research article performance characterization of...

Research ArticlePerformance Characterization of Polymer ModifiedAsphalt Binders and Mixes

Nikhil Saboo and Praveen Kumar

Department of Civil Engineering Indian Institute of Technology Roorkee 247667 India

Correspondence should be addressed to Nikhil Saboo niksiitkgp88gmailcom

Received 3 November 2015 Revised 12 January 2016 Accepted 19 January 2016

Academic Editor Ghassan Chehab

Copyright copy 2016 N Saboo and P Kumar This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Fatigue sensitivity of four different asphalt binders and three different asphalt mixes was evaluated in the study Binders weresubjected to Linear Amplitude Sweep (LAS) test at three temperatures of 10 20 and 30∘C Four-point beam bending test (4PBBT)was conducted on the asphalt mixes at a temperature of 20∘C for strain amplitudes varying from 200 to 1000microstrains Tests likeretained Marshall Stability and indirect tensile strength (ITS) were also carried out to judge the mix performance Experimentalstudies demonstrated that elastomeric modified binder and mixes gave the best performance in fatigue Plastomeric modificationwas found to be highly strain susceptible and resulted in poor fatigue performance The fatigue life of stone mastic asphalt (SMA)was found to be almost five times higher than the dense graded mixes For similar strain levels the results of LAS test could belinearly correlated with the 4PBBT results

1 Introduction

High stresses due to heavy vehicular loading increase in tem-perature and introduction of new axle configuration demandeffective strengthening of pavementsUse ofmodified bindersis among themost common techniques employed to improvethe strength characteristics of bituminous mixes [1ndash3] Amidvarious forms of modification polymers tend to increase theviscoelastic response of binder and reduce its temperaturesusceptibility [4ndash8] Polymer increases the stiffness of thebinder at higher temperature while upholding flexibility atlower temperatures

The current superpave specification for performancegrading was developed mainly for unmodified binders andhas been proved to be misleading for predicting rutting andfatigue properties of modified bitumen [9ndash13] The methodemploys the parameter |119866

lowast

| sdot sin 120575 to quantify the asphaltbinder fatigue resistance |119866

lowast

| is the complex shear moduluswhile 120575 is the phase lag between the stress and strainamplitudes It is based on the concept that lower dissipatedenergy per loading cycle (120587 sdot 120574

0

2

sdot |119866lowast

| sdot sin 120575) will lead tolower distress accumulation 120574

0is the strain amplitude for

constant strain testing Hence the intermediate temperature

is determined such that |119866lowast

| sdot sin 120575 is less than 5000 kPa [14]This stiffness based parameter which is a development ofStrategic Highway Research Program (SHRP) is measuredat a fixed frequency (10 radsec) ensuring the strain to bebelow the linear viscoelastic regime of the bitumen Therecommended strain value is 1-2 The test was developedbased on the speculation that binder in pavements functionsmostly in the linear viscoelastic range and is not likely to affectbitumenrsquos properties This simple test cannot describe theactual complicated fatigue phenomena in which the binderis exposed to higher strain levels and varied frequency levels

Fatigue is one of the three (rutting fatigue cracking andlow temperature cracking) major failure modes in flexiblepavements which results in degradation of the pavementmaterials and finally the pavement structure [15] The mate-rials in pavement are subjected to short time load amplitudesupon passage of a vehicle Higher amplitudes of this repeatedloading result in reduction of material stiffness and itssubsequent accumulation with time may lead to completefailure [16]

Over the past 40 years different test methods havebeen developed to simulate the fatigue behavior of hotmix asphalt (HMA) materials with varying success [17ndash24]

Hindawi Publishing CorporationAdvances in Civil EngineeringVolume 2016 Article ID 5938270 12 pageshttpdxdoiorg10115520165938270

2 Advances in Civil Engineering

Tangella et al [25] listed the general categories of differenttest methodologies which included simple flexure supportedflexure diametral test triaxial test direct axial test fracturetest and wheel tracking test In the SHRP-A-404 report [26]a comprehensive evaluation was performed based on whichthe repeated flexure beam test (thirdfour-point bending)wasgiven the highest rank Usually two types of loading modesare adopted in laboratory fatigue testing constant stress(controlled-stress) mode and constant strain (controlled-strain) mode In the constant stress loading mode the stressis kept constant and the strain increases with load cycleswhereas in the constant strain mode of loading the strainis maintained constant in all the loading cycles and the stressdecreases subsequently In the field the loading conditionsaremore complex and are usually combinedmodes of loading[27] Researchers [25 28] have suggested that controlled-strain testing might be used for relatively thin pavementswith HMA less than 50mm (2 in) because the strain inthin asphalt layer is governed by the underneath layers andis merely affected by the decrease in stiffness of the asphaltmix The controlled-stress testing might be more appropriatefor thicker pavements of more than 152mm (6 in) wherethe main load-carrying component is the top layer Forintermediate thicknesses a combination of constant stressand constant strain exists It has been found that the fatiguelife obtained from constant stress testing condition is shorterthan the life obtained from constant strain testing condition[26] In this study constant strain mode has been adoptedassuming that the thickness of the wearing course is not high

A plethora of studies have indicated the improvementin rheological and mechanical properties of bitumen withaddition of polymers [8 29ndash31] In general elastomeric mod-ification has been found to improve the lower temperaturesusceptibility of binders while plastomeric modified binderstend to improve the high temperature properties [8 32ndash34] Few studies also demonstrated the increase in fatigueproperties with use of plastomeric modified binders [35]Specifically the change in properties are a function of thetype and amount of modifier used and also the base chemicalproperties of the base bitumen Study on variation of fatiguelife with change in strain amplitudes for modified binders ishowever a new area to be explored

(1) Objective of the Study Although studies have reported thefatigue characteristics of different asphalt binders and mixesvery few have focused on correlating and comparing thebinders fatigue life using LAS test with the fatigue behaviorof asphalt mixes Since LAS is a new test method a criticalstudy is required using different binders and checking itsvalidity with the fatigue performance of different asphaltmixes The main objective of the study is to compare andcorrelate the fatigue response of different asphalt binders andmixes corresponding to different strain levels

2 Materials

21 Bitumen Four binders were used in the study VG 10and VG 30 were the viscosity graded (VG) binder VG10 was being modified with elastomeric Styrene Butadiene

DBMBC

SMA

01 1 10 100001Sieve size (mm)

0

20

40

60

80

100

120

Pass

ing

()

