 pressure = 1 loading = 20 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value
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2 10 3.461 1.634 2.119 0.3008 2 20 5.106 1.634 3.125 0.0378 3 10 8.183 1.634 5.010 0.0002 3 20 8.933 1.634 5.469 0.0001 pressure = 2 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 2 20 1.644 1.634 1.007 0.9127 3 10 4.722 1.634 2.891 0.0657 3 20 5.472 1.634 3.350 0.0217 pressure = 2 loading = 20 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 3 10 3.078 1.634 1.884 0.4279 3 20 3.828 1.634 2.343 0.2038 pressure = 3 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 3 20 0.7500 1.634 0.4591 0.9972
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E 5. Shear Modulus (2 MPa stress difference) General Linear Model: SM2 versus binder, pressure, loading Factor Type Levels Values binder fixed 3 0, 5, 10 pressure fixed 2 2, 3 loading fixed 2 10, 20 Analysis of Variance for SM2, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P binder 2 4.76 4.76 2.38 0.21 0.813 pressure 1 589.68 589.68 589.68 51.66 0.000 loading 1 18.20 18.20 18.20 1.59 0.219 binder*pressure 2 3.47 3.47 1.73 0.15 0.860 binder*loading 2 0.38 0.38 0.19 0.02 0.984 pressure*loading 1 32.30 32.30 32.30 2.83 0.106 binder*pressure*loading 2 56.96 56.96 28.48 2.50 0.104 Error 24 273.95 273.95 11.41 Total 35 979.70 S = 3.37854 R-Sq = 72.04% R-Sq(adj) = 59.22% Unusual Observations for SM2 Obs SM2 Fit SE Fit Residual St Resid 31 40.4000 32.1667 1.9506 8.2333 2.98 R 32 25.4000 32.1667 1.9506 -6.7667 -2.45 R 36 27.0000 33.9333 1.9506 -6.9333 -2.51 R R denotes an observation with a large standardized residual.
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E 6. Failure Stress General Linear Model: FS versus binder, pressure, loading Factor Type Levels Values binder fixed 3 0, 5, 10 pressure fixed 3 1, 2, 3 loading fixed 2 10, 20 Analysis of Variance for FS, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P binder 2 0.00852 0.00852 0.00426 0.76 0.476 pressure 2 6.24131 6.24131 3.12066 554.77 0.000 loading 1 0.11966 0.11966 0.11966 21.27 0.000 binder*pressure 4 0.03173 0.03173 0.00793 1.41 0.250 binder*loading 2 0.00423 0.00423 0.00211 0.38 0.689 pressure*loading 2 0.48629 0.48629 0.24314 43.22 0.000 binder*pressure*loading 4 0.01380 0.01380 0.00345 0.61 0.656 Error 36 0.20251 0.20251 0.00563 Total 53 7.10804 S = 0.0750012 R-Sq = 97.15% R-Sq(adj) = 95.81% Unusual Observations for FS Obs FS Fit SE Fit Residual St Resid 26 2.12100 1.96700 0.04330 0.15400 2.51 R 27 1.80900 1.96700 0.04330 -0.15800 -2.58 R 30 1.21000 1.33333 0.04330 -0.12333 -2.01 R 31 1.54000 1.41667 0.04330 0.12333 2.01 R 52 1.86500 1.99033 0.04330 -0.12533 -2.05 R R denotes an observation with a large standardized residual. Least Squares Means for FS pressure*loading Mean SE Mean 1 10 1.015 0.02500 1 20 1.378 0.02500 2 10 1.871 0.02500 2 20 1.830 0.02500 3 10 1.990 0.02500 3 20 1.950 0.02500 Tukey 95.0% Simultaneous Confidence Intervals Response Variable FS All Pairwise Comparisons among Levels of pressure*loading pressure = 1 loading = 10 subtracted from: pressure loading Lower Center Upper 1 20 0.2563 0.3626 0.4688 2 10 0.7492 0.8554 0.9617 2 20 0.7091 0.8153 0.9216 3 10 0.8684 0.9747 1.0809 3 20 0.8284 0.9347 1.0409
