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PARTICLE DEFORMATION DURING STIRRED MEDIA MILLING

By

RHYE GARRETT HAMEY

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008

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© 2008 Rhye Garrett Hamey

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My family and fiancé Yun Mi Kim, for their encouragement

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ACKNOWLEDGMENTS

I would like to acknowledge the friendship and the wisdom of the late Professor Brian

Scarlett, whose instruction and support were the reasons for the pursuit of a Ph. D. Dr. Brian

Scarlett, taught me how to be a better engineer and a better person.

I am grateful for the help of Dr. Hassan El-Shall for his countless hours of guidance

through out this study. Dr. El-Shall was a constant inspiration. I would also like to thank Dr.

Mecholsky, Dr. Fuchs, Dr. Whitney, and Dr Svoronos for serving as committee members and for

their guidance and discussions during this Ph..D. study.

A special thanks goes out to all the friends I have made during this study, Maria

Palazeulos, Scott Brown, Milorad Djomlija, Vijay, Krishna, Stephen Tedeschi, Nate Stevens,

Kerri-Ann Hue, and Dauntel Specht. I would like to acknowledge Marco Verwijs for being a

great friend and roommate for so many years. I would also like to thank Yun Mi Kim for her

love and support.

I would like to acknowledge the financial support of the Particle Engineering Research

Center (PERC) at the University of Florida, The National Science Foundation (NSF) and the

Industrial Partners of the PERC for support of this research. Thanks are extended to the US

Army for their support of the project.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS ...............................................................................................................4

LIST OF TABLES...........................................................................................................................8

LIST OF FIGURES .......................................................................................................................10

ABSTRACT...................................................................................................................................14

CHAPTER

1 INTRODUCTION ..................................................................................................................16

Impact of Milling Metallic Powders.......................................................................................16 Research of Particle Deformation during Milling ..................................................................18 Method for Understanding Particle Deformation during Milling...........................................18

2 BACKGROUND ....................................................................................................................21

Comminution Equipment........................................................................................................22 Crushers...........................................................................................................................23 Grinders ...........................................................................................................................23 Ultrafine Grinders............................................................................................................24 Cutting Machines.............................................................................................................24

Particle Deformation and Particle Breakage...........................................................................24 Particle Deformation .......................................................................................................24 Particle Breakage.............................................................................................................27 Cracks and Defects ..........................................................................................................28 Particle Deformation during Milling ...............................................................................29 Effect of Milling Parameters on Particle Deformation....................................................31 Particle Breakage during Milling ....................................................................................32 Effect of Milling Parameters on Particle Breakage .........................................................33 Summary..........................................................................................................................35

3 MATERIALS, CHARACTERIZATION AND EXPERIMENTAL PROCEDURE.............41

Materials .................................................................................................................................41 Metal Powders .................................................................................................................41 Milling Media..................................................................................................................41

Experimental Procedures ........................................................................................................42 Media Mill .......................................................................................................................42 Milling Procedure............................................................................................................42 Drying of Aluminum Slurry and Milling Samples..........................................................43 Sample Preparation by Dispersion of Dry Powder..........................................................44

Statistical Design of Experiment ............................................................................................45

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Characterization......................................................................................................................45 Light Scattering ...............................................................................................................46 Microscopy and Image Analysis .....................................................................................47

Electron microscopy.................................................................................................47 Optical microscopy ..................................................................................................48 Occhio optical particle sizer .....................................................................................48

Surface Area Analysis (BET)..........................................................................................48 Inductively Couple Plasma Spectroscopy (ICP) .............................................................49 Fourier Transform Infrared Spectroscopy (FTIR)...........................................................49

Light Scattering Results..........................................................................................................50 Results of Aluminum Powder .........................................................................................50 Results for Aluminum Flake ...........................................................................................51 Summary of Characterization and Light Scattering ........................................................52

Milling Condition Selection ...................................................................................................52 Preliminary Milling Study...............................................................................................52 Preliminary Milling Results ............................................................................................53 Establishing Milling Conditions......................................................................................54

Milling medium........................................................................................................54 Mill loading and grinding aids .................................................................................55 Milling time and temperature...................................................................................56 Media properties and rotational rate.........................................................................57

4 RESULTS AND DISCUSSION.............................................................................................72

Experimental Results of Stirred Media Milling......................................................................72 Effect of Mill Parameters ................................................................................................72 Kinetic Energy Model .....................................................................................................73 Stress Model ....................................................................................................................75 Deformation Rate ............................................................................................................79

Strain Energy and Milling Efficiency.....................................................................................81 Strain Energy ...................................................................................................................81 Mill Efficiency.................................................................................................................83

Empirical Modeling of Particle Deformation through Statistical Design of Experiment ......88 Microstructure Analysis..........................................................................................................92 Summary.................................................................................................................................93

5 CASE STUDY: MATERIAL SELECTION AND DEVELOPMENT FOR INFRARED OBSCURANTS....................................................................................................................127

Introduction...........................................................................................................................127 Development of New Obscurant Materials ..........................................................................128 Material Characterization and Obscurant Performance Measurement Method ...................131 Production of Infrared Obscurant .........................................................................................132 Summary...............................................................................................................................135

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6 SUMMARY, CONCLUSIONS, AND FUTURE WORK ...................................................143

Summary and Conclusions ...................................................................................................143 Future Work..........................................................................................................................146

LIST OF REFERENCES.............................................................................................................149

BIOGRAPHICAL SKETCH .......................................................................................................154

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LIST OF TABLES

Table page 3-1 Statistical data comparison for light scattering and image analysis performed using

the Occhio particle counter. ...............................................................................................66

3-2 Stirred media milling equipment variables. .......................................................................67

3-3 Stirred media milling operating variables..........................................................................67

3-4 Experimental parameters used in the hexagonal statistical design of experiment.............67

3-5 Milling conditions for preliminary study...........................................................................68

4-1 Calculated stress intensity for experiments performed in this study. The table indicates that it is possible to achieve equivalent energies and different milling conditions.........................................................................................................................101

4-2 Maximum mean particle size of milling experiments. Even though the kinetic energy of some of the milling experiments are equivalent the maximum particles sizes differ.................................................................................................................................101

4-3 Force, radius of contact area, and stress acting on the milling media as a function of media size and rotation rate (calculated using Hertz theory)...........................................103

4-4 Number of particles stressed in a single collision between grinding media and the stress exerted on an individual particles. .........................................................................103

4-5 Stress frequency as calculated from Kwade’s model. The frequency is the number of times milling media collide with each other. ...................................................................103

4-6 The time required to reach the maximum particle diameter. As milling speed increases the time it takes to obtain the maximum particle diameter decreases. .............104

4-7 Total number of particle compressions in 60 minutes, as calculated using stress frequency and number of particles, Equation 4-2 and 4-6. ..............................................104

4-8 Strain energy per particle for deformation study. ............................................................107

4-9 Total strain energy for deformation study. The 1.5 mm media milling experiments resulted in the largest amount of stain energy. ................................................................108

4-10 List of constants for equations used to calculate milling power......................................108

4-11.Milling efficiency as a function of percent amount of strain the material has experienced at 1000 rpm and varying media size. The 1.5 mm media reaches over 60 % of the maximum strain while milling at 37% efficiency. The last few percent of the maximum strain result in the most inefficient milling...............................................113

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4-12 Experimental design for central composite design 1. ......................................................114

4-13. Analysis of variance for the central composite design 1 described in table 4-12. .............114

4-14 Experimental design for central composite design 2. ......................................................118

4-15 Analysis of variance for the central composite design 2 described in table 4-10............118

5-1 Experimental parameters used in the statistical design of experiment used to determine milling parameters. .........................................................................................137

5-2 Experimental parameters used in the full 2 factorial (22) statistical design of experiment........................................................................................................................139

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LIST OF FIGURES

Figure page 1-1 Methodology for understanding particle deformation during stirred media milling. ........20

2-1 1) Particle stressed by compression or shear, 2) particle stressed by impaction on rigid surface, and 3) particle stressed in shear flow...........................................................36

2-2 Milling efficiency variations by machine type. .................................................................36

2-3 Types of grinding mills......................................................................................................37

2-4 Diagram of a stirred media mill, energy is supplied to the grinding media by the rotation of the agitator........................................................................................................37

2-5 Face centered unit cell for aluminum.................................................................................38

2-6 Slip planes and directions for FCC aluminum...................................................................38

2-7 True stress- true strain curve for a material undergoing plastic deformation and strain hardening............................................................................................................................39

2-9 Effect of impact..................................................................................................................40

3-1 Particle size distribution of as received H-2 aluminum, along with particle size data, obtained from Coulter LS 11320. ......................................................................................59

3-2 Image of Yttria-stabilized zirconia grinding media obtained form an optical microscope, 1mm in diameter............................................................................................60

3-3 Union Process stirred media mill use in study...................................................................61

3-4 Phase diagram for carbon dioxide, indicating the region of supercritical fluid formation............................................................................................................................62

3-5 SPI pressure vessel used for supercritical drying of powder samples taken from milling ................................................................................................................................63

3-6 Galia partial vacuum chamber used to disseminate powder..............................................63

3-7 Scanning electron microscope image of as received H-2 aluminum powder. ...................64

3-8 Differential volume and number distributions for as received H-2 spherical aluminum powder measured by light scattering. ...............................................................65

3-9 Volume particle size distribution of milled aluminum flake as measure by light scattering. ...........................................................................................................................65

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3-10 Volume particle size distribution of milled aluminum flake as measured by the Occhio image analysis. ......................................................................................................66

3-11 SEM image of US Bronze “as received” brass flake used in preliminary milling experiments. .......................................................................................................................68

3-12 Surface response of figure of merit with respect to media loading and RPM. .................69

3-13 Stearic acid a saturated fatty acid found in many animal fats and vegetable oils..............69

3-14 Cumulative undersized versus particle size as at varying milling time for H-2 aluminum. ..........................................................................................................................70

3-15 Scanning electron microscope images of a) as received aluminum, b) milled for 240 minutes aluminum and c) milled for 600 minutes aluminum. ...........................................71

4-1 Volume percent particle size distributions for experiments using 1.0 mm grinding media at 2000 rpm. Bimodality in the particle size distribution is indicative of particle deformation and particle breakage occurring simultaneously. .............................95

4-2 Volume percent particle size distributions for the experiments with 1.5 mm grinding media at 1000 rpm, a visible shift in the particle size distribution to larger sizes is seen due to particle deformation. .......................................................................................96

4-3 Maximum mean particle size achieved for each milling experiment versus media size, the 1.5 mm milling media produced the largest amount of deformation...................97

4-4 Particle deformation versus milling time at a milling speed of 1000 rpm for varying grinding media sizes. .........................................................................................................98

4-5 Particle deformation versus milling time at a milling speed of 1500 rpm for varying grinding media sizes.. ........................................................................................................99

4-6 Particle deformation versus milling time at a milling speed of 2000 rpm for varying grinding media sizes.. ......................................................................................................100

4-7 Mean particle size versus milling time as a function of rotation rate ..............................101

4-8 Contact between colliding elastic spheres. Aluminum particles are caught in the contact area between the media. ......................................................................................102

4-9 Diagram of the change in dimensions of particle and the measurements used to calculate stress and strain.................................................................................................104

4-10 Stress-strain behavior for experiments performed at 1000 rpm.......................................105

4-11 Stress-strain behavior for experiments performed at 1500 rpm.......................................106

4-12 Stress-strain behavior for experiments performed at 2000 rpm.......................................107

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4-13 A plot of milling efficiency as a function of milling time at 1000 rpm, for all media sizes..................................................................................................................................109

4-14 A plot of milling efficiency as a function of milling time at 1500 rpm, for all media sizes..................................................................................................................................110

4-15 A plot of milling efficiency as a function of milling time at 2000 rpm, for all media sizes..................................................................................................................................111

4-16 A plot of milling efficiency as a function of milling time for the 1.5 mm at varying rotational rates..................................................................................................................112

4-17 A plot of milling efficiency at failure, right side of figure 4-13 used for comparison of efficiencies as a function of rotational rate..................................................................113

4-18 Contour plot for central composite design 1, a minimum strain of 2.17 can be seen at approximately 0.9 mm milling media..............................................................................115

4-19 Surface response for central composite design 1, a trough exists at the 1.0 mm media size. ..................................................................................................................................116

4-20 Standard error associated with central composite design 1, error increases at the limits of the study.............................................................................................................117

4-21 Contour plot for central composite design 2, shows a maximum at approximately the 1.6 mm media...................................................................................................................119

4-22 Surface response for central composite design 2, a peak can be seen at intermediate media size.........................................................................................................................120

4-23 A plot of the interaction between the media size and rotation rate, it can be seen that there is only a slight interaction at low. ...........................................................................121

4-24 Standard error associated with central composite design 2. ............................................122

4-25 Transmission electron microscope image of “as received” aluminum particle. ..............123

4-26 Diffraction pattern obtained from particle in Figure 4-20. ..............................................124

4-27 Transmission electron microscope image of sectioned flake after 4 hours of milling. ...125

4-28 Single crystalline diffraction pattern of sectioned flake after 4 hour sof milling. ...........126

5-1 A chart of relevant material properties of materials for use as an infrared obscurant. High values in each property are preferred for candidate materials. ...............................136

5-2 The performance of various milled metals, the copper has the highest performance to due to the properties being the highest in all the desired area. ........................................137

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5-3 The results of the initial design of experiment, indicating that higher media loading increase the performance of the material. ........................................................................138

5-4 Plot of FOM for as received and ground brass at specific milling condition of 480ml media volume and 700 rpm rotational speed ...................................................................139

5-5 The results of the affect of varying media size and rotation rate on the performance of a milled brass flake. .....................................................................................................140

5-6 Differential volume particle size distribution at increasing milling times.......................141

5-7 Figure of merit versus IR wavelength for increasing milling times. ...............................141

5-8 Mean particle size as a function of milling time for different density milling media, zirconia (6 g/cc), stainless steel (9.8 g/cc), and tungsten carbide (16 g/cc)....................142

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

PARTICLE DEFORMATION DURING STIRRED MEDIA MILLING By

Rhye Garrett Hamey

August 2008

Chair: Hassan El-Shall Major: Materials Science and Engineering

Production of high aspect ratio metal flakes is an important part of the paint and coating

industry. The United States Army also uses high aspect ratio metal flakes of a specific dimension

in obscurant clouds to attenuate infrared radiation. The most common method for their

production is by milling a metal powder. Ductile metal particles are initially flattened in the

process increasing the aspect ratio. As the process continues, coldwelding of metal flakes can

take place increasing the particle size and decreasing the aspect ratio. Extended milling times

may also result in fracture leading to a further decrease in the particle size and aspect ratio. Both

the coldwelding of the particles and the breakage of the particles are ultimately detrimental to the

materials performance. This study utilized characterization techniques, such as, light scattering

and image analysis to determine the change in particle size as a function of milling time and

parameters.

This study proved that a fundamental relationship between the milling parameters and

particle deformation could be established by using Hertz’s theory to calculate the stress acting on

the aluminum particles. The study also demonstrated a method by which milling efficiency could

be calculated, based on the amount of energy required to cause particle deformation. The study

found that the particle deformation process could be an energy efficient process at short milling

times with milling efficiency as high as 80%. Finally, statistical design of experiment was used

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to obtain a model that related particle deformation to milling parameters, such as, rotation rate

and milling media size.

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CHAPTER 1 INTRODUCTION

In today’s market there is a need to develop new and improved products at an increasing

rate. Particle deformation by milling is important to many areas of product development, such as,

powder metallurgy (P/M), paints and coatings, and military applications. Understanding and

predicting particle deformation during milling, will lead to more rapid development of products

in which these materials are used.

Impact of Milling Metallic Powders

Generally, milling is used to reduce the size of a material or for the processing of brittle

materials. However, large quantities of ductile metals used in the powder metallurgy industry

(P/M) are processed through milling [1]. Powder metallurgy is estimated to be a $1.8 billion

industry annually with an estimated 70 % spent in the automotive industry [2]. Below is a list of

reasons for the milling of materials in the P/M industry [1]:

• Particle size reduction (comminution or grinding) for sintering

• Particle size growth

• Shape change (flaking)

• Agglomeration

• Solid-state alloying (mechanical alloying)

• Solid-state blending (incomplete alloying)

• Modifying, changing, or altering properties of a material (density, flowability, or work hardening)

• Mixing or blending of two or more materials or mixed phases

• Nonequilibrium processing of metastable phases such as amorphous alloys, extended solid solutions, and nanocrystalline structures

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During the processing and subsequent stressing of metallic powders, several phenomena

may occur; the metal can fracture, deform, coldwork, coldweld, or transform into other

polymorphs [3]. Coldwelding is used to mechanically alloy (MA) and refine the microstructure

of immiscible metals [4]. Coldworking is used to strengthen metallic particles. This study will

focus on deformation of metallic particles during milling. This technique is used to make

metallic flakes for paints, coating, and obscurants [5-9]. The metallic flakes in paints give what is

termed a “metallic look” which means the randomly oriented flakes in the paint will give a

“shiny” appearance. Radiation shielding in devices such as cell phones will use metallic particles

to form a conductive coating. The US Army uses metallic flakes in smoke bombs to obscure

infrared light (IR). The conductive metallic particles are capable of attenuating the IR signal

which provides a shield against missiles and IR imaging devices.

The most common metallic pigment is aluminum, which when milled deforms into flakes

with highly reflective surfaces. In order for the metallic flakes to be effective at scattering and

reflecting light, the particle size, size distribution, particle shape, and particle morphology must

be controlled. The particle size and size distribution affect the optical reflectance and light

scattering properties of the flake. If the particle size distribution of these paints is broad the

reflectiveness will be diminished and the paint will appear dull. The particle morphology and

surface roughness also affect the optical reflectance i.e. the smoother the surface the more

reflective the pigment. An additional difficulty to this processing method is that most of the

aluminum pigments are produced in batch milling processes and there exists large batch to batch

variations due to lack of process knowledge [10]. In the end, these variations lead to additional

processing costs from classification.

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Research of Particle Deformation during Milling

Most milling studies focus on particle breakage with limited research on particle

deformation. The particle deformation studies have focused on the mechanical alloying process

and do not investigate optimizing the flake dimensions, which are necessary for paints and

coatings. Zoz showed how the dimensions of flakes are affected by the material hardness[11].

Several researchers have investigated the change in the microstructure and material properties of

metals during milling [12-14]. None of these studies has shown the effect of milling parameters

on particle deformation. The research to date does not provide any methodology for predicting

the magnitude or extent of particle deformation during milling. In order to improve the

production and quality of the products it is important to understand the effects of milling

parameters on the materials being processed. Even though particle breakage during milling has

been studied extensively, there is very little knowledge of the particle deformation process

during milling. This study will attempt to apply some of the knowledge gained from particle

breakage during milling to the deformation process and to fill the gaps in the theories between

the two processes.

Breakage during milling has been studied at nearly every length scale [15-19]. Numerous

researchers have modeled milling kinetics and energetics for particle breakage [20-22]. Others

have used population balance modeling to predict particle size during milling [19, 23]. The

response of the product material to nearly every milling parameter has been investigated for

particle breakage. Wear on equipment and process optimization studies have also been

researched [24, 25].

