Engineering Fracture Mechanics

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1 Engineering Frcture Mechnics 93 (2012) Contents lists vilble t SciVerse ScienceDirect Engineering Frcture Mechnics journl homepge: Mixed mode frcture resistnce of sphlt concrete mixtures M. Ameri,b,c, A. Mnsourin b,, S. Pirmohmmd d, M.R.M. Alih d,e, M.R. Aytollhi d School of Civil Engineering, Irn University of Science nd Technology, Irn b Trnsporttion Reserch Institute, Irn University of Science nd Technology, Irn c Center of Excellence of PMS, Trnsporttion nd Sfety, Irn d Ftigue nd Frcture Lb., School of Mechnicl Engineering, Irn University of Science nd Technology, Irn e Welding nd Joining Reserch Center, School of Industril Engineering, Irn University of Science nd Technology, Irn rticle info bstrct Article history: Received 20 December 2011 Received in revised form 23 My 2012 Accepted 24 June 2012 Keywords: Frcture resistnce Hot mix sphlt (HMA) Semi-circulr bend (SCB) Mixed mode I/II frcture Frcture resistnce of hot mix sphlt (HMA) is n importnt prmeter for chrcterizing the sphlt concrete probble performnce in cold climtes. In this reserch study, two types of semi-circulr bend (SCB) specimens contining n edge verticl crck re used nd subjected to symmetric three-point bending lod to mesure the criticl lod needed for clcultion of HMA frcture resistnce. The numericl nd experimentl results indicte tht the proposed test specimens would llow the mesurement of criticl lods under complete combintions of mixed mode deformtion rnging from pure mode I to pure mode II nd therefore cn be used s suitble specimens for investigting mixed mode crck deformtion of HMA mixtures t low tempertures. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Hot mix sphlt (HMA) concrete is perhps the most complicted mteril in flexible pvement system since its properties depend upon temperture nd loding conditions. Crcking is common mode of filure in sphlt concrete pvements especilly in cold regions. Therefore, investigtion of crck growth behvior in pvements is n importnt issue for design, construction nd mintennce of pvements in cold climtes. To investigte the crck growth behvior of HMA, frcture toughness is considered s one of the most importnt properties of HMA mixtures. Experimentlly, frcture toughness of HMA cn be computed using single edge notched specimen loded in three-point bending in ccordnce with Eqs. (1) nd (2) [1]. K IC ¼ P f tw 3 2 f W f 1 3 W ¼ W h 2 1:99 1 n oi W W 2:15 3:93 W þ 2:7 2 W ð2þ 21þ2 3 W 1 2 W In Eqs. (1) nd (2), P f is the criticl lod to filure, t nd W re the specimen thickness nd width respectively. is the initil crck length nd K IC is fundmentl mteril property tht mesures mteril resistnce ginst crck growth due to therml or externl mechnicl lods. A higher vlue of K IC indictes tht n sphlt mixture hs better resistnce to crck growth nd propgtion of pre-existing flws in rel pvement structures. ð1þ Corresponding uthor. Tel.: ; fx: E-mil ddress: _mnsourin@iust.c.ir (A. Mnsourin) /$ - see front mtter Ó 2012 Elsevier Ltd. All rights reserved.