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pressure loading ----+---------+---------+---------+-- 1 20 (--*--) 2 10 (--*--) 2 20 (--*--) 3 10 (--*--) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 1 loading = 20 subtracted from: pressure loading Lower Center Upper 2 10 0.3866 0.4929 0.5991 2 20 0.3465 0.4528 0.5590 3 10 0.5059 0.6121 0.7184 3 20 0.4659 0.5721 0.6784 pressure loading ----+---------+---------+---------+-- 2 10 (--*--) 2 20 (--*--) 3 10 (--*---) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 2 loading = 10 subtracted from: pressure loading Lower Center Upper 2 20 -0.1464 -0.04011 0.06614 3 10 0.0130 0.11922 0.22547 3 20 -0.0270 0.07922 0.18547 pressure loading ----+---------+---------+---------+-- 2 20 (--*--) 3 10 (--*--) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 2 loading = 20 subtracted from: pressure loading Lower Center Upper 3 10 0.05308 0.1593 0.2656 3 20 0.01308 0.1193 0.2256 pressure loading ----+---------+---------+---------+-- 3 10 (--*--) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 3 loading = 10 subtracted from: pressure loading Lower Center Upper
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3 20 -0.1463 -0.04000 0.06625 pressure loading ----+---------+---------+---------+-- 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 Tukey Simultaneous Tests Response Variable FS All Pairwise Comparisons among Levels of pressure*loading pressure = 1 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 1 20 0.3626 0.03536 10.25 0.0000 2 10 0.8554 0.03536 24.20 0.0000 2 20 0.8153 0.03536 23.06 0.0000 3 10 0.9747 0.03536 27.57 0.0000 3 20 0.9347 0.03536 26.44 0.0000 pressure = 1 loading = 20 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 2 10 0.4929 0.03536 13.94 0.0000 2 20 0.4528 0.03536 12.81 0.0000 3 10 0.6121 0.03536 17.31 0.0000 3 20 0.5721 0.03536 16.18 0.0000 pressure = 2 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 2 20 -0.04011 0.03536 -1.134 0.8637 3 10 0.11922 0.03536 3.372 0.0205 3 20 0.07922 0.03536 2.241 0.2449 pressure = 2 loading = 20 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 3 10 0.1593 0.03536 4.507 0.0009 3 20 0.1193 0.03536 3.375 0.0203 pressure = 3 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 3 20 -0.04000 0.03536 -1.131 0.8651
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Appendix F: Analysis of Variance (ANOVA) and Analysis of Covariance (ANCOVA) for Granulated Powder Formulations F 1. Bulk Modulus General Linear Model: BM_gr versus Binder, Loading rate Factor Type Levels Values Binder fixed 2 5, 10 Loadingrate fixed 2 10, 20 Analysis of Variance for BM_gr, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Pressure 1 271408 271408 271408 297.37 0.000 Binder 1 1253 263 263 0.29 0.595 Loadingrate 1 36405 44 44 0.05 0.828 Binder*Pressure 1 1393 1393 1393 1.53 0.227 Binder*Loadingrate 1 4724 2 2 0.00 0.964 Loadingrate*Pressure 1 11987 11987 11987 13.13 0.001 Binder*Loadingrate*Pressure 1 1467 1467 1467 1.61 0.215 Error 28 25555 25555 913 Total 35 354192 S = 30.2107 R-Sq = 92.78% R-Sq(adj) = 90.98% Term Coef SE Coef T P Constant 92.34 10.68 8.64 0.000 Pressure 27.847 1.615 17.24 0.000 Pressure*Binder 5 1.995 1.615 1.24 0.227 Pressure*Loadingrate 10 5.852 1.615 3.62 0.001 Pressure*Binder*Loadingrate 5 10 -2.047 1.615 -1.27 0.215 Unusual Observations for BM_gr Obs BM_gr Fit SE Fit Residual St Resid 7 491.500 421.217 16.808 70.283 2.80 R 9 339.900 421.217 16.808 -81.317 -3.24 R R denotes an observation with a large standardized residual.