Method for Understanding Particle Deformation during Milling

The goal of this study is to understand and predict particle deformation during stirred

media milling. Figure 1-1 shows the methodology that was used to accomplish this goal. The

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study investigated the affects of mill speed and media size on the particle size and morphology of

an aluminum powder. The study shows how milling breakage models fail to describe particle

deformation during milling. New models were derived from the stress-strain behavior of

aluminum during milling to describe particle deformation. Hertz theory was used to calculate the

stress acting on a particle during. The stress acting on a particle and the affect it had on particle

deformation was then determined. Statistical analysis was used to determine the magnitude of the

interaction between milling parameters. Design of experiment was used to construct a model

that relates milling parameters to particle deformation. From these studies a more comprehensive

understanding of particle deformation during milling was achieved. This may ultimately lead to a

method to better predict and optimize milling processes where the deformation of metallic flakes

is desired.

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Figure 1-1. Methodology for understanding particle deformation during stirred media milling.

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CHAPTER 2 BACKGROUND

Comminution is arguably the oldest material processing technique. Earlier civilizations

employed simple mortars and pestles to reduce the size of agricultural and medicinal products.

Even though there have been significant changes in technology, these simple devices that were

employed thousands of years ago can still be found in nearly every lab today. A simple definition

of comminution is the reduction in particle size through the application of an applied load. In

order to study and improve a milling process it is important to understand how the load is applied

and to analyze the response of the material to that load. Rumpf suggested four modes by which

stress can cause particle breakage [26]:

1. Compression-shear stressing 2. Impact stressing 3. Stressing in shear flow 4. Stressing by other methods of energy transmission (electrical, chemical, or heat)

Figure 2.1 is a representation of the modes of stressing a material as indicated by Rumpf.

The first two modes are caused by contact forces and are important for milling. Mode 3 is

important for the dispersion of materials under shear, and only exerts enough force to break apart

weak agglomerates [26]. The fourth mode is not applicable to milling where mechanical

stressing is important. There are several types of machines designed to apply stress to a material

by modes 1 and 2.

The beginning of this chapter will describe the types of milling equipment used today. A

review of literature on single and multi particle breakage will be presented. Followed by a

discussion of the response of a material to the load applied during milling. This information will

be used as a basis for this study and it will shed light on the deformation process during milling,

which has not been studied as thoroughly. This chapter will conclude by discussing material

deformation and reviewing deformation during milling processes. Ultimately, this study will

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compile what has already been done to study particle deformation during milling and use that

knowledge, combined with particle breakage and further experimentation, to more accurately

develop the understanding of particle deformation during milling.

Comminution Equipment

Comminution is a diverse process, found in nearly every industry. Therefore there are

numerous types of milling equipment. The equipment must be able to operate in rigorous, high

throughput environments of the mineral processing industry and in the ultra pure, contamination

free pharmaceutical industry. McCabe, Smith and Harriott identified four classes of milling

equipment each with subclasses [27]:

A. Crushers (coarse and fine)

a. Jaw crushers

b. Gyratory crushers

c. Crushing roll

B. Grinders (intermediate and fine)

a. Hammer mills, impactors

b. Rolling-compression mills

i. Bowl mills

ii. Roller mills

c. Attrition mills

d. Tumbling mills

i. Rod mills

ii. Ball mills; pebble mills

iii. Tube mills; compartment mills

C. Ultrafine grinders

a. Hammer mills with internal classification

b. Fluid-energy mills

c. Agitated mills

D. Cutting machines

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a. Knife cutters; dicers; slitters

The differences in equipment are due to the mode in which stress is applied to the material

and the final achievable particle size. Some of the equipment may work in clean environments

and process small quantities of products while other may process large amounts of material in

wet and dry environments. Schonert has shown that some of these machines can operate at high

energy efficiencies >90% while others operations are a fraction of a percent efficient. Most of

this inefficiency is associated with the increase in energy required to achieve smaller particle

size. Examples of the efficiency of select mills can be seen in Figure 2-2, obtained from

tabulated data given by Prasher for the energy consumption associated with milling to a specific

size [28].

Crushers

Jaw crushers, gyratory crushers and crushing roll mills are used to process large quantities

of materials. They are often used in the mineral processing and cement industries to reduce the

size of rock and ore for further processing.

Grinders

Grinders are one of the most diverse sets of milling equipment. They are most often used

to reduce large aggregates to a powder. Grinding mills can supply a load to a material by

impaction, attrition, or compression. Hammer mills apply a load via impaction by dropping a

weight repeatedly on a bed of material. Attrition mills wear away a material by the breakage of

small fragments from the surface. Roll mills and ball mills apply a load through compression by

trapping material between colliding media or in between two heavy rollers. Figure 2-3 is a

diagram of a ball mill and a roller mill. Ball mills have been the subject of a considerable amount

of research because they can be used in wet and dry environments and their large capacities. Ball

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mills operate by rotating a drum containing hard dense balls and product material. The balls fall

from a height equal to the diameter of the drum and compress the material.

Ultrafine Grinders

Ultrafine grinders have recently become very popular due to there ability to produce

nanoparticles. The most popular ultrafine grinders are fluid energy mills such as jet mills and

agitated mills such as stirred media mills. Jet mills stress a material by entraining particles in a

gas stream and impacting the particles on a hard surface or against each other. Jet mills are used

extensively in the pharmaceutical industry due to their ability to produce fine particles without

the wear of mechanical parts. Another class of mills used to produce fine particles, are the stirred

media mills, which are similar to ball mills except they contain an agitator, which supplies the

necessary energy instead of rotation of the vessel. The agitator allows the media to collide with a

much higher force than is possible in the ball mill. Due to their importance in this study, stirred

media mills and particle breakage during stirred media mills will be discussed in more detail

later. Figure 2-4, is a diagram of a stirred media mill. Products in a stirred media mill are often

ground in a wet environment to allow for easier stabilization of the product.

Cutting Machines

Cutting machines are used to reduce the size of resilient materials that are not easily

fractured [27]. Some examples of materials that are processed using cutting machines are tire

rubber for recycling, paper products, and plant materials. Cutting machines apply a shear stress

to materials, which causes them to fail or break.

Particle Deformation and Particle Breakage

Particle Deformation

Plastic deformation in a metal occurs when the material is stressed beyond its yield stress;

the atomic bonds inside a material are broken and then reformed as planes of atoms are moved

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past each other. Plastic deformation results in a perment change in the shape of the object being

stressed. Plastic deformation is affected by the stress (σ), strain rate (dε/dt), temperature (T), and

the microstructure of the material [29, 30]. This study focuses on the deformation of aluminum

particles when subjected to a compressive stress.

Aluminum is a crystalline material with a face center cubic (FCC) structure with atoms at

each corner and in the center of each face of a cube. Figure 2-5 is a sketch of a FCC unit cell. For

such a structure, deformation often occurs by slip, the process of plastic deformation by

dislocation motion, along the preferred crystal planes. The {111} plane for aluminum is the most

atomically dense plane and it is in this plane, along the <110> direction, that slip occurs [31].

There are 4 slip planes for aluminum and 3 slip directions this means that there are 12 total slip

systems for dislocation motion to occur in. Figure 2-6 show the highlighted {111} plane and the

<110> direction is denoted by the arrows beneath the highlighted areas.

When dislocations encounter each other and a strengthening of the material will occur

resulting in a loss of ductility. This strengthening is called work hardening, cold working, or

stain hardening; and is due to the increase in dislocation density and decrease in the allowable

dislocation motion. Equation 2-1 is the work hardening equation, σy is the true yield stress, ε is

the true strain of the material, Kw is the strengthening or work hardening coefficient, and n is the

work hardening exponent. In the equation the stress and strain are true stress and true strain. The

exponent and coefficient for the work hardening equation are generally obtained experimentally.

Many researchers have calculated the exponent for numerous materials under numerous

conditions [32-34].

nwy K εσ = 2-1

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According to this relationship, higher stresses are required to obtain greater amounts of

deformation. The material will eventually work harden to the extent that no additional

deformation may be achieved and the material will ultimately fail.

In a milling process, a material will undergo multiple loading and unloading cycles. This

behavior can be characterized by a stress strain curve. Figure 2-7 is a generic representation of a

stress-strain curve for plastic deformation followed by failure. When the material is unloaded

after experiencing plastic deformation, it will remain in the deformed state. The area under the

elastic region of the curve is called resilience. It is the strain energy due to elastic deformation of

the material. The total area under the curve until fracture is called toughness. This is the same

toughness discussed earlier for particle breakage. The area under the curve represents the amount

of energy the material can absorb before it will fracture, or the strain energy due to plastic

deformation. It should be noted that the area under the linear part of the curve is the energy due

to elastic deformation.

Strain rate, dε/dt, is the rate at which a material is deformed. Schönert referred to strain

rate as stress velocity and theorized that it could affect material breakage. The strain rate also

affects deformation. Several researchers have investigated the effects of strain rate on the

deformation of materials [35-37]. Tome and Canova investigated the stress strain response of

aluminum and copper at different strain rates[37]. They showed that over the strain rate range

tested, copper did not appear to have strain rate dependence. However, aluminum did have strain

rate dependence; lower strain rates resulted in less deformation before failure. Nieh observed

superplastic-like behavior, also known as extended ductility, of aluminum composites at very

high strain rates. Meyers has also shown that at very high strain rates it is possible for a material

to even recrystallize and form new grains [38]. Hines also observed this result in copper [39]. In

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order to achieve a greater understanding of particle deformation during milling it is important to

review particle breakage and to correlate these results to deformation.

Particle Breakage

Numerous authors have studied single particle and multi particle breakage [40-43]. They

have found that particles can break in different ways depending on the method in which the load

is applied. In a stirred media mill, load is applied to particles trapped between colliding grinding

media, media and the wall of the vessel, and between the stirrer and media. Therefore, particle

breakage is a complex phenomenon with numerous stages to study. Schönert extensively studied

breakage, crack propagation, and crack velocity for many particulate materials and found that the

strain rate or stressing velocity can influence material failure [44]. Polymer materials, for

example, are strongly affected by strain rate. Metals also have been shown to have some strain

rate dependence, however, the effect is much less than that of polymers [44].

There are three modes by which a material can fracture, which are a function of the

material as well as the stress applied to the material.

(1) Opening mode that corresponds to an applied tensile load (2) Sliding mode where the force is applied in the plane of the defect or crack (3) Tearing mode where a force is applied in a direction out of the plane of the crack or defect

For most particles, breakage is considered to take place in the first mode of failure. This

may be due to artifacts in the techniques developed to measure particle breakage. For this reason,

most techniques for measuring particle failure involve stressing the particle in tension. If a

normal load is applied to a particle a load equal in magnitude is acting internally in the direction

perpendicular to the load and can then be considered to be a tensile load. Tensile failure is more

likely than compressive failure for many materials.

Particle breakage can take place through many different mechanisms of loading. These

mechanisms of loading as well as the material being stressed can affect how the particle will

28

break. The mechanisms of breakage were alluded to earlier when discussing the types of milling

machines and now will be discussed in more detail. Rumpf suggested there are three ways by

which a particle can break, which are fracture, cleavage or attrition [26]. During fracture a

mother particle will break into daughter particles or fragments that have a wider size distribution.

During cleavage a mother particle will break into smaller daughter particles of roughly the same

sizes.

Attrition takes place when a mother particle has surface asperities removed from the

particle. This leads to much smaller daughter particles. Figure 2-8 represent the three different

mechanisms of particle breakage. If a brittle material experiences a normal load such as

impaction in a milling process it would undergo a fracture or attrition mechanism of breakage. If

a ductile material experiences a shear force, it is most likely to fail by a cleavage mechanism

[45].

Cracks and Defects

Understanding crack formation and propagation is of fundamental importance to the study

of particle breakage. Particle breakage is preceded by crack growth, which is preceded by crack

formation. Crack formation is enhanced by local defects in a material. Defects are separated into

four classes, which correspond to their dimensions.

(1) Point defects (vacancies, interstitials, or substitution) (2) Line dislocations (screw or edge) (3) Interfacial (4) Volume

The strength of a material is related to the number, size and types of defects present. Most

materials are only a fraction as strong as the theoretical strength would predict due to the

presence of defects. A method by which cracks are initiated is when the applied stress exceeds

the strength of the material. Following crack initiation is crack growth, which leads to particle

29

breakage. Schönert extensively studied crack growth and found that crack velocity can vary

widely depending on the material, environment, and mode of stressing [46]. Schönert also

studied particle breakage during milling, however few researchers have studied deformation

during milling [47].

Particle Deformation during Milling

A significant amount of work has gone into investigating particle deformation during

milling, however, that work has focused on the mechanical alloying process[1]. This process is

important because it is used to make alloys that can be made in no other way. Beside the

formation of novel alloys, mechanical alloying can be used to refine the microstructure of the

materials to increase their strength. Mechanical alloying and microstructure refinement involves

adding a metallic powder(s), fatty acid/dispersant, and grinding media to a ball mill. The mixture

is then milled until an equilibrium particle size is reached [4]. The particles generally produced

in this process are semi-spherical agglomerates.

Benjamin is the pioneering researcher of mechanical alloying. The author was the first to

form an indium alloy [48]. Since then numerous authors have studied mechanical alloying (MA)

[49-53]. Most of the studies on MA have focused either on alloying or on refinement of

microstructure. Weeber studied the effect of different ball milling operations on the final product

and found that the milling equipment can affect the final product [52]. The author found

microstructure can vary using different types of ball mills. Gilman investigated the effect of

additives on the alloying process and found that if too little quantity of dispersant was added that

the metal would coldweld together and not effectively alloy[4].

Even though mechanical alloying and the production of metallic flakes involve similar

equipment and similar physics, the final product for flake production is very different. The

desired product of the flake making process is a powder with a large major dimension and a

30

narrow particle size distribution. It is not possible to run a flaking process to an equilibrium

particle size, as is the case with MA. Further milling will cause the flakes to break, no longer

scatter light effectively, and perform poorly as metallic effect pigments. The major differences

between the MA and flaking process are the use of dispersant and the grinding time. Many

flaking processes mill in a solvent to prevent the metal particle from coldwelding together and

the processes are run for shorter lengths of time to limit breakage.

The production of metallic flakes for use as pigments has been ongoing for over 50 years.

Some of the first available works are patents for devises made to produce metallic flakes [54].

More recently metallic flakes have found increasing use in other applications such as conductive

and electromagnetic resistant coatings and infrared obscurants [7, 8]. It is important for flakes to

have a large major dimension in order to function in the specific part of the electromagnetic

spectrum desired for these applications. Breakage during milling of these metallic particles

ultimately leads to poorly performing obscurants and paints. It is necessary to understand the

relationship between particle deformation and milling.

Moshksar has shown that when milling aluminum powder that the aspect ratio of the

material [major dimension divided by minimum dimension (d/t)] increases to some maximum,

then begins to decrease at longer milling times [55]. The decrease is due to particle breakage and

a subsequent reduction in aspect ratio. The results suggest that an ideal product may be produced

by monitoring the aspect ratio as a function of milling time. The author also found that the cold

welding and agglomeration of the powder particles was hindered by the fracture of the flakes at

longer milling times. Zoz showed that the maximum value of the d/t ratio varies with the

hardness of the metal being milled [56]. The lesser the hardness of the metal and the greater the

d/t ratio, the more likely the material will form flakes. Material selection and strain rate can

31

significantly affect whether the material breaks or deforms. It may also be possible to relate

material properties such as hardness and strain rate to the aspect ratio. This relationship would

enable the development of a model that relates material properties, and milling parameters to

particle deformation.

Effect of Milling Parameters on Particle Deformation

The deformation process has yet to be studied as extensively as the breakage process; the

studies that have been performed are mainly focused on a specific application. Much of the

research that has been performed is directed at understanding the microstructure development

during mechanical alloying (MA) [4]. For the paint industry, changes in particle morphology are

important and not the change in the microstructure of the material [57]. Few researchers have

investigated the milling of metals for use in the paint industry [5, 56, 58]. Zoz’s work was

discussed above [11]. Sung studied the affect of particle morphology on the reflectance and

quality of the paint.

Hashimoto studied the effect of milling media diameter on the total energy consumption as

well as the energy per impact on a metal powder in a simple vibratory mill [14]. From this, the

average energy per collision was calculated. The author found that the total energy consumption

was higher for larger media. The author also found that as media loading increased, the average

energy per collision is reduced due to ball-ball interactions. Kwade’s models of stress frequency

and stress intensity neglect ball-ball interactions. Hashimoto measured the change in the

hardness of the metal with milling time, the work hardening of the metal, and found that the

increase in the hardness of the powder was greater with larger media. This increase was

attributed to cold working of the material during the milling process. Riffel determined that an

optimum media size existed when mechanically alloying (MA) Mg2Si compounds. The author

determined that if the media was too small it did not provide enough kinetic energy to alloy or

32

reduce the size of the material [59]. Riffel’s results for MA also agree with the Kwade’s

predictions of an optimum stress value (milling conditions) for particle breakage. Kwade and

Riffel’s result suggest that it may be possible to use particle breakage equations to describe the

particle deformation process.

Rodriguez milled aluminum in a stirred ball mill, and measured the hardness as a function

of milling time [60]. The researcher found an initial increase in Vickers hardness which reached

a maximum at a value of 130 kg/mm2. The increase in hardness measured by Rodriguez agrees

with the increase also observed by Hashimoto. Huang also measures an increase in hardness with

milling time in copper [12]. Huang used the change in the diffraction pattern measured from the

high-resolution transmission electron microscope (HRTEM) to determine the lattice strain and

measured a 0.2% increase in lattice strain. Hwang also used powder x-ray diffraction data

(XRD) to investigate the effect of milling time on lattice strain and determined that it

increased[13]. Huang and Hwang’s results agree and provide other methods of characterizing the

work hardening of a material during milling.

Particle Breakage during Milling

Prasher gives a chronology of proposed laws relating energy for breakage to simple

parameters such as changes in surface area or change in particle size [28]. Two of the most

notable relationships are Rittinger’s and Kick’s Law. Rittinger states that, energy E, to break

particles is equal to the new surface area times a constant as described by Equation 2.1.

sKxx

E Δ=⎟⎟⎠

⎞⎜⎜⎝

⎛−∝ 1

12

11 2-1

The terms x1 and x2 describe the particle diameter of the feed and product material

respectively, K1 is a constant and Δs is the change in surface area. Kick’s Law, Equation 2.2,

33

finds the energy to break a particle is equal to a constant, K2, times the log of the starting particle

size divided by the ending particle size.

⎟⎟⎠

⎞⎜⎜⎝

⎛=

2

12 log

xx

KE 2-2

These relationships apply to a limited number of cases with precise particle sizes and specific

materials and have not been shown to apply to processes where particle deformation is desired

[28].

Figure 2-9 shows a comparison of brittle materials and ductile materials trapped between

impinging grinding media. Brittle particles are compressed and fractured by the media, whereas

ductile particles are plastically deformed and flattened. Both processes represent an increase in

overall surface area, however, during particle deformation the volume of the particle is

conserved.