2 154 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Nomenclture B HMA K I K If K II K IIf L P P cr R S 1, S 2 SCB t W Y I Y II crck length specimen height hot mix sphlt stress intensity fctor for mode I criticl stress intensity fctor for Mode I stress intensity fctor for mode II criticl stress intensity fctor for Mode II distnce of verticl crck from center of specimen criticl lod to filure frcture lod rdius of specimen distnces of supports from verticl crck position semi-circulr bend specimen thickness of specimen Width of specimen Shpe fctor for mode I Shpe fctor for mode II Greek symbols crck ngle At subzero nd very low tempertures, HMA mixture behvior my be considered liner elstic [2 5]. Force displcement digrms obtined experimentlly by Li nd Mrstenu [4] s well s the experimentl reserch works conducted by Kim et l. [5] show tht t very low tempertures, HMA behves in liner elstic mnner up to the mximum lod nd thus the frmework of liner elstic frcture mechnics (LEFM) would be pplicble to this type of mteril t very low tempertures [4,6]. In recent numericl study conducted by uthors, it ws shown tht crcked pvement experiences mixed mode I/II (tensile-sher) deformtion when vehicle psses from the neighborhood of crck [7]. Consequently, ll deformtion modes cn ffect the frcture behvior of rel crcked sphlt pvement. For such conditions, stress intensity fctors cn be used s fundmentl prmeters to chrcterize pvement filure due to brittle frcture nd/or ftigue crck growth deformtion. A review of pst experimentl reserch works indictes tht Bhgt nd Herrin, Mjidzdeh, Monismith et l. nd Witczk nd his coworkers were of the pioneered reserchers who hve conducted experimentl works to obtin frcture resistnce of sphltic mterils [8]. They ll hve used prismtic rectngulr bem specimens with verticl edge crck t the center subjected to three or four-point bending lods. In recent yers, Molenr nd his coworkers [9 11] conducted both experimentl nd numericl studies to investigte crck growth resistnce of vrious sphlt mixtures. They used different test specimens such s the semi-circulr bend (SCB) specimen, the verticl edge crcked rectngulr prismtic bem specimen subjected to four-point bending lods nd the center crck plte under tension. Chen et l. [12] lso employed the SCB specimen to study the effect of temperture on the tensile strength nd frcture toughness of HMA mixtures. Some reserchers hve lso investigted the crck growth in sphltic mterils using some other test smples such s rectngulr nd disc shpe compct tension specimens [1,13]. In most of the mentioned studies, crck growth of sphlt mixtures hs been investigted only under mode I or tensile lods. Among the few vilble investigtions in this re, Brhm nd Buttlr [14] studied the pure Mode II or sher mode crck growth resistnce of n sphlt mixture experimentlly using prismtic bem specimens with two opposing verticl edge crcks on ech side of the bem subjected to nonsymmetricl four-point bending lods. They conducted their experimentl study t 10 C nd concluded tht t this temperture, the HMA behvior for pure mode II frcture is liner elstic. In nother experimentl study conducted by Brhm nd his coworkers [15], to evlute the crck growth resistnce of HMA under pure mode I nd pure mode II loding, they concluded tht 4 to 5 times more frcture energy is required to promote the crck extension in pure mode I thn it is needed for pure mode II frcture. There re generlly two pproches for investigting the mechnicl behvior of sphlt mixtures: (1) micro-structurl models in which the ggregtes, voids, nd in some extent, rndomicity hve to be considered. (2) mcro-structurl models in which the bulk mteril is often ssumed to behve like uniform or homogeneous mteril. While mny ppers (including the present pper) hve dopted the second pproch when deling with sphlt mixture in mcro-scle, some reserchers hve lso ttempted to study the crck growth behvior of HMA under mixed mode I/II loding using micro- nd meso-mechnicl frcture models (see for exmple [16,17]). Since finite element method is powerful tool for simulting nd investigting crck growth of HMA mixtures, Ameri et l. [7] recently performed severl 3D finite element nlyses of pvement structure to configure predominnt modes of deformtion in n sphlt lyer tht contins top-down trnsverse crck [7]. They found tht depending on the vehicle loction reltive to the crck plne, sher modes sometimes ply n importnt role in the crck deformtion. Therefore, it is

