International Journal of Fatigue 55 (2013) 213–219

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International Journal of Fatigue

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Comparison of fatigue failure criterion in flexural fatigue test

0142-1123/$ - see front matter � 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.ijfatigue.2013.07.004

⇑ Corresponding author. Tel.: +1 505 277 6083.E-mail addresses: tarefder@unm.edu (R.A. Tarefder), balami7@unm.edu

(D. Bateman), akswamy@unm.edu (A.K. Swamy).1 Tel.: +1 505 730 1793.2 Tel.: +1 505 277 5901.

Rafiqul A. Tarefder ⇑, Damien Bateman 1, Aravind K. Swamy 2

Department of Civil Engineering, University of New Mexico, MSC 01 1070, Albuquerque, NM 87131, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 9 October 2012Received in revised form 15 June 2013Accepted 4 July 2013Available online 11 July 2013

Keywords:Flexure fatiguePseudostiffnessViscoelastic continuum damageStiffness

This study compares traditional stiffness and energy based fatigue failure criteria with the fatigue failurecriterion based on the viscoelastic continuum damage (VECD) approach. In traditional approach, fatiguefailure is defined as the number of cycles at which the stiffness of a material reduces by 50% (Nf50). Inenergy based approach, fatigue failure is defined by the number of cycles at the maximum energy ratioor Rowe’s maximum stiffness defined by stiffness multiplied by the corresponding number of the cycle(E � N). In VECD approach, fatigue failure is defined by the number of loading cycles at the inflection pointof the normalized pseudostiffness (C) versus damage variable (S) curve. It is shown that a correlation exitsbetween traditional criteria and VECD criteria. It is shown that maximum energy ratio or Rowe’s maxi-mum stiffness based fatigue life is higher than the traditional fatigue life (Nf50). This indicates the tradi-tional approach is conservative. A strong correlation of fatigue was observed between the VECD fatiguecriterion and energy ratio based fatigue criteria. However, the fatigue life by VECD approach is always lessthan the fatigue life by energy ratio or Rowe’s maximum stiffness.

� 2013 Elsevier Ltd. All rights reserved.

� �

1. Introduction

Fatigue cracking is the most common form of distress in flexiblepavement. Due to the repeated application of damage inducingstress (and strain), the integrity of the asphalt concrete materialis lost. This loss of material integrity starts with the initiation ofmicrocracks. In the absence of sufficient healing time (or mecha-nism), these microcracks coalesce to form macrocracks, whichfinally lead to pavement failure.

Traditionally, third point loaded beam fatigue test has beenused to characterize fatigue performance under laboratory con-ditions [1]. This test includes subjecting beams to damage inducingcyclic loading (displacement control) and monitoring its stress his-tory. Using beam geometry, applied displacement and measuredload, stress and strain in the beam are calculated. Further, stiffnessof material is calculated using stress and strain history. Finally, thenumber of cycles at 50% reduction in stiffness is recorded as failureof the beam. This procedure is repeated at other strain levels to ob-tain a relationship between the applied strain and the number ofcycles to failure. The same relationship is given in Eq. (1). Some-times, initial stiffness of material is also incorporated into the fati-gue model and is given in Eq. (2).

Nf ¼ k11e

k2

ð1Þ

Nf ¼ k11e

� �k2 1E

� �k3

ð2Þ

where Nf is the number of cycles at failure, e the maximum tensilestrain in beam, E the initial stiffness and ki is the regressioncoefficients.

Under a controlled displacement mode of loading, stress in thebeam reduces with an increase in loading cycles. Due to the testingdifficulties, it is difficult to monitor development and propagationof cracks in the beam. Often, it takes a large number of load repe-titions to see macro-cracking in the beam. Due to the nature of theloading, the measured load might not decrease beyond a certainvalue. Additionally, a 50% reduction in stiffness has been arbitrarilydefined as the failure point. Such an approach might not indicatebetter utilization of the material and time resources available.

Several researchers have proposed energy based approaches toanalyze fatigue data. Due to their simplistic natures, the dissipatedenergy, cumulative dissipated energy and dissipated energy ratioapproaches are popular among the pavement engineering commu-nity [19,14,12,13,8,16,5]. However, these approaches fail to ac-count for the viscoelastic nature of asphalt concrete. On the otherhand, the viscoelastic continuum damage (VECD) approach hasshown promising results in terms of robustness and efficient utili-zation of available resources [9,6,7,17,18].