Effect of Milling Parameters on Particle Breakage

Choosing the proper milling parameters can have a significant effect on the breakage rate,

energy consumption, and efficiency of the milling process. Grinding media density and size, for

example, directly affects the magnitude of the load on the particles, and thus can be expected to

alter milling. Many authors have studied the effects of milling parameters on particle breakage in

a stirred media mill [21, 25, 61, 62]. Kwade formulated a simple equation (eq. 2-3) to

mathematically relate media size, media density, and rotational rate to the stress intensity.

Kwade’s stress intensity term is merely a representation of the kinetic energy of the media and is

not a representation of the actual stress acting on the particles. Stress intensity (SI) is directly

proportional to circumferential velocity v, media size Dp, and media density ρp less the fluid

density ρf through Equation 2-3 [63]:

34

( ) 23 υρρ fppDSI −= 2-3

Kwade then showed that at a specific energy input an optimum in stress intensity existed

that provided minimum particles size for a minimum energy input. The optimum energy input

for producing a maximum fineness exists between a stress intensity of 0.01 Nm and 0.1 Nm.

Kwade also derived an expression that relates the stress frequency (SF) to media size [63]. The

stress frequency is a representation of the number of media-particles interactions, i.e. the number

of times a particle is contacted by the media, and described by Equation 2-4.

TDDSF

p

ss

2

⎟⎟⎠

⎞⎜⎜⎝

⎛= ω 2-4

Here, T is milling time, Dp is the diameter of grinding media, Ds is diameter of the stirrer, and ωs

is angular velocity. Kwade showed that the greatest stress frequency results from the smallest

media size. Large stress frequency also results in the smallest particle size. The author was able

to provide a method for optimizing and even scaling a milling process. However, these results

have only been shown to apply to a system where particle size reduction is desired. The effect of

stressing velocity on the deformation of materials in a milling system has not been studied.

Stressing velocity and strain rate in a mill can be assumed to be equivalent terms as previously

discussed by Schönert [44]. Using Kwade’s model of SI it is now possible to relate specific

milling parameters (media size, media density, and rotational rate) to the strain rate. This would

be the first step in obtaining a realistic model to describe the deformation process in a stirred

media mill.

Eskin et al. developed a more sophisticated approach to modeling the energetics of a

milling process. The authors calculated granular temperature, and used it to represent the

velocity of the grinding media in their process [20]. The authors then calculated the force, and

35

stress of the grinding media based on Hertz’s theory and rigid body impact. Equation 2-5

demonstrates how force, F, is related to media size, R, granular temperature(velocity), Θ, and

materials properties, such as, Poisson’s ratio, η, density, ρ, and modulus of elasticity, Y [20].

( ) ( ) ( ) ( )532

535

2

2196.1 Θ⎥

⎦

⎤⎢⎣

⎡−

= RYF ρη

2-5

Eskin derived a relationship determining the number of compressions a particle would

experience as a function of media size. This relationship is similar to Kwade’s stress frequency

term. Eskin concluded by calculating a milling efficiency term based on the energy input into the

mill. The work by Eskin was found to be important to this study and the equation and derivations

of his work will be revisited in more detail in Chapter 4.

Summary

In summary, Kwade has provided models that describe the stress intensity and stress frequency

in a stirred media milling process for particle breakage. These models may also be valid for

describing the stress intensity in a milling process where deformation is desired. It is known that

some metals have a strain rate dependent behavior and that greater deformation may be achieved

from a lower strain rate. Zoz showed that the amount of deformation a material can undergo in a

milling experiment is also related to the hardness of the material. Researchers have also shown

that the extent of work hardening varies with media size, concentration and milling time. The

researchers have provided three methods by which work hardening can be characterized,

including indentation, XRD, and HRTEM. From these studies, it is now possible to begin to

construct models that can predict material deformation based on the hardness of the material,

deformation, milling time, media size, media density and rotational rate of the stirred media mill.

36

Figure 2-1. 1) Particle stressed by compression or shear, 2) particle stressed by impaction on rigid surface, and 3) particle stressed in shear flow.

0 10 20 30 40 50 60 70 80 90 100

Fluid Energy 2%

Pin Mill 5%

Ball Mill 8%

Ball Roce Mill 13%Swing Hammer Mill 22%

Roll Crusher 80%

Free Crusher 100%

0 10 20 30 40 50 60 70 80 90 100

Fluid Energy 2%

Pin Mill 5%

Ball Mill 8%

Ball Roce Mill 13%Swing Hammer Mill 22%

Roll Crusher 80%

Free Crusher 100%

Figure 2-2. Milling efficiency variations by machine type.

1) 2) 3)

37

Ball Mill Roll mill

A) B)

Ball Mill Roll millBall Mill Roll mill

A) B)

Figure 2-3. Types of grinding mills, A) ball mill and B) roll mill.

Figure 2-4. Diagram of a stirred media mill, energy is supplied to the grinding media by the rotation of the agitator.

Stirred media

38

Figure 2-5. Face centered unit cell for aluminum.

Figure 2-6. Slip planes and directions for FCC aluminum.

39

σy

σUTS

Elastic region

Plastic region

Unloading

Stress

Strain

σy

σUTS

Elastic region

Plastic region

Unloading

Stress

Strain

Figure 2-7. True stress- true strain curve for a material undergoing plastic deformation and strain hardening.

40

Increasing relative particle sizeIncreasing relative particle size

Figure 2-8. Relative particle size distributions for attrition, cleavage, and fracture, respectively.

Figure 2-9. Effect of impact (a) brittle single particle, and (b) ductile single spherical particle.

a) b)

41

CHAPTER 3 MATERIALS, CHARACTERIZATION AND EXPERIMENTAL PROCEDURE

The goal of the study was to understand and predict particle deformation during milling. In

order to achieve this goal it was necessary to develop experimental procedures and

characterization techniques for performing and assessing particle deformation. This chapter

describes the milling equipment and procedures used in this study. Characterization techniques

and validation of the results are discussed in this chapter. In addition, the chapter describes the

statistical analysis techniques used for predicting particle deformation during stirred media

milling. The chapter concludes with identification of the milling parameters used in this study.

Materials

Metal Powders

The aluminum powder (product name H-2) used in this study was purchased from Valimet

Inc, which is generally used in the production of metal effect paints and aluminum based

explosives. Valimet manufactures the aluminum by atomization. Molten aluminum is sprayed

through a high pressure nozzle and solidifies when it is exposed to argon atmosphere forming

semi-spherical aluminum particles. The aluminum is then classified to obtain the desired size

distribution. The powder has a purity of 99.7 weight percent aluminum and a median particle

size of 3.2 μm as measured by the manufacture. In house measurements of the particle size using

light scattering determined the median size to be 3.8 μm, and a mean of 4.2 μm. Figure 3-1

shows the size distribution of the “as received” H-2 aluminum as measured by the Coulter

LS13320 light scattering particle sizer.

Milling Media

The milling media used in this study was yttria-stabilized zirconia, purchased from Advanced

Materials Inc. in sizes of 0.5, 1.0, 1.5, and 2.0 mm. The density of the media is 6.0 g/cm3. Figure

42

3-2 is an image of the 1.0 mm grinding media used in this study. In order to maintain a consistent

size distribution the media was sieved after each experiment to remove fines and fragments

caused by fracture and wear [1].

Experimental Procedures

Media Mill

The mill used in this study was a bench top Union Process attrition mill as seen in Figure 3-3.

The mills operational speed is between 500-5500 rpm. Numerous types of milling vessels and

stirrers can be equipped on this model. This study used a 750 ml stainless steel milling vessel and

a 4 bar stainless steel agitator, the bars of the agitator are approximately 60 mm in length. It is

important to note that the length of the agitator arm and the rotational rate was used to calculate

the tip speed of the mill and ultimately the kinetic energy of the grinding media. The vessel is 90

mm in diameter and 90 mm in height. Figure 3-3 is a picture of the milling vessel and the

agitator used in the study. The mill is attached to a recirculation reservoir that maintains the

temperature of the mill contents at 25oC. The mill is attached to a digital controller, which

provides speed and power control over the mill.

Milling Procedure

The mill was assembled according the specification provided in the mill manual. To assure

experimental continuity, the volume of material used and the distance between the bottom of the

agitator and the bottom of the milling vessel (1/4 in.) was maintained in all experiments. The

contents and milling sequence were performed in the following order:

1. 25 grams of H-2 aluminum powder 2. 5 grams of stearic acid 3. 300 ml of isopropyl alcohol 4. Initial dispersion 5. 400 ml of grinding media 6. Start milling experiment (sample at appropriate times)

43

The milling medium used in this study was isopropanol with 5g of stearic acid dispersant. A

more detailed description of these materials will come later in the chapter. Prior to the loading of

milling media, the mill was run for 5 min at 500 rpm to disperse the metal powder in the medium

(liquid suspension). Following the 5 minutes of dispersion the mill was ramped up to the desired

milling rotational rate. It was then shut off. The milling experiment was then restarted when the

milling media was added. Samples were taken from the mill at times of 1, 3, 5, 8, 12, 15, 30 45,

and 60 minutes then at 1.5, 2, 4, 6, 8, and 10 hours. In order to reduce the effect of the change in

volume on milling kinetics the samples removed from the mill were less than 1.0 ml. Samples

were diluted with 20 ml of isopropyl alcohol, sealed and then stored for either drying or

characterization.

At the end of each experiment, the mill was stopped and dissembled. The contents of the

mill were pored through two sieves, one of sufficient size (i.e. 1.0 mm mesh for 1.5 mm media)

to catch grinding media and another of 90 μm to catch fragments of grinding media. After the

slurry was separated form grinding media it was placed in a Nalgen® bottle for storage and later

drying. Every part of the mill that was exposed to the aluminum slurry was rigorously cleaned

with soap and water and allowed to dry in an oven before performing another experiment. The

grinding media caught in the sieve was placed in a 1000 ml Erlenmeyer flask and washed with a

3 M hydrochloric acid (HCl) solution. The contents of the flask was then emptied into a sieve

and placed in a sonic water bath. The sonicator was flushed repeatedly with water to remove

HCl. The media was then placed in an oven and allowed to dry.

Drying of Aluminum Slurry and Milling Samples

There has been a considerable amount of effort put into establishing the best way to dry a

liquid suspension. A review of the work can be found in a dissertation on dry dispersion by

44

Stephen Tedeschi [64]. This study will use a supercritical drying technique to dry samples

obtained from the milling process. When liquid CO2 is heated to above 31.2 oC in a confined

volume, CO2 becomes a meta stable fluid termed a supercritical fluid Figure 3-4. The

supercritical drying method involves solvent exchanging the suspensions fluid with that of liquid

CO2, then heating the pressure vessel above 31.2oC and releasing the meta stable fluid. The

importance of drying across each phase boundary was discussed in Tedeschi work; it was found

that supercritical drying reduced capillary forces that are present in conventional drying

techniques [64]. Figure 3-5 is the pressure vessel used in this study, it was purchased from SPI

Inc. The vessel is capable of sustaining a pressure of 2000 psi and a temperature of 50oC.

The method we used is as follows. The particle suspension samples removed during

milling was placed in a 25,000 Dalton dialysis bag and diluted with isopropyl alcohol. The

dialysis bag was used to allow diffusion of solvents, while capturing the particles. The bags were

then placed in the pressure vessel, which was then filled with liquid CO2 and allowed to sit for 2

hours. After two hours, approximately 70% of the fluid inside the vessel was released and the

vessel was again filled with CO2. The step of emptying and refilling the vessel was continued

until all the isopropyl alcohol was removed, which took approximately 10 washes. After the final

solvent exchange, the vessel was heated to above 31.2 oC and the meta stable fluid was slowly

released as a gas. The samples were then removed from the vessel and placed in Nalgen bottles

for storage and later analysis and testing.

Sample Preparation by Dispersion of Dry Powder

For many of the characterization and analytical techniques used in this study the milled

product must be dispersed in the dry form. A particle vacuum chamber was used to disperse the

powder. Samples prepared in this way were used in image analysis, obscuration tests, and mass

measurements. They were also used for calculating IR obscurant performance. Obscurant results

45

will be discussed later in the case study. The device used for this study was a Galai partial

vacuum chamber. Approximately 2 mg of supercritically dried sample was dispersed in the

chamber using 5 bars of vacuum. The amount of sample used was found by trail and error, and

was determined to be enough to give a near monolayer of particles. Figure 3-6, shows a) the

Galia chamber, as well as, b) a glass slide used for mass and image analysis measurements, c) a

silicone wafer chip used for scanning electron microscope measurements, and d) a double pass

transmission (DPT) slide used for Fourier transform infrared spectroscopy measurements

(FTIR). The exact use and importance of the samples prepared by this method will be discussed

in the appropriate characterization section.

Statistical Design of Experiment

Statistical design of experiment (DoE) is a powerful tool used to optimize and analyze

many industrial and commercial processes. This study first used statistical design to understand

and choose the parameters that are important to particle deformation during stirred media

milling. The variables studied were rotation rate, media loading, and media size. Additional

designs and analysis were used to determine the interaction between milling parameters and

define their significance. A central composite design was used to analyze the measured material

response to milling (strain) as a function of milling parameters. The DoE software used in this

study was purchased from Stat-Ease, and is called Design-Expert 7. The software is capable of

performing statistical analysis of the data, based on analysis of variance (ANOVA). It is also

capable of developing and experimental design that can then be modeled by the software.

Characterization

Characterization is a vital part of any study, it is important to understand and relate process

variable to product qualities. By characterizing and interpreting the product materials, it is

possible to determine and predict the behavior of a material or process. This study used

46

characterization techniques to measure the response of aluminum to process parameters before,

during, and after mill. The characterization techniques used in this study and the sample there

importance are discussed in the following sections.

Light Scattering

Light scattering has been used to rapidly and accurately measure particle size and size

distributions. The main principle of light scattering for particle size analysis is that light scatters

at different angles based on the size of the particle. A detector measures the angle and intensity

of the scattered light and is able to reconstruct a particle size distribution from that data. One

limitation of light scattering is that it assumes all particles are spherical for size calculations. This

limitation will be addressed in more detail in chapter 4. This study uses the Coulter LS11320

which is capable of measuring particle sizes from 40 nm to 2,000 µm. The Coulter measures the

particles size distribution of the samples taken from the mill. In order to achieve accurate

measurements, the samples from the mill are further diluted with isopropyl alcohol to a

concentration fit for size measurement. To achieve an accurate measurement from the LS11320,

light must be able to pass through the sample, the approximate concentration must be <1 %. The

data from the Coulter is used for calculations of stress, strain energy, strain, milling efficiency

and strain rate, these results will be shown in chapter 4.

The LS11320 is capable of providing data output in number, surface area, and volume

distributions. The differences in these measurements are due to how they are calculated. If the

particle size distribution were narrow, these three methods would provide equivalent. However,

if the distribution is bi-model or broad a number would appear to have smaller particles size and

a volume distribution would appear larger.

47

Microscopy and Image Analysis

This study produced high aspect ratio metallic flakes with major dimensions as large as 10

μm and minimum dimension sizes as small as 10 nm. This led to challenges in obtaining clear

images from one specific device. Some of these challenges were getting both quantitative and

qualitative flake thickness measurements due to difficulty in getting the flakes to stand

perpendicular to the surface. There were also challenges in getting quantitative particles size

measurements of the flake diameter to verify light scattering data. This challenge will be

addressed later in this chapter.

Electron microscopy

Most of the images used in this study were taken using a scanning electron microscope

(SEM). The SEM functions by focusing a beam of electrons onto a surface. The beam of

electrons then excites and emits electrons from the surface that are then detected and used to

reconstruct the surface topography. The microscope used in this study was a JEOL 6330 cold

field emission microscope. Samples for the SEM image were prepared by disseminating the

powder onto a silicone wafer and attaching the wafer to an aluminum stub with carbon tape. This

procedure allows for a conductive contact between the flakes and the instrument. SEM images

were used to verify light scattering data using image analysis software called ImagePro®. The

software was capable of thresholding the images and counting and measuring the particles. SEM

was used to study particle morphology and determine when particle breakage occurred.

Transmission electron microscope (TEM) was used in this study to measure particles size,

and crystallinity. TEM image materials by passing an electron beam through a thin slice of

sample. TEM can also determine crystallinity and microstructure of materials. Two TEMs were

used in this study, the JEOL TEM 200CX was capable of imaging at high magnification, and the

JEOL TEM 2010F was capable of measure crystallinity over a broad size range. Samples were

48

prepared for the TEM analysis by mixing the dry powder with an epoxy. The epoxy was then

allowed to cure. After curing, the epoxy was sectioned using a microtome to cut slices

approximately 100 nm thick.

Optical microscopy

Imaging was also done on an Olympus BX60 optical microscope equipped with a SPOT

Insight Digital CCD camera. The microscope was capable of magnifying and image between 2 to

100 times. This microscope requires very little sample preparation to obtain images. Optical

microscopy provided a quick way to estimate particle size and morphology. However, it was

challenging to measure particles of less than 5 μm due to the low magnification and low

resolution at that length scale.

Occhio optical particle sizer

The Occhio optical particle sizer was also used in this study. The instrument passes a

sample below a fixed high magnification CCD camera capable of imaging thousands of particles

in seconds. It then analyzes the images with Calisto software. The Occhio instrument specifies

that it is capable of measuring particles as small as 0.5 microns and as large as 3 mm. A

comparison of data between the Occhio and light scattering will be shown later.

Surface Area Analysis (BET)

Surface area analysis by gas adsorption was first achieved by Stephen Brunauer, Paul

Hugh Emmett and Edward Teller in 1938 and was later termed the BET technique [65]. BET

involves measuring the amount of gas condensed on the surface of a sample at low temperatures

and pressures. This study used the Quantachrome Autosorb 1C-MS to measure the specific

surface area of samples taken before, during, and after milling. Samples for BET analysis were

allowed to outgas under vacuum at 60oC for 12 hours before being placed in the BET for

analysis. The particle size of the before milling samples were verified by image analysis and

49

light scattering techniques. The after and during milling samples were used to study the change

in particle size as a function of milling time and were used to determine IR obscurant

performance.

Inductively Couple Plasma Spectroscopy (ICP)

Inductively coupled plasma spectroscopy is used to measure the elemental composition of

an organic or aqueous liquid. The ICP ionizes atoms is an argon plasma, the ionized atoms emit

light when electrons return to the ground state. The light is detected and correlated to specific

atoms. The instrument used in this study was the Perkin-Elmer 3200 Inductively Coupled Plasma

Spectroscope. It has the capability to measure contents to less than 1 part per million. ICP was

used to verify the purity of the starting material and to determine the mass used in the case study.

As mentioned previously approximately 2 mg of sample was disseminated into the particle

vacuum chamber. However, only a fraction of the would end up on the DPT slide, this lead to

difficulty in accurately determining the mass-transmission relation necessary for measuring

material performance as an IR obscurant. This was resolved by also disseminating on to a glass

slide of known dimensions then measuring the concentration of metal dissolved off the slide.

From the mass an accurate measurement of mass per area was obtained, which was then equated

to the mass per area of the DPT slide. The measurement of mass and obscuration values were

then used to determine the performance of the material.