3 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) importnt to investigte mixed mode I/II frcture in crcked sphlt smples using pproprite test specimens. In this pper, two new SCB specimens re used to conduct series of mixed mode I/II frcture tests on n sphlt mixture smple. The crck prmeters re clculted for these specimens using finite element method nd the dvntges of new specimens re discussed. 2. Selection of pproprite specimen geometry Selection of pproprite compcted HMA test specimen tht would properly simulte the rel sttus of crck growth in pre-crcked sphlt lyer is essentil. The dvntge of using SCB specimen to conduct frcture tests is tht its fbriction is simple nd the edge crck my be cut verticlly or t ny inclined ngle. One my use cored specimen tken from pvement structure or fbricte it using conventionl Gyrtory Compctor Mchine. Aytollhi nd Alih [18] numericlly investigted the clssicl SCB specimen contining n inclined edge crck subjected to three-point bending (shown in Fig. 1) under different combintions of mode I nd mode II loding. For wide rnges of crck lengths nd crck ngles, they performed numerous finite element nlyses nd clculted the stress intensity fctors for pure mode I, pure mode II nd mixed mode I/II crck deformtions. They lso obtined geometric shpe fctors for ech of these frcture modes nd concluded tht the SCB specimen shown in Fig. 1 is good cndidte for conducting experimentl tests to mesure frcture resistnce of brittle nd qusi-brittle mterils like rock. However, cutting n inclined edge crck in sphlt mixtures is often difficult nd sometimes leds to brekge of some ggregtes in the shrp corner t the center of semi-circle. Therefore, cutting n edge crck norml to the flt side of the SCB specimen is preferred for HMA mixtures. Two types of modified SCB specimens re suggested here in which crck is norml to the dimetrl edge of specimen (see Fig. 1b nd 1c). In these specimens, the mode mixity is controlled through the positions of the two bottom supports. Fig. 1 shows the loding configurtions tht would simulte mixed mode I/II (tensile-sher) deformtion in the SCB specimen tht contin verticl or n inclined crck. From this Figure, it cn be observed tht by chnging the crck ngle or by chnging the distnce of bottom support from the verticl crck position, or by cutting n off-centered verticl notch, sttus of the mixed mode I/II deformtion chnges. Pure mode I deformtion occurs when inclintion of the crck line to the pplied lod is zero ( = 0) (or the supporting distnces re symmetric with respect to the loding position nd lso position of the verticl crck). By grdully incresing inclintion of the crck ngle from zero or by chnging one of the two supports distnce from the verticl crck position, mixed mode deformtion occurs. At specific inclintion ngle (or supporting distnce from the verticl crck position) pure mode II deformtion will occur. Fig. 2 shows typicl finite element mesh used for modeling the SCB specimen with bout 2800 eight-node rectngulr plne stress elements. Considering the subzero working temperture, liner elstic mteril model with homogenous prop-clssicl SCB specimen b-modified specimen SCB-1 c-modified specimen SCB-2 Fig. 1. Different loding configurtions tht simulte mixed mode I/II for three types of SCB specimens. Fig. 2. Typicl finite element mesh used for modeling SCB specimen nd crck tip region.

4 156 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) erties ws ssumed for the modeled HMA. The Young s modulus nd Poisson s rtio of the SCB mteril were tken s MP nd 0.35, respectively. The specimen ws subjected to 1 kn concentrted sttic lod s reference vlue pplied t mid-spn on the top surfce of the specimen. The boundry conditions for this model is considered in such wy tht displcements in both directions re constrined in the left support nd is verticlly constrined in the right support. Finlly, the stress intensity fctors were directly derived from the results of the numericl nlyses performed by ABAQUS softwre which uses the properties of pth-independent contour integrls for clculting the stress intensity fctors. In ech numericl nlysis, knowing the vlues of S 1,S 2 nd the crck length, the vlues of stress intensity fctors re clculted by chnging the reltive position of the crck to the disc center (i.e. the length L in the Fig. 1b) SCB-1 specimen For most modeling cses, mixed mode I/II loding tkes plce. There exist some specific situtions of loding tht pure modes occur. The corresponding situtions re presented in Tble 1 for the SCB-1 specimen. For this specimen, the stress intensity fctors (K I nd K II ) cn be written s: K I ¼ P pffiffiffiffiffiffi p YI 2Rt R ; L R ; S 1 R ; S 2 R K II ¼ P pffiffiffiffiffiffi p YII 2Rt R ; L R ; S 1 R ; S 2 R : In which Y I nd Y II re the shpe fctors of mode I nd mode II, respectively. Other prmeters re shown in Fig. 1b. Knowing the loding condition, geometry nd lso the stress intensity fctors obtined from the softwre, the shpe fctors of modes I nd II were clculted in ccordnce with Eq. (3). Selected numericl results re presented in Figs. 3 8 s exmples. More detils of numericl results cn be found in [19]. ð3þ 2.2. SCB-2 specimen The finite element nlyses were lso conducted for clculting the shpe fctors of the SCB-2 shown in Fig. 1c. This cse is ctully specil sitution in the SCB-1 specimen which ws ddressed erlier. All the modeling procedures of the two cses re the sme, except tht in the SCB-2 specimen the crck is considered in the center of the semicircle nd only the supports re moved. After clculting the stress intensity fctors, the shpe fctors re clculted by the following eqution: Tble 1 Pure mode I nd pure mode II situtions in the SCB-1 specimen nd the respective vlues of stress intensity fctors for P = 1 kn. Loding conditions nd geometry Sitution of pure mode I (mm) p K I ðmp ffiffiffiffi m Þ Sitution of pure mode II (mm) p KII ðmp ffiffiffiffi m Þ (S 1,S 2 ) = (30,30) nd /R = 0.2 L = L = (S 1,S 2 ) = (30,30) nd /R = 0.4 L = L = (S 1,S 2 ) = (40,20) nd /R = 0.2 L = L = (S 1,S 2 ) = (40,20) nd /R = 0.4 L = L = (S 1,S 2 ) = (40,10) nd /R = 0.2 L = L = (S 1,S 2 ) = (40,10) nd /R = 0.4 L = Fig. 3. Mode I shpe fctor in the SCB-1 specimen for loding condition (S 1,S 2 ) = (30,30).