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F 2. Compression Index General Linear Model: CI_gr versus Binder, Pressure, Loadingrate Factor Type Levels Values Binder fixed 2 5, 10 Pressure fixed 3 2.5, 5.0, 10.0 Loadingrate fixed 2 10, 20 Analysis of Variance for CI_gr, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Binder 1 0.007611 0.007611 0.007611 3.75 0.065 Pressure 2 0.021532 0.021532 0.010766 5.30 0.012 Loadingrate 1 0.003406 0.003406 0.003406 1.68 0.208 Binder*Pressure 2 0.008034 0.008034 0.004017 1.98 0.160 Binder*Loadingrate 1 0.006529 0.006529 0.006529 3.21 0.086 Pressure*Loadingrate 2 0.007930 0.007930 0.003965 1.95 0.164 Binder*Pressure*Loadingrate 2 0.005924 0.005924 0.002962 1.46 0.252 Error 24 0.048739 0.048739 0.002031 Total 35 0.109705 S = 0.0450643 R-Sq = 55.57% R-Sq(adj) = 35.21% Unusual Observations for CI_gr Obs CI_gr Fit SE Fit Residual St Resid 30 0.728966 0.839051 0.026018 -0.110085 -2.99 R R denotes an observation with a large standardized residual. Least Squares Means for CI_gr Pressure Mean SE Mean 2.5 0.8383 0.01301 5.0 0.7875 0.01301 10.0 0.8404 0.01301 Tukey 95.0% Simultaneous Confidence Intervals Response Variable CI_gr All Pairwise Comparisons among Levels of Pressure Pressure = 2.5 subtracted from: Pressure Lower Center Upper 5.0 -0.09670 -0.05078 -0.004856 10.0 -0.04378 0.00214 0.048060 Pressure ------+---------+---------+---------+ 5.0 (-------*------) 10.0 (------*-------) ------+---------+---------+---------+ -0.060 0.000 0.060 0.120 Pressure = 5.0 subtracted from: Pressure Lower Center Upper ------+---------+---------+---------+
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10.0 0.006995 0.05292 0.09884 (-------*------) ------+---------+---------+---------+ -0.060 0.000 0.060 0.120 Tukey Simultaneous Tests Response Variable CI_gr All Pairwise Comparisons among Levels of Pressure Pressure = 2.5 subtracted from: Difference SE of Adjusted Pressure of Means Difference T-Value P-Value 5.0 -0.05078 0.01840 -2.760 0.0283 10.0 0.00214 0.01840 0.116 0.9926 Pressure = 5.0 subtracted from: Difference SE of Adjusted Pressure of Means Difference T-Value P-Value 10.0 0.05292 0.01840 2.876 0.0218
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F 3. Spring-back Index General Linear Model: SI_gr versus Binder, Loadingrate Factor Type Levels Values Binder fixed 2 5, 10 Loadingrate fixed 2 10, 20 Analysis of Variance for SI_gr, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P Pressure 1 0.0008742 0.0008742 0.0008742 21.79 0.000 Binder 1 0.0012649 0.0002668 0.0002668 6.65 0.015 Loadingrate 1 0.0000964 0.0000029 0.0000029 0.07 0.792 Binder*Pressure 1 0.0000002 0.0000002 0.0000002 0.01 0.939 Binder*Loadingrate 1 0.0002098 0.0004156 0.0004156 10.36 0.003 Loadingrate*Pressure 1 0.0000513 0.0000513 0.0000513 1.28 0.268 Binder*Loadingrate*Pressure 1 0.0002364 0.0002364 0.0002364 5.89 0.022 Error 28 0.0011234 0.0011234 0.0000401 Total 35 0.0038566 S = 0.00633413 R-Sq = 70.87% R-Sq(adj) = 63.59% Term Coef SE Coef T P Constant 0.045218 0.002239 20.19 0.000 Pressure 0.001580 0.000339 4.67 0.000 Pressure*Binder 5 -0.000026 0.000339 -0.08 0.939 Pressure*Loadingrate 10 -0.000383 0.000339 -1.13 0.268 Pressure*Binder*Loadingrate 5 10 0.000822 0.000339 2.43 0.022 Unusual Observations for SI_gr Obs SI_gr Fit SE Fit Residual St Resid 33 0.070858 0.057244 0.002185 0.013614 2.29 R R denotes an observation with a