Fourier Transform Infrared Spectroscopy (FTIR)

Fourier transform infrared spectroscopy (FTIR) is most often associated with

measurements used to identify compounds in liquids and on solid surfaces. The equipment used

was the Thermo Electron Magna 760. The FTIR is capable of measuring the transmission, and

reflectance of light at wavelengths from 400-4000 cm-1. This study used the FTIR to determine

the percent obscuration of light in the infrared (IR) spectrum for the development of IR

50

obscurants. The development of IR will be discussed in detail in chapters 7 & 8. As discussed

previously, sample was disseminated onto DPT slides, which were then place in the FTIR. Light

was then passed through the sample and a percent transmission was measured. This value was

then used to calculate the performance of the material, the calculation will be shown later.

Light Scattering Results

In this study, it was important to utilize techniques to characterize the response (particle

size) to varying milling conditions. This study used light scattering to measure particle size and

used image analysis to validate the techniques.

Results of Aluminum Powder

Experimental studies were performed on an aluminum powder (H-2) that deforms as a

function of milling time. It was also important to confirm light scattering particle size results for

the powders used in this study. Figure 3-7 shows an SEM image of the as received spherical

aluminum powder. The powder is roughly spherical with few non-spherical agglomerates. The

image also indicates that the particle size distribution for this particular powder may be broad as

can be seen by the large number of particles that are less than a micron and the large number that

are greater than a micron. The particle size of this powder was measured by light scattering.

Figure 3-8 gives the differential volume and number distribution data from this measurement.

Figure 3-8 also shows the error bars that represent the standard deviation obtained from three

separate measurements of the as received aluminum powder. The error bars are barely visible

due to the very low sample-to-sample variations in the measurement technique. A difference in

the volume and number distributions is apparent in Figure 3-8. If the particle size distribution

was narrow and mono dispersed the number and volume distributions would overlay each other.

However, the distribution is broad, as indicated by the SEM image. In addition, when there are

many fine particles present the number distribution tends to shift to the smaller particle size

51

range. The mean particle size diameter as measured from the number and volume distributions

are 1.0 μm and 4.2 μm, respectively.

Surface area measurements were performed on the “as received” H-2 aluminum powder

using a BET. This measurement was compared with the calculations of the specific surface area

based on the mean particle size obtained from the light scattering data. The mass of an individual

aluminum particle was calculated from the density (2700 kg/m3) for particles of mean diameters

of 1.0 μm and 4.2 μm. The calculated specific surface areas for the mean number and volume

particle sizes of 1.0 μm and 4.2 μm are 2.22 m2/g and 0.53 m2/g respectively. The measured

surface area from the BET was determined to be 1.55 m2/g. The measured and calculated values

are close only for the 4.2 micron particle indicating that the BET and light scattering techniques

are in close agreement.

Results for Aluminum Flake

However, this study focused on disk-shaped particles obtained from the deformation of the

spherical particles. It was therefore necessary to verify the light scattering techniques used in this

study with image analysis. To obtain a more accurate measurement of the aluminum flake we

employed the use of the Occhio® particle sizing system (specifications and functionality

discussed in chapter 3). Figures 3-9 and 3-10 are the particle size distribution data obtained from

light scattering and image analysis using the Occhio®. The data is for aluminum flakes that

were milled for 10 hrs. The figures show an agreement between the distributions obtained from

both measurement techniques. The mean particle size data obtained from the Occhio and light

scattering measurements were 4.6 and 6.9 μm, respectively. The Occhio counted over 16000

particles; this makes the measure more statistically significant [66]. Table 3-1 gives a

52

comparison between the light scattering and image analysis data. It can be seen that the d10, d50

and d90 have a close values.

Summary of Characterization and Light Scattering

In any application where particle size is a critical parameter, it is important to determine

what the desired form of the particle size distribution is for a process. If the number of particles

in the process is a key variable for quality control then a number distribution might be

considered. However, if the mass of the material being processed is an important process

condition the volume distribution may be important. This study will show later how the volume

of the particle is important for modeling the milling process. In this study the volume distribution

obtained from light scattering data was determined to be the most applicable.

Even though there are challenges with using light scattering to measure the particle size

and size distribution of disk shaped particles, the above work validating the technique shows that

can be used in this work. Particle size distribution of aluminum flakes obtained from light

scattering and image analysis techniques were comparable. This indicates that light scattering is

a valid technique for characterizing the major dimension of disc shaped materials.

Milling Condition Selection

Preliminary Milling Study

Stirred media milling is a complex process with numerous operating and equipment

variables affecting the performance of the mill and the final product. Some of the equipment

variables that can be manipulated are listed in Table 3-2. The vessel size, geometry, stirrer size,

and geometry were fixed. Table 3-3 gives a list of operating variables. Those variables were

media size and density, solvent, material, and surfactants. However, many other operating

variables need to be manipulated or determined in order to conduct a milling experiment.

53

Preliminary Milling Results

The best way to understand the effect of milling parameters is to vary conditions during a

series of experiments. A preliminary study of the effect of media loading on mill performance

was carried out using brass flakes obtained from US Bronze. The flake is the current material

used in infrared obscurant. Scanning electron microscope images of the starting material can be

seen in Figure 3-11. Statistical design of experiments was used to determine the effect of media

loading on deformation. A two factor design was used in this experiment. This design involves

varying the factor A (media loading) between five different concentrations (levels) and a second

factor B (rotational rate) between 3 different speeds (levels), then measuring a response (particle

size). Table 3-4 gives the experimental details used in this study. Experiments 4a-4c were used to

confirm the repeatability of the experiments. The other parameters such as milling medium and

medium volume, milling media size, material concentration and surfactant usage were held

constant; Table 3-5 gives the specific milling conditions used in this study.

The response variable used to measure mill performance was the figure of merit (FOM).

Figure of merit is a measure of how efficiently a material obscures infrared light (IR) and is an

indication of the specific surface area of the material. Equation 3-1 describes FOM where

transmission, T, is obtain from FTIR measurements, mass, m, is measured using the ICP and SA,

is the surface area of a microscope slide. The material constant, Cm, is considered proprietary.

m

slide

C

SAm

TLNFOM *

*2

100⎟⎠⎞

⎜⎝⎛

−= 3-1

A surface response plot of figure of merit versus the factors listed above can be seen in

Figure 3-12. The figure shows that as media loading is increased the figure of merit is also

increased. Higher media loading results in a larger number of grinding media that can impart

54

energy on the particles. The highest figure of merit was obtained at 21% media loading. These

results suggest that even higher media loading may further improve mill performance. However,

it was found that if media loading was increased to greater that 70% that the vessel contents

would overflow at velocities higher than 1000 rpm due to the turbulent environment inside the

mill. It was then possible to maximize mill performance by maximizing media loading, this also

allowed for the study of addition milling parameters by fixing media loading at a constant value.

Establishing Milling Conditions

This study also focused on using a specific mill and milling accessories described in Table

3-2. All milling experiments were conducted using the same mill geometry, vessel size and

stirrer geometries. Therefore, all the equipment variables used in this study were held constant.

We have established the importance of some of the operating variables on mill performance from

the preliminary study. However, numerous other operating variables can be manipulated and

may have a significant effect on mill performance.

Milling medium

The milling medium is also an important parameter for a wet stirred media milling process.

The medium affects the viscosity of the system, which in turn affects the energetic of the milling

process. The medium can also affect the ability to disperse particles during milling and the

selection of grinding aids used in particle dispersion. In this study, we milled an aluminum

material exposing a very reactive native aluminum surface in the process. It was important to

choose a milling medium that would have a favorable reaction with the exposed native aluminum

surface. Experiments performed using water as a medium led to the rapid oxidation of the native

aluminum surface. This caused the material to become brittle and fracture. It also led to the

production of hydrogen gas and the generation of large amounts of heat. It was decided that this

was not a favorable condition to make high aspect ratio metallic flakes due to the production of a

55

large amount of alumina particles. Instead, nonpolar solvents such as isopropyl alcohol or

heptane were considered. After consulting with Dr. Kremer at Silberline Inc. and reviewing

literature on metallic flake production, the explosive hazards of high surface area aluminum

powders were brought to light [10]. Milling in heptane would produce particles of high specific

surface area with a minimum amount of passivation. This could potentially be extremely

explosive. Therefore, isopropyl alcohol, which would provide a limited amount of passivation

during the milling process, was used to reduce the threat of explosions.

Mill loading and grinding aids

One of most important parameters in a wet milling study is the viscosity of the slurry. The

slurry viscosity is likely to change as a function of milling time due to increased surface area of

the product from deformation and/or particle breakage. Many researchers have investigated the

effect of viscosity on mill performance [67-69]. Viscosity directly effects the energetic of

milling. The higher the viscosity the more energy lost to viscous friction. One method for

improving performance is by using grinding aids [70]. In order to minimize the effect of

viscosity on experiments milling was done at very low solids loading to reduce any changes in

viscosity as a function of milling time. The solids loading is the amount of material that is to be

milled, in this case, it is the amount of aluminum powder added to the mill. In this experiment 25

g of aluminum was used which amounts to a solids loading of 8.3%.

At high solids loading it becomes important to select the proper grinding aid that reduce

the viscosity of the system. As stated above, this study maintained a low solids loading in the

mill thus eliminating the need for a viscosity reducing grinding aid. Generally, grinding aids are

used to disperse particles broken during stirred media milling and to prevent particle

agglomeration.

56

Dry ball mills use grinding aids to prevent coldwelding of metallic particles. The most

common grinding aid used to prevent coldwelding is stearic acid. Figure 3-13 shows the

chemical structure of stearic acid. Stearic acid is a saturated fatty acid used in firework

production to coat metallic particles and prevent oxidation. In this study, the wet milling

environment prevented the coldwelding of the metallic particles. However, stearic acid was used

to prevent oxidation of the metal during milling and after drying the product. An added benefit of

the stearic acid was that it aided in the dry dispersion of the metallic particles when used for IR

obscurants.

Milling time and temperature

Milling time is one of the most significant factors when running a milling experiment.

Time affects the overall amount of energy consumption of the mill, which will ultimately define

milling efficiently. The final product and final product quality is highly dependent on the amount

of time it has been milled. On the laboratory scale, it is possible to sample the milling process at

varying milling times in order to evaluate the temporal effects on the product. In this study,

samples were taken though out the milling experiment to identify when particle deformation

and/or particle breakage occurs. Figure 3-14 represents a typical particle size distribution data

obtained from a milling experiment where particle deformation and breakage occur. The graph

shows that samples taken from the mill up to 240 minutes show an increase in particle size, this

is due to particle deformation and an increase in the major dimensions. After 240 minutes, the

particle size begins to decrease due to particle breakage. From these results it is possible to

identify at what time particle deformation is the dominate mechanism and at what time particle

breakage was dominate. It is possible to see this effect in SEM images of samples taken at

different milling times. Figure 3-15 a-c are SEM images taken at a) 0 minutes, b) 240 minutes,

and c) 600 minutes of milling. At 0 minutes, the aluminum particles appear to be roughly

57

spherical. As milling time increases to 240 minutes the spherical particles were deformed and are

now disk shaped “silver dollar” particles. It is important to note that at roughly 240 minutes the

edges of the particles are smooth and rounded indicating that particle breakage has not occurred,

it is also important to note that since particle breakage has not occurred that the volume of the

particles in image a) and b) are equal. This observation of constant volume is important for

calculations and models developed later in this study. After 600 minutes of milling the particles

are much thinner and nearly transparent to the electron beam. They have irregular edges

indicating that breakage has occurred and the particles can no longer be taken to have the same

volume as the “as received” aluminum powder. This study focuses on the particle deformation

process; therefore, it is important to understand when deformation stops or slows and when

breakage begins. Experiments performed in this study were milled for 10 hrs with sample taken

at times of 1, 3, 5, 8, 12, 15, 30, 45 minutes and 1, 1.5, 2, 4, 6, 8, 10 hours. The time of 10 hrs

was selected because it was the longest time required to cause particle breakage.

Temperature can affect mill performance by changing the properties of the environments

such as viscosity of the medium. This study found that temperature has an added effect from the

humid Florida environment where the experiments were preformed. Initial experiments were

performed at a constant temperature of 150C; however, condensation occurred and caused large

amounts of water to be added to the vessel. This problem was solved by increasing the milling

temperature to 250C.

Media properties and rotational rate

The preliminary study showed the effect of media loading on mill performance. It was

found that greater media loading improved mill performance. This was an intuitive result

because the greater media loading, the larger the frequency of contacts that result in deformation.

For this study, the media loading was fixed at 40% for all milling experiments. There are

58

additional properties of the grinding media that affect the milling process. Those properties are

hardness, density and media size. If the media hardness is not greater than the product material

then deformation and breakage will be difficult. This study uses yttria-stabilized zirconia

grinding media (mohs hardness 9.0) to mill aluminum powder (mohs hardness 2-3). Another

property of the media that can affect its performance is the media size. In previous studies,

Hamey showed that if the media is not of sufficient size it fails to impart enough energy on the

material to cause particle breakage. The author also showed that if the media is too large it does

not perform as optimally as smaller media [71]. This study will focus on grinding media of sizes,

0.5, 1.0, 1.5, and 2.0 mm, these sizes are several orders of magnitude larger than that of the

product material (mean particle size of as received aluminum powder 4.2 μm) . Media density

can significantly affect mill performance; higher density media possess more momentum. Kwade

showed the effect of media density on particle size, higher density media yielded better mill

performance for particle breakage [72]. This study focuses on one media density for the

aluminum experiments (zirconia 6 g/cm3).

Rotation rate of the stirrer directly affects the energy of the grinding media and in turn the

amount of energy the product material experiences. For this study, rotation rate was varied from

a high of 2000 rpm to 1000 rpm. Rotational rates higher than 2000 rpm also resulted in leakage

from the vessel, similar to the effect of very high media loadings. Many authors have

investigated the affect of rotational rate on breakage [61, 72]. They found that the greater the

rotational rate the more breakage that occurred. However, it is still unknown what effect rotation

rate will have on deformation. It is even difficult to postulate this effect due to the complex

nature of media-particle-media contacts. Chapter 4 will provide results of the effect of rotational

rate on deformation.

59

Figure 3-1. Particle size distribution of as received H-2 aluminum, along with particle size data, obtained from Coulter LS 11320.

60

Figure 3-2. Image of Yttria-stabilized zirconia grinding media obtained form an optical microscope, 1mm in diameter.

61

a)

b)

Union Process Attrition Mill

Vessel Stirrer

a)

b)

a)

b)

Union Process Attrition Mill

Vessel Stirrer

Figure 3-3. Union Process stirred media mill use in study, a) stirred media mill, and b) milling vessel and agitator.

62

Figure 3-4. Phase diagram for carbon dioxide, indicating the region of supercritical fluid

formation.

63

Figure 3-5. SPI pressure vessel used for supercritical drying of powder samples taken from milling

Figure 3-6. Galia partial vacuum chamber used to disseminate powder a) chamber, b) glass slide, c) silicone wafer chip, and d) DPT slide.

64

Figure 3-7. Scanning electron microscope image of as received H-2 aluminum powder.

65

0123456789

0.1 1 10 100Particle diameter (μm)

Diff

eren

tial

%

Volume distributionNumber distribution

Figure 3-8. Differential volume and number distributions for as received H-2 spherical aluminum powder measured by light scattering.

0

1

2

3

4

5

6

7

8

9

10

1 10 100

Particle diameter (μm)

Volu

me

perc

ent (

%)

Volume percent light scattering

Cummulative volume percentdivided by 10 light scattering

Figure 3-9. Volume particle size distribution of milled aluminum flake as measure by light scattering.

66

0

1

2

3

4

5

6

7

8

9

10

1 10 100

Particle diameter (μm)

Volu

me

perc

ent (

%)

Volume percent image analysis

Cummulative volume percentdivided by 10 image analysis

Figure 3-10. Volume particle size distribution of milled aluminum flake as measured by the Occhio image analysis.

Table 3-1. Statistical data comparison for light scattering and image analysis performed using the Occhio particle counter.

Image analysis Light scatteringmean 6.6 11.2d10 5.4 3.6d50 10.1 9.6d90 22.9 20.5

67

Table 3-2. Stirred media milling equipment variables.

Mill geometry (horizontal or vertical)Mill sizeVessel size

Equipment variable

Vessel material Stirrer geometryStirrer sizeStirrer material

Table 3-3. Stirred media milling operating variables. Operating variables

Mill speed (rotational rate)Media sizeMedia material (density, hardness)

TemperatureTime

Media loading (volume fraction)Liquid medium (viscosity, density, polarity)Material loading (volume fraction)Surfactant, grinding aids, lubricants, and dispersants

Table 3-4. Experimental parameters used in the hexagonal statistical design of experiment. Experiment number Media loading (%) Rotational rate (rpm)

1 0.0 20002 5.3 7003 5.3 3300

4a 8.0 20004b 8.0 20004c 8.0 20005 16.0 7006 16.0 33007 21.3 2000

68

Table 3-5. Milling conditions for preliminary study.

Milling parameter LevelMedia size 0.5 mmMeda type ZirconaMaterial Brass flake/90gMill temperature 20 CSurfactant Steric Acid/5gMedium 2-propanol/300ml

Figure 3-11. SEM image of US Bronze “as received” brass flake used in preliminary milling experiments.

69

Rotational rate (RPM)

Figu

re o

f mer

it

Media loading (%)

Rotational rate (RPM)

Figu

re o

f mer

it

Media loading (%)

Figure 3-12. Surface response of figure of merit with respect to media loading and RPM.

O

O

HH

H

H H

HH

H H

HH

H H

HH

HH

HH

HH

HH

H H

HH

H H

HH

H H

HH

H

Figure 3-13. Stearic acid a saturated fatty acid found in many animal fats and vegetable oils.

5.38.0

16.021.3

70

0

20

40

60

80

100

0.1 1 10 100Particle size (μm)

Vol

ume

per

cent

(%)

As recieved15 min.45 min240min 600 min

Figure 3-14. Cumulative undersized versus particle size as at varying milling time for H-2 aluminum.

71

a) b) c)a) b) c)

Figure 3-15. Scanning electron microscope images of a) as received aluminum, b) milled for 240 minutes aluminum and c) milled for 600 minutes aluminum.

72

CHAPTER 4 RESULTS AND DISCUSSION

In order to understand and predict particle deformation during milling it is important to

study and thoroughly characterize the milling experiments. Prediction of deformation can be

obtained by modeling the milling process and the change in particle size. By combining these

two methods of studies, it is possible to establish a more comprehensive understanding of the

flaking process during milling. This chapter will discuss the empirical, semi-empirical and

theoretical results obtained from milling. These results will then be used to construct models that

explain and predict the effect of milling parameters on particle deformation during milling.

