Construction and Building Materials 26 (2012) 694–700

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Construction and Building Materials

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Development of a double-torsion fracture test to predict channelized crackbehaviors of asphalt concrete

Hyunwook Kim ⇑, Manfred N. PartlEmpa, Swiss Federal Laboratories for Materials Testing and Research, CH-8600 Dübendorf, Switzerland

a r t i c l e i n f o

Article history:Received 29 June 2010Received in revised form 20 June 2011Accepted 23 June 2011Available online 19 July 2011

Keywords:Bituminous materialsFractureDouble-torsionComplianceStress intensity factor

0950-0618/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.conbuildmat.2011.06.076

⇑ Corresponding author. Tel.: +41 44 823 4474; faxE-mail addresses: hyunwook.kim@empa.ch, hkim2

a b s t r a c t

Fracturing of asphalt concrete paving surfaces and overlays is a significant cause of premature pavementdeterioration. Fracture mechanics and the proper handling of crack propagation are much needed tounderstand the mechanisms that are relevant for increasing pavement life. The topic is still quite widein the field of asphalt pavement design and analysis. This paper shows the experimental developmentof a double-torsion fracture test for predicting fundamental fracture properties of bituminous materials.Double-torsion test specimens were prepared from a model asphalt material using an automatic Frenchslab compactor. Double-torsion tests were performed at low temperatures to investigate brittle and/orquasi-brittle behavior of bituminous materials. A constant displacement control method was appliedto obtain reliable fracture properties of bituminous materials. Test geometry with different notch lengthswas considered to obtain a standard specimen configuration without any unexpected failure. Character-istic fracture properties from double-torsion tests were determined based on the linear elastic fracturemechanics theory including compliance. Experimental results showed that the notch length was not asignificant factor in the determination of stress intensity factor properties from double-torsion fracturetests on the model material used in this study.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Asphalt concrete is a quasi-brittle composite material, which iscomposed of brittle aggregates and viscous bituminous binder.Asphalt concrete becomes more brittle at low temperatures,especially under high frequency loading conditions, as shown inprevious studies on the fracture behavior of asphalt concrete atlow temperatures. Different test methods were used. Three-pointbending beam tests were the popular application for investigatingthe fracture mechanism of asphalt concrete [1,2]. Also, disk-shapedcompact tension tests and semi-circular tests were applied tostudy the fracture toughness of asphaltic materials [3–5]. However,a new fracture test method for considering the longitudinal crackbehavior caused by traffic wheel loads was needed. In reality, thereare many repeated traffic wheel loads on the pavement and theywill make fatigue cracks through the direction of traffic loading.Authors wanted to develop a realistic fracture test to considerthe channelized cracking by repeated traffic wheel loads as shownfrom the conceptual insight in Fig. 1.

For a wide range of materials including ceramics [6–8], glasses[9], composites [10], cement concrete [11], polymers [12,13], steels

ll rights reserved.

: +41 44 821 6244.9@gmail.com (H. Kim).

[14], and rocks [15,16], the double-torsion (DT) approach has beenused in the fracture mechanics field for investigating both criticalcrack growth (fracture toughness measurement) and subcriticalcrack propagation. However, surprisingly, this method has notbeen applied for bituminous materials so far. Crack can start froma critical defect, growing very slowly at first, and then acceleratingunder further load until the part finally fails. This behavior isknown as subcritical crack propagation. The advantages of DT testsare following: (1) the test configuration consists of simple speci-men geometry and inexpensive experimental set-up; (2) theobtaining fracture property, the stress intensity factor, is the firstapproximation and independent of crack length for a range of cracklengths in DT specimens; (3) comprehensive crack measurementsmay not be needed when the constant loading techniques; and(4) DT tests can characterize both the crack channeling, which isa typical pavement longitudinal crack behavior, and fatigue crack-ing under repeated traffic loads. In this study, a DT fracture test forbituminous materials was developed and implemented to predictthe crack channelizing and to obtain the fracture properties. Inthe beginning of study, there were many trial test configurationsand specimen geometries for obtaining the reliable test results atlow temperatures. DT tests were performed with different notchlengths and loading speeds to investigate the response dependen-cies of fracture behavior.