Figure 1 Aggregate gradation adopted in the study

Styrene (SBS) and plastomeric Ethylene Vinyl Acetate (EVA)at various percent of modification level An earlier studydone by the authors [36] found that the interlocked phaseof polymer with the base binder is obtained using 3 SBSand 5 EVA Higher percentages yielded binders whichwere susceptible to phase separation Moreover using lowerpercentages did not fully optimize the properties of thebase binder which resulted in an uneconomical blend Sofor comparison only 3 SBS and 5 EVA are consideredin the study The conventional properties along with thehigh temperature performance grade (PG) specification andtrue intermediate grade temperature for these binders arepresented in Table 1 In this paper the polymer modifiedbitumen will be represented as PMB (E) and PMB (S)indicating modification with EVA and SBS The authors alsostudied the optimum blending requirements for both thepolymers Following the study PMB (S) was modified at atemperature of 180∘C using a high shear mixture operatedat 1500 rpm for 60 minutes PMB (E) on the other hand wasmodified at 190∘C at a shear rate of 600 rpm for 30 minutes

22 Aggregate Quartzite aggregates were used and obtainedfrom a local quarry The conventional properties of aggre-gates were measured which followed the specifications inaccordance with Ministry of Road Transport and Highways(MoRTampH) India

23 Gradations Adopted Three gradations were adopted inthe study namely bituminous concrete (BC) dense bitu-minous macadam (DBM) and stone mastic asphalt (SMA)The nominal maximum aggregate sizes (NMAS) of 19mm265mm and 19mm were used respectively The gradationrequirements are as perMoRTampH BC andDBMare amongstthe dense graded mixes most commonly used in India forthe surface and binder courses respectively SMA on theother hand is a gap-graded mix used as a wearing coursewith high rut resistant properties Usually SMA is used atplaces with extreme conditions of temperature and loadingFigure 1 presents the sieve size distribution for the respectivemixes Each type of mix was prepared with all the fourbinders For SMA first the drain-down test was carried

Advances in Civil Engineering 3

Table 1 Conventional properties of binders used in the study

Binders Penetrationdmm

Softeningpoint ∘C

Penetrationindex

Viscosity at60∘C Pasdots

Storagestability

ΔSoft point∘C

Hightemperature PG

grade

True gradeintermediate

temperature ∘C

VG 10 75 47 minus101 258 mdash PG 58-XX 253VG 30 62 49 minus095 375 mdash PG 64-XX 201PMB (S) 56 60 131 2120 15 PG 70-XX 157PMB (E) 49 65 192 6120 13 PG 76-XX 122

Table 2 Drain-down test results

Type of mix Type of binder Drain-down ()(max 03)

SMA VG 10 057SMA VG 30 043SMA PMB (S) 028SMA PMB (E) 026

out using all the binders As SMA is a gap-graded mixthe binders are susceptible to flow out of the mix at highhandling temperatures (near about 163∘C)This phenomenonis known as drain-downwhich should be less than 03 as perspecification outlined in Indian Roads Congress (IRC) SP-79 2008 Drain-down test was carried out using Schellenbergmethod [37] It was found that only the modified binders(PMB (S) and PMB (E)) satisfied the maximum drain-downcriteria So VG 10 and VG 30 were not used for preparingSMA samples Moreover SMA should have high resistanceproperties and thus it should have a stiff binder which in thiscase cannot be VG 10 or VG 30 as shown by the results inTable 1 Table 2 presents the results of the drain-down test

24 Mix Design All the bituminous mixes in the study wereprepared using Marshall Mix design procedure Samples forBC and DBM were compacted by applying 75 blows on eachface while SMA was compacted through application of 50blows on each face respectively Sampleswere prepared at fivebinder contents for eachmix typewith three identical samplesat each binder content The procedure as recommended byNAPAwas used for the determination of the optimumbindercontent (OBC) According to the method the binder contentcorresponding to 4 air void (by weight of the mix) isdetermined first and this binder content is used to determinethe values of Marshall Stability voids in mineral aggregates(VMA) flow and percent voids filled with bitumen (VFB)Each value is compared against the specification value for thatproperty and if all are found to be within the specificationrange the asphalt content at 4 percent air void is considered asthe optimumAfter determination of theOBC correspondingto 4 air void threemore samples at that binder content wereprepared for Marshall testing

3 Experimental Investigation

31 Linear Amplitude Sweep (LAS) Test Linear AmplitudeSweep test following AASHTO TP 101-14 was conducted todetermine the parameters 119860 and 119861 to assess the fatiguelife of the binders at different strain levels 119860 and 119861 arethe model parameters of the fatigue equation This test wasdone at 10 20 and 30∘C for all the binders The resultsreported in the study are an average of three samples for eachtemperature The test requires conducting a frequency sweeptest followed by a Linear Amplitude Sweep The frequencysweep is conducted at a very low strain level of 01 to obtainundamaged material properties which is used as an input inthe analysis of amplitude sweep test The amplitude sweeptest is conducted by linearly varying strain from 0 to 30through 3100 loading cycles at a fixed frequency of 10HzThetest begins with 100 cycles of sinusoidal loading at 01 strainfollowed by incremental load steps of 100 cycles each at a rateof 1 increment in strain level

The frequency sweep test (02ndash30Hz) is used for thedetermination of the parameter alpha (120572) which is later usedin the analysis of strain sweep data 120572 is the reciprocal ofthe straight line slope (119898) of log119866

1015840 (120596) versus log120596 curveFrequency sweep is conducted at a strain level of 01 so asto ensure the linear viscoelastic range for the bitumen

120572 =1

119898 (1)

Amplitude or strain sweep test is conducted at a frequencyof 10Hz with loading increasing from zero to 30 over thecourse of 3100 cycles of loadingThe damage accumulation inthe specimen is calculated using the formulae [38]

119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(119862119894minus1

minus 119862119894)]120572(1+120572)

(119905119894minus 119905119894minus1

)1(1+120572)

(2)

where 119862(119905) is the ratio of |119866lowast

|(119905) to |119866lowast

|initial which are thevalue of complex shear modulus at any time 119905 and the initialundamaged |119866

lowast

|Further the calculated 119862(119905) and 119863(119905) are used to fit a

relation of the form

119862119905

= 1198620

minus 1198621

(119863)1198622 (3)

where 1198620 1198621 and 119862

2are evaluated using curve fitting 119862 at

peak stress is used to calculate the value of119863(119905) at failure (119863119891)

using the above equation


Thebinder fatigue life119873119865is calculated using the equation

119873119865

= 119860 (120574max)119861

(4)

where 119860 and 119861 are the model parameters and are evaluatedusing the following equations

119860 =119891 (119863119891)119896

119896 (12058711986211198622)120572

119861 = 2120572

(5)

In the above equations 119891 is the frequency (10Hz) and 119896 iscalculated as follows

119896 = 1 + (1 minus 1198622) 120572 (6)

The above method for characterizing the fatigue is generatedfrom the viscoelastic continuum damage (VECD) principlewhich starts from the basic Schaperyrsquos equation for damage(119863) rate written as [39]

119889119863

119889119905= minus

120597119882

120597119863 (7)

The above equation for viscoelastic materials was modified toobey power law based on Paris Law of crack growth

119889119863

119889119905= (minus

120597119882

120597119863)

120572

(8)

119882 is the materials energy potential while 120572 is the exponentdetermining the energy release rate