Experimental Results of Stirred Media Milling

Effect of Mill Parameters

The goal of this study was to develop a better understanding of particle deformation during

stirred media milling. An observation was made from preliminary milling studies that indicated

certain milling parameters resulted in larger diameter flakes and less particle breakage than other

parameters. This was an important observation because most processes that use metal flakes

prefer flakes with high aspect ratios that have not been broken. The particle size distributions

shown in Figure 4-1 are for 1.0 mm milling media at 1000 rpm. In this figure samples were taken

at different milling times. The bimodality seen in the figure is due to particle breakage. It can be

seen that bimodality was present at short milling times. This indicates that the experiment

resulted in breakage at short milling times. Figure 4-2 shows the particle size distributions for an

experiment, which used 1.5 mm milling media and 1000 rpm. In this figure, the distribution was

monomodal and shifted to larger particle sizes indicating that the particle deformation occurred

and there was only limited breakage. The differences in the effects of milling media on the

aluminum flakes were also seen visually. The samples milled with 1.0 mm media appeared dull

73

and non-reflective and showed limited pearlescence. Whereas, the 1.5 mm media produced

flakes that were highly reflective showed a high amount of pearlescence[57, 73]. Figure 4-3

shows a comparison of the maximum particle diameter achieved in each milling experiment. It

can be seen that for all rotational rates the 1.5 mm result in the largest particle size. This result

correlates well with the visual observations. In order to understand the deformation process

during milling it was necessary to study the temporal effects of media size on mean particle

diameter.

The grinding curves (mean particle size versus milling time) for this study are shown in

Figures 4-4 to 4-6. In all the experiments the mean particle size increases to some maximum

value due to the flattening of the particles. This maximum particle size was than followed by a

decrease in particle size at long milling times, which can be attributed to breakage of the

particles. It can be seen that the 1.0 mm grinding media results in breakage at the shortest

milling times and that the 1.5 mm results in the largest particle diameter. Figure 4-7 shows that

rotational rate does not have a strong influence on maximum particle size. However, rotation rate

does affect how rapidly the maximum particle size was reached. The influence of rotation rate

on deformation will be discussed in more detail later in the chapter. At first, it was not

completely understood why certain media sizes resulted in larger diameter particles and

ultimately a greater amount of deformation before breakage. However, this study developed a

theory and methodology to explain the relationship between particle deformation and milling

parameters such as media size and rotational rate. The next section compares and contrasts data

using existing models for particle breakage to the deformation data.

Kinetic Energy Model

For particle breakage, researchers have related kinetic energy to the fineness of the

product. Several researchers have shown that the size of grinding media can significantly affect

74

the particle breakage and particle deformation process during milling [14, 21, 63, 71]. Media size

is an important parameter in Kwade’s equations of stress intensity (SI) (Equations 4-1). Stress

intensity is simply the kinetic energy (KE) of the grinding media in liquid slurry. In Equation 4-

1, Dp is the diameter of the milling media, υ is the linear velocity of the media, and ρf and ρp are

the density of the fluid medium and milling media respectively. A more detailed discussion of

Kwade’s equations can be found in chapter 2.

( ) 23 υρρ fppDSI −= 4-1

This equation has been the basis for the scaling up of many particle breakage processes.

However, there is no data or models relating grinding media size to particle deformation during

stirred media milling. As a first step, this study applied Kwade’s models to particle deformation.

The hypothesis, equivalent to that for particle breakage, is that if higher stress intensity (KE)

resulted in a greater amount of particle breakage, than higher stress intensity (KE) may also

result in a greater amount of deformation. Selection of the milling parameters chosen for this

study was discussed in chapter 3. The effect of four grinding media sizes (0.5, 1.0, 1.5, and 2.0

mm), and three rotation rates (1000, 1500, and 2000 rpm) on the resulting deformation. Table 4-

1 gives the calculated stress intensities for all the experiments performed in this study. As media

size and rotation rate increase, the stress intensity (KE) also increases. This is due to the higher

kinetic energy resulting from the larger mass and greater velocity objects. Kwade verified the

results with experimental data for breakage, however, no one has shown whether the models are

verifiable with deformation data. Table 4-2 shows the maximum mean particle size for each

milling experiment. By comparing the data in Tables 4-1 and 4-2 it is possible to determine if

there is a relationship between kinetic energy (stress intensity) and deformation (mean particle

size). It is logical that kinetic energy is dependent on both media size and rotation rate. Thus,

75

equivalent kinetic energies could be obtained at different combinations of these milling

conditions. However, it can be seen in Figure 4-3 and Table 4-2 that deformation does not vary

with rotation rate. The energies for the [1.5 mm, 1500 rpm] and [2.0 mm, 1000 rpm] are

equivalent. Thus, according to this theory the particles sizes for these experiments should also be

equivalent. However, the maximum particle sizes differ indicating that kinetic energy can not be

used to predict deformation. This result led to develop of a new model that was not based on

kinetic energy of the grinding media, such as a contact mechanic model based on Hertz’s theory

discussed in the next section.

Stress Model

Eskin et al. derived a model that relates milling parameters to particle breakage [20]. The

basis for Eskin’s model was the use of Hertz theory to calculate a contact area, which was then

used to calculate milling efficiency. Eskin used a term called granular temperature as a

representation of velocity was used to calculate the force. In this investigation the linear velocity

is used so a more direct comparison between this model and stress intensity (KE) could be

established[74].

In order to apply Hertz theory, the contact of the colliding bodies must be elastic. In this

research, the colliding objects are spherical zirconia grinding media with an elastic modulus of

approximately 200GPa and a Poisson’s ratio of 0.31. Thus, the assumption of elastic contact is

valid. The following equations were derived from Johnson’s book “Contact mechanics”, and can

also be found in Eskin [20, 74]. In Equation 4-2 the average normal force, Fb, of identical

elastic beads is related to the Young’s modulus of the bead, Yb, the Poisson’s ratio of the bead,

ηb, multiplied by the density, ρb, times the velocity, υ, and radius of the bead, Rb.

76

( ) ( ) bbb

bb R

YF 5

65

35

2

2 215

76.0 νπρη ⎥

⎦

⎤⎢⎣

⎡−

= 4-2

The radius of the contact area, αb, was calculated from the force acting on the bead and the area

of a circle. Dividing the force by the contact area is the stress, σb, exerted at the center of the

contact area by the beads, as described by Equation 4-3 and 4-4.

( ) 31

2143

⎥⎦

⎤⎢⎣

⎡ −= bb

b

bb FR

Yη

α 4-3

2)(23

b

bb

Fαπ

σ = 4-4

Figure 4-8 is a schematic of the collision of elastic spheres. Table 4-3 gives the force,

contact radius and stress calculated from Equations 4-2, 4-3, and 4-4. It was determined that the

force increases with increasing media size and rotational rate. The media size and rotational rate

also increase the contact area. The stress for a specific rotational rate is equivalent for all media

size. This indicates that stress exerted by the grinding media is not sufficient to describe the

variations in deformation from varying media size. However, the important quantity to know is

the magnitude of the stress exerted on the particle and not the stress acting on the media.

The stress acting on the particle ultimately results in the deformation of the material. A

schematic of the particles trapped in the region between two colliding grinding media can be

seen in Figure 4-8. From the size of the contact area of colliding media and the concentration of

particles inside the mill, it was possible to calculate the number of particles in the contact area

and subsequently, the stress acting on each particle. The stress exerted on the particle, σp, was

calculated by dividing the contact stress by the number of particles in the contact area for a

specific media size, as given by Equation 4-5 and Equation 4-6. The number of particle, Np, was

77

calculated by dividing the contact area by the projected area of the particle and then multiplying

by the solids volumetric concentration of aluminum particles in the mill, c.

cR

Np

bp 2

2α= 4-5

p

bp N

σσ = 4-6

Table 4-4 gives the values for number particles in the contact area and stress acting on the

particles as a function of media size and rotational rate. It can be seen that the stress acting on the

particle decreases with increasing media size due to the larger number of particles in the contact

area. Also, the number of particles in the contact area increases with increasing rotation rate due

to the increase in contact radius, which is attributed to the milling media colliding with greater

force. The yield stress and tensile strength of aluminum are 35 MPa and 90 MPa, respectively.

However, the aluminum in this study was heavily strained, therefore, it may be more appropriate

to consider the strain hardened values of aluminum for comparison purposes. The strained

harden values of yield strength and tensile strength of aluminum are 117 MPa and 124 MPa,

respectively [31].

Using the strained hardened values and Equations 4-2 to 4-6, data was calculated and the

following results were obtained. The 0.5 mm grinding media exerts the most stress on the

material, nearly two orders of magnitude greater than the strength of the material. Such high

stress could be responsible for low amount of deformation before breakage, this result can be

seen in Figure 4-7. In the figure the maximum particle size achieved for the 0.5 mm for any

rotation rate was approximately 13 μm. It should also be noted that out of all the media size the

0.5 mm milling media result in the longest amount of time to reach the maximum amount of

deformation as can be seen by the figure, where, the 100 rpm experiment took almost 10 hrs to

78

reach the maximum particle size. This result will be explained in the next section, which will

discuss deformation rate.

Similarly, the stress of the 1.0 mm grinding media is higher than the tensile strength of

the material thus resulting in particle breakage and a minimum amount of deformation. The high

normal stress of the 1.0 mm media resulted in rapid particle breakage, which can also be seen in

Figure 4-7 and in more detail in Figure 4-1. Conversely, the 1.5 mm media exerts a stress that is

closest to the yield stress of a strain hardened aluminum material. Each compression event for

the 1.5 mm media could be considered a loading to the yield strength of the particle resulting in

finite amount of deformation. Media of this size can therefore apply the maximum amount of

deformation to the material without failure. The largest media, 2.0 mm, apply a stress to the

particle that is below the yield stress of the material and thus resulting in less deformation then

the 1.5 mm media. These results can also be seen in Figure 4-7 where the 1.5 mm results in the

most rapid deformation and the largest magnitude of deformation.

However, it can be seen in Table 4-4 that the stress acting on the particles for a specific

media size does not change significantly with rotation rate. This stability in stress values may

explain the data in Figure 4-7, which shows that the maximum deformation was not significantly

affected by rotation rate. These results are in contrast to the breakage models that state rotation

rate has a large effect on breakage. The models described above give a fundamental

interpretation of particle deformation as a function of mill parameters. However, this study has

so far neglected the influence of number frequency of media collisions on particle deformation.

The next section will discuss the effect of media size on the frequency of media collisions and

the resulting affect on deformation and deformation rate.

79

Deformation Rate

This study demonstrated that rotation rate affected the rate at which deformation was

achieved. Eskin and Kwade developed models that expressed the rate at which collisions

between grinding media take place. Kwade’s Equation 4-7, was used to determine the rate at

which media collide. In Equation 4-7, stress frequency, SF, is equal to angular velocity, ωs, times

diameter of the stirrer, Ds, divided by the diameter of the bead, Db, multiplied by milling time, T.

TDD

SFb

ss

2

⎟⎟⎠

⎞⎜⎜⎝

⎛= ω 4-7

Kwade determined the necessary stress frequency for reaching a specific material fineness. The

author found a specific fineness could be obtained by using a high stress frequency and low

kinetic energy of grinding media, or vise versa. In addition, Kwade found this relationship held

up to a point of a minimum amount of kinetic energy. Kwade considered a constant volumetric

media loading, for comparisons of stress frequency. Eskin derived a similar model, but chose to

measure the number of times a particle encounters the media. Both authors found that the

frequency was dependent on the media size and rotational rate. Table 4-5 gives the values of

stress frequency for this study as calculated using Kwade’s model. The model shows that stress

frequency increases with media size. The model also gives a linear relationship between

frequency of collisions and rotation rate. However, values in the table refer to the collision of the

media and fail to give the number of compressions the particles experiences.

The time at which the particle size begins to decrease for each experiment, was estimated

from the data in Figure 4-7, and was recorded in Table 4-6. Kwade’s model indicates that smaller

media size had the largest collision frequency, as shown in Table 4-5. When this result is coupled

with the high stress acting on the particle associated with the 0.5 mm one would expect this

experiment to approach the maximum amount of particle deformation more rapidly than the

80

larger media sizes. However, it was shown in the previous section that the 0.5 mm reached the

maximum deformation slowly. It is challenging to compare the effect of media size on the onset

of particle breakage for all the media sizes due to the complex nature of breakage. However, it is

certain that rotational rate affects particle breakage. Higher rotation rates result in a more rapid

onset of particle breakage. In addition, Kwade’s model would predict a more direct correlation

between media size and breakage, which is not the case for particle deformation as observed in

this study. In order to explain the discrepancies in these models with the experimental data it

was necessary to formulate a new model.

Therefore, in this investigation the stress frequency (Table 4-5 and Equation 4-7) was

multiplied by the number of particles in the contact area (Table 4-4 and Equation 4-5) to obtain

the total number of particles stressed as a function of milling time, Table 4-7 gives the total

number of particles stressed in 60 minutes. From Table 4-6, it can be seen that the total number

of stressing events does not change as a function of media size. However, the total number of

stressing events does change as a function of rotation rate. These results explain the increase in

the breakage as the rotation rate increases, as shown by the experimental data in Table 4-6. The

frequency model suggests that the number of collisions is only a function of rotation rate and not

of media size. This is way rotation rate only effects the time it take to achieve the maximum

amount of deformation and does not effect the actual maximum deformation achieved.

In summary, it has been found that milling media size determines the maximum amount

of particle deformation until failure. This was explained by calculating the stress acting on the

particles using Hertz’s theory. Rotational rate was found to have only a minor effect on the

maximum achievable particle size, Table 4-2. The calculation of stress acting on the particle

showed that there was a minimal amount of change in stress as a function of rotational rate. Thus

81

confirming the result that rotation rate did not have a significant effect on maximum particle

deformation. The time it took a particle to break was modeled using stress frequency. Rotation

rate was shown to affect the rate of deformation. Existing models failed to explain how rotation

rate affects particle breakage. Therefore, a new model was derived that showed rotation rate

directly influenced the number of stressing events. The models give the fundamental relationship

between media size, and rotational rate on particle deformation.

However, the models above do not predict the energy efficiency of the milling process or

give any indication on how the milling parameters affect efficiency.

Strain Energy and Milling Efficiency

Strain Energy

One of the greatest challenges in any milling operation is the measurement and calculation

of milling efficiency. It is relatively easy to measure the amount of energy input to a milling

process, however, it is very difficult to determine how the energy is utilized. Many authors have

studied the amount of energy required to break either a single particle or an ensemble, a review

of this work was given in Chapter 2 [43, 47, 75]. However, the milling process consists of

numerous breakage events and a particle will likely fracture several times before it reaches the

desired particle size. It is then difficult to determine the energy required for a particle to break to

a specific size then break again to another size. This makes calculating the energy of breakage

difficult. Generally, milling efficiency is estimated by measuring the energy input and

subtracting the energy that is expended as heat. Most mills are cooled to maintain a constant

temperature, and the heat is usually measured from the coolant. This method does not directly

establish how much of the energy went into the material itself, only the energy dissipated as heat.

Efficiency calculated from this method does not represent the milling efficiency to cause particle

breakage, thus making it difficult to optimize the milling process.

82

However, the particle deformation process is unique in that the number of particles does

not change and the energy that goes into deformation is stored in the material as strain energy.

From measurements of the amount of deformation the material experienced, it was possible to

calculate the strain of the material. From the strain, it was then possible to determine the strain

energy. The strain energy was then used to calculate milling efficiency as a function of milling

parameters.

Usually strain is directly measured by studying the change in dimensions of the object. In

this study, it is difficult to measure all the dimensions of the particles being strained. It was

shown in Chapter 3 that light scattering could be used to characterize that major dimension of the

particles. However, there is no direct method for characterizing the minimum dimension, i.e.,

thickness of the flakes. Thickness was calculated by considering there was no change in the

volume of the material up to the point where the material fails. Failure is taken to be the point at

which the mean particle size begins to decrease. Equations 4-8, 4-9, and 4-10 were used to

calculate the thickness of the flake by calculating the volume of the “as received” particles. In

Equation 4-8, Vs is the volume of the “as received” spherical aluminum particles and Dp,o is the

diameter of the “as received” aluminum particles. The volume of the “as received” sphere is

equal to the volume of the flake in Equation 4-9. The volume of the flake was calculated using

the equation for the volume of a cylinder, Vcyl (a flake is essentially a cylinder with a small

height, ie., thickness), and the diameter of the flake, Dp,f, at some sampling time; tp,f is the

thickness of the flake at the corresponding sampling time. The thickness of the flake was

calculated by equating the volume of the sphere to the volume of the flake using Equation 4-10.

3,

234

⎟⎟⎠

⎞⎜⎜⎝

⎛= op

s

DV π 4-8

83

fpfp

cyl tD

V ,

2,

2 ⎟⎟⎠

⎞⎜⎜⎝

⎛= π 4-9

2,

3,

,

2

234

⎟⎟⎠

⎞⎜⎜⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛

=fp

op

fpD

D

t

π

π 4-10

The strain, ε, was then calculated form thickness of the flake by using the true stain,

Equation 4-11. A diagram for the change of the spherical particle to a flake can be seen in Figure

4-9. The true strain was calculated for every sampling time up to the point where the particle size

decreases.

op

fp

Dt

,

,ln=ε 4-11

The work hardening equation, Equation 4-12, was used to calculate the stress. The coefficient

and exponent (K and n, 180 MPa and 0.2 respectively) for the work hardening equation were

obtained form literature for aluminum [31].

nKεσ = 4-12

Figure 4-10 is the stress-strain curves at 1000 rpm for each media sizes. The 1.5 mm media

yields the highest strain for all the experiments at 1000 rpm rotational rate. Similar behavior can

be seen in the 1500 rpm and 2000 rpm stress-strain curves, as seen in Figure 4-11 and 4-12,

respectively. The number of data points on each set of data decreases as rotational rate increases

due to the more rapid particles breaking at the high rotational rates and thus shorter milling time.

Mill Efficiency

As discussed in Chapter 2, stirred media milling processes have been estimated to operate

at energy efficiencies of less than 2%. These estimates are for particle breakage processes and

84

are generally obtained from monitoring heat generated in a mill. There is no research, which

measures the amount of energy supplied to the material. The following section will demonstrate

that milling processes do not innately operate at low energy efficiencies, and will describe

methods of improving the milling efficiency for particle deformation. This study used

measurements of particle deformation to calculate the amount of energy stored in the material.

Strain energy was obtained by integrating the stress-strain curves and dividing by the

volume (volume of the particle remains constant at this point on the stress-strain curve) of the

particles. Table 4-8 is the strain energy as a function of media size and rotation rate. It is clear

that the particles milled with the 1.5 mm grinding media have the highest strain energy. It is

important to note that nearly the same strain energies were obtained at the higher rotational rates

in a much shorter amount of time.

The total strain energy divided by the energy input to the mill is milling efficiency. The

total strain energy was obtained by multiplying the strain energy by the total number of particles

in the mill. Table 4-9 gives the total strain energy from each milling experiment. The 1.5 mm

milling media resulted in the highest strain energy values, which was due to the large amount of

deformation produced by the media. The energy input into the mill was calculated using the

equations developed in Eskin [20]. In order to determine the energy input Eskin calculated the

energy for a stirred mixing tank modeled by Nagata [76]. Equation 4-13 describes the power

input, Pw, to the mill calculated from tank geometry, mill speed, and slurry density. The terms N,

H, D, and Δ, are the rotation rate, tank height, stirrer diameter and tank diameter, respectively.

HDNMP mw 2

33

Δ= ρ 4-13

Slurry density, ρm, was calculated from the density of media, ρb, liquid density, ρL, and media

solids loading, c as shown in Equation 4-14.