Fig. 1. Fatigue crack behavior caused by repeated traffic loads.

Fig. 2. Aggregate gradation of asphalt mixture.

Table 1Marshall properties of AC4.

Asphalt mixture (AC4)Percentage of binder 8.0 Mass%Density 2407 kg/m3

Area density (SSD) 2296 kg/m3

Percentage of air void 4.6 vol.%Voids in the mineral aggregate (VMA) 22.5 vol.%Voids filled with asphalt (VFA) 79.4 vol.%

Marshall propertiesMarshall stability 11.1 kNMarshall flow 2.7 mm

H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700 695

2. Materials

Asphalt binder, bitumen 70/100, based on the penetration grade system accord-ing to the European standard EN 12591 [17] and commonly used for asphalt pave-ment surface mixtures in Switzerland was selected for this study. According toEuropean Standard EN 13108-1 [18], asphalt mixture, AC4, with relatively smallnominal maximum aggregate size was used as a model material to obtain homoge-neous and repeatable test results. The aggregate gradation curve of asphalt mixtureis shown in Fig. 2. Table 1 shows material properties of the asphalt mixture andMarshall test results following the series of European standards EN 12697-34[19] and EN 12697-35 [20].

3. Experimental procedure

3.1. Specimen preparation

Asphalt concrete slabs were compacted by an automatic steelroller compactor, developed by Laboratoire Central des Ponts etChaussées (LCPC) in France [21]. The asphalt slabs were 500 mmlong with a rectangular cross section of 180 width and 20 mmthickness. The constant load magnitude of the steel roller was5 kN. The bottom plate of steel mold is gradually lifted during com-paction such that the contact surface of the steel roller with thespecimen always remains at a constant level during the roller pass-ing. For compacting asphalt specimens, the hot asphalt concretemixture was firstly filled into a pre-heated steel mold with an alu-minum bottom plate and compacted until obtaining the targeted20 mm specimen thickness.

There have been some studies for finding proper DT specimengeometries with other materials. Evans and Wiederhorn [22] andAtkinson [23] showed experimentally that specimen width wshould be 12 times greater than thickness d. Pletka et al. [24]suggested that the specimen length l should be greater than twicethe value of w. Therefore, the size of the DT specimen should be

12d < w < l=2 ð1Þ

In addition, Trantina [25] used a finite element analysis to showthat KI (the stress intensity factor in mode-I, pure tensile mode)was independent in an operational range with 5% deviations ofKI. The operational range was

0:55w < a < l� 0:65w ð2Þ

According to the above constraint, the experimental study ofShetty and Virkar [26] determined as operational the followingranges of crack lengths:

0:50w < a < l� 1:0w ð3Þ

0:4w < a < l� 0:8w ð4Þ

Most recently, Ciccotti et al. [27] performed detailed three-dimensional finite element analyses for various range of DT testspecimens (170 mm < l < 250 mm and 60 mm < w < 100 mm). Theyanalyzed both the range determined by Trantina [25] and thedimension proposed by Shetty and Virkar [26]. Based on theirinvestigations, the operational ranges were not consistent due todifferent loading conditions and different thickness. Also, they con-cluded that appreciable deviations can be from the classical analyt-ical predictions of strain energy release rate (g). A guide groove isnecessary to control the crack path in DT specimens due to the het-erogeneity of materials. There were some studies related to thenotch shape effects in DT fracture tests [15,28]. Swanson [29] men-tioned that the guide groove geometries (sizes and shapes) had nosignificant effects of reducing the scatter of DT test on rocks. How-ever, Nara and Kaneko [16] later tested rock DT specimens withthree different groove shapes using rectangular, semi-circular,and the triangular section grooves. They concluded that the levelof reproducibility was highest for the rectangular guide groovespecimens.