Further the work done by Park and coworkers [39] formonotonic loading was implemented for harmonic loadingas typical in flexible pavements For strain controlled cyclicshear loading the dissipated energy during each cycle wasused in place of119882 in (8) [12]The dissipated energy is derivedfrom the work done per unit volume by the material whensubjected to cyclic loading It could be written as

119882 = 120587 sdot 1205740

2

sdot1003816100381610038161003816119866lowast1003816100381610038161003816 sdot sin 120575 (9)

Using this equation in the above equation yields the solutionas

119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894minus1minus

1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894)]120572(1+120572)

sdot (119905119894minus 119905119894minus1

)1(1+120572)

(10)

Further using (3) in (9) will give119889119882

119889119863= minus120587119862

11198622

(119863)1198622minus1

(120574max)2

(11)

Equations (11) and (8) create a differential equation which onsolving will give

119863 (119905) = [1

(minus1205721198622

+ 120572 + 1) 119905]

(1(1205721198622minus120572minus1))

sdot [1

(120587119862111986221205872)

]

(120572(1205721198622minus120572minus1))

(12)

This equation is finally transformed to (4)

(a) Load configuration (b) Failure of specimen

Figure 2 Indirect tension strength test loading and failure process

32 Moisture Susceptibility Test The susceptibility of asphaltmixtures to moisture is another measure of the durabilityRetained Marshall Stability test was employed for evaluatingthe sensitivity of the mixes and binders to moisture Ten-sile strength ratio (TSR) was also calculated for assessingthe moisture susceptibility of bituminous mixes MoRTampHrequires a minimum of 80 TSR to make the mix resistive tomoisture damage Marshall Stability of compacted specimenswas determined after conditioning them by keeping in watermaintained at 60∘C for 24 h prior to testing This stabilityexpressed as percentage of the stability ofMarshall Specimensdetermined under standard conditions is the retained sta-bility of the mix Tensile strength ratio (TSR) is the averagestatic indirect tensile strength of the conditioned specimensexpressed as percentage of the average static indirect tensilestrength of unconditioned specimens Conditioning wasdone by keeping the specimens in water maintained at 60∘Cfor 24 h and by curing at 25∘C for 2 h before commencingthe test The test was conducted at 25∘C Three samples wereprepared for checking the consistency in the results and theaverage value was calculated

33 Indirect Tension Strength (ITS) Test In the study ITStest was conducted in accordance with ASTM D 6931 2012at 25∘C Indirect tensile strength test procedure consists ofapplying a load along cylindrical specimenrsquos diametrical axisat a fixed deformation rate of 51 cmmin until failure anddetermining the total vertical load at failure of the specimenat 25∘C Failure is defined as the point after which there is noincrease in load A nearly uniform tensile stress is developednormal to the direction of the applied load along the samevertical plane causing the specimen to fail by splitting alongthe vertical diameter Figure 2 shows the loading and failurephenomena in the test The maximum load sustained by thespecimen is used to calculate the indirect tensile strengthusing the following expression

119878119879

=2119865

314 (ℎ119889) (13)

where

119878119879is indirect tensile strength

119865 is total applied vertical load at failure Nℎ is height of specimen mm119889 is diameter of specimen mm


Table 3 Test condition adopted for 4PBB test

S number Test parameter Test condition1 Test temperature (∘C) 20 plusmn 052 Strain amplitude (10minus6m) 200ndash10003 Loading frequency (Hz) 104 Air void content () 4 plusmn 025 Type of loading Sinusoidal

6 Failure conditionWhen the flexural stiffness is reduced to 50 ofthe initial flexural stiffness or 200000 loading

cycles have been applied whichever occurs first

34 Four-Point Beam Bending Test (4PBBT) The flexuralfatigue testing protocol of AASHTO T321-2003 and SHRPM-009 requires preparation of oversized beam specimensthat have to be sawed to the required dimensions Thefinal required dimensions are 380 plusmn 6mm (15 plusmn 14 in) inlength 50 plusmn 6mm (2 plusmn 14 in) in height and 63 plusmn 6mm(25 plusmn 14 in) in width No specific procedure is mentionedfor beam preparation However several methods includingfull scale rolling wheel compaction miniature rolling wheelcompaction and vibratory loading have been used over years

In this study the beams were prepared adopting a newmethod of loading and unloading The mold used for beampreparation had an inside dimension of 382mm times 50mm times

70mm The final dimension was fixed as 382mm times 50mmtimes 50mm to achieve uniform beam sizes for all the types ofmixtures All the specimens were prepared to achieve a targetair void content of 4byweight of the totalmix As the heightof beam was fixed the weight of the mixture required toachieve the target air void was precalculated The aggregatesand bitumen were mixed at the required mixing temperatureand was placed in the preheated mold A compression testingmachine was used for applying load till the desired heightwas reached The loading was accompanied by an unloadingprocess to avoid breaking of aggregates due to static loadingAfter compaction the specimen was allowed to cool for 24hours The beam was extracted from the mold and the airvoid content was measured using the saturated surface-dryprocedure (AASHTO T166) Compacting the specimens isone of themost difficult tasks when the target air void contentis fixed This may be possible but would require many trialsSo an allowance of plusmn02 was given to the required airvoid content The testing protocol mentioned in Table 3 wasadopted for conducting the four-point beam bending (4PBB)test Two samples were prepared for each combination ofbinder and mix

The maximum tensile stress and strain were calculatedusing the following equations

120590119905

=0382 sdot 119875

119887 sdot ℎ2

120576119905

=12 sdot 120575 sdot ℎ

3 sdot 1198712 minus 4 sdot 1198862

(14)

where

120590119905is maximum tensile stress Pa

120576119905is maximum tensile strain mm

119875 is applied load N119887 is average specimen width mℎ is average specimen height m120575 is maximum deflection at the center of the beam119871 is length of the specimen 382mm119886 is length between the clamps (1198713 = 12733mm)

The flexural stiffness phase angle dissipated energy andcumulative dissipated energy are calculated as follows

119878 =120590119905

120576119905

120601 = 360 sdot 119891 sdot 119904

119863 = 120587 sdot 120590119905sdot 120576119905sdot sin (120601)

CDE =

119873

sum119894=1

119863119894

(15)

where

119878 is flexural stiffness Pa120601 is phase angle degrees119891 is load frequency Hz119904 is time lag seconds119863 is dissipated energy per cycle Jm3CDE is cumulative dissipated energy Jm3

4 Results and Analysis

41 Fatigue Behavior of Binders Figure 3 shows the compari-son of fatigue lives for all the binders at the three temperaturesconsidered in the study It can be seen that PMB (S) outper-forms all the binders irrespective of any test temperaturesAt 10 and 20∘C for low strain levels PMB (E) had higherfatigue life thanVG 10 andVG30As the strain level increased(typically after 10) the fatigue life decreased steeply forPMB (E) giving lower values than the conventional bindersThis describes the higher strain susceptibility for plastomericPMB (E) Due to higher stiffness at lower temperature PMB(E) tends to undergo brittle failure when strained to higher