85

( )cc Lbm −+= 1ρρρ 4-14

M is a coefficient calculated using Equations 4-15 through 4-20. In Equation 4-15, Re is the

Reynolds number for the tank, which is calculated by Equation 4-16. The coefficients A, B, and

exponent h, are empirically determined constants [76].

h

BAM ⎟⎟⎠

⎞⎜⎜⎝

⎛++

+= 66.03

66.03

Re2.310Re2.110

Re 4-15

m

mNDμ

ρ2

Re = 4-16

In Equation 4-17, b is total stirrer diameter, and for this study b is equal to the diameter of the

stirrer multiplied by the number of stirrer, four (four stirrer arms on the agitator).

⎥⎥⎦

⎤

⎢⎢⎣

⎡+⎟

⎠⎞

⎜⎝⎛ −

ΔΔ+= 1856.067014

2DbA 4-17

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛

Δ−⎟

⎠⎞

⎜⎝⎛ −

Δ−

=Db

B14.15.043.1

2

10 4-18

42

75.05.241.1 ⎟⎠⎞

⎜⎝⎛

Δ−⎟

⎠⎞

⎜⎝⎛ −

Δ−

Δ+=

bDbh 4-29

The dynamic slurry viscosity, μm, used in Equation 4-16 was calculated by Equation 4-20.

( )[ ]cccLm 20exp0019.0105.21 2 +++= μμ 4-20

Table 4-10 gives the values of the mill geometry and mill operating constants used in Equations

4-13 through 4-20. Mill power was then multiplied by the mill volume and milling time to obtain

the energy of the mill as a function of time. Equation 4-21 gives milling efficiency, η, which is

equal to total strain energy, SET, divided by mill energy, Em.

100*m

T

ESE

=η 4-21

86

The mill energy was estimated for a stirred tank, which may underestimate the true mill

energy. This is because a mill requires more power to move the high mass of milling media in

the chamber. This is not a major concern, because most milling processes can measure milling

energy directly from measurements of torque or power draw and therefore obtain a better

measurement of milling power and efficiency.

Figure 4-13 shows a plot milling efficiency versus milling time to breakage for the 0.5, 1.0,

1.5, and 2.0 mm media at 1000 rpm. At short milling times, the milling efficiency is very high

due to the rapid deformation of the material. It also can be seen that for the 1.5 mm media the

efficiency approaches 100 percent. This result is due to the method for estimating mill energy. It

was observed that the 1.5 mm milling process is much more efficient than the rest of the media

sizes, due to the more rapid and greater amount of deformation than the other media sizes. Figure

4-13 gives the efficiency for 1 hour of milling, however, the milling experiments were conducted

for 10 hours. It can be seen at 1 hour of milling that the efficiencies begin to approach the values

reported in literature of <2%. Further milling leads to an even more inefficient process. This

result would suggest that milling time is the leading cause of inefficiency. Therefore, it is

important to select parameters that will result in the most rapid deformation, such as, a high

rotation speeds.

Similar results are observed at rapid rotational rates as shown in Figures 4-14 and 4-15,

for 1500 and 2000 rpm respectively. The 1.5 mm media results in the most efficient milling

process, however it is difficult to determine from these plots whether efficiency was affected by

rotational rate. In order to understand the effect of rotational rate on mill efficiency, the results

for the 1.5 mm media was plotted in Figure 4-16 at varying rotational rates. By plotting the

milling efficiency at maximum strain, it is possible to obtain a relationship between rotational

87

rate and efficiency. Figure 4-17 is milling efficiency as a function of rotational rate. The plot

focuses on the data as it approaches particles breakage. It can be seen from the graph that the

2000 rpm speed resulted in a greater efficiency. This is due to the more rapid rate of particle

deformation. Ultimately, milling at rapid rotation rate would result in energy saving due to

increased efficiency. Rapid rotation rates would also increase time saving due to reduced

processing time. This study has shown that the benefits can be realized with no detrimental effect

to the product quality, i.e. strain. By investigating milling efficiency it was also possible to

determine the mechanisms by which energy is wasted, as discussed below.

As mentioned earlier milling processes are generally considered inefficient processes,

with efficiencies of approximately a fraction of a percent. Usually, most of the energy was

considered lost to viscous friction. This study found that milling could be a very efficient process

at short milling times, indicating that energy lost to viscous friction was grossly overestimated. It

can be assumed that the energy lost to friction is constant throughout the milling process due to

the low solids loading in the mill, and minimal change in viscosity during the milling process.

This indicates the low efficiency observed at longer milling times in this study must be due to

another mechanism. Table 4-11 shows the milling efficiency as a function of percent strain, and

table indicates that the efficiency decreases as percent strain increases. This could be explained

by the fact that it becomes increasingly difficult to cause plastic deformation in the material, due

to the increase in strain hardening with increased strain. The media contacts with the powder

results in increased elastic contacts that do not cause strain and result in a waste of energy or in

efficient milling.

In summary, this study has determined the most effective milling parameters for

maximizing particle deformation. The study demonstrated how stress acting on the particle

88

ultimately determines deformation. The strain energy stored in the material during processing

was also calculated , and the effect of milling parameters on efficiency was identified. However,

one of the goals of this study was to develop a model that predicts particle deformation based on

milling parameters. In order to achieve this goal, statistical design of experiments was used to

develop a milling model for predicting particle deformation.

Empirical Modeling of Particle Deformation through Statistical Design of Experiment

Statistical design of experiment (DOE) is a powerful tool used for, identification of

significant process parameters, development of semi-empirical models, and process optimization.

Many industries regularly employ the use of DOE in the development and implementation of

new process [77]. In Chapter 3, screening designs were used to identify the significant variables

affecting particle deformation. These designs successfully determined the effect of grinding

media loading on deformation. The results of these designs were used to plan future experiments

to study other milling parameters. The data presented in this chapter was the result of using DOE

to develop a model capable of predicting particle deformation. A central composite design

(CCD) was used for this purpose. The CCD was used to obtain the coefficients to a quadratic

model and to obtain a response surface. The surface response was used to obtain a relationship

between design variables (milling parameters) and the response variable (strain). A detailed

description of the CCD methodology can be found in Montgomery and in the design of

experiment software package Stat-Ease® [78].

Two CCD designs were used to model the milling experiments. Both designs were two-

factor designs. The first design’s data can be seen in Table 4-12. The media size for this design

was varied from 0.5 to 1.5 mm and the rotation rate was varied from 1000 to 2000 rpm.

Repetitions were used for the [0.5 mm, 1500 rpm], [1.0 mm, 1000], and [1.0 mm, 2000rpm] to

insure repeatability. The total design involved 12 experiments and the parameters modeled in this

89

study were rotation rate, media size, and the interaction between media size and rotation rate.

The analysis of variance (ANOVA) results are shown in Table 4-13. This study used a

significance level of 5 % or a confidence interval of 95 %, because this is a standard method of

determining statistical significance. It can be seen that the p-value for the model is 0.0165, which

means the model is statistically significant .When the p-value is less than 0.05 then it means the

terms in the model (media size and rotation rate) have a significant effect on the response

variable (strain). Equation 4-22 is developed based on the DOE and is in terms of coded factors.

The coded factors allow for a direct comparison of the coefficients in the equation. If the terms

were uncoded or the actual terms it would be necessary to normalize the equations by the

magnitude of the factors in order to evaluated there affects. For example, rotational rate has a

numerical value three orders greater than that of the media size 1000 rpm compared to 1.0 mm.

Which means the coefficient of the rotational rate in actual terms would need to be three orders

of magnitude less for the media and rotation rate to have a similar effect on strain.

The coefficients of the coded equation represent the significance of that factor effect on the

response, higher magnitudes of the coefficients indicate greater significance. In Equation 4-22, A

is the coefficient for rotation rate, B is the media size, and ε is the strain at failure.

22 54.0062.0067.02.012.018.2 BAABBA +−−+−=ε 4-22

From the equation, it can be seen that the media size (B) has the greatest effect on strain

and that the interaction between media size and rotation rate (A) has the smallest effect on strain.

To accurately model the mill performance it is important to model the process with respect to the

actual milling parameters.

90

Equation 4-23, models the design in terms of the mill parameters. The model was used to

predict the strain with respect to rotation rate and media size, within the framework of this design

(i.e. between 1000-2000 rpm and 0.5-1.5 mm media).

22744 18.210*48.210*70.256.310*65.738.3 BAABBA ++−−+= −−−ε 4-23

The contour plots and surface response can be seen in Figures 4-18 and 4-19, respectively.

Figure 4-20 is a plot of standard error associated with the experiments. It can be seen that the

error was low at the center points in the study but increased towards the limits. From the surface

response, Figure 4-19, a minimum strain at failure was obtained from the 1.0 mm media. The

existence of the minimum correlates with the analysis performed previously, that also showed

that 1.0 mm media resulted in the least amount of deformation. The surface response further

confirms the result that rotational rate does not significantly influence strain. This result can be

seen by the effect on strain at different rotational rates and constant media sizes. One of the

problems with this design is that extrapolation beyond the limits of the design may provide

misleading information. For example, the surface response and model indicate larger media size

will result in higher strains. However, this study has shown from empirical and theoretical data

that this does not occur. In order to develop a stronger model a second central composite design

was constructed that would investigate the effect of milling parameters on strain, beyond the

limits of the first design.

The second composite design investigated the effect of a larger media size on strain. Table

4-14 gives a list the experiments and response used in the second design. There were 11

experiments modeled in this design with repetitions of [1.0 mm, 1000 rpm], and [1.0 mm, 2000

rpm]. Table 4-15 gives the analysis of variance results for the second design. The p-value for this

design was 0.008, which means the model is statistically significant. Coded variable were used to

91

determine the significance of the milling parameters on strain. Equation 4-24 is the second

design’s model in terms of coded variables.

22 58.005.0045.018.012.085.2 BAABBA −−−+−=ε 4-24

The coefficients of the coded equation indicate the magnitude of the effect on the strain.

The rotation rate has a negative affect on strain meaning increasing rotational rate will decrease

strain. However, the media size has a greater effect than rotational rate, with a strong negative

second order effect. The second order effect of media size ultimately leads to a maximum in

strain at intermediate media sizes. The interaction term AB has a small coefficient, which means

that there is only a minor effect on strain from the combination of media size and rotational rate.

Equation 4-25 is the model for the second central composite design in actual terms. This model

can be used to predict maximum deformation within limits of the design.

22743 32.210*01.210*80.104.710*11.168.1 BAABBA −+−+−−= −−−ε 4-25

Figures 4-21 and 4-22 are the contour and surface response plots for the second model. Both

graphs indicate that an optimum amount of stress may be obtainable with grinding media of

approximately 1.6 mm. The plots also show that there is little effect on the deformation with

respect to rotational rate, which further confirms the qualitative result observed earlier in Figure

4-7. Figure 4-23 give a plot of the interaction between media size and rotational rate. If there was

a significant interaction the curves would intersect, but as they are, there is only a slight

interaction at the 1000 rpm rotation rate.

The small interaction terms seen in the first and second designs shown here strengthens the

hypothesis that stress determines the magnitude of particle deformation. This is because stress is

a function of media size and only moderately effected by rotational rate. It also strengthens the

theory that stress frequency is constant as a function of media size. The stress frequency only

92

varies as a function of rotational rate and constant as a function of media size. Both the proposed

models for stress and frequency indicate only a small interaction between the rotational rate and

media size. The standard error for the second central composite design can be seen in Figure 4-

24. In this model, the error increase at the limits of the rotation rate and at the highest media size.

In summary, design of experiments is a powerful tool for process optimization. In this

study, this experimental methodology enabled the development of models capable of predicting

particle deformation. This was proven by Equation 4-25 that relates media size and rotation rate

to strain. Design of experiments also allowed for the validation of the proposed milling theory

discussed previously by quantifying the effect and interaction of milling parameters. One more

method of validating the above results was to look at the changes in the microstructure of the

aluminum flake. If the number of dislocation is quantified as a function of milling time, it may

be possible to recalculate strain energy, which would offer another source of validation of the

milling models. However, this study only was able to perform a qualitative analysis with respect

to dislocation density as shown below.

Microstructure Analysis

The study of the microstructure and change to microstructure is an extensive part of

material science research. If the change in the number of dislocations could be characterized, it

may be possible to determine the energy per dislocation and ultimately the strain energy. An

attempt was made in this study to characterize the dislocations in the material by using

transmission electron microscopy (TEM). However, only information of crystallinity and flake

thickness were obtained, and the quantification of dislocation density was unsuccessful. It was

determined that the study of dislocation density was beyond the scope of this research.

Many of the processes that deform metallic flakes plan on the material to coldwelding to

refine the microstructure[48]. This study did not observe coldwelding taking place, and that the

93

wet milling process used in this study prevented the coldwelding of the metal powder. In order to

confirm these results transmission microscope images and diffraction patterns of the powder

before and after milling were taken. Figure 4-25 is a TEM image of an “as received” aluminum

particle and Figure 4-26 is the diffraction pattern for the particle. It can be seen from the

diffraction pattern that the aluminum particle in this study is single or nearly a single crystal.

Many more pictures would be needed to obtain a statistical representation of crystallinity,

however, the particles sampled here all gave similar results for crystallinity. Upon initial

inspection of the images, the dark regions in the image were thought to be grains; however,

Figure 4-26 shows a single crystal diffraction pattern which means they cannot be grains. The

discrete points indicate a single crystal pattern; a polycrystalline material would have filled or

nearly filled rings. Samples from the 1.5 mm, 1000 rpm milling experiments after 4 hr of milling

were sectioned and then imaged using a transmission electron microscope. The flakes in Figure

4-27 are approximately 100-200 nm thick after 4 hours of milling and this compares closely with

the estimated thickness from calculation of 200 nm. This indicates that the assumption that only

a small amount of failure has occurred and that the flakes maintain a constant volume was

correct. Figure 4-28 gives the diffraction pattern of a milled flake, which appears to be that of a

single crystal material as described above. This result confirms that coldwelding has not taken

place. If coldwelding was present the diffraction pattern of the milled flake would be

polycrystalline due to the welding of multiple particles together. It is possible to obtain

information about lattice strain and dislocation density from the TEM. However, this work was

beyond the scope of this dissertation.

Summary

This study has developed a fundamental relationship between milling parameters and

particle deformation. Through investigations of milling mechanics, it was possible to determine

94

the stress exerted on a particle as a function of rotational rate and grinding media size. The study

determined, for the first time, the frequency at which a particle was stressed during milling. It

also established a relationship between milling parameters and frequency. A novel approach was

used to calculate milling efficiency based on strain measurements and strain energy calculations.

Conformation of the frequency and stress models were obtained from statistical design of

experiment. A predictive model for particle deformation as function of milling parameters was

also developed using statistical design. Finally, TEM studies were performed that confirmed the

thickness calculations used in the strain measurements and the crystallinity of the material. The

above work is a significant step in the understanding of the deformation process during milling.

95

0

1

2

3

4

5

6

7

8

0.1 1 10 100Particle diameter (μm)

Volu

me

perc

ent (

%)

"as received" 15 minutes2 hours4 hours10 hours

Particle breakage

Particle deformation

0

1

2

3

4

5

6

7

8

0.1 1 10 100Particle diameter (μm)

Volu

me

perc

ent (

%)

"as received" 15 minutes2 hours4 hours10 hours

Particle breakage

Particle deformation

Figure 4-1. Volume percent particle size distributions for experiments using 1.0 mm grinding media at 2000 rpm. Bimodality in the particle size distribution is indicative of particle deformation and particle breakage occurring simultaneously.

96

0

1

2

3

4

5

6

7

8

9

0.1 1 10 100

Particle diameter (μm)

Volu

me

perc

ent (

%)

"as received" 15 minutes2 hours4 hours10 hours

Particle deformation

0

1

2

3

4

5

6

7

8

9

0.1 1 10 100

Particle diameter (μm)

Volu

me

perc

ent (

%)

"as received" 15 minutes2 hours4 hours10 hours

Particle deformation

Figure 4-2. Volume percent particle size distributions for the experiments with 1.5 mm grinding media at 1000 rpm, a visible shift in the particle size distribution to larger sizes is seen due to particle deformation.

97

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5

Media SIze (mm)

Mea

n pa

rticl

e si

ze (

m)

1000 rpm1500 rpm2000 rpm

Mill Speed

6

8

10

12

14

16

18

0 0.5 1 1.5 2 2.5

Media SIze (mm)

Mea

n pa

rticl

e si

ze (

m)

1000 rpm1500 rpm2000 rpm

Mill SpeedMill Speed

Figure 4-3.Maximum mean particle size achieved for each milling experiment versus media size, the 1.5 mm milling media produced the largest amount of deformation.

98

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

( μm

)

0.5 mm zirconia media1.0 mm zirconia media1.5 mm zirconia media2.0 mm zirconia media

Figure 4-4. Particle deformation versus milling time at a milling speed of 1000 rpm for varying grinding media sizes.

99

0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

( μm

)

0.5 mm zirconia media1.0 mm zirconia media1.5 mm zirconia media2.0 mm zirconia media

Figure 4-5. Particle deformation versus milling time at a milling speed of 1500 rpm for varying grinding media sizes.

100

0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

( μm

)0.5 mm zirconia media1.0 mm zirconia media1.5 mm zirconia media2.0 mm zirconia media

Figure 4-6. Particle deformation versus milling time at a milling speed of 2000 rpm for varying grinding media sizes.

101

0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μm

)

1000 rpm

1500 rpm

2000 rpm

0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μm

)

1000 rpm

1500 rpm

2000 rpm

0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μ

m)

1000 rpm

1500 rpm

2000 rpm0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μ

m)

1000 rpm

1500 rpm

2000 rpm

a) 0.5 mm mediab) 1.0 mm media

d) 2.0 mm mediac) 1.5 mm media

0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μm

)

1000 rpm

1500 rpm

2000 rpm

0

2

4

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8

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14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μm

)

1000 rpm

1500 rpm

2000 rpm

0

2

4

6

8

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12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μ

m)

1000 rpm

1500 rpm

2000 rpm0

2

4

6

8

10

12

14

16

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Mea

n pa

rtic

le d

iam

eter

(μ

m)

1000 rpm

1500 rpm

2000 rpm

a) 0.5 mm mediab) 1.0 mm media

d) 2.0 mm mediac) 1.5 mm media

Figure 4-7. Mean particle size versus milling time as a function of rotation rate, a) 0.5 mm grinding media, b) 1.0 mm grinding media, c) 1.5 mm grinding media, and d) 2.0 grinding media.

Table 4-1. Calculated stress intensity for experiments performed in this study. The table indicates that it is possible to achieve equivalent energies and different milling conditions.

Table 4-2. Maximum mean particle size of milling experiments. Even though the kinetic energy of some of the milling experiments are equivalent the maximum particles sizes differ.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 3 21 69 1601500 6 46 160 3702000 10 82 280 660

Stress intensity *10^-5 (joule)

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 11 11.0 +/- 0.6 16 121500 13.0 +/- 0.3 9 15 122000 11 9.4 +/- 0.8 14 11

Maximum mean particle diameter at failure (μm)

102

Fb

Fb

bα

Rb

Aluminum particles

Media

Media

Fb

Fb

bα

Rb

Aluminum particles

Media

Media

Figure 4-8. Contact between colliding elastic spheres. Aluminum particles are caught in the contact area between the media.