large standardized residual. Means for Covariates Covariate Mean StDev Pressure 5.833 3.162 Least Squares Means for SI_gr Binder*Loadingrate Mean SE Mean 5 10 0.04446 0.002111 5 20 0.05256 0.002111 10 10 0.06114 0.002111 10 20 0.05959 0.002111 Tukey 95.0% Simultaneous Confidence Intervals Response Variable SI_gr All Pairwise Comparisons among Levels of Binder*Loadingrate Binder = 5 Loadingrate = 10 subtracted from: Binder Loadingrate Lower Center Upper 5 20 -0.000049 0.008101 0.01625 10 10 0.008533 0.016683 0.02483
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10 20 0.006978 0.015128 0.02328 Binder Loadingrate +---------+---------+---------+------ 5 20 (-------*-------) 10 10 (-------*-------) 10 20 (-------*-------) +---------+---------+---------+------ -0.010 0.000 0.010 0.020 Binder = 5 Loadingrate = 20 subtracted from: Binder Loadingrate Lower Center Upper 10 10 0.000432 0.008582 0.01673 10 20 -0.001123 0.007027 0.01518 Binder Loadingrate +---------+---------+---------+------ 10 10 (--------*-------) 10 20 (-------*-------) +---------+---------+---------+------ -0.010 0.000 0.010 0.020 Binder = 10 Loadingrate = 10 subtracted from: Binder Loadingrate Lower Center Upper 10 20 -0.009705 -0.001555 0.006595 Binder Loadingrate +---------+---------+---------+------ 10 20 (-------*--------) +---------+---------+---------+------ -0.010 0.000 0.010 0.020 Tukey Simultaneous Tests Response Variable SI_gr All Pairwise Comparisons among Levels of Binder*Loadingrate Binder = 5 Loadingrate = 10 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 5 20 0.008101 0.002986 2.713 0.0520 10 10 0.016683 0.002986 5.587 0.0000 10 20 0.015128 0.002986 5.066 0.0001 Binder = 5 Loadingrate = 20 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 10 10 0.008582 0.002986 2.874 0.0363 10 20 0.007027 0.002986 2.353 0.1101 Binder = 10 Loadingrate = 10 subtracted from: Difference SE of Adjusted Binder Loadingrate of Means Difference T-Value P-Value 10 20 -0.001555 0.002986 -0.5207 0.9534
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F 4. Shear Modulus General Linear Model: SM_gr versus binder, pressure, loading Factor Type Levels Values binder fixed 2 5, 10 pressure fixed 3 1, 2, 3 loading fixed 2 10, 20 Analysis of Variance for SM_gr, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P binder 1 14.4 14.4 14.4 0.47 0.497 pressure 2 12223.1 12223.1 6111.5 201.76 0.000 loading 1 5.0 5.0 5.0 0.17 0.687 binder*pressure 2 306.9 306.9 153.4 5.07 0.015 binder*loading 1 1323.1 1323.1 1323.1 43.68 0.000 pressure*loading 2 371.0 371.0 185.5 6.12 0.007 binder*pressure*loading 2 1178.4 1178.4 589.2 19.45 0.000 Error 24 727.0 727.0 30.3 Total 35 16148.9 S = 5.50375 R-Sq = 95.50% R-Sq(adj) = 93.43% Unusual Observations for SM_gr Obs SM_gr Fit SE Fit Residual St Resid 15 73.5000 86.1667 3.1776 -12.6667 -2.82 R R denotes an observation with a large standardized residual. Least Squares Means for SM_gr binder*pressure*loading Mean SE Mean 5 1 10 26.12 3.178 5 1 20 26.65 3.178 5 2 10 32.57 3.178 5 2 20 30.17 3.178 5 3 10 86.17 3.178 5 3 20 49.42 3.178 10 1 10 12.15 3.178 10 1 20 25.72 3.178 10 2 10 37.35 3.178 10 2 20 38.52 3.178 10 3 10 55.18 3.178 10 3 20 74.58 3.178 Tukey 95.0% Simultaneous Confidence Intervals Response Variable SM_gr All Pairwise Comparisons among Levels of binder*pressure*loading binder = 5 pressure = 1 loading = 10 subtracted from: binder pressure loading Lower Center Upper 5 1 20 -15.67 0.53 16.739 5 2 10 -9.76 6.45 22.656