Fatigue life 10∘C Fatigue life 20∘C

Fatigue life 30∘C

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1

10

100

1000

10000

100000

1000000

10000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1 10Strain ()

1 10Strain ()

1 10Strain ()

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

Figure 3 Variation of fatigue life at different temperatures

amplitudes This is attributed to the crystalline nature of thepolyethylene segment in EVA which imparts brittle natureto the binder at lower temperatures However at 30∘C thefatigue life of PMB (E)was found to be higher thanVG30 It ishence recommended that plastomeric modified binders suchas EVA should not be used at regions with lower pavementtemperatures and heavily stressed areas The conventionalbinders displayed interesting behavior VG 10 and VG 30had lower fatigue lives at lower strain amplitudes But therate of decrease in fatigue life with increase in strain levelwas lower than the modified binders VG 10 had the loweststrain susceptibility and gave better results than PMB (E)and VG 30 at higher strain amplitudes This phenomenonwas compounded in the traditional method of determiningfatigue life As can be seen in Table 1 the true intermediatetemperature for |119866

lowast

| sdot sin 120575 to be lower than 5000 kPa isthe lowest for PMB (E) indicating that it would performbetter than all other binders This is contrary to the rankingof binder as demonstrated by LAS test results Moreover inthe traditionalmethod thewide spectrumof fatigue behaviorwith change in strain level cannot be evaluated Hence LAStest is a better way of judging the relative fatigue performanceof different binders A statistical test was carried out to seeif the data obtained using LAS test for different combinationof temperature and strain levels were significantly different

It was found that the 119865 statistics values (697 365 and335) were higher than the 119865 critical value (159) at all thetemperatures (10 20 and 30∘C) at different strain levels(1ndash30) which indicates that the results are significantlydifferentThe tables are not presented in this paper for brevity

The fatigue life for all the binders using LAS methodwas found to be sensible to the value of 120572 and 119860 A lowervalue of 120572 and a higher value of 119860 are desirable for superiorperformance in fatigue ldquo120572rdquo indicates the rate of reductionin fatigue life with increase in strain amplitude A lowervalue would indicate lower strain susceptibility In general 120572

decreases and 119860 increases with increase in temperature forall the binders But the change in the respective values withchange in temperature is different for each binder Also it isobserved that the value of 120572 has dependence on the stiffnessof binder The value increased with increase in stiffness withPMB (E) having the highest value Table 4 presents the valuesof the 119860 and 120572 at all the test temperatures

Variation of fatigue life with temperature was also eval-uated corresponding to two different strain levels as canbe seen in Figure 4 Usually it is assumed that the strainin the binder is about 50 times that in the mixture [40]Hence the fatigue life at two strain levels was evaluated forcomparison 25 and 5 corresponding to 500 microstrainsand 1000 microstrains were reported In general the fatigue


25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)

15 25 355Temperature (∘C)


Figure 4 Variation of fatigue life with temperature at two different strain levels

Table 4 Values of fatigue parameters 120572 and 119860

Binders 120572 119860

10∘C 20∘C 30∘C 10∘C 20∘C 30∘CVG 10 16048405 14582551 03822351 1689232 37431015 65396962VG 30 17922338 16402502 03409223 47259719 5453401 83388288PMB (S) 18680149 18391338 02876897 14840075 37825185 12799364PMB (E) 20018136 18236637 02922775 14712968 13279917 70209328

life increases with increase in temperature for all the bindersThe increase in fatigue life with increase in temperaturewas the highest for VG 10 indicating higher temperaturesusceptibility

42 Marshall Mix Results Table 5 presents the result of theoptimum binder content and the corresponding MarshallMix parameters The stability of mixes prepared with mod-ified binders was higher than those prepared with conven-tional binders Amongst different mixes SMA had the loweststability values attributed to higher VMA and binder contentThe retained Marshall Stability values were found to behigher for mixes prepared with modified binders Moreoveramongst all the mixes SMA had the highest retained stabilityvalue Two outcomes can be derived from this observationFirst the modified binders have lower temperature suscepti-bility and secondly higher binder content (as in SMA mixes)tends to increase the film thickness making the mix moredurable and resistant to moisture damage

43 Indirect Tensile Strength (ITS) Figure 5 presents the ITSresults for the three types of mixes prepared using differentbinders The results revealed that modified binders havehigher values as compared to mixes prepared with conven-tional binders Dense graded mixes such as BC displayed

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)

Figure 5 ITS values for different mixes

higher values as compared to gap-graded SMA Though theITS values for BC andDBMmixes are higher than SMA theywill develop cracks due to lower binder content It is hencenecessary to determine the resistance to cracking for differentmixes from repeated bending test The TSR values were alsoplotted on the secondary axis Modified binders were foundto be least susceptible to moisture damage The minimum


Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000

400 microstrains 600 microstrains

1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A

Figure 6 Fatigue life at different strain levels

Table 5 Results of Marshall Mix design

Mix properties BC DBM SMAVG 10 VG 30 PMB (S) PMB (E) VG 10 VG 30 PMB (S) PMB (E) PMB (S) PMB (E)

119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886

399 406 403 407 403 402 402 398 405 404VMA 1395 1399 1423 142 1373 1363 1358 1368 1999 1995VFB 7139 7098 7167 7134 7068 7048 7042 7089 7976 7973Stability Kg 1275 1359 1588 1675 1182 1278 1450 1570 970 1015Flow mm 31 29 32 34 36 34 31 31 38 37Marshall quotient 411 468 496 492 328 375 467 506 255 274Retained Marshall Stability 62 67 79 82 67 66 80 85 95 96

specification criteria of 80 TSR were not satisfied for mixesprepared with VG 10 For DBM VG 30 also displayed slightlylower value than the minimum required Hence for thesemixes antistripping agent should be used to protect it frombeing vulnerable to moisture effects

44 Fatigue Life from 4PBBT Figure 6 presents the compar-ison of the fatigue life of different mixes for each binder typeThe results of 200 microstrains are not shown because all themixes exhibited fatigue life higher than 2 times 105 cycles At

400 microstrains SMA mixes prepared with PMB (S) andPMB (E) also had higher fatigue life It was found that atlower strain levels (lt600 microstrains) mixes prepared withpolymer modified binders exhibited higher fatigue life thanthose prepared using conventional binders Amongst thepolymer modified binders PMB (S) gave superior results Asthe strain level increased the fatigue life of PMB (E) reduceddrastically and was almost close to the behavior shown byconventional binders PMB (S) on the other hand displayedthe best performance at all the strain levels Amongst all