103

Table 4-3. Force, radius of contact area, and stress acting on the milling media as a function of media size and rotation rate (calculated using Hertz theory).

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 3.5 14 32 561500 5.7 23 52 922000 8.1 32 73 130

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 1.4 2.9 4.3 5.71500 1.7 3.4 5.0 6.72000 1.9 3.8 5.7 7.5

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 8300 8300 8300 83001500 9700 9700 9700 97002000 11000 11000 11000 11000

Force of milling media (N)

Radius of contact area of milling media *10^-5 (m)

Stress acting on milling media (MPa)

Table 4-4. Number of particles stressed in a single collision between grinding media and the

stress exerted on an individual particles.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 7 30 67 1191500 10 41 92 1642000 13 52 116 206

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 1115 279 124 701500 948 237 105 592000 845 211 94 53

Stress acting on an individual particle (MPa)

Number of 4.2 μm diameter "as received" aluminum particles in contact area

Table 4-5. Stress frequency as calculated from Kwade’s model. The frequency is the number of

times milling media collide with each other.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 54 14 6 31500 81 20 9 52000 110 27 12 7

Stress frequency (Hz) *10^8 in 60 minutes of milling

104

Table 4-6. The time required to reach the maximum particle diameter. As milling speed increases the time it takes to obtain the maximum particle diameter decreases.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 36000 14400 36000 280001500 14400 1800 14400 54002000 14400 3600 3600 2700

Milling time at breakage (second)

Table 4-7. Total number of particle compressions in 60 minutes, as calculated using stress frequency and number of particles, Equation 4-2 and 4-6.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 4 4 4 41500 8 8 8 82000 14 14 14 14

Number of particle compressions in 60 minutes *10^10 (Hz)

Dp,0

Dp,f

tp,f

Dp,0

Dp,f

tp,f

Figure 4-9. Diagram of the change in dimensions of particle and the measurements used to calculate stress and strain.

105

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

a)

c) d)

b)

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

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250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

a)

c) d)

b)

Figure 4-10. Stress-strain behavior for experiments performed at 1000 rpm a) 0.5 mm media, b) 1.0 mm media, c) 1.5 mm media, and d) 2.0 mm media.

106

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

a)

c) d)

b)

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

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250

0 1 2 3

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

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250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

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250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

a)

c) d)

b)

Figure 4-11. Stress-strain behavior for experiments performed at 1500 rpm a) 0.5 mm media, b) 1.0 mm media, c) 1.5 mm media, and d) 2.0 mm media.

107

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

0.5 mm media

a)

c) d)

b)

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

0.5 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

2.0 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

1.0 mm media

0

50

100

150

200

250

0 1 2 3

Strain

Stre

ss (M

Pa)

1.5 mm media

0

50

100

150

200

250

0 0.5 1 1.5 2 2.5

Strain

Stre

ss (M

Pa)

0.5 mm media

a)

c) d)

b)

Figure 4-12. Stress-strain behavior for experiments performed at 2000 rpm a) 0.5 mm media, b) 1.0 mm media, c) 1.5 mm media, and d) 2.0 mm media.

Table 4-8. Strain energy per particle for deformation study.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 1.6 1.5 2.2 1.71500 1.9 1.3 2.1 1.82000 1.6 1.2 2 1.7

Strain energy per particle *10^-8 (joule)

108

Table 4-9. Total strain energy for deformation study. The 1.5 mm media milling experiments resulted in the largest amount of stain energy.

Rotation rate (rpm) 0.5 mm media 1.0 mm media 1.5 mm media 2.0 mm media1000 3900 3700 5300 42001500 4400 3100 5000 43002000 3800 2970 4700 4000

Total strain energy for each milling experiment (joule)

Table 4-10. List of constants for equations used to calculate milling power

0.533

0.00286 kg/(m*s)

0.028 m

785 kg/m^3

6000 kg/m^3

0.09 m

0.06 m

0.05 m

1000, 1500, 2000 rpm

ValuesConstants

0.533

0.00286 kg/(m*s)

0.028 m

785 kg/m^3

6000 kg/m^3

0.09 m

0.06 m

1000, 1500, 2000 rpm

ValuesConstants

c

b

DHN

L

L

b

μ

ρ

ρ

Δ

109

0

20

40

60

80

100

120

0 500 1000 1500 2000

Milling time (sec)

Milli

ng e

ffici

ency

, η (%

)

0.5 mm media, 1000 rpm1.0 mm media, 1000 rpm1.5 mm media, 1000 rpm2.0 mm media, 1000 rpm

Figure 4-13. A plot of milling efficiency as a function of milling time at 1000 rpm, for all media sizes.

110

0

5

10

15

20

25

30

35

40

0 500 1000 1500 2000

Milling time (sec)

Milli

ng e

ffici

ency

, η (%

)

0.5 mm media, 1500 rpm1.0 mm media, 1500 rpm1.5 mm media, 1500 rpm2.0 mm media, 1500 rpm

Figure 4-14. A plot of milling efficiency as a function of milling time at 1500 rpm, for all media sizes.

111

0

5

10

15

20

25

0 500 1000 1500 2000

Milling time (sec)

Milli

ng e

ffici

ency

, η (%

)

0.5 mm media, 2000 rpm1.0 mm media, 2000 rpm1.5 mm media, 2000 rpm2.0 mm media, 2000 rpm

Figure 4-15. A plot of milling efficiency as a function of milling time at 2000 rpm, for all media sizes.

112

0

10

20

30

40

50

60

70

80

90

100

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Milli

ng e

ffici

ency

, η (

%) 1.5 mm media, 2000 rpm

1.5 mm media, 1500 rpm

1.5 mm media, 1000 rpm

Efficiency at failure

0

10

20

30

40

50

60

70

80

90

100

0 5000 10000 15000 20000 25000 30000 35000 40000

Milling time (sec)

Milli

ng e

ffici

ency

, η (

%) 1.5 mm media, 2000 rpm

1.5 mm media, 1500 rpm

1.5 mm media, 1000 rpm

Efficiency at failure

Figure 4-16. A plot of milling efficiency as a function of milling time for the 1.5 mm at varying rotational rates.

113

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1000 10000 100000

Milling time (sec)

Milli

ng e

ffici

ency

, η (

%)

1.5 mm media, 2000 rpm

1.5 mm media, 1500 rpm

1.5 mm media, 1000 rpm

Figure 4-17.A plot of milling efficiency at failure, right side of Figure 4-13 used for comparison of efficiencies as a function of rotational rate.

Table 4-11.Milling efficiency as a function of percent amount of strain the material has experienced at 1000 rpm and varying media size. The 1.5 mm media reaches over 60 % of the maximum strain while milling at 37% efficiency. The last few percent of the maximum strain result in the most inefficient milling.

Percent of total strain Mill efficiency Percent of total strain Mill efficiency Percent of total strain Mill efficiency23 8 37 14 64 3750 2 57 9 76 1769 0.8 76 3 83 491 0.4 92 1 91 2

0.5 mm media 1.0 mm media 1.5 mm media

114

Table 4-12. Experimental design for central composite design 1. Factor 1 Factor 2 Response

Run A: Rotation rate (rpm) B: Media size (mm) Strain at failure

1 1500 1.5 2.89

2 1000 1 2.41

3 2000 1.5 2.72

4 1500 1 1.95

5 1000 1 2.26

6 1500 0.5 2.70

7 2000 0.5 2.31

8 2000 1 2.17

9 2000 1 1.88

10 1000 1.5 3.04

11 1000 0.5 2.36

12 1500 0.5 2.63

Table 4-13. Analysis of variance for the central composite design 1 described in Table 4-12. Sum of Degrees of Mean F p-value

Source Squares Freedom Square Value Prob>F

Model 1.222 5 0.244 7.141 0.0165

A: Rotation rate 0.123 1 0.123 3.579 0.1074

B: Media Size 0.261 1 0.261 7.613 0.0329

AB 0.018 1 0.018 0.532 0.4931

A^2 0.009 1 0.009 0.276 0.6182

B^2 0.812 1 0.812 23.715 0.0028

115

1000 1250 1500 1750 2000

0.50

0.75

1.00

1.25

1.50Strain at failure

2.17

2.34

2.34

2.52

2.52

2.702.88

Rotation rate (rpm)

Med

ia si

ze (m

m)

1000 1250 1500 1750 2000

0.50

0.75

1.00

1.25

1.50Strain at failure

2.17

2.34

2.34

2.52

2.52

2.702.88

Rotation rate (rpm)

Med

ia si

ze (m

m)

Figure 4-18.Contour plot for central composite design 1, a minimum strain of 2.17 can be seen at approximately 0.9 mm milling media.

116

1000 1250

1500 1750

2000

0.50

0.75

1.00

1.25

1.50

1.9

2.2

2.5

2.8

3.1

A: Rotation rate

a size Media size (mm)

Rotation rate (rpm)

Stra

in a

t fai

lure

1000 1250

1500 1750

2000

0.50

0.75

1.00

1.25

1.50

1.9

2.2

2.5

2.8

3.1

A: Rotation rate

a size Media size (mm)

Rotation rate (rpm)

Stra

in a

t fai

lure

Figure 4-19. Surface response for central composite design 1, a trough exists at the 1.0 mm media size.

117

1000 1250

1500 1750

2000

0.50

0.75

1.00

1.25

1.50

0.094

0.11075

0.1275

0.14425

0.161

Media size Media size (mm)

Rotation rate (rpm)

Stan

dard

err

or (u

nits

of s

train

)

1000 1250

1500 1750

2000

0.50

0.75

1.00

1.25

1.50

0.094

0.11075

0.1275

0.14425

0.161

Media size Media size (mm)

Rotation rate (rpm)

Stan

dard

err

or (u

nits

of s

train

)

Figure 4-20. Standard error associated with central composite design 1, error increases at the limits of the study.

118

Table 4-14. Experimental design for central composite design 2. Factor 1 Factor 2 Response

Run A: Rotation rate (rpm) B: Media size (mm) Strain at failure

1 1000 1 2.41

2 1000 1 2.26

3 1500 1.5 2.98

4 1500 2 2.55

5 2000 2 2.39

6 2000 1.5 2.72

7 1000 2 2.50

8 1500 1 1.95

9 2000 1 1.88

10 2000 1 2.17

11 1000 1.5 3.04

Table 4-15. Analysis of variance for the central composite design 2 described in Table 4-10. Sum of Degrees of Mean F p-value

Source Squares Freedom Square Value Prob>F

Model 1.216 5 0.243 11.921 0.008

A: Rotation rate 0.106 1 0.106 5.175 0.072

B: Media Size 0.230 1 0.230 11.254 0.020

AB 0.011 1 0.011 0.546 0.493

A^2 0.005 1 0.005 0.265 0.629

B^2 0.717 1 0.717 35.129 0.002

119

1000 1250 1500 1750 2000

1.00

1.25

1.50

1.75

2.00Strain at failure

2.152.33

2.50

2.50

2.68

2.68

2.85

Med

ia s

ize

(mm

)

Rotation rate (rpm)

1000 1250 1500 1750 2000

1.00

1.25

1.50

1.75

2.00Strain at failure

2.152.33

2.50

2.50

2.68

2.68

2.85

Med

ia s

ize

(mm

)

Rotation rate (rpm)

Figure 4-21. Contour plot for central composite design 2, shows a maximum at approximately the 1.6 mm media.

120

1000 1250

1500 1750

2000

1.00 1.25

1.50 1.75

2.00

1.9

2.2

2.5

2.8

3.1

A: Rotation rat B: Media size Media size (mm) Rotation rate (rpm)

Stra

in

1000 1250

1500 1750

2000

1.00 1.25

1.50 1.75

2.00

1.9

2.2

2.5

2.8

3.1

A: Rotation rat B: Media size Media size (mm) Rotation rate (rpm)

Stra

in

Figure 4-22. Surface response for central composite design 2, a peak can be seen at intermediate media size.

121

B: Media size

1000 1250 1500 1750 2000

Interaction

1.70

2.05

2.40

2.75

3.10

Rotation rate (rpm)

Stra

in a

t fai

lure

2.0 mm milling media1.0 mm milling media

B: Media size

1000 1250 1500 1750 2000

Interaction

1.70

2.05

2.40

2.75

3.10B: Media size

1000 1250 1500 1750 2000

Interaction

1.70

2.05

2.40

2.75

3.10

Rotation rate (rpm)

Stra

in a

t fai

lure

2.0 mm milling media1.0 mm milling media

Figure 4-23. A plot of the interaction between the media size and rotation rate, it can be seen that there is only a slight interaction at low.

122

1000

1250

1500

1750

2000

1.00

1.25

1.50

1.75

2.00

0.073

0.08675

0.1005

0.11425

0.128

A: Rotation rate B: Media size Media size (mm) Rotation rate (rpm)

Stan

dard

err

or (u

nits

of s

train

)

1000

1250

1500

1750

2000

1.00

1.25

1.50

1.75

2.00

0.073

0.08675

0.1005

0.11425

0.128

A: Rotation rate B: Media size Media size (mm) Rotation rate (rpm)

Stan

dard

err

or (u

nits

of s

train

)

Figure 4-24. Standard error associated with central composite design 2.

123

Figure 4-25. Transmission electron microscope image of “as received” aluminum particle.

124

Figure 4-26. Diffraction pattern obtained from particle in Figure 4-20.

125

Figure 4-27. Transmission electron microscope image of sectioned flake after 4 hours of milling.

126

Figure 4-28. Single crystalline diffraction pattern of sectioned flake after 4 hour sof milling.

127

CHAPTER 5 CASE STUDY: MATERIAL SELECTION AND DEVELOPMENT FOR INFRARED

OBSCURANTS

Introduction

U.S. Army has used obscurant smokes and clouds as a defense against spectral targeting

for many years. Recent advancements in technology have led to communication and detection

systems functioning in the infrared and microwave region of the electromagnetic spectrum and

new obscurant materials are needed to meet these wavelengths. According to

“globalsecurity.org”, virtually all nations have access to sensors and guided munitions utilizing

the infrared portion of the electromagnetic spectrum. The widespread availability of these

devices has led the United States Military to search for the best countermeasures to mitigate their

effectiveness.

Janon Embury measured the mass extinction coefficients of many materials and later

theoretically calculated the extinction coefficients for materials depending on their shape and

size [7, 8, 79-82]. The calculations indicated that electrically conductive high aspect ratio

particles with the minor dimension in the nanometer size range and the major dimension of about

1/3rd the wavelength of light would exhibit many fold improvement over the materials currently

available. The method of choice for this purpose is to disperse fine metal flakes or rods into the

atmosphere between friendly forces and the enemy. With higher obscuration efficiency, less material

will be required, thus reducing the weight or volume of obscurant munitions carried by soldiers

or combat vehicles. Attenuation by a particulate cloud follows Beer-Lambert law, Equation 5-1,

where Io and I are incident and attenuated light intensities, α is the extinction coefficient, C is the

concentration of the particles in the light path of length L.

128

lno

I C LI α⎛ ⎞ = − ⋅ ⋅⎜ ⎟⎝ ⎠

5-1

In Equation 5-1, α is dependant on size and optical properties of the particles and its units may

be expressed on either mass or volume basis with the use of corresponding concentration and

path length units.

The goal of this study was to obtain a four fold improvement over the existing IR

obscurant material. In order to achieve this goal the army uses Equation 5-2 to gauge the

performance of the obscurant.

Figure of Merit = FoM = Y Pα ρ⋅ ⋅ ⋅ 5-2

In Equation 5-2, α is the extinction coefficient on the mass basis, ρ is the material density, Y is

the yield factor that is a measure of the ease of a material to be disseminated and is the ratio of

the mass of particulates successfully disseminated and the total mass of the material in a grenade.

The factor P is the packing factor that measures the mass fraction of material in the fill volume.

From these terms it can be seen that the figure of merit is a function of the type of material,

material properties, loading of the grenade and dissemination of the powder in the grenade. The

Particle Engineering Research Center applied a systems approach to achieve this goal by

improving every factor in the figure of merit equation (FOM). However, this study will only

focus on the selection and development of obscurant materials, for example, thinner flakes will

be used that will increase the area of coverage at a cost of less material. The other aspects of the

FOM equation can be found in a thesis by Tedeschi [64].

Development of New Obscurant Materials

In order to achieve the improvement goal, the FOM has to increase four fold. The right

hand terms in the Equation 5-2 are not mutually exclusive. First, the α is dependant on the

material. Higher α values are achieved by using high aspect ratio and electrically conductive

129

particles. Based on previous work, metal flakes and rods were expected to be ideal candidates [7,

8, 79-82]. The best shape and size of materials are flakes and rods with a major dimension

greater then 3 μm and a minimum dimension of less than 100nm and lower the better. These

high aspect ratio materials (major/minor dimension) are difficult to manufacture. The cost of the

material and processing into desired shape and dimensions must be minimized to reduce the

overall cost of the grenade. Metal nanorods with these dimensional requirements are difficult and

expensive to produce. Entanglement of fibers also results in poor dispersion and dissemination.

On the other hand, flakes nearing these dimensions have been manufactured in large quantities

for decades by milling. Metal ductility plays a significant roll in the aspect ratio of the flake that

can be produced. It is possible to obtain a higher aspect ratio with softer materials, which means

that softer materials can be made thinner, thus increasing the aspect ratio. Higher density

materials have been shown to have greater dissemination efficiencies, resulting in higher

performance. It was possible then to construct a chart of relevant material properties (ductility,

electrical conductivity, and density) to aid in the selection of candidate materials.

The relative magnitudes of density, ductility, and conductivity for several materials can be

seen in Figure 5-1. Theoretically, a material with high values in each of these areas would be and

ideal infrared obscurant. The figure shows that one such material is copper, which has a high

ductility, conductivity and density. Another possible candidate would be silver; however, silver

is a precious metal and is expensive. Aluminum is also a good candidate with respect to

conductivity and ductility; however, its low density will hurt its overall performance on a volume

basis. It is also possible to use alloys of some of these materials to increase performance.

As shown above the data presented in Figure 5-1 is a useful tool for selecting possible

materials, however, density, ductility, and conductivity are not the only material properties that

130

are important to material selection. As mentioned earlier, cost of the raw and processed material

is also important. Aluminum has been found to be pyrophoric, which means that it is possible to

ignite the aluminum powder. Copper powder does not form a passivation later, which means it

will eventually oxidize to copper oxide which will reduce its conductivity. There are also

environmental concerns for all the materials. Additional work in coating the material also being

performed in this project, however, this work is beyond the scope of this specific study.

Several materials were selected for processing from Figure 5-1. A comparison of the

experimentally measured performance of different materials is shown in Figure 5-2. This figure

shows that copper gives the highest performance followed by silver-coated copper and

aluminum. The reason for the high performance of copper is due to its high ductility, high

density and high conductivity. The performance of aluminum is relatively low because of its low

density (roughly a third that of copper). Even though tin has a high ductility and high density, it

has a low performance due to it low electrical conductivity.