The objective of this paper is to compare the fatigue failure cri-terion based on stiffness reduction with the VECD approach. Such a

214 R.A. Tarefder et al. / International Journal of Fatigue 55 (2013) 213–219

comparison can aid the phenomenological approach in describingfatigue performance in a rational manner.

2. Background

American Association of State Highway Transportation Officials(AASHTO) defines fatigue failure as the number of cycles at whichstiffness of material decreases by 50% [1]. Initial stiffness of a beamis measured at the 50th loading cycle. This is to account for the ini-tial setting of the beam. However, one might expect stiffnessreduction from the first cycle itself. Thus, in this approach, damagein the initial few cycles is ignored. This often leads to unrealisticvalues especially at higher strain amplitude levels because at high-er strain, stiffness reduces significantly even after a few loading cy-cles [15].

Other researchers have used dissipated energy to model fatiguebehavior [19,14,12,13]. Dissipated energy is defined as energy lostto the system during each cycle of loading. Energy loss is due todamping, viscoelastic effects and damage growth. Dissipated en-ergy can be calculated by determining the area within the load-ing–unloading portion of the stress–strain curve. Mathematically,dissipated energy in each cycle i is given by Eq. (3). Further dissi-pated energy in each cycle is summed to obtain cumulative dissi-pated energy as shown in Eq. (4).

wi ¼ prampeamp sin u ð3Þ

Wi ¼XN

1

wi ð4Þ

where wi is the dissipated energy in cycle i, ramp the stress ampli-tude, eamp the strain amplitude, / the phase angle between stressand strain and Wi the cumulative dissipated energy up to cycle i.Eq. (3) is accurate when the applied strain and measured stresscurves are sinusoidal. It can be noted that these curves are con-formed to perfect sinusoidal shapes for a successful fatigue test fol-lowing the AASHTO Standard T 321 procedure.

Van Dijk and Vesser [19] found a strong relation between num-bers of cycles and cumulative dissipated energy. Pronk andHopman [12] refined the dissipated energy approach by definingthe energy ratio to check for linearity. Energy ratio is defined asthe ratio of initial dissipated energy to the dissipated energy in cy-cle i multiplied by the number of cycles. Deviation from thestraight line in the plot of dissipated energy ratio against the num-ber of cycles indicates the transition from micro-cracking tomacro-cracking in the beam. However, deviation from the straightline is subjected to individual judgment.

Ghuzlan and Carpenter [8] used the Dissipated Energy Ratio(DER) to quantify the relative change in the dissipated strain en-ergy. DER is defined as a change in the dissipated energy betweensubsequent cycles divided by the dissipated energy in the previouscycle. The expression for the DER is given in Eq. (5). Ghuzlan andCarpenter [8] found a strong relationship between DER and thenumber of cycles to failure.

DER ¼ wa �wb

wað5Þ

where wa is the dissipated energy in cycle a, wb the dissipated en-ergy in cycle b and DER is the dissipated energy ratio.

A plot of the dissipated energy ratio vs. the number of cyclesindicates three distinct regions. In the first region, the rapidlydecreasing DER indicates ‘settling’ of the beam. In the second re-gion, the DER remains fairly constant. The average DER in the sec-ond region is known as the plateau value. In the third region, DERrapidly increases. The rapid increase in the DER is considered to bethe failure point. Research by Shen and Carpenter [16] indicated a

linear relationship between the plateau value and the number ofcycles to 50% initial stiffness (both on log scale). However, due tothe overly sensitive dissipated energy difference, the plot of theDER vs. the number of cycles indicates scatter. Thus it is difficultto interpret the failure location visually as well as mathematically.

Rowe and Bouldin [15] introduced the Energy Ratio for model-ing fatigue behavior. The Energy Ratio is obtained by multiplyingstiffness by the corresponding number of the cycle (E � N) and ismeasured in kPa. For this study, the Energy Ratio is referred to asRowe’s stiffness parameter due to the fact that the failure criterionis not presented as a ratio. Rowe’s stiffness parameter is cross plot-ted against the number of cycles to find the failure location. Such aplot has two distinct regions. In the first region, the curve is mono-tonically increasing whereas in the second region it is monotoni-cally decreasing. The junction of these two regions indicates thepeak value of the stiffness parameter and represents a transitionfrom micro-cracking to macro-cracking. The peak value for thiscurve can be identified visually or by systematic search. A system-atic search locates the maximum value of E � N and then back-cal-culates the number of cycles equivalent to this peak value.