5 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Fig. 4. Mode II shpe fctor in the SCB-1 specimen for loding condition (S 1,S 2 ) = (30,30). Fig. 5. Mode I shpe fctor in the SCB-1 specimen for loding condition (S 1,S 2 ) = (40,20). Fig. 6. Mode II shpe fctor in the SCB-1 specimen for loding condition (S 1,S 2 ) = (40,20). K I ¼ P pffiffiffiffiffiffi p YI 2Rt R ; S 1 R ; S 2 R K II ¼ P pffiffiffiffiffiffiffi p YII 2Rt R ; S 1 R ; S ð4þ 2 R

6 158 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Fig. 7. Mode I shpe fctor in the SCB-1 specimen for loding condition (S 1,S 2 ) = (40,10). Fig. 8. Mode II shpe fctor in the SCB-1 specimen for loding condition (S 1,S 2 ) = (40,10). For brevity, only the finl FE results which contin the geometry shpe fctors re presented. The vritions of mode I nd mode II shpe fctors in the SCB-2 specimen re shown in Figs for /R = 1/2 nd 1/3. More numericl results cn be found in [19]. As it cn be seen from Figs. 9 12, the SCB-2 specimen cn develop different cses of mixed mode loding conditions from pure mode I to pure mode II. In this specimen, moving from symmetric loding (S 1 =S 2 ), the crck deformtion stte chnges 6 /R=1/2 5 4 Y I S1/R=2/3 S1/R=1/2 S1/R=1/3 S1/R=1/ S2/R Fig. 9. Mode I shpe fctor in the SCB-2 specimen for crck length rtio of /R = 1/2.

7 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Y II /R=1/2 S1/R=2/3 S1/R=1/2 S1/R=1/3 S1/R=1/ S2/R Fig. 10. Mode II shpe fctor in the SCB-2 specimen for crck length rtio of /R = 1/2. Y I /R=1/ S1/R=2/3 S1/R=1/2 S1/R=1/ S2/R Fig. 11. Mode I shpe fctor in the SCB-2 specimen for crck length rtio of /R = 1/3. 2 /R=1/3 Y II S1/R=2/3 S1/R=1/2 S1/R=1/ S2/R Fig. 12. Mode II shpe fctor in the SCB-2 specimen for crck length rtio of /R = 1/3. to mixed cse of opening nd shering nd finlly to pure sher deformtion mode. Also by incresing the crck length nd S 1, the dimensionless vlue of Y I increses. Incresing S 2 will decrese Y II. Therefore, the two proposed SCB specimens cn potentilly be pproprite for ssessing the crck growth behvior in tensile-sher mode deformtion of sphlt mixtures.