In this paper, the selected proper specimen dimension relied onprevious DT studies but the specimen dimension was not limitedto the definition from the previous studies because of differentmaterial characteristics, e.g. different level of heterogeneity likethe relatively large aggregates embedded in asphalt mixtures andthe viscous behavior from bituminous binder. Fig. 3 shows thespecimen geometry for DT fracture tests. DT specimens were cutfrom asphalt slabs compacted by French roller compactor withdimensions as shown in Table 2. The thickness of 20 mm was cho-sen because the double-torsion fracture test concept was based onthe thin plat theory and DT specimens should have enough thick-ness, more than three times than the maximum aggregate size, toreduce the aggregate dependency on test results. Beam length of300 mm, twice than the width and more than six times than thethickness, was chosen to produce reasonable bending conditionswithin the size limitation of the temperature chamber. In thisstudy, the rectangular guide groove was made on the bottomsurface of DT specimen and the notch lengths (a) were varied with0, 30, 60, and 85 mm.

gw

A A

Groovegd

dl

w

l

dA A

wm

a

wpx

wo

Groove

Notch

wpy

Fig. 3. Double-torsion specimen geometry.

Table 2Dimension of double-torsion specimen (unit: mm).

w w0 wm l d U wpx wpy a dl gd gw

150 10 65 300 20 10 20 20 0, 30, 60, 85 17 3 3

696 H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700

3.2. Testing method

DT asphalt specimens were placed on simple supported bars in-side of a temperature chamber under the mechanical loadingframe and round-shape point loading pins with 10 mm diameters(U) applied on the top of DT specimens with 1 mm/min monotonicloading speed. The span length of supporting bars was 130 mm andthe two loading bars were 40 mm apart. The distance betweenpoint loading positions and the outer edge of DT specimen was20 mm. The diameter of supporting steel rollers was 10 mm. Inmost cases, two to four replicates were used for experiments.Mechanical loading was applied and monitored at �10 �C using a10 kN load cell and the loading was controlled by the crossheadmovement. The beam deflection was measured by A linear variable

Fig. 4. DT test configurations: test set-ups and measurement (left) a

differential transducer (LVDT) placed on the top surface in the mid-dle of steel loading plate as shown in Fig. 4 (left). Fig. 4 (right)shows the details of DT loading point area and small pieces of rect-angular steel plates on the bottom of loading points for avoidingpunching effects at the loading positions. The test was conductedin a refrigerated environmental chamber capable of maintainingair temperature within ±0.2 �C during the test. The groove surfacewas located at the bottom surface of DT specimens because thecritical cracking usually starts from the crack tip of bottom surface.

3.3. Determination of fracture parameters

The DT fracture tests have received considerable attention as adirect method to determine the fracture toughness and the behav-ior of subcritical crack growth due to its simplicity and the possi-bility of conducting extensive crack propagation in a wide rangeof crack propagation rates under constant loading conditions orload relaxation tests [30]. A compliance analysis of DT fracture testindicates that the stress intensity factor, KI, is independent of thecrack length a [12]. The compliance C of solid materials, definedas the ratio of load point displacement (D) to the load (P), varieslinearly with crack length:

C ¼ DP¼ Baþ D ð5Þ

where B and D are empirical constants depending on materials.The expression for stress intensity factor takes the following

form:

KI ¼ Pwm3ð1þ mÞ

wd3dlwðd=wÞ

!1=2

ð6Þ

where P is the applied force, m is Poisson’s ratio, dl is the ligamentlength after subtracting the groove depth from d, and w(d/w) is acorrection factor for the specimen thickness [31] but thin speci-mens can be assumed as 1/3 [32]. The correction factor can be sig-nificant for beams thick relative to wide. The function of correctionfactor is

wðd=wÞ ¼ 1� 0:63022dw

� �þ 1:20

2dw

� �exp

pd

� �ð7Þ

The instantaneous crack length (ai) can be obtained then by thefollowing equation:

ai ¼ aþ Dai ¼ aþ Ci � C0

Bð8Þ

nd a double-torsion specimen under loading conditions (right).

H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700 697

where a is the initial notch length, C0 was calculated for each testfrom the initial slope of P–D curve in its elastic portion, Ci was ob-tained from lines radiating from the origin as shown in Fig. 5.

The theoretical crack propagation velocity (Vthe) can be calcu-lated based on the following equation [22]:

V the ¼dD=dt

PBð9Þ

where dD/dt is the velocity of loading bar during the crack propaga-tion test.