In all of the above cases, material is considered to be elastic.However, asphalt concrete exhibits rate-dependent and tempera-ture-dependent behavior. Kim [9] successfully applied theelastic–viscoelastic correspondence principle for modeling sand-asphalt mixture behavior under multi-level cyclic loading. Kim[9] found that the secant pseudostiffness (stress corresponding tomaximum pseudostrain divided by maximum pseudostrain in eachcycle) value decreases with increasing damage. Daniel [6], [7]found that the relationship between the normalized pseudostiff-ness (C1) and the damage parameter (S1) is unique for a given as-phalt concrete mix (hereafter referred to as damage characteristiccurve) under uniaxial mode of loading. The normalized pseudo-stiffness (C1), is obtained by dividing the secant pseudostiffnessby the initial pseudostiffness, while the damage parameter (S1) isa function of normalized pseudostiffness, time and material prop-erties. These parameters, C1 and S1 are explained in greater detailin the Analysis Procedure section. Swamy [17] extended the VECDmode to the flexure mode of loading (as oppose to uniaxial load-ing) and found that the damage characteristic curve is unique at gi-ven temperatures under the flexure mode of loading. Swamy andDaniel [18] found a point of inflection in the damage characteristiccurve beyond which the material loses its structural integrity at afaster rate. Also, it was observed that normalized pseudostiffness atthis inflection point depends on the mixture properties. This studyinvestigates the VECD approach to defining fatigue failure in as-phalt concrete by comparing it with traditional criterion andRowe’s stiffness approach to fatigue failure.

3. Mixtures, specimen preparation and fatigue testing

Two plant produced Hot Mix Asphalt (HMA) concrete mixturestypically used in major highways in the State of New Mexico wereused in this study. These were 25 mm and 19 mm Nominal Maxi-mum Aggregate Size (NMAS) mixtures and are designated as SP-IIand SP-III mixtures respectively. PG 64-22 and PG 70-22 binderwas used in SP-II and SP-III mixtures respectively.

Plant produced HMA mixtures were obtained in accordancewith AASHTO T 168 [2] specifications and filled in paper bags. Eachbag contained around 20 kg of loose mixture. The loose mixturewas tested for theoretical maximum specific gravity, aggregategradation and binder content. The details for aggregate gradationare presented in Table 1.

The loose HMA mixture was heated in an oven for at least 1 h tobring it to compaction temperature (151 �C). Once the loose mix-ture reached the compaction temperature, the mold in a linear

Table 1Material properties of HMA mixtures.

Specified mixture properties HMA mix design

SP-II SP-IIIMax. theoretical specific gravity (Gmm) 2.439 2.430Binder content 4.4 4.6

Percent passing sieve size 38.0 mm 100 10025.0 mm 94 10019.0 mm 85 9412.5 mm 69 809.5 mm 60 674.75 mm 35 340.075 mm 3.4 3.4

Fig. 2. Dynamic modulus mastercurves of SP-II samples.

Fig. 3. Dynamic modulus mastercurves of SP-III samples.

R.A. Tarefder et al. / International Journal of Fatigue 55 (2013) 213–219 215

kneading compactor was filled with the loose mixture. Then theloose mixture was compacted using a hydraulically operated com-pactor. Usually two beams of size 18 in. � 6 in. � 3 in. were fabri-cated at a time. Once the beams cooled to room temperature,each compacted beam was cut into two test specimens of size15 in. � 2.5 in. � 2.0 in. using a saw cutting tool. Then the bulk spe-cific gravity of the beam and percentage of air voids in the beamwere measured according to AASHTO T 166 [3] and AASHTO T269 [4] specifications respectively. As per NMDOT specifications,any beams with air voids between 5% and 6% were used for subse-quent testing.

In this study, traditional four-point bending beam fatigue test-ing apparatus was used. AASHTO T 321 [1] standards were usedfor fatigue testing. For determining the viscoelastic properties, sstrain controlled cyclic loading mode was used (See Fig. 1).