8 160 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) The prcticl cpbility nd performnce of these specimens in mesuring frcture resistnce of sphlt mixtures should be investigted through lbortory experiments on these specimens. 3. Shpe fctors for test specimens The lbortory specimens were 15 cm in dimeter nd the crck length ws 2 cm. It should be mentioned tht Molenr nd Molenr [9] hve shown tht the criticl stress intensity fctor in sphlt mixtures is independent of the thickness of the specimen in the rnge of mm. Therefore, in this reserch study the thickness of SCB specimens ws bout 30 mm in order to fll within this rnge. Molenr nd Molenr [9] lso performed series of experiments on the SCB specimens of dimeters 10, 15 nd 22 cm t subzero tempertures nd showed tht the specimen size hs negligible effects on the frcture resistnce of sphlt mixtures under the mentioned conditions. Thus, no size limittion study ws performed in the present reserch nd the dimeter of 15 cm ws dopted for the SCB specimens bsed on the results reported in [9]. The vlues of shpe fctors of the selected specimens tested in this reserch study were obtined through finite element nlysis of the specimens with specific dimensions mentioned bove. In ddition to pure mode I nd pure mode II loding, four cses of mixed mode I/II loding were lso evluted. The vlues of S 1,S 2 nd the prmeter of distnce between crck nd middle line of specimen (L) together with the vlues of shpe fctors for the SCB-1 specimens re presented in Tble 2. Tble 3 shows the vlues of S 1 nd S 2 used for creting different loding cses for the SCB-2 specimens. The shpe fctors obtined through finite element (FE) nlyses re lso presented in Tble 2. As shown in Tbles 2 nd 3, in ll experiments S 1 ws fixed nd equl to 50 mm. The SCB-1 tests were lso performed ll with S 2 = 20 mm. Different mixed mode conditions were provided by chnging L in the SCB-1 specimen nd by chnging S 2 in the SCB-2 specimens. For esy understnding, the specimens re designted s SCB-x-y in which x indictes the type of specimen (i.e. 1 or 2) nd y indictes the vlues of L in the SCB-1 nd S 2 in the SCB-2 specimens. The SCB-x-y designtion hs been used in Tbles 2 nd 3 nd Tbles 5 7 for describing the specimens tested under pure mode I, pure mode II nd mixed mode I/II loding. In the mentioned Tbles, M e is the mixity prmeter nd is defined by the Eq. (5) [18]. M e ¼ 2 K I p tn 1 ð5þ K II The mixity prmeter M e defines the reltive contribution of modes I nd II. For pure mode I, M e = 1 nd for pure mode II the prmeter M e is zero. For ech test specimen, the finite element nlysis ws performed for reference lod of P = 1000 N, thickness t = 30 mm, specimen rdius R = 75 mm nd crck length = 20 mm. The stress intensity fctors K I nd K II were obtined directly from ABAQUS. The shpe fctors Y I nd Y II were then clculted by Eq. (6). The results re given in Tbles 2 nd 3 for both lbortory test specimens. Y I ¼ K I pffiffiffiffiffiffi 2Rt p P Y II ¼ K II pffiffiffiffiffiffi 2Rt ð6þ p P Tble 2 FE results of shpe fctors for the SCB-1 specimens used in experiments. Specimen Loding mode S (mm) Shpe fctor for mode I (Y I ) Shpe fctor for mode II (Y II ) M e SCB-1-0 Mixed mode I/II (S 1,S 2 ) = (50,20) nd L = SCB-1-3 Mixed mode I/II (S 1,S 2 ) = (50,20) nd L = SCB-1-7 Mixed mode I/II (S 1,S 2 ) = (50,20) nd L = SCB-1-11 Mixed mode I/II (S 1,S 2 ) = (50,20) nd L = SCB-1-17 Pure mode II (S 1,S 2 ) = (50,20) nd L = Tble 3 FE results of shpe fctors for the SCB-2 specimens used in experiments. Specimen Loding mode S (mm) Shpe fctor for mode I (Y I ) Shpe fctor for mode II (Y II ) M e SCB-2-50 Pure mode I ðs 1 ; S 2 Þ¼ð50; 50Þ SCB-2-22 Mixed mode I/II ðs 1 ; S 2 Þ¼ð50; 22Þ SCB-2-18 Mixed mode I/II ðs 1 ; S 2 Þ¼ð50; 18Þ SCB-2-15 Mixed mode I/II ðs 1 ; S 2 Þ¼ð50; 15Þ SCB-2-12 Mixed mode I/II ðs 1 ; S 2 Þ¼ð50; 12Þ SCB-2-9 Pure mode II ðs 1 ; S 2 Þ¼ð50; 9Þ