The averaged experimental crack propagation velocity (Vexp)can be determined based on the stable crack propagation lengthand measured time as following:

Vexp ¼Dac

Dt¼ Dc � D0

Dtð10Þ

where Dac is the stable crack propagation length until reaching thecatastrophic point (Dc) and Dt is the time spent for crackpropagation.

To determine the specific work of fracture, cwork, the work per-formed by the mechanical loading on the specimen can be calcu-lated based on the entire stable crack propagation path [33].From Fig. 6, the total energy was split into the critical energy(Uc) and the elastic energy (Uel). As shown in Eq. (11), the area un-der the force versus displacement curve up to the catastrophicpropagation point was divided by the corresponding projectedfracture surface area. The elastic energy stored in the system atthe catastrophic propagation point was also subtracted from thework performed by the test machine. The work of fracture at cata-strophic point is given by the following equation:

Fig. 5. Schematic of P–D curve and compliance.

Fig. 6. Graphic representation of the calculation of work of fracture.

cwork ¼Uc

2dlDac¼R Dc

0 ðP � DÞdD� 12 PcDc

2dlDacð11Þ

where Pc and Dc are, respectively, the loading force and the verticaldisplacement at the point where catastrophic propagation begins,and Dac = ac�a0, with ac obtained from the compliance curve. Uc

is presented in Fig. 6.

4. Results and discussion

4.1. Fracture behavior for DT specimens with different notch length

The applied force versus displacement curves in DT tests repre-sent the region of elastic deformation in the beginning of the curveand the region of stable crack propagation where the points beginto deviate from the straight line of elastic region including the pla-teau and the failure. Fig. 7 shows the applied force versus displace-ment curves for tested DT asphalt specimens with different notchlengths at �10 �C. In general, the length of stable cracking plateaubecomes shorter as the notch length increases. It is understandablethat specimens with longer ligaments can resist more against theapplied force and have more displacement at the displacementmeasurement or loading position. Also, the change of initial slopein Fig. 7 showed that DT specimens with longer notches can havehigher compliance or lower stiffness. However, the notch lengthdid not significantly or systematically contribute the values ofmaximum force.

Fig. 8 shows typical crack propagation through the guide grovemade on the bottom surface of DT specimen and also the side viewthrough the crack path of cracked specimens. The subcritical crackgrowth was not investigated in this paper because of using rela-tively thin specimens. From Fig. 8, the channelized crack in DTspecimens well followed the guide groove path but was not astraight line. The crack propagation still showed the arbitrary crackpath along the guide groove line to avoid the aggregates and/or tofollow the weakest material points. In future, some crack detectionor measurement approaches will be applied to determine the crackvelocity and investigate the behavior of subcritical crack growth inthick DT specimens.

The materials constants B and D were determined from theaveraged compliance values and notch length as shown in Fig. 9.The determined equations for the compliance of test specimens ex-tracted from the force versus displacement curves are:

C0 ¼ 3:2 � 10�6aþ 3:609� 10�7 ð12Þ

Cc ¼ 2:8 � 10�6ac þ 7:660� 10�7 ð13Þ

Fig. 7. Applied force versus displacement curves for asphalt concrete.

Fig. 8. Cracked DT specimens: crack path through the guide groove (left) and cracked area surface along groove lines (right).

698 H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700

As already discussed, the critical stress intensity factor, KIC, canbe determined from Eqs. (6) and (7). The assumed Poisson’s ratiowas 0.35. Fig. 10 shows the critical stress intensity factor versusnotch length plots with the average value of 1.351 MPa m1/2. Theaveraged deviation from KIC was 5% from the averaged KIC.

As shown in Fig. 11, theoretical and experimental crack propa-gation velocities were determined by Eqs. (9) and (10) and mea-sured experimental data. There was a good agreement betweentheoretical and experimental velocities. Averaged experimentalcrack propagation velocity can be determined based on the cracklength (Dac), as shown in Fig. 12, determined by initial and criticalcompliances and measured time at each compliance value. The

Fig. 9. Averaged compliance versus notch length for asphalt concrete.