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5 2 20 -12.16 4.05 20.256 5 3 10 43.84 60.05 76.256 5 3 20 7.09 23.30 39.506 10 1 10 -30.17 -13.97 2.239 10 1 20 -16.61 -0.40 15.806 10 2 10 -4.97 11.23 27.439 10 2 20 -3.81 12.40 28.606 10 3 10 12.86 29.07 45.272 10 3 20 32.26 48.47 64.672 binder pressure loading --------+---------+---------+-------- 5 1 20 (--*--) 5 2 10 (--*---) 5 2 20 (--*--) 5 3 10 (--*--) 5 3 20 (---*--) 10 1 10 (--*--) 10 1 20 (--*--) 10 2 10 (--*--) 10 2 20 (--*---) 10 3 10 (--*--) 10 3 20 (---*--) --------+---------+---------+-------- -50 0 50 binder = 5 pressure = 1 loading = 20 subtracted from: binder pressure loading Lower Center Upper 5 2 10 -10.29 5.92 22.122 5 2 20 -12.69 3.52 19.722 5 3 10 43.31 59.52 75.722 5 3 20 6.56 22.77 38.972 10 1 10 -30.71 -14.50 1.706 10 1 20 -17.14 -0.93 15.272 10 2 10 -5.51 10.70 26.906 10 2 20 -4.34 11.87 28.072 10 3 10 12.33 28.53 44.739 10 3 20 31.73 47.93 64.139 binder pressure loading --------+---------+---------+-------- 5 2 10 (--*--) 5 2 20 (---*--) 5 3 10 (--*--) 5 3 20 (---*--) 10 1 10 (--*--) 10 1 20 (--*--) 10 2 10 (--*--) 10 2 20 (--*---) 10 3 10 (---*--) 10 3 20 (---*--) --------+---------+---------+-------- -50 0 50 binder = 5 pressure = 2 loading = 10 subtracted from: binder pressure loading Lower Center Upper 5 2 20 -18.61 -2.40 13.806
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5 3 10 37.39 53.60 69.806 5 3 20 0.64 16.85 33.056 10 1 10 -36.62 -20.42 -4.211 10 1 20 -23.06 -6.85 9.356 10 2 10 -11.42 4.78 20.989 10 2 20 -10.26 5.95 22.156 10 3 10 6.41 22.62 38.822 10 3 20 25.81 42.02 58.222 binder pressure loading --------+---------+---------+-------- 5 2 20 (---*--) 5 3 10 (---*--) 5 3 20 (--*---) 10 1 10 (--*--) 10 1 20 (---*--) 10 2 10 (--*--) 10 2 20 (--*--) 10 3 10 (---*--) 10 3 20 (--*---) --------+---------+---------+-------- -50 0 50 binder = 5 pressure = 2 loading = 20 subtracted from: binder pressure loading Lower Center Upper 5 3 10 39.79 56.00 72.206 5 3 20 3.04 19.25 35.456 10 1 10 -34.22 -18.02 -1.811 10 1 20 -20.66 -4.45 11.756 10 2 10 -9.02 7.18 23.389 10 2 20 -7.86 8.35 24.556 10 3 10 8.81 25.02 41.222 10 3 20 28.21 44.42 60.622 binder pressure loading --------+---------+---------+-------- 5 3 10 (--*--) 5 3 20 (--*--) 10 1 10 (--*---) 10 1 20 (--*--) 10 2 10 (--*---) 10 2 20 (---*--) 10 3 10 (--*--) 10 3 20 (--*--) --------+---------+---------+-------- -50 0 50 binder = 5 pressure = 3 loading = 10 subtracted from: binder pressure loading Lower Center Upper 5 3 20 -52.96 -36.75 -20.54 10 1 10 -90.22 -74.02 -57.81 10 1 20 -76.66 -60.45 -44.24 10 2 10 -65.02 -48.82 -32.61 10 2 20 -63.86 -47.65 -31.44 10 3 10 -47.19 -30.98 -14.78 10 3 20 -27.79 -11.58 4.62
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binder pressure loading --------+---------+---------+-------- 5 3 20 (---*--) 10 1 10 (--*--) 10 1 20 (--*--) 10 2 10 (--*--) 10 2 20 (--*---) 10 3 10 (--*--) 10 3 20 (---*--) --------+---------+---------+-------- -50 0 50 binder = 5 pressure = 3 loading = 20 subtracted from: binder pressure loading Lower Center Upper 10 1 10 -53.47 -37.27 -21.06 10 1 20 -39.91 -23.70 -7.49 10 2 10 -28.27 -12.07 4.14 10 2 20 -27.11 -10.90 5.31 10 3 10 -10.44 5.77 21.97 10 3 20 8.96 25.17 41.37 binder pressure loading --------+---------+---------+-------- 10 1 10 (---*--) 10 1 20 (--*---) 10 2 10 (---*--) 10 2 20 (--*--) 10 3 10 (--*--) 10 3 20 (--*--) --------+---------+---------+-------- -50 0 50 binder = 10 pressure = 1 loading = 10 subtracted from: binder pressure loading Lower Center Upper 10 1 20 -2.639 13.57 29.77 10 2 10 8.994 25.20 41.41 10 2 20 10.161 26.37 42.57 10 3 10 26.828 43.03 59.24 10 3 20 46.228 62.43 78.64 binder pressure loading --------+---------+---------+-------- 10 1 20 (---*--) 10 2 10 (--*--) 10 2 20 (--*---) 10 3 10 (---*--) 10 3 20 (--*---) --------+---------+---------+-------- -50 0 50 binder = 10 pressure = 1 loading = 20 subtracted from: binder pressure loading Lower Center Upper 10 2 10 -4.572 11.63 27.84 10 2 20 -3.406 12.80 29.01
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10 3 10 13.261 29.47 45.67 10 3 20 32.661 48.87 65.07 binder pressure loading --------+---------+---------+-------- 10 2 10 (--*---) 10 2 20 (---*--) 10 3 10 (--*--) 10 3 20 (--*--) --------+---------+---------+-------- -50 0 50 binder = 10 pressure = 2 loading = 10 subtracted from: binder pressure loading Lower Center Upper 10 2 20 -15.04 1.167 17.37 10 3 10 1.63 17.833 34.04 10 3 20 21.03 37.233 53.44 binder pressure loading --------+---------+---------+-------- 10 2 20 (--*--) 10 3 10 (---*--) 10 3 20 (--*---) --------+---------+---------+-------- -50 0 50 binder = 10 pressure = 2 loading = 20 subtracted from: binder pressure loading Lower Center Upper 10 3 10 0.4610 16.67 32.87 10 3 20 19.8610 36.07 52.27 binder pressure loading --------+---------+---------+-------- 10 3 10 (--*---) 10 3 20 (--*--) --------+---------+---------+-------- -50 0 50 binder = 10 pressure = 3 loading = 10 subtracted from: binder pressure loading Lower Center Upper 10 3 20 3.194 19.40 35.61 binder pressure loading --------+---------+---------+-------- 10 3 20 (--*--) --------+---------+---------+-------- -50 0 50 Tukey Simultaneous Tests Response Variable SM_gr All Pairwise Comparisons among Levels of binder*pressure*loading binder = 5 pressure = 1 loading = 10 subtracted from:
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Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 5 1 20 0.53 4.494 0.119 1.0000 5 2 10 6.45 4.494 1.435 0.9441 5 2 20 4.05 4.494 0.901 0.9984 5 3 10 60.05 4.494 13.363 0.0000 5 3 20 23.30 4.494 5.185 0.0013 10 1 10 -13.97 4.494 -3.108 0.1381 10 1 20 -0.40 4.494 -0.089 1.0000 10 2 10 11.23 4.494 2.500 0.3851 10 2 20 12.40 4.494 2.759 0.2576 10 3 10 29.07 4.494 6.468 0.0001 10 3 20 48.47 4.494 10.785 0.0000 binder = 5 pressure = 1 loading = 20 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 5 2 10 5.92 4.494 1.317 0.9685 5 2 20 3.52 4.494 0.783 0.9996 5 3 10 59.52 4.494 13.244 0.0000 5 3 20 22.77 4.494 5.066 0.0017 10 1 10 -14.50 4.494 -3.227 0.1096 10 1 20 -0.93 4.494 -0.208 1.0000 10 2 10 10.70 4.494 2.381 0.4531 10 2 20 11.87 4.494 2.641 0.3119 10 3 10 28.53 4.494 6.350 0.0001 10 3 20 47.93 4.494 10.667 0.0000 binder = 5 pressure = 2 loading = 10 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 5 2 20 -2.40 4.494 -0.534 1.0000 5 3 10 53.60 4.494 11.928 0.0000 5 3 20 16.85 4.494 3.750 0.0366 10 1 10 -20.42 4.494 -4.543 0.0059 10 1 20 -6.85 4.494 -1.524 0.9190 10 2 10 4.78 4.494 1.064 0.9936 10 2 20 5.95 4.494 1.324 0.9673 10 3 10 22.62 4.494 5.033 0.0018 10 3 20 42.02 4.494 9.350 0.0000 binder = 5 pressure = 2 loading = 20 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 5 3 10 56.00 4.494 12.462 0.0000 5 3 20 19.25 4.494 4.284 0.0108 10 1 10 -18.02 4.494 -4.009 0.0204 10 1 20 -4.45 4.494 -0.990 0.9965 10 2 10 7.18 4.494 1.599 0.8934 10 2 20 8.35 4.494 1.858 0.7719