Initially, the prepared specimen was tested for its viscoelasticproperties and subsequently tested for its fatigue properties. Dur-ing the determination of viscoelastic properties, the specimen wassubjected to low strain amplitude cyclic loading to obtain itsdynamic modulus and phase angle fingerprint at different temper-atures and frequencies. The maximum strain in the specimen waslimited to 75 microstrains. Dynamic modulus and phase anglemeasurements were obtained at �10 �C to 30 �C in 10 �C incre-ments. Within each temperature, load was applied at frequenciesof 15, 10, 5, 2, 1, 0.5, 0.2 and 0.1 Hz. Using time–temperaturesuperposition principles, dynamic modulus and phase angle mas-tercurves were constructed. Dynamic modulus mastercurves forSP-II and SP-III mixtures are shown in Figs. 2 and 3 respectively.Using dynamic modulus and phase angle mastercurve coefficients,the relaxation modulus mastercurve was obtained using intercon-version technique proposed by Park and Kim [11]. Relaxation mod-ulus mastercurves for SP-II and SP-III mixtures are shown in Fig. 4.

In the second stage, fatigue testing was conducted on speci-mens to obtain fatigue properties on the mixture. All specimenswere tested at the damage inducing strain level. In this research,

Fig. 1. Preparation of asp

strain amplitudes used were in the range of 400–1200 microstrain.Table 2 presents the test parameters such as strain amplitude andpercent air voids, as well as test results such as fatigue life. It can beseen here that the percent of air voids varied from 3% to 6.5%. Thefirst five samples listed are of SP-II mixture, while the remainingsamples are of SP-III mixture.

4. Analysis procedure

Using the deflection history, load response history and geome-try of the test specimen, the maximum stress and strain in thespecimens are calculated using Eqs. (6) and (7) respectively.

e ¼ 12hd

3L2 � 4a2ð6Þ

r ¼ PL

bh2 ð7Þ

halt beam samples.

Fig. 4. Relaxation modulus mastercurves of SP-II and SP-II mixtures.

Table 2Test results from fatigue testing.

Beam ID Beam ID Gmb %AV Applied microstrain le Nf

N2 SP-II-1 2.311 5.2 400 79,008M2 SP-II-2 2.294 5.9 400 723,711I2 SP-II-3 2.315 5.1 800 11,700K1 SP-II-4 2.354 3.5 1000 1684K2 SP-II-5 2.366 3.0 1000 14,625F2 SP-III-1 2.309 5.0 800 114,001I2 SP-III-2 2.339 3.8 800 90,001E2 SP-III-3 2.273 6.5 1200 17600D1 SP-III-4 2.361 2.8 1200 2050

216 R.A. Tarefder et al. / International Journal of Fatigue 55 (2013) 213–219

where P is the load applied by actuator at time t, b the average spec-imen width and h the average specimen height, d the deflection atcenter of beam at time t, a the distance between inside clampsand L is the distance between outside clamps. Table 3 presentsthe values of these constants shown in the above equations.

Further, the relaxation modulus mastercurve is obtained usingthe dynamic modulus and the phase angle mastercurve coefficientsthrough the interconversion technique. Using the computed strainhistory and relaxation modulus mastercurve, the pseudostrain iscomputed using Eq. (8). This pseudostrain accounts for all visco-elastic effects and separates the effects of damage and healingwithin the specimen.

eRðtÞ ¼ 1ER

Z t

0Eðt � sÞ de

dsds ð8Þ

where ER is the reference modulus, E(t) the relaxation modulus, ethe computed physical strain, t the elapsed time between the timeloading began and the time of interest and s is the time variable.

In a fatigue test, loops are seen in the cross plot of the measuredstress vs. pseudostrain. Further, the slope of these loops decreasesas testing progresses. The secant pseudostiffness (SR

i ) in any cycle iis calculated by dividing the measured stress by the maximumpseudostrain in cycle i. To account for specimen to specimen vari-ation, secant pseudostiffness is divided by the secant pseudostiff-ness in the first cycle of loading. From here onward forsimplicity, this value will be referred to as normalized pseudostiff-ness (C1). Due to the continuous growth of damage, the numericalvalue of normalized pseudostiffness continuously decreases (has avalue of 1 at the undamaged condition, 0 at complete failure). The

Table 3Fixed measurements used in beam fatigue test.

Test parameter Symbol Units (mm)

Length between outside clamps L 357Length between inside clamps a 119Height of beam h 50.8Width of beam b 63.5

variation of normalized pseudostiffness during a fatigue test isshown in Fig. 5. Using the histories of normalized pseudostiffnessand computed physical strain, the damage parameter is computed.The equation to compute damage parameter is presented in Eq. (9).