9 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Tble 4 HMA ggregte grdtion. Sieve size(mm) Requirements Percent pssing Min Mx Tble 5 Results of pure mode I frcture tests on sphlt mixture using SCB-2 specimen. Specimen type M e p t (cm) P cr (kn) K If MP ffiffiffiffi m p K IIf MP ffiffiffiffi m Averge K v p If MP ffiffiffiffi m SCB K v p IIf MP ffiffiffiffi m Tble 6 Criticl stress intensity fctors K IIf for HMA specimens under pure mode II loding. Specimen types M e p t (cm) P cr (kn) K If MP ffiffiffiffi m SCB-1-17 S 1 =50mm S 2 =20mm L =17mm SCB-2-9 S 1 =50mm S 2 =9mm p K IIf MP ffiffiffiffi m Averge K v p If MP ffiffiffiffi m K v p IIf MP ffiffiffiffi m * * * * * * * * * * Test results re not reported becuse the mode II frcture tests conducted re not vlid (becuse frcture did not initite from the crck tip). 4. Mteril nd testing procedure Asphlt cement with penetrtion grde of (widely used in the Irn pvement systems) ws utilized s binder. The nominl mximum ggregte size of 12.5 mm nd the ir void content of 4% were used for prepring the HMA mixture. Tble 4 shows the ggregte grdtion of the sphlt concrete specimens. After determining the crck position in the semi-circulr test specimens, for ech specific mixed mode I/II condition, crcks were generted using rotry bldes in lower edge of semi-circulr specimens nd on pproprite loctions designted through the FE clcultions. In this wy, the SCB lbortory specimens were crcked in the SCB-1 nd SCB-2 smples under six loding conditions noted in Tbles 2 nd 3. For ech loding condition, t lest 6 lbortory specimens were mde to be used in the frcture tests nd ll the specimens were mintined in freezer so the testing temperture would be t -10 C.

10 162 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Tble 7 Criticl stress intensity fctors of HMA specimens (K If nd K IIf ) under different cses of mixed mode loding. Specimen type M e p t (cm) P cr (kn) K If MP ffiffiffiffi m p K IIf MP ffiffiffiffi m Averge K v p If MP ffiffiffiffi m K v p IIf MP ffiffiffiffi m SCB SCB SCB SCB SCB SCB SCB SCB

11 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Tble 7 (continued) Specimen type M e p t (cm) P cr (kn) K If MP ffiffiffiffi m p K IIf MP ffiffiffiffi m Averge K v p If MP ffiffiffiffi m K v p IIf MP ffiffiffiffi m SCB SCB SCB Fig. 13. Loding frme nd smple pth of frcture. Ech specimen ws loded in constnt rte three-point bending test till its finl fcture. Fig. 13 depicts the loding nd frcture procedure of typicl lbortory specimen. In this reserch, the loding rte ws similr to the one used by Molenr nd Molenr [9] for 15 cm dimeter specimens nd ws 3 mm/min. During the tests, the lod displcement curve for ech specimen ws recorded by personl computer. A smple lod displcement curve is presented in Fig. 14. The liner reltionship between the lod nd displcement nd sudden frcture indicte brittle behvior of sphlt mixtures t 10 C. In this cse, the frcture resistnce vlues of ech specimen cn be clculted by obtining the criticl frcture lod. 5. Test results In this prt of reserch, the purpose of lbortory testing is to obtin the frcture resistnce of conventionl sphlt concrete mixtures tht is used in construction of Irnin pvement network nd ssess its strength ginst crcking. Therefore,