Fig. 10. Mode-I stress intensity factor (KIC) versus notch length.

averaged stable crack propagation length for DT specimens withdifferent notch length was 112 mm. Fig. 12 shows that the notchlength did not have any influence on the critical crack length. Figs.13 and 14 show the distributions of applied energy, elastic energy,Uc, and work of fracture at different notch length. The averagedpercentage of elastic energy from the applied energy to DT speci-mens was 64.3%. The averaged work of fracture was 235 J/m2.

4.2. Fracture behavior for DT specimens under different loading speeds

Four different loading speeds, 0.5, 1, 2.5, and 5 mm/min, wereapplied to AC specimens at �10 �C with 30 mm notch length to

Fig. 11. Crack propagation velocity versus notch length.

Fig. 12. Stable crack propagation length versus notch length.

Fig. 13. Averaged energies obtained from DT specimens with different notchlength.

Fig. 14. Work of fracture for DT asphalt specimens with different notch length.

Fig. 15. P–d curves with different loading speeds.

Table 3Calculated averaged fracture parameters under different loading speeds at �10 �C.

Loading speed(mm/min)

Appliedenergy (N m)

Uel (N m) Uc (N m) cwork

(J/m2)KIC

(MPa m1/2)

0.5 2.52 1.64 0.88 245.57 1.3771 2.38 1.64 0.74 265.69 1.4602.5 2.16 1.59 0.57 224.70 1.5985 2.32 1.93 0.39 233.84 1.545

Average 2.35 1.70 0.65 242.45 1.491

H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700 699

investigate the dependency of loading speed to the fracture behav-ior of DT specimens. From Fig. 15, different loading speed affectsthe whole fracture behavior of DT specimens including initial stiff-ness and the length of stable crack propagation. Fracture parame-ters obtained from DT specimens under different loading speedscan be found in Table 3.

As shown in Fig. 16, the variation of work of fracture becomeslarger with increasing loading speed. This means that the repeat-ability of DT fracture tests is better in the condition of slower load-ing speed. Also, the averaged stable crack propagation lengthbecomes longer as the loading speed becomes slower (Fig. 17).

Fig. 16. Work of fracture in DT asphalt specimens under different loading speeds.

Fig. 17. Stable crack propagation length under different loading speeds.

Fig. 18. Experimental and theoretical crack propagation velocity under differentloading speeds.

700 H. Kim, M.N. Partl / Construction and Building Materials 26 (2012) 694–700

The favorable aspect of DT fracture is that DT tests should havelong enough stable crack propagation length to obtain betterrepeatable test results. From Fig. 18 you see above, the theoreticalcrack propagation velocity becomes diverge from experimentalcrack propagation velocity as the loading speed becomes faster.Based on the data trends from Figs. 17 and 18, slower loadingspeeds will be better than fast loading speeds to predict the frac-ture behavior of asphalt materials using DT tests.

5. Summary and conclusions

In this study, a double-torsion (DT) fracture test was developedand implemented to investigate the fracture behavior of asphaltconcrete. DT test was initiated for understanding the channelizedcrack propagation and for obtaining various fracture parameters.One selected model asphalt mixture, AC4, was tested with differentnotch lengths to testify the developed DT fracture test set-ups andto find the proper DT specimen geometry and test configurations.Some conclusive remarks are:

– Double-torsion fracture test was a suitable method to charac-terize the crack propagation along the longitudinal dimensionof thin plate asphalt specimen.

– The compliance approach with different notch lengths showedthe strong benefits for obtaining characteristic material param-eters from DT fracture tests without comprehensive measure-ments. The material constants for AC4 were 3.2 � 10�6 for Band 3.609 � 10�7 for D at �10 �C.

– The constant fracture toughness KIC was obtained from DT spec-imens tested with different notched lengths. In other words, thefracture property obtained from DT tests was independent onthe initial notch length of DT specimen. The averaged criticalstress intensity factor of AC4 was 1.351 MPa m1/2.

– DT specimens tested under slower loading speeds showedlonger stable crack propagation length, which is favorable inDT fracture tests.

More DT fracture tests at different temperatures should be con-ducted to characterize various asphalt materials and these are oneof ongoing studies by authors. Also, there are further research top-ics related to DT fracture tests, which are fatigue fracture tests withDT specimens, advanced crack measurements using optical meth-ods, and numerical modeling approaches for DT fracture tests tounderstand more detail fracture mechanisms.

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