S1i ffiXN

i¼1

12ðeR

maxÞ2ðC1i�1 � C1iÞ

� � a1þa

ðti � ti�1Þ1

1þa ð9Þ

where eRmax;i is the maximum pseudostrain in cycle i, C1i the normal-

ized pseudostiffness in cycle i, S1i the damage parameter in cycle i, athe material constant and t is the time to maximum pseudostrain incycle i.

Due to the continuous growth of damage, the numerical valueof the damage parameter continuously increases (with initial valueof 0). Further, the normalized pseudostiffness is plotted against thedamage parameter to obtain the damage characteristic curve. Thiscurve was fitted with the Generalized Exponential Model (GEM)presented in Eq. (10).

C1 ¼ ek1�ðS1Þk2 ð10Þ

where C1 is the normalized pseudostiffness, S1 the damage param-eter and ki is the regression coefficients.

Visual examination of the actual damage characteristic curveand predicted values from the GEM indicated that the GEM over-predicted at lower normalized pseudostiffness values. Thus, usingdata points below which the deviation was seen were fitted withthe second order polynomials. The composite mode consisting ofthe GEM and second order polynomial was used for further analy-sis. The point of intersection of the GEM and second order polyno-mial is referred to as the point of inflection. The characteristicdamage curve obtained for the SP-II-5 specimen (SP-II mixture)is shown in Fig. 6. The same figure shows the fitted GEM and thesecond order polynomial. The number of cycles corresponding tothis inflection point has been documented as failure criterion bySwamy and Daniel [18]. In general, the damage parameter, S con-tains the state of micro-damage within the asphalt concrete (dam-age evolution law). At the inflection point, the damage parameter, Scan be related to a physical quantity such as crack length. Indeed,randomly distributed micro cracks start to coalesce to form macrocracks at the inflection point. Therefore the S-value at inflectionpoint can be used as a measure of the relative fatigue failure ofan asphalt mixture. Similarly, VECD based S-value at inflectionpoint can be compared to traditional fatigue criterion that relatesto the number of loading cycles to failure based on the applied ten-sile strain and the initial stiffness of material. More details aboutthe VECD approach as applied to the flexure mode of loading canbe found elsewhere [17], [18].

Using the computed stress and strain, stiffness in each cycle ofloading was computed. Furthermore, the stiffness ratio was com-

Fig. 5. Variation of normalized pseudostiffness and stiffness ratio with number ofrepetitions.

Fig. 6. Damage characteristic curve for SP-II-5 specimen.

Fig. 8. Damage characteristic curves for SP-III mixture.

R.A. Tarefder et al. / International Journal of Fatigue 55 (2013) 213–219 217

puted using both the initial stiffness and the stiffness correspond-ing to the number of cycles. The formula to compute the stiffnessratio is Eq. (11). The variation of Rowe’s stiffness parameter com-pared with the number of cycles is shown in Fig. 5. During thecourse of the fatigue test, Rowe’s stiffness parameter increases ini-tially and then decreases. The number of cycles corresponding tothe maximum value has been considered to be the failure pointby several researchers [15].

SR ¼ Si

S0

� �Ni ð11Þ

where SR is the stiffness ratio, Si the stiffness in cycle Ni, and S0 isthe initial stiffness.

5. Results and discussion

Damage characteristic curves for SP-II and SPIII mixtures usingalpha = 1 + 1/n are shown in Figs. 7 and 8 respectively. Alpha is amaterial constant used to determine the relaxation modulus mas-tercurve, ER, shown in Eq. (10). The slope of the ER is = n. If thematerial’s fracture energy and failure stress are constant, thenthe material constant, a, equals 1 + 1/n. On the other hand, if thefracture process zone size and fracture energy are constant, thematerial constant, a equals 1/n. Lee and Kim [10] suggested thatthe material constant forms a = 1 + 1/n, and a = 1/n, are more suit-able for the controlled strain amplitude test and controlled stressamplitude test respectively.

5.1. Comparison of parameters at maximum stiffness ratio

The number of cycles for 50% reduction in stiffness is comparedwith the number of cycles at Rowe’s maximum stiffness for SP-IIand SP-III mixtures in Figs. 9 and 10 respectively. Overall, the num-ber of cycles at Rowe’s maximum stiffness parameter was higher

Fig. 7. Damage characteristic curves for SP-II mixture.

than the number of cycles for 50% reduction in stiffness (Nf50). Thisindicates that the traditional approach of 50% stiffness isconservative.