A wet stirred media milling process was used to produce high aspect ratio flakes from the

raw material. This is the same process that was the focus of this dissertation, however, it was

found that milling just beyond the point of particle breakage gave the best obscurant material,

this result will be discussed later in this chapter. The milling equipment and procedures for this

study are the same that were used in the dissertation work with the exception that most of the

experiments in the case study involved longer milling times. Several of the characterization

techniques discussed in Chapter 3 were developed specifically for the measurements of the

figure of merit of the materials. However, the next section will give a brief review of these

techniques and how they were used to calculate FOM.

131

Material Characterization and Obscurant Performance Measurement Method

Particle size characterization was performed on the samples using the Coulter LS Model

13320 laser diffraction particle sizer. The specific surface area measurements are obtained from a

Quantachrome NOVA 1200 gas sorption instrument. Images of the particles were taken using a

JEOL 6330 field emission scanning electron microscope.

The FOM values were calculated from transmission data obtained from the FTIR using a

dual pass transmission (DPT) cell and from measurement of the amount of material per area. In

this measurement the powder was dispersed onto DPT slides and the transmission of IR light

through the slide was measured in a reflection mode. By this method the degree of dispersion

and material performance could be evaluated. The amount of powder used was within the

measurement error of lab balance so for a higher degree of accuracy Inductively Coupled Plasma

Spectroscopy (ICP) was used and is described in detail below. This allowed the accurate

measurement of masses well below those seen for these experiments. The material performance

was determined based on the material FOM, or the improvement of the new materials compared

to a standard material (brass flakes) supplied by the US Army.

The standard procedure used for FOM measurements is as follows. The dry powders were

dispersed in a Galai® vacuum dispersion chamber onto a glass microscope slide and a DPT

slide. The powder was allowed to settle for forty five minutes after which the DPT slide was

placed in the FTIR for measurement. The glass microscope slide was placed in a Nalgene®

bottle with a 1M HCL acid solution to dissolve the metal in order to accurately measure the

concentration using the ICP. Mass was calculated by measuring the concentration of Al in

solution, and normalized by the area of the glass slide.

The Perkin-Elmer Plasma 3200 Inductively Coupled Plasma Spectroscopy (ICP) system is

equipped with two monochromators covering the spectral range of 165-785 nm with a grated

132

ruling of 3600 lines/mm. The ICP operates on the principle of atomic emission by atoms ionized

in the argon plasma. Light of specific wavelengths is emitted as electrons return to the ground

state of the ionized elements, quantitatively identifying the species present. The system is

capable of analyzing materials in both organic and aqueous matrices with a detection limit range

of less than one part per million. This detection limit is well below the concentrations used in

these experiments and therefore allowed accurate measurement of the material mass

disseminated.

Production of Infrared Obscurant

In this project several metallic materials were measured, their FOM was compared with the

current obscurant material brass which has a FOM of 1. This study evolved over a several years,

the first material chosen to work with was the current brass material. Further milling was used to

improve the current material. The starting material was brass flake obtained from US Bronze.

The flake was produced by dry ball milling with the addition of stearic acid to prevent oxidation.

The stearic acid coating also aids in the dispersion of the brass by making the brass surface

hydrophobic.

A screening design of experiment (DOE) was followed to determine the effects of media

loading and rotational rate on the massed based FOM of brass. The milling media used in all

experiments was high-density yttria stabilized zirconia with a mean particle size of 500 microns.

The rotational rate was varied from 700, 2000, and 3300 rpm. The experimental parameters for

this study can be found in Table 5-1.

The results of the initial screening design can be seen in Figure 5-3. It was determined that

rotational rate had very little effect on FOM value and showed that as media loading increased

FOM increased. It should be noted that the effect of rotational rate on FOM is similar to that

observed in the theoretical study of deformation of aluminum. An increase of 25% in the FOM

133

was obtained from the screening design. The DOE determined that larger media loading

increased the FOM. Using the information obtained form the DOE, Figure 5-4 gives FOM for

the “as received” material, and that milled with a media volume of 480 ml of milling media. It

can be seen in Figure 5-4 that a much larger FOM is obtained when the media volume was

increased. However, it can also be seen that at high wavelengths the FOM value for high media

loading decreases more rapidly. The decrease at high wavelengths is due to the reduction in

particle size form milling. When the particle sizes become less than 1/3 the size of that

wavelength no longer scatters light at the wavelength [7, 8]. This design enabled future

experiments to set the media loading at a high concentration.

The second design used in this study was a full factorial (22) design; this involves choosing

two factors (rotational rate and media size) and two levels per factor for a total of 4 experiments.

Table 5-2 is a list of the milling parameters used in the 22 statistical design. The media loading in

this experiment was fixed at 300 ml, which is the maximum capacity of the mill. This design

measured responses of FOM and particle size at milling times of 6,12, 18, and 24 hrs. The

surface response of figure merit versus the design factors can be seen in Figure 5-5. At

increasing media sizes the figure merit increased. It was determined that the 1.5 mm media

resulted in the highest figure of merit. The increase in the FOM is due to the increased

deformation of particles.

It is important to note that particle sizes roughly 1/3 the wavelength of IR light do not

effectively scatter light at that wavelength [8]. Particle breakage in the mill can reduce the

effectiveness of the material at longer wavelengths. Figure 5-6 gives the effect of milling time on

the particle size distribution of brass. As received brass has a mean particle size of 10 μm with a

nearly normal distribution and as milling time increases the particle size decreases. The particle

134

size distribution becomes bi-modal, which is indicative of a breakage mechanism. After 24 hr the

mean particle size was approximately 2.3 μm. This means that the flakes should no longer

effectively scatter light above 7 μm. Figure 5-7 is a plot of FOM versus wavelength at varying

milling times. As milling time increased the FOM increased, this is due to increase in particle

deformation. At a milling time of 18 hrs the FOM begins to decrease at the higher wavelengths,

due to particle breakage, the affect of particle breakage on the decrease in more dramatic at 24

hrs of milling time. At 24 hrs the particle size is 2.3 μm and the wavelength where the FOM

begins to decrease is 7 μm, this agrees with the calculations made by Embury. The combination

of these designs and the theoretical studies established a basis for empirically relating milling

parameters to FOM. The designs determined that high media loadings and that the 1.5 mm

grinding media resulted in the highest performing flake. Rotation rate was found to have only a

minimal affect on FOM. These results correlate with the theoretical study of particle

deformation.

Media density was not investigated in the study of deformation of aluminum particles,

however, density is a component of all the models. Theoretically media density should affect the

stress acting on the particle and in turn affect particle deformation. Experiments were performed

to mill copper with stainless steel, zirconia, and tungsten carbide grinding media (densities of

9.8, 6.0, and 16 g/cc, respectively), Figure 5-8 gives these results. Tungsten carbide media

results in the largest amount of deformation before breakage, followed by stainless steel, and

zirconia. That indicates the highest density media, tungsten carbide density (16 g/cc), performed

the best and, zirconia, the lowest density media (6 g/cc) was the worse.

135

Summary

The above studies proved that is possible to improve the obscuration properties of existing

materials and to produce new and improved obscurants by stirred media milling. It was found

that high aspect ratio flakes could be produced by milling soft metals, that the softer the metal

the thinner the flake that could be produced. A relationship based on fundamental material

properties was derived for selecting materials that would produce the best infrared obscurant.

The relationship suggested that copper, aluminum, and silver would yield the best flakes from

milling. The study found that larger media produced a larger thinner flake; the results indicate

that the smaller media fractured the materials causing the materials to have a lower aspect ratio

that was detrimental to their performance. Denser media yield higher aspect ratio in shorter

milling time. The shorter milling times would ultimately result in economic saving if the process

was scaled up. Milling speed did not appear to have any effect on the quality of the product;

however, greater rotational rate resulted in much faster deformation. Greater rotational rates

would result in energy and time saving if the process was scaled up. During this study particle

size was closely monitor by sample from the milling during the experiments. All the experiments

showed and initial increase in the particle size at short milling times due to deformation followed

by a decrease due to particle breakage. This study found that a final optimum particle size of

approximately 5 μm yielded the highest performing obscurant.

136

Iron

Tita

nium

Tung

sten

Zinc Ti

n

Bra

ss

Al-B

ronz

e

Alu

min

um

Cop

per

Silv

er

Densi t y ( g/ cc)

Conduct i vi t y *10^-7 ( ohm-cm)

Duct i l i t y ( %)

0

10

20

30

40

50

60Density (g/cc) Conductivity *10 -̂7 (ohm-cm) Ductility (%)

Figure 5-1.A chart of relevant material properties of materials for use as an infrared obscurant.

High values in each property are preferred for candidate materials.

137

Figure 5-2. The performance of various milled metals, the copper has the highest performance to

due to the properties being the highest in all the desired area.

Table 5-1. Experimental parameters used in the statistical design of experiment used to

determine milling parameters.

Experiment Media volume (ml) Rotation rate (rpm)1 0 20002 40 7003 40 3300

4a 60 20004b 60 20004c 60 20005 120 7006 120 33007 160 2000

138

Rotation rate (rpm)Media volume (ml)

Figu

reof

Mer

it

Rotation rate (rpm)Media volume (ml)

Figu

reof

Mer

it

Figure 5-3. The results of the initial design of experiment, indicating that higher media loading

increase the performance of the material.

139

0.7

0.9

1.1

1.3

1.5

1.7

1.9

3 5 8 10 13 15wavelength (um)

Figu

re o

f Mer

it

Brass As ReceivedRun 8 (480ml/700rpm)As received brassMedia volume of 480 ml

0.7

0.9

1.1

1.3

1.5

1.7

1.9

3 5 8 10 13 15wavelength (um)

Figu

re o

f Mer

it

Brass As ReceivedRun 8 (480ml/700rpm)As received brassMedia volume of 480 ml

Figure 5-4. Plot of FOM for as received and ground brass at specific milling condition of 480ml

media volume and 700 rpm rotational speed

Table 5-2. Experimental parameters used in the full 2 factorial (22) statistical design of

experiment. Experiment Media size (mm) Rotation rate (rpm)

1 0.5 5002 0.5 1500

3a 1.0 10003b 1.0 10004 1.5 5005 1.5 1000

140

1.67

2.04

2.40

2.78

3.13

500

7501000

12501500

0.50

0.75

1.00

1.25

1.50

Media size (mm)Rotation rate (rp

m)

Figu

re o

f Mer

it

1.67

2.04

2.40

2.78

3.13

500

7501000

12501500

0.50

0.75

1.00

1.25

1.50

1.67

2.04

2.40

2.78

3.13

500

7501000

12501500

0.50

0.75

1.00

1.25

1.50

Media size (mm)Rotation rate (rp

m)

Figu

re o

f Mer

it

Figure 5-5. The results of the affect of varying media size and rotation rate on the performance of

a milled brass flake.

141

0

1

2

3

4

5

6

7

8

0.1 1 10 100

Particle diameter (μm)

Volu

me

perc

ent (

%)

As Received (10.3um)6hr (7.5um)12h (5.4um)r18hr (3.4um)24hr (2.3um)

Figure 5-6. Differential volume particle size distribution at increasing milling times.

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

3 5 7 9 11 13 15

Wavelength(μm)

Mas

s ex

tinct

ion

(m^2

/g)

6hr

12hr

18hr

24hr

Figure 5-7. Figure of merit versus IR wavelength for increasing milling times.

142

0

5

10

15

20

25

30

0 5 10 15 20

Milling time (hr)

Mea

n pa

rticl

e di

amet

er ( μ

m)

Tungsten Carbide Stainless Steel Zirconia

Figure 5-8. Mean particle size as a function of milling time for different density milling media,

zirconia (6 g/cc), stainless steel (9.8 g/cc), and tungsten carbide (16 g/cc).

143

CHAPTER 6 SUMMARY, CONCLUSIONS, AND FUTURE WORK

Summary and Conclusions

The goal of the study was to develop a fundamental and predictable understanding of

particle deformation during stirred media milling. This study confirmed that particle deformation

during stirred media milling is a complex phenomenon. It is difficult to understand and predict

the interaction of milling parameters with each other and the material being processed. Novel

characterization techniques and methods were used to understand the deformation process.

Statistical analysis and design of experiments were used to interpret data, develop predictive

models, and develop screening experiments for determining the most significant milling

parameters and their effect on deformation. Relationships between milling parameters, particle

deformation, and milling efficiency were established based on the fundamental theories of

contact mechanics and mechanical behavior of materials. Finally, knowledge gained from this

study was then used to develop a material for the US Army to obscure infrared light.

In order to achieve the goals of this study a systematic approach was used to study the

process including:

• Development of characterization techniques and sample preparation methods capable of measuring high aspect ratio particles

• Determine the milling parameters that have the most significant affect on particle deformation

• Establish a relationship, based on fundamental theories between, milling parameters and particle deformation

• Calculate milling efficiency with respect to milling parameters

• Develop milling models capable of predicting particle deformation

To achieve these objectives it was necessary to develop particle sizing techniques capable

of measuring high aspect particles. The predominate characterization technique used in this study

144

to measure particle size was light scattering, which was designed for measuring spherical

particles. The results proved that light scattering was capable of measuring the major dimension

of high aspect ratio particles.

The case study required the ability to measure the capability of metallic flakes to obscure

IR light. The measurement needed to be representative of how the metallic flakes would perform

in an aerosolized cloud in a combat environment. In order to obtain this measurement three

challenges had to be addressed:

• Obtain a dry dispersible powder • Disperse powder • Characterize the dispersed powder

A dry powder was obtained through supercritical drying. This technique involved the

exchange of the solvent (alcohol) to liquid carbon dioxide. Following the solvent exchanges, the

sample was then dried using the supercritical drying technique described in Chapter 3, this

method yielded an easily dispersible powder. The sample was then disseminated onto a dual pass

transmission slide and placed into and FTIR for characterization. These procedures allowed for a

measurement of grenade performance that closely relates to that observed in the field.

Several statistical designs of experiments were performed in this study. Preliminary

designs were used to determine which milling parameters were significant and required a more

rigorous study and which variables could be held constant. The preliminary designs determined

that a maximum media loading was important for causing the maximum amount of particle

deformation. The early designs also showed that rotation rate and media size could affect media

loading and required further investigation to determine their exact behavior. Milling studies at

varying media size and rotation rate showed that the 1.5 mm milling particles resulted in the

highest amount of deformation. Rotation rate was found to affect the rate of particle deformation

145

and had little to no influence over the maximum attainable deformation. Hertz’s theory was used

to explain the relationship between rotation rate, media size and particle deformation.

Hertz’s theory was used to determine the stress acting on the media, the theory was then

expanded to determine the stress acting on the particle by calculating the number of particles in

the contact area between colliding milling media. The data indicated that as media sizes

decreased the stress acting on the particle increased. The 1.5 mm media resulted in the highest

amount of deformation, due to the stress being close to the yield stress of the aluminum material.

The media sizes smaller than 1.5 mm caused stresses greater than the yield stress and thus

resulted in an early onset of particle breakage. Models that describe media frequency of contacts

failed to describe the rotation rate effects on deformation observed in this study. New models

were derived that demonstrated that media size had no effect on the number of times that

particles were stressed during the experiment. The new models also determined that rotation rate

effect the number of times a particle was stressed during the milling experiments. The empirical

data agreed with the results of the rotational rate models, however, further experimentation

would be required to obtain a strong validation of the rotation rate models.

The strain energy was calculated from assumptions of the conservation of volume of the

particles during deformation. For the first time it was possible to calculate milling efficiency

based on the strain energy. The study found that milling efficiency was the greatest for the 1.5

mm media and that efficiency decreased with milling time. A rotation rate of 2000 rpm resulted

in the highest efficiency at the point of particle breakage. The study also determined the reasons

for inefficiency during the milling processes. Previous studies had proposed that viscous friction

and heat generated in the milling process were the leading cause of inefficiency. This study

found that elastic collision which resulted in no deformation led to the inefficiency.

146

Statistical design of experiment was used to develop an empirical model capable of

predicting particle deformation during milling based on rotation rate and media size. The model

also validated the fundamental theories used to explain the behavior of milling parameters on

deformation. The statistical design showed that the interactions between media size and rotation

rate had a minimal effect on deformation. This result was also obtained by the fundamental

theory based on contact mechanics which showed the stress acting on the particle only varied

slightly with rotation rate. The statistical design predicted that a media size of 1.5 mm would

yield the most strain in the particle.

For the first time relationships between particle deformation and milling parameters based

on fundamental theories were established using Hertz’s theory and collision frequency. The

relationship between milling parameters and the stress acting on the particle could be used as a

scaling parameter to improve and design milling processes. Results of this investigation showed

that it was possible to predict milling efficiency, which could be directly applied to many milling

operations currently in use. The case study proved that the understanding developed in this study

could be directly applied to developing products used in real world applications.

Future Work

This study developed a knowledge base for milling processes where particle deformation is

desired. However, most milling processes involve particle breakage, a suggestion for future work

would be to determine correlation between the models developed in this study and the particle

breakage models. An example of this is that many researches have recognized the non linear

breakage rate kinetics in a milling process [83, 84]. A similar relation would exist between stress

acting on a particle and particle size as a function of milling time. As particle size decreases in a

breakage process, the number of particles in the contact area would increase, thus decreasing the

stress acting on the particle. It is also known that as particle size decrease the number of defects

147

in the particle also decreases, requiring higher stress to fracture the particle. These results could

be the reason that a so called “grinding limit” is observed in many milling process. One method

of testing the applicability of the models developed in this study to breakage processes would be

to reduce the number concentration of particles during the milling process, thus maintaining a

constant level of stress acting on the particles.

Another area of interest for future work would be to investigate the effect of media density

on particle deformation. Density has a direct effect on the stress acting on the particle, it would

be interesting to determine if the effect on deformation is as predicted by the models. One area,

which requires more study, is that of the frequency of media and particle contacts. The results

obtained in this study were not sufficient and conclusive enough to make up a significant theory.

More empirical data and short sampling intervals would be required to obtain a more robust

model capable of describing the effect of media size on frequency of particle contact.

One of the most novel aspects of this study was the ability to obtain an actual value for

milling efficiency. It is possible to test this method of measuring milling efficiency by

manipulating other milling variables such as viscosity and determine the effect on energy

utilization. It would also be interesting to further investigate the mechanisms of milling

efficiency such as the result of elastic collisions and their effect on inefficiency. Further work is

needed to construct milling models that are capable of predicting deformation of materials based

on milling parameters and material properties.

Finally, the goal of this study was to develop a fundamental understanding of particle

deformation during milling and develop a predictive model. In most respects this goal was

accomplished, however, it is important to develop a model that includes a time parameter. It may

148

also be possible to construct a model that includes a material property parameter and properties

of milling media, such as, media density, and hardness.

149

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BIOGRAPHICAL SKETCH

Rhye Garrett Hamey was born in Medina, Ohio. He attended Cloverleaf High

School. After high school he obtained a degree in chemical engineering at The Ohio State

University. While at Ohio State, Rhye attended a class on particle technology instructed

by visiting Professors Brian Scarlett and Dr. Brij Moudgil. Through continued contact

with Professor Scarlett, Rhye became interested in particle technology and chose to

pursue a graduate degree from the Department Materials Science and Engineering at the

University of Florida. He performed his study while working at the Particle Engineering

Research Center. In 2005, Rhye obtained a Master’s degree in Materials Science and

Engineering. After receiving his Master’s Rhye decided to continue his Ph.D. study under

the supervision of Dr. Hassan El-Shall.