500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000

500000Fatigue life DBM

500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

Figure 7 Fatigue life of different type of bituminous mixes

the mixes SMA had the highest fatigue life which wasalmost 5 times the fatigue life of BC and DBM This may beattributed to the volumetric of the bituminous mixture SMAbeing a gap-graded mix has high VMA (17ndash22) which canaccommodate ample amount of bitumen for a fixed air voidcontent of 4 This increases the film thickness inside themix making the mix more durable to the induced strain

Figure 7 illustrates the fatigue life as a function of strainThe slope of the curve indicates the sensitivity of the bindersto the change in the magnitude of strain PMB (E) showedhighest susceptibility to this change while PMB (S) wasfound to be least susceptible It was found that at lowerstrain levels (le400 120583m) PMB (E) had fatigue life very closeto PMB (S) But as the strain increased the fatigue life ofPMB (E) decreased very sharply At higher strain amplitudes(ge800120583m) the fatigue life of PMB (E) mixes was evenlower than that of the mixes prepared using conventionalbinders This behavior of PMB (E) may be explained asfollows In PMB (E) the crystalline nature of the polymerstiffens the binder inducing viscous behavior At low strainsdue to high stiffness the binder can take higher number of

load repetitions without any damage But due to the rigidnature it cannot be stretched to higher strain which willresult in formation of cracks On the other hand in PMB(S) the polymers are cross-linked to a three-dimensionalnetwork The polystyrene end-blocks impart strength whilethe butadiene mid-blocks impart exceptional elasticity Thismakes the binder more flexible and increases its capability toresist higher strains

45 Correlation of LAS and 4PBBT Results It was attemptedto correlate the fatigue results of asphalt binders with thefatigue life of asphalt mixtures Assuming that the strainin binder is about 50 times the strain in mixtures fourstrain levels (2 3 4 and 5) of LAS test were chosencorresponding to four similar strain levels (400 600 800and 1000 microstrains) of 4PBBT Plotting the results ofthe binders against the fatigue life of mixes it can be seenfrom Figure 8 that linear correlation is achieved for all themixes For PMB (E) and PMB (S) the fatigue life for SMAis also shown It can be seen that the slope for SMA deviates


VG 10

BCDBM

Linear (BC)Linear (DBM)

VG 30

PMB (S)

BCDBMSMA

Linear (BC)Linear (DBM)Linear (SMA)

PMB (E)

BCDBM


BCDBMSMA


50000 100000 150000 2000000Fatigue life of mixes

R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der

50000 100000 1500000Fatigue life of mixes

50000 1000000Fatigue life of mixes

0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der

Figure 8 Correlation of fatigue life of asphalt binders and mixes

considerably compared to that of BC and DBMThis may beattributed to the higher VMA for SMAmixes as compared toBC and DBM The correlation equation however varies withthe type of mix for each binder

5 Conclusions

Based on the results of the experimental and analyticalinvestigations on fatigue behavior of different unmodified

and modified bituminous binders and mixes the followingconclusions have been drawn

(1) LAS test was found to bemore practical than the exist-ing intermediate performance criteria of 119866

lowast

sdot sin 120575By LAS test it was possible to evaluate the complexbehavior of the binder at a wide range of loadinglevels Elastomeric polymer modified binder (PMB(S)) displayed the highest fatigue life at all the testtemperatures PMB (E) was found to be susceptible


to strain amplitudes at 10 and 20∘C at which theperformance degraded at higher strain levels VG 10and VG 30 had lower fatigue lives at lower strainamplitudes But the rate of decrease in fatigue life withincrease in strain level was lower than the modifiedbinders VG 10 had the lower strain susceptibilityand gave better results than PMB (E) and VG 30 athigher strain amplitudes However at 30∘C PMB (E)performed better than the conventional binders

(2) TheMarshall test results indicated higher stability fordense graded mixtures prepared with polymer mod-ified bitumen SMA mixes displayed lower stabilityvalues attributed to high VMA and increased bindercontent

(3) The moisture susceptibility as shown by the retainedMarshall Stability test was higher for conventionalbinders The retained Marshall Stability values forSMA mixes were found to be higher than the densegradedmixesThis is attributable to the higher bindercontentwhich increases the film thicknessmaking themix water resistant ITS values for BC and DBMwerefound to be higher than SMA Mixes prepared withmodified binders displayed higher strength values incomparison to viscosity graded binders VG 10 did notsatisfy the minimum TSR criteria required to satisfythe moisture susceptibility criteria

(4) At lower strain levels mixes prepared with polymermodified binders had higher fatigue life as comparedto mixes prepared with conventional viscosity gradedbinders At high strain amplitude mixes preparedwith PMB (E) gave poor performance in fatigue Thefatigue life PMB (E) mixes were even lower thanthe mixes prepared using conventional binders Thisis attributed to the high strain sensitivity of PMB(E) PMB (S) on the other hand gave best results incomparison to other binders

(5) Amongst all the mixes SMA gave the best perfor-mance in fatigue The fatigue life of SMA mixes wasalmost five times higher as compared to other bitu-minous mixtures This is attributed to the high VMApercentage which can accommodate large amount ofbinder for a fixed air void content This increases thefilm thickness which reduces the stress and increasesthe durability

(6) It was found that for similar strain levels the fatiguelife of asphalt binders could be linearly correlatedwith the fatigue life of asphalt mixes The correlationequation varies with the type of mix for each binder

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] E Santagata O Baglieri D Dalmazzo and L TsantilisldquoEvaluation of the anti-rutting potential of polymer-modifiedbinders by means of creep-recovery shear testsrdquo Materials andStructures vol 46 no 10 pp 1673ndash1682 2013

[2] Y Becker and M P Mendez ldquoPolymer modified asphaltrdquoVisionary Technologies vol 9 pp 39ndash50 2001

[3] F Cardone G Ferrotti F Frigio and F Canestrari ldquoInfluenceof polymer modification on asphalt binder dynamic and steadyflow viscositiesrdquo Construction and Building Materials vol 71pp 435ndash443 2014

[4] X Lu U Isacsson and J Ekblad ldquoRheological properties ofSEBS EVA and EBA polymer modified bitumensrdquo Materialsand Structures vol 32 no 216 pp 131ndash139 1999

[5] B Sengoz and G Isikyakar ldquoEvaluation of the properties andmicrostructure of SBS and EVA polymer modified bitumenrdquoConstruction and Building Materials vol 22 no 9 pp 1897ndash1905 2008

[6] G D Airey ldquoRheological evaluation of ethylene vinyl acetatepolymer modified bitumensrdquo Construction and Building Mate-rials vol 16 no 8 pp 473ndash487 2002

[7] G D Airey Rheological Characteristics of PolymerModified andAged Bitumens University of Nottingham Nottingham UK1997

[8] U Isacsson and X Lu ldquoCharacterization of bitumens modifiedwith SEBS EVA and EBA polymersrdquo Journal of MaterialsScience vol 34 no 15 pp 3737ndash3745 1999