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10 3 10 25.02 4.494 5.567 0.0005 10 3 20 44.42 4.494 9.884 0.0000 binder = 5 pressure = 3 loading = 10 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 5 3 20 -36.75 4.494 -8.18 0.0000 10 1 10 -74.02 4.494 -16.47 0.0000 10 1 20 -60.45 4.494 -13.45 0.0000 10 2 10 -48.82 4.494 -10.86 0.0000 10 2 20 -47.65 4.494 -10.60 0.0000 10 3 10 -30.98 4.494 -6.89 0.0001 10 3 20 -11.58 4.494 -2.58 0.3435 binder = 5 pressure = 3 loading = 20 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 10 1 10 -37.27 4.494 -8.293 0.0000 10 1 20 -23.70 4.494 -5.274 0.0010 10 2 10 -12.07 4.494 -2.685 0.2907 10 2 20 -10.90 4.494 -2.426 0.4270 10 3 10 5.77 4.494 1.283 0.9737 10 3 20 25.17 4.494 5.600 0.0005 binder = 10 pressure = 1 loading = 10 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 10 1 20 13.57 4.494 3.019 0.1632 10 2 10 25.20 4.494 5.608 0.0005 10 2 20 26.37 4.494 5.867 0.0003 10 3 10 43.03 4.494 9.576 0.0000 10 3 20 62.43 4.494 13.893 0.0000 binder = 10 pressure = 1 loading = 20 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 10 2 10 11.63 4.494 2.589 0.3378 10 2 20 12.80 4.494 2.848 0.2216 10 3 10 29.47 4.494 6.557 0.0001 10 3 20 48.87 4.494 10.874 0.0000 binder = 10 pressure = 2 loading = 10 subtracted from: Difference SE of Adjusted
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binder pressure loading of Means Difference T-Value P-Value 10 2 20 1.167 4.494 0.2596 1.0000 10 3 10 17.833 4.494 3.9684 0.0224 10 3 20 37.233 4.494 8.2855 0.0000 binder = 10 pressure = 2 loading = 20 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 10 3 10 16.67 4.494 3.709 0.0400 10 3 20 36.07 4.494 8.026 0.0000 binder = 10 pressure = 3 loading = 10 subtracted from: Difference SE of Adjusted binder pressure loading of Means Difference T-Value P-Value 10 3 20 19.40 4.494 4.317 0.0100
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F 5. Failure Stress General Linear Model: FS versus binder, pressure, loading Factor Type Levels Values binder fixed 3 0, 5, 10 pressure fixed 3 1, 2, 3 loading fixed 2 10, 20 Analysis of Variance for FS, using Adjusted SS for Tests Source DF Seq SS Adj SS Adj MS F P binder 2 0.00852 0.00852 0.00426 0.76 0.476 pressure 2 6.24131 6.24131 3.12066 554.77 0.000 loading 1 0.11966 0.11966 0.11966 21.27 0.000 binder*pressure 4 0.03173 0.03173 0.00793 1.41 0.250 binder*loading 2 0.00423 0.00423 0.00211 0.38 0.689 pressure*loading 2 0.48629 0.48629 0.24314 43.22 0.000 binder*pressure*loading 4 0.01380 0.01380 0.00345 0.61 0.656 Error 36 0.20251 0.20251 0.00563 Total 53 7.10804 S = 0.0750012 R-Sq = 97.15% R-Sq(adj) = 95.81% Unusual Observations for FS Obs FS Fit SE Fit Residual St Resid 26 2.12100 1.96700 0.04330 0.15400 2.51 R 27 1.80900 1.96700 0.04330 -0.15800 -2.58 R 30 1.21000 1.33333 0.04330 -0.12333 -2.01 R 31 1.54000 1.41667 0.04330 0.12333 2.01 R 52 1.86500 1.99033 0.04330 -0.12533 -2.05 R R denotes an observation with a large standardized residual. Least Squares Means for FS pressure*loading Mean SE Mean 1 10 1.015 0.02500 1 20 1.378 0.02500 2 10 1.871 0.02500 2 20 1.830 0.02500 3 10 1.990 0.02500 3 20 1.950 0.02500 Tukey 95.0% Simultaneous Confidence Intervals Response Variable FS All Pairwise Comparisons among Levels of pressure*loading pressure = 1 loading = 10 subtracted from: pressure loading Lower Center Upper 1 20 0.2563 0.3626 0.4688 2 10 0.7492 0.8554 0.9617 2 20 0.7091 0.8153 0.9216 3 10 0.8684 0.9747 1.0809 3 20 0.8284 0.9347 1.0409
