effect of specimen thickness on the fracture resistance of
TRANSCRIPT
Construction and Building Materials 160 (2018) 487–496
Contents lists available at ScienceDirect
Construction and Building Materials
journal homepage: www.elsevier .com/locate /conbui ldmat
Effect of specimen thickness on the fracture resistance of hot mix asphaltin the disk-shaped compact tension (DCT) configuration
https://doi.org/10.1016/j.conbuildmat.2017.11.0410950-0618/� 2017 Elsevier Ltd. All rights reserved.
⇑ Corresponding author.E-mail address: [email protected] (C.M. Stewart).
Calvin M. Stewart ⇑, Chinedu W. Oputa, Eduardo GarciaDepartment of Mechanical Engineering, The University of Texas at El Paso, 500 West University Avenue, Suite A126, El Paso, TX 79968-0521, United States
h i g h l i g h t s
� The plane-strain condition does not exist in 50 mm thick DCT specimen.� Linear elastic fracture mechanics theory can be used to optimize layer thicknesses.� Fracture surfaces do not distinguish between the plane-stress and strain conditions.
a r t i c l e i n f o
Article history:Received 6 July 2017Received in revised form 29 September2017Accepted 10 November 2017Available online 21 November 2017
Keywords:Fracture toughnessFracture energyCoefficient of variationPlane-stressPlane-stainHot mix asphaltDisk-shaped compact tension3D scanningLinear elastic fracture mechanicsElastic-plastic fracture mechanics
a b s t r a c t
In this study, the effect of specimen thickness on the fracture resistance of a dense-graded hot mixasphalt (HMA) is investigated. The fracture toughness, Kc and fracture energy, Gf in triplicate DCT spec-imens with width-to-thickness ratios ranging from 1.46 to 4.4 is measured at 27 �C. The coefficient ofvariation (COV) of Kc and Gf is calculated to determine reliability as a function of thickness. Photos ofcracked specimens and 3D surface scans are employed to study how the crack path and fracture surfacechanged with thickness. The ASTM specifications and linear-elastic fracture mechanics theory are appliedto show that Kc does not reach a plane-strain condition, Kc–KIc , for the given ratios. The average Kc
increases with thickness while the COV is inconsistent with thickness. The average Gf is independentof thickness but the COV decreases with thickness; thus, Gf is thickness-dependent. The crack pathand fracture surface cannot be used to identify the plane-stress or plane-strain condition due to largeaggregates dominating the fracture process. A method for estimating the specimen thickness requiredfor the plane-strain condition and a method to estimate the thickness at which fracture toughness ismaximized is demonstrated.
� 2017 Elsevier Ltd. All rights reserved.
1. Introduction
Cracking is the most commonmode of degradation contributingto failure in flexible pavements. The rapid initiation of cracks short-ens the service life of pavement and increases maintenance costs.Hot mix asphalts (HMAs) offer low construction and maintenancecosts when compared to concrete yet the problem of cracking per-sists. There is a need to elucidate the cracking behavior of HMAs toenable proactive maintenance management of transportationinfrastructure. HMA layers are subjected to out-of-phase thermo-mechano-chemical fatigue due to the varying types of roads, trafficpatterns, and climate across the world. Due to the complex natureof HMA’s (an irregular distribution of aggregates in a bitumen
matrix) fracture tests exhibit low repeatability. A systematic inves-tigation into the factors that contribute to this problem is needed.Previous work has shown that specimen geometry plays a key rolein repeatability [1]. The current paper investigates specimen thick-ness as a factor of interest.
Hot mix asphalts are heterogeneous composites consisting ofbrittle aggregates heldwithin a viscoelastic-plastic bitumenmatrix.The aggregates include crushed stone (large), sand (fine), and min-eral (filler) at varied sizes and spatial distributions. Fracture is drivenby the friction between interlocked aggregates coated with binderthat are responsible for the material dilation and nucleation ofmicro-cracks. The micro-cracks propagate into major cracks due tooverload, repeated mechanical loading, thermal cycling, and syner-gistic effects. At low temperature, the probability of crack initiationis increased due to the quasi-brittle response of the binder andthermal-expansion mismatch with the aggregate as opposed to
488 C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496
the ductile response observed at elevated temperature [2,3]. Com-position andaggregate gradationplay an integral role in the repeata-bility of