[9] F Zhou W Mogawer H Li A Andriescu and A CopelandldquoEvaluation of fatigue tests for characterizing asphalt bindersrdquoJournal of Materials in Civil Engineering vol 25 no 5 pp 610ndash617 2013

[10] C M Johnson H U Bahia and A Coenen ldquoComparisonof bitumen fatigue testing procedures measured in shear andcorrelations with four-point bending mixture fatiguerdquo in Pro-ceedings of the 2nd Workshop on Four Point Bending PaisUniversity of Minho Guimaraes Portugal 2009

[11] C M Johnson H Bahia and H U Wen ldquoPractical applicationof viscoelastic continuum damage theory to asphalt binderfatigue characterizationrdquo Journal of the Association of AsphaltPaving Technologists vol 78 pp 597ndash638 2009

[12] C Hintz R Velasquez C Johnson andH Bahia ldquoModificationand validation of linear amplitude sweep test for binder fatiguespecificationrdquoTransportation Research Record vol 2207 pp 99ndash106 2011

[13] C Hintz and H Bahia ldquoUnderstanding mechanisms leading toasphalt binder fatigue in the dynamic shear rheometerrdquo RoadMaterials and Pavement Design vol 14 supplement 2 pp 231ndash251 2013

[14] D A Anderson and T W Kennedy ldquoDevelopment of SHRPbinder specificationrdquo Journal of the Association of AsphaltPaving Technologists vol 62 pp 481ndash507 1993

[15] H Ziari R Babagoli and A Akbari ldquoInvestigation of fatigueand rutting performance of hot mix asphalt mixtures preparedby bentonite-modified bitumenrdquo Road Materials and PavementDesign vol 16 no 1 pp 101ndash118 2015

[16] H Di Benedetto C de La Roche H Baaj A Pronk and RLundstrom ldquoFatigue of bituminous mixturesrdquo Materials andStructures vol 37 no 3 pp 202ndash216 2004

[17] J B Sousa J C PaisM Prates R Barros P Langlois andA-MLeclerc ldquoEffect of aggregate gradation on fatigue life of asphalt


concrete mixesrdquo Transportation Research Record vol 1630 pp62ndash68 1998

[18] J T Harvey J A Deacon B Tsai and C LMonismith ldquoFatigueperformance of asphalt concrete mixes and its relationship toasphalt concrete pavement performance in Californiardquo TechRep RTA-65W485-2 Berkeley Calif USA 1995

[19] S Adhikari S Shen and Z You ldquoEvaluation of fatigue modelsof hot-mix asphalt through laboratory testingrdquo TransportationResearch Record vol 2127 pp 36ndash42 2009

[20] D Bodin C de La Roche and A Chabot ldquoPrediction ofbituminous mixes fatigue behavior during laboratory fatiguetestsrdquo in Proceedings of the 3rd Eurasphalt and EurobitumeCongress pp 1935ndash1945 Vienna Austria May 2004

[21] M E Kutay VECD (Visco-Elastic Continuum Damage) State-of-the-Art Technique to Evaluate Fatigue Damage in AsphaltPavements History of the ViscoelasticContinuum Damage(VECD)Theory Michigan State University East Lansing MichUSA

[22] A A A Molenaar ldquoPrediction of fatigue cracking in asphaltpavements do we follow the right approachrdquo TransportationResearch Record vol 2001 pp 155ndash162 2007

[23] Z Suo andWGWong ldquoAnalysis of fatigue crack growth behav-ior in asphalt concretematerial inwearing courserdquoConstructionand Building Materials vol 23 no 1 pp 462ndash468 2009

[24] P J Yoo and I L Al-Qadi ldquoA strain-controlled hot-mix asphaltfatigue model considering low and high cyclesrdquo InternationalJournal of Pavement Engineering vol 11 no 6 pp 565ndash574 2010

[25] S C S Tangella J Craus J A Deacon and C L MonismithSummary Report on Fatigue Response of Asphalt Mixtures 1990

[26] C Monismith Fatigue Response of Asphalt-Aggregate MixesUniversity of CAB 1994

[27] S Shen Dissipated energy concepts for HMA performancefatigue and healing [ProQuest DissTheses] University of Illinoisat Urbana-Champaign Champaign Ill USA 2006

[28] YHHuangPavement Analysis andDesign Pearson Education2nd edition 2010

[29] F Merusi F Giuliani and G Polacco ldquoLinear viscoelas-tic behaviour of asphalt binders modified with polymerclaynanocompositesrdquo ProcediamdashSocial and Behavioral Sciences vol53 pp 335ndash345 2012

[30] V O Bulatovic V Rek and K J Markovic ldquoRheologicalproperties and stability of ethylene vinyl acetate polymer-modified bitumenrdquoPolymer Engineering and Science vol 53 no11 pp 2276ndash2283 2013

[31] T Alatas and M Yilmaz ldquoEffects of different polymers onmechanical properties of bituminous binders and hotmixturesrdquoConstruction and Building Materials vol 42 pp 161ndash167 2013

[32] X Lu and U Isacsson ldquoModification of road bitumens withthermoplastic polymersrdquo Polymer Testing vol 20 no 1 pp 77ndash86 2000

[33] J Zhu B Birgisson and N Kringos ldquoPolymer modification ofbitumen advances and challengesrdquo European Polymer Journalvol 54 no 1 pp 18ndash38 2014

[34] G D Airey ldquoRheological properties of styrene butadienestyrene polymer modified road bitumensrdquo Fuel vol 82 no 14pp 1709ndash1719 2003

[35] M Ameri A Mansourian and A H Sheikhmotevali ldquoLabo-ratory evaluation of ethylene vinyl acetate modified bitumensand mixtures based upon performance related parametersrdquoConstruction and Building Materials vol 40 pp 438ndash447 2013

[36] N Saboo and P Kumar ldquoOptimum blending requirementsfor EVA modified binderrdquo International Journal of PavementResearch and Technology vol 8 no 3 pp 172ndash178 2015

[37] IRC-SP79 Tentative Specifications for Stone Matrix AsphaltIndian Roads Congress New Delhi India 2008

[38] AASHTO ldquoEstimating damage tolerance of asphalt bindersusing linear amplitude sweeprdquo TP 101 2014

[39] S W Park Y R Kim and R A Schapery ldquoA viscoelastic con-tinuum damage model and its application to uniaxial behaviorof asphalt concreterdquo Mechanics of Materials vol 24 no 4 pp241ndash255 1996

[40] E Masad N Somadevan H U Bahia and S Kose ldquoModel-ing and experimental measurements of strain distribution inasphalt mixesrdquo Journal of Transportation Engineering vol 127no 6 pp 477ndash485 2001