12 164 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) Fig. 14. Lod displcement curve for one of the sphlt concrete specimens. in this section, the wy of clculting criticl stress intensity fctors bsed on the vlue of criticl frcture lod (obtined through the results of tests conducted on HMA specimens) is explined first. The criticl stress intensity fctors for modes I nd II i.e. K If nd K IIf re computed using Eqs. (7 nd 7b): K If ¼ Y I P cr 2Rt K IIf ¼ Y II P cr 2Rt pffiffiffiffiffiffi p pffiffiffiffiffiffi p in which R is the rdius of specimens (R = 7.5 cm), is the crck length ( = 2 cm) nd t is the thickness of specimens given in Tbles 5 7. P cr is the frcture lod which is obtined from the experiments. The vlues of Y I nd Y II re given in Tbles 2 nd 3. Therefore, by using these dt the vlues of K If nd K IIf cn be clculted. A totl number of 8 SCB-2 specimens cooled in freezer t the temperture of 10 C were used for pure mode I frcture tests. The specimens were loded in such wy tht the lower supports were symmetric reltive to crck position nd the crck ws exctly in the center of the bottom edge. The criticl lod ws recorded for ech specimen nd finlly the mode I criticl stress intensity fctor (or K If ) ws clculted ccording to Eq. (7). The vlues of mode I frcture resistnce K If with their verge re given in Tble 5. A smple specimen frctured under pure mode I is shown in Fig. 15. Pure mode II frcture tests were performed on both SCB-1 nd SCB-2 specimens while frozen t 10 C. Eight SCB-1 specimens nd six SCB-2 specimens were used for mode II frcture tests on the HMA mixture. The test specimens were loded ð7þ ð7bþ Fig. 15. A smple HMA specimen frctured under pure mode I loding.

13 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) SCB-1 SCB-2 Fig. 16. Smples of HMA specimens frctured under pure mode II loding. Fig. 17. A mode II frcture test on HMA using SCB-2 specimen with uncceptble frcture trjectory. SCB-1-3 SCB-1-0 SCB-1-11 SCB-1-7 Fig. 18. Smple SCB-1 specimens frctured under different combintions of mode I nd mode II.

14 166 M. Ameri et l. / Engineering Frcture Mechnics 93 (2012) SCB-2-18 SCB-2-22 SCB-2-12 SCB-2-15 Fig. 19. Smple SCB-2 specimens frctured under different combintions of mode I nd mode II. using three-point loding fixture ccording to the geometricl properties mentioned in Tbles 2 nd 3. For ech test smple, the criticl frcture lod ws recorded nd the criticl stress intensity fctor ws clculted using Eq. (7b). The vlues of mode II frcture resistnce (K IIf ) together with the verge vlue obtined from ech specimen re given in Tble 6. Fig. 16 shows two smples frctured under pure mode II loding for ech of the SCB-1 nd SCB-2 specimens. In some of the SCB-2 specimens, mode II frcture ws not initited from the crck tip. Insted, new crck ws nucleted from the bottom right support nd propgted towrds top loding point. Fig. 17 shows smple of mode II test specimens with uncceptble pttern of crck growth. These cses (designted by sign in Tble 6), were considered s invlid tests. To conduct the experiments under mixed mode loding (tension-sher loding), the specimens were prepred nd were put in freezer t -10 C. The loding ws in ccordnce with the vlues of S 1 nd S 2, nd L given in Tbles 2 nd 3, nd the criticl lods were recorded. Finlly the frcture resistnce ws clculted using Eqs. (7 nd 7b). The vlues of K If nd K IIf together with their verges for ech mixed mode cse re given in Tble 7. The specimens frctured under mixed mode I/II re shown in Fig. 18 for SCB-1 specimen nd in Fig. 19 for SCB-2 specimen. It is seen in Tble 7 tht gin in some of the SCB-2 test cses, frcture did not initited from the crck tip nd the tests were invlid. Such invlid tests (designted by sign) were more frequent for mode II dominted loding conditions. Therefore, one my suggest tht the SCB-1 specimen is more pproprite for performing mixed mode frcture tests on HMA mixture. 6. Conclusions In this pper, finite element method ws used to clculte the vlues of shpe fctors for two types of SCB specimens proposed for mesuring the mixed mode frcture resistnce of HMA mixtures. Cutting norml crck insted of n inclined crck is one of the dvntges of the proposed SCB specimens compred with the clssicl SCB specimens. Both types of specimens used in this reserch study hve similr potentil for mesuring mixed mode frcture resistnce of HMA, lthough the SCB-1 specimen ws found to be more suitble. The testing procedure presented in this reserch study cn be used to determine the mixed mode frcture resistnce of HMA t low tempertures. Typicl vlues of K If nd K IIf presented in Tble 7, my be used to evlute the HMA resistnce ginst mixed mode crck growth. Acknowledgement The uthors would like to cknowledge the finncil support for this reserch provided by the Trnsporttion Reserch Institute under the contrct 88B5T2P28 (RP).

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