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pressure loading ----+---------+---------+---------+-- 1 20 (--*--) 2 10 (--*--) 2 20 (--*--) 3 10 (--*--) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 1 loading = 20 subtracted from: pressure loading Lower Center Upper 2 10 0.3866 0.4929 0.5991 2 20 0.3465 0.4528 0.5590 3 10 0.5059 0.6121 0.7184 3 20 0.4659 0.5721 0.6784 pressure loading ----+---------+---------+---------+-- 2 10 (--*--) 2 20 (--*--) 3 10 (--*---) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 2 loading = 10 subtracted from: pressure loading Lower Center Upper 2 20 -0.1464 -0.04011 0.06614 3 10 0.0130 0.11922 0.22547 3 20 -0.0270 0.07922 0.18547 pressure loading ----+---------+---------+---------+-- 2 20 (--*--) 3 10 (--*--) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 2 loading = 20 subtracted from: pressure loading Lower Center Upper 3 10 0.05308 0.1593 0.2656 3 20 0.01308 0.1193 0.2256 pressure loading ----+---------+---------+---------+-- 3 10 (--*--) 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 pressure = 3 loading = 10 subtracted from: pressure loading Lower Center Upper
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3 20 -0.1463 -0.04000 0.06625 pressure loading ----+---------+---------+---------+-- 3 20 (--*--) ----+---------+---------+---------+-- 0.00 0.35 0.70 1.05 Tukey Simultaneous Tests Response Variable FS All Pairwise Comparisons among Levels of pressure*loading pressure = 1 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 1 20 0.3626 0.03536 10.25 0.0000 2 10 0.8554 0.03536 24.20 0.0000 2 20 0.8153 0.03536 23.06 0.0000 3 10 0.9747 0.03536 27.57 0.0000 3 20 0.9347 0.03536 26.44 0.0000 pressure = 1 loading = 20 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 2 10 0.4929 0.03536 13.94 0.0000 2 20 0.4528 0.03536 12.81 0.0000 3 10 0.6121 0.03536 17.31 0.0000 3 20 0.5721 0.03536 16.18 0.0000 pressure = 2 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 2 20 -0.04011 0.03536 -1.134 0.8637 3 10 0.11922 0.03536 3.372 0.0205 3 20 0.07922 0.03536 2.241 0.2449 pressure = 2 loading = 20 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 3 10 0.1593 0.03536 4.507 0.0009 3 20 0.1193 0.03536 3.375 0.0203 pressure = 3 loading = 10 subtracted from: Difference SE of Adjusted pressure loading of Means Difference T-Value P-Value 3 20 -0.04000 0.03536 -1.131 0.8651
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VITA
Anuranjan Pandeya received his Bachelor of Technology in Agricultural Engineering
from Rajendra Agricultural University, Pusa (India) in 1995. He received Master of
Technology from Indian Institute of Technology, Kharagpur in 1997. After that he
worked as Production Engineer at R. T. Exports Ltd, Sonepat (India) for three years. He
joined as a Research Associate in Indian Agricultural Research Institute, New Delhi in
2001 and worked there for three years. His last job was as an Application Engineer with
Scientific and Digital Systems. He is a member of American Society of Agricultural &
Biological Engineering (ASABE), Gamma Sigma Delta, and American Association of
Pharmaceutical Scientists.