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



Tangella et al [25] listed the general categories of differenttest methodologies which included simple flexure supportedflexure diametral test triaxial test direct axial test fracturetest and wheel tracking test In the SHRP-A-404 report [26]a comprehensive evaluation was performed based on whichthe repeated flexure beam test (thirdfour-point bending)wasgiven the highest rank Usually two types of loading modesare adopted in laboratory fatigue testing constant stress(controlled-stress) mode and constant strain (controlled-strain) mode In the constant stress loading mode the stressis kept constant and the strain increases with load cycleswhereas in the constant strain mode of loading the strainis maintained constant in all the loading cycles and the stressdecreases subsequently In the field the loading conditionsaremore complex and are usually combinedmodes of loading[27] Researchers [25 28] have suggested that controlled-strain testing might be used for relatively thin pavementswith HMA less than 50mm (2 in) because the strain inthin asphalt layer is governed by the underneath layers andis merely affected by the decrease in stiffness of the asphaltmix The controlled-stress testing might be more appropriatefor thicker pavements of more than 152mm (6 in) wherethe main load-carrying component is the top layer Forintermediate thicknesses a combination of constant stressand constant strain exists It has been found that the fatiguelife obtained from constant stress testing condition is shorterthan the life obtained from constant strain testing condition[26] In this study constant strain mode has been adoptedassuming that the thickness of the wearing course is not high

A plethora of studies have indicated the improvementin rheological and mechanical properties of bitumen withaddition of polymers [8 29ndash31] In general elastomeric mod-ification has been found to improve the lower temperaturesusceptibility of binders while plastomeric modified binderstend to improve the high temperature properties [8 32ndash34] Few studies also demonstrated the increase in fatigueproperties with use of plastomeric modified binders [35]Specifically the change in properties are a function of thetype and amount of modifier used and also the base chemicalproperties of the base bitumen Study on variation of fatiguelife with change in strain amplitudes for modified binders ishowever a new area to be explored

(1) Objective of the Study Although studies have reported thefatigue characteristics of different asphalt binders and mixesvery few have focused on correlating and comparing thebinders fatigue life using LAS test with the fatigue behaviorof asphalt mixes Since LAS is a new test method a criticalstudy is required using different binders and checking itsvalidity with the fatigue performance of different asphaltmixes The main objective of the study is to compare andcorrelate the fatigue response of different asphalt binders andmixes corresponding to different strain levels

2 Materials

21 Bitumen Four binders were used in the study VG 10and VG 30 were the viscosity graded (VG) binder VG10 was being modified with elastomeric Styrene Butadiene

DBMBC

SMA

01 1 10 100001Sieve size (mm)

0

20

40

60

80

100

120

Pass

ing

()

Figure 1 Aggregate gradation adopted in the study

Styrene (SBS) and plastomeric Ethylene Vinyl Acetate (EVA)at various percent of modification level An earlier studydone by the authors [36] found that the interlocked phaseof polymer with the base binder is obtained using 3 SBSand 5 EVA Higher percentages yielded binders whichwere susceptible to phase separation Moreover using lowerpercentages did not fully optimize the properties of thebase binder which resulted in an uneconomical blend Sofor comparison only 3 SBS and 5 EVA are consideredin the study The conventional properties along with thehigh temperature performance grade (PG) specification andtrue intermediate grade temperature for these binders arepresented in Table 1 In this paper the polymer modifiedbitumen will be represented as PMB (E) and PMB (S)indicating modification with EVA and SBS The authors alsostudied the optimum blending requirements for both thepolymers Following the study PMB (S) was modified at atemperature of 180∘C using a high shear mixture operatedat 1500 rpm for 60 minutes PMB (E) on the other hand wasmodified at 190∘C at a shear rate of 600 rpm for 30 minutes

22 Aggregate Quartzite aggregates were used and obtainedfrom a local quarry The conventional properties of aggre-gates were measured which followed the specifications inaccordance with Ministry of Road Transport and Highways(MoRTampH) India

23 Gradations Adopted Three gradations were adopted inthe study namely bituminous concrete (BC) dense bitu-minous macadam (DBM) and stone mastic asphalt (SMA)The nominal maximum aggregate sizes (NMAS) of 19mm265mm and 19mm were used respectively The gradationrequirements are as perMoRTampH BC andDBMare amongstthe dense graded mixes most commonly used in India forthe surface and binder courses respectively SMA on theother hand is a gap-graded mix used as a wearing coursewith high rut resistant properties Usually SMA is used atplaces with extreme conditions of temperature and loadingFigure 1 presents the sieve size distribution for the respectivemixes Each type of mix was prepared with all the fourbinders For SMA first the drain-down test was carried




Softeningpoint ∘C

Penetrationindex


Storagestability

ΔSoft point∘C

Hightemperature PG

grade


temperature ∘C











120572 =1

119898 (1)


119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(119862119894minus1

minus 119862119894)]120572(1+120572)

(119905119894minus 119905119894minus1

)1(1+120572)

(2)


|(119905) to |119866lowast


lowast



119862119905

= 1198620

minus 1198621

(119863)1198622 (3)

where 1198620 1198621 and 119862






119873119865

= 119860 (120574max)119861

(4)


119860 =119891 (119863119891)119896

119896 (12058711986211198622)120572

119861 = 2120572

(5)


119896 = 1 + (1 minus 1198622) 120572 (6)


119889119863

119889119905= minus

120597119882

120597119863 (7)


119889119863

119889119905= (minus

120597119882

120597119863)

120572

(8)



119882 = 120587 sdot 1205740

2



119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894minus1minus

1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894)]120572(1+120572)

sdot (119905119894minus 119905119894minus1

)1(1+120572)

(10)


119889119863= minus120587119862

11198622

(119863)1198622minus1

(120574max)2

(11)


119863 (119905) = [1

(minus1205721198622

+ 120572 + 1) 119905]

(1(1205721198622minus120572minus1))

sdot [1

(120587119862111986221205872)

]

(120572(1205721198622minus120572minus1))

(12)






119878119879

=2119865

314 (ℎ119889) (13)

where












120590119905

=0382 sdot 119875

119887 sdot ℎ2

120576119905


3 sdot 1198712 minus 4 sdot 1198862

(14)

where





119878 =120590119905

120576119905

120601 = 360 sdot 119891 sdot 119904


CDE =

119873

sum119894=1

119863119894

(15)

where






Fatigue life 30∘C

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1

10

100

1000

10000

100000

1000000

10000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1 10Strain ()

1 10Strain ()

1 10Strain ()

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10



lowast







25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)





Binders 120572 119860





VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)




Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Softeningpoint ∘C

Penetrationindex


Storagestability

ΔSoft point∘C

Hightemperature PG

grade


temperature ∘C











120572 =1

119898 (1)


119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(119862119894minus1

minus 119862119894)]120572(1+120572)

(119905119894minus 119905119894minus1

)1(1+120572)

(2)


|(119905) to |119866lowast


lowast



119862119905

= 1198620

minus 1198621

(119863)1198622 (3)

where 1198620 1198621 and 119862






119873119865

= 119860 (120574max)119861

(4)


119860 =119891 (119863119891)119896

119896 (12058711986211198622)120572

119861 = 2120572

(5)