The number of cycles at the inflection point in the damagecharacteristic curve (using alpha = 1 + 1/n) is compared with thenumber of cycles at the maximum stiffness parameter for SP-IIand SP-III mixtures in Figs. 11 and 12 respectively. In general, astrong correlation was found between the number of cycles atthe inflection point in the damage characteristic curve and thenumber of cycles at Rowe’s maximum stiffness parameter. Further,the number of cycles at the inflection point in the damage charac-teristic curve was always less than the number of cycles at Rowe’smaximum stiffness parameter.

6. Comparison of VECD method with traditional method

A scatter plot of the number of cycles at the inflection point inthe damage characteristic curve vs. the number of cycles at 50%reduction in stiffness for SP-II and SP-III mixtures are presentedin Figs. 13 and 14 respectively. The coefficient of correlation (withpower fit, both on log scales) was in the range of 0.6575–0.9245. R2

values and visual interpretation indicates a strong correlation be-tween these two parameters.

6.1. Effect of strain amplitude

The effect on the strain amplitude on the number of cycles wasinvestigated for SP-II and SP-III mixtures. Failure criteria such as50% reduction in stiffness, maximum stiffness ratio and inflectionpoint in the damage characteristic curve were used in evaluation.The plots for SP-II and SP-III mixtures are shown in Fig. 15 andFig. 16 respectively.

Fig. 9. Comparison of number of cycles at Rowe’s maximum stiffness parameterand number of cycles for 50% stiffness reduction for SP-II mixture.

Fig. 10. Comparison of number of cycles at Rowe’s maximum stiffness parameterand number of cycles for 50% stiffness reduction for SP-III mixture.

Fig. 11. Comparison of number of cycles at inflection point and number of cycles atRowe’s maximum stiffness parameter for SP-II mixture.

Fig. 12. Comparison of number of cycles at inflection point number of cycles atRowe’s maximum stiffness parameter for SP-III mixture.

Fig. 13. Comparison of number of cycles at inflection point and number of cycles for50% stiffness reduction for SP-II mixture.

Fig. 14. Comparison of number of cycles at inflection point and number of cycles for50% stiffness reduction for SP-III mixture.

Fig. 15. Effect of strain amplitude on failure criteria for SP-II mixture.

Fig. 16. Effect of strain amplitude on failure criteria for SP-III mixture.

218 R.A. Tarefder et al. / International Journal of Fatigue 55 (2013) 213–219

In the case of the SP-II mixture, with the decrease in strainamplitude, the number of cycles increased for all three cases. How-ever, this was not the case for the SP-III mixture. In the case of theSP-II mixture, R2 value was 0.797, 0.738 and 0.8195 for 50% reduc-tion in stiffness, maximum stiffness ratio and inflection point in thedamage characteristic curve respectively. For the SP-III mixture,the R2 value was 0.219, 0.403 and 0.5904 for 50% reduction in stiff-ness, the maximum stiffness ratio and the inflection point in thedamage characteristic curve respectively. This indicates that thereis better correlation between the strain amplitude and number ofcycles at the inflection point in the damage characteristic curve.

7. Conclusions

Fatigue failure criterion developed using the stiffness based ap-proach was compared with the VECD approach. The conclusions ofthis study are as follows;

R.A. Tarefder et al. / International Journal of Fatigue 55 (2013) 213–219 219

� Using the VECD approach, a point of inflection was identified inthe damage characteristic curve beyond which the materialloses its structural integrity at faster rate. This point was consid-ered the fatigue failure of the sample.� A strong correlation of fatigue was found between the VECD cri-

terion and the maximum energy ration or Rowe’s maximumstiffness criteria. Further, the fatigue life of the VECD approachwas always less than the maximum energy ratio or Rowe’s max-imum stiffness fatigue life.� A strong correlation was also found between the VECD criterion

and the traditional criterion (Nf50).� In general, maximum energy ratio or Rowe’s maximum stiffness

fatigue life was higher than the traditional fatigue life (Nf50).This indicates the traditional approach is conservative.� The effect of the strain amplitude on the fatigue life of SP-II and

SP-III mixtures was analyzed using the three different failureapproaches. In case of the SP-II mixture, with decrease in strainamplitude, the number of cycles increased for all three cases.However, this was not the case for the SP-III mixture. HigherR2 values for the inflection point in the damage characteristiccurve suggest that there is better correlation between strainamplitude and the number of cycles at inflection point in thedamage characteristic curve.

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