119896 = 1 + (1 minus 1198622) 120572 (6)


119889119863

119889119905= minus

120597119882

120597119863 (7)


119889119863

119889119905= (minus

120597119882

120597119863)

120572

(8)



119882 = 120587 sdot 1205740

2



119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894minus1minus

1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894)]120572(1+120572)

sdot (119905119894minus 119905119894minus1

)1(1+120572)

(10)


119889119863= minus120587119862

11198622

(119863)1198622minus1

(120574max)2

(11)


119863 (119905) = [1

(minus1205721198622

+ 120572 + 1) 119905]

(1(1205721198622minus120572minus1))

sdot [1

(120587119862111986221205872)

]

(120572(1205721198622minus120572minus1))

(12)






119878119879

=2119865

314 (ℎ119889) (13)

where












120590119905

=0382 sdot 119875

119887 sdot ℎ2

120576119905


3 sdot 1198712 minus 4 sdot 1198862

(14)

where





119878 =120590119905

120576119905

120601 = 360 sdot 119891 sdot 119904


CDE =

119873

sum119894=1

119863119894

(15)

where






Fatigue life 30∘C

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1

10

100

1000

10000

100000

1000000

10000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1 10Strain ()

1 10Strain ()

1 10Strain ()

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10



lowast







25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)





Binders 120572 119860





VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)




Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119873119865

= 119860 (120574max)119861

(4)


119860 =119891 (119863119891)119896

119896 (12058711986211198622)120572

119861 = 2120572

(5)


119896 = 1 + (1 minus 1198622) 120572 (6)


119889119863

119889119905= minus

120597119882

120597119863 (7)


119889119863

119889119905= (minus

120597119882

120597119863)

120572

(8)



119882 = 120587 sdot 1205740

2



119863 (119905) cong

119873

sum119894=1

[1205871205740

2

(1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894minus1minus

1003816100381610038161003816119866lowast1003816100381610038161003816 sin 120575

119894)]120572(1+120572)

sdot (119905119894minus 119905119894minus1

)1(1+120572)

(10)


119889119863= minus120587119862

11198622

(119863)1198622minus1

(120574max)2

(11)


119863 (119905) = [1

(minus1205721198622

+ 120572 + 1) 119905]

(1(1205721198622minus120572minus1))

sdot [1

(120587119862111986221205872)

]

(120572(1205721198622minus120572minus1))

(12)






119878119879

=2119865

314 (ℎ119889) (13)

where












120590119905

=0382 sdot 119875

119887 sdot ℎ2

120576119905


3 sdot 1198712 minus 4 sdot 1198862

(14)

where





119878 =120590119905

120576119905

120601 = 360 sdot 119891 sdot 119904


CDE =

119873

sum119894=1

119863119894

(15)

where






Fatigue life 30∘C

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1

10

100

1000

10000

100000

1000000

10000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1 10Strain ()

1 10Strain ()

1 10Strain ()

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10



lowast







25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)





Binders 120572 119860





VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)




Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















120590119905

=0382 sdot 119875

119887 sdot ℎ2

120576119905


3 sdot 1198712 minus 4 sdot 1198862

(14)

where





119878 =120590119905

120576119905

120601 = 360 sdot 119891 sdot 119904


CDE =

119873

sum119894=1

119863119894

(15)

where






Fatigue life 30∘C

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1

10

100

1000

10000

100000

1000000

10000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1 10Strain ()

1 10Strain ()

1 10Strain ()

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10



lowast







25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)





Binders 120572 119860





VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)




Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











Fatigue life 30∘C

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

01

1

10

100

1000

10000

100000

1000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1

10

100

1000

10000

100000

1000000

10000000

Fatig

ue L

ife (

traffi

c ind

icat

or)

1 10Strain ()

1 10Strain ()

1 10Strain ()

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10

VG 30PMB (S)

PMB (E)VG 10



lowast







25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)





Binders 120572 119860





VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)




Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










25 strain

VG 30PMB (S)

PMB (E)VG 10

50

500

5000

5 strain

VG 30PMB (S)

PMB (E)VG 10

500

5000

50000

Fatig

ue li

fe (

traffi

c ind

icat

or)

Fatig

ue li

fe (

traffi

c ind

icat

or)





Binders 120572 119860





VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

VG 1

0

VG 3

0

PMB

(S)

PMB

(E)

PMB

(S)

PMB

(E)

BC DBM SMAITSTSR

50

80

110

TSR

()

0500

100015002000250030003500400045005000

ITS

(kPa

)




Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

020000400006000080000

100000120000140000160000


1000 microstrains

VG 30

PMB (S)PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

VG 30

PMB (S)

PMB (E)

VG 10

0

20000

40000

60000

80000

100000

120000

140000

0

2000

4000

6000

8000

10000

12000

14000

BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM BC

DBM SM

A BCD

BM SMA

Fatig

ue li

feN

F

800 microstrains

VG 30

PMB (S)

PMB (E)

VG 100

500010000150002000025000300003500040000

BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A BC

DBM BC

DBM BC

DBM SM

A BC

DBM SM

A




119866119904119887

2712 2712 271119866119887

102 102 103 104 102 102 103 104 103 104119866119898119887

2454 2458 2451 2452 2455 2458 2462 2459 2324 2325119866119898119898

2556 2562 2554 2556 2558 2561 2565 2561 2422 2423OBC 49 51 51 51 47 47 48 48 67 67119881119886






500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










500

5000

50000

500000

Fatigue life BC

VG 10VG 30

PMB (S)PMB (E)

VG 10VG 30

PMB (S)PMB (E)

500

5000

50000


500

5000

50000

500000

Fatigue life SMA

PMB (S)PMB (E)

Fatig

ue li

feN

F

Fatig

ue li

feN

F

Fatig

ue li

feN

F

600 700 800 900 1000 1100500Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)

500 700 900 1100300Strain (10minus6 mm)







VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










VG 10

BCDBM


VG 30

PMB (S)

BCDBMSMA


PMB (E)

BCDBM


BCDBMSMA



R2 = 09873

y = 00572x + 10105

R2 = 09935

y = 00709x + 70153

R2 = 09947

y = 00724x + 67238

R2 = 09992

y = 00485x + 47814

R2 = 09982

y = 02063x + 74194

R2 = 09991

y = 0192x + 60915

R2 = 09975

y = 00666x + 34208

R2 = 09981

y = 0061x + 34445R2 = 09919

y = 00609x + 49753

R2 = 09948

y = 00598x + 46973

0

5000

10000

15000

20000

25000

30000

35000

Fatig

ue li

fe o

f bin

der

0

2000

4000

6000

8000

10000

12000

Fatig

ue li

fe o

f bin

der



0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der


0

1000

2000

3000

4000

5000

6000

Fatig

ue li

fe o

f bin

der



5 Conclusions




lowast











References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation


















References













































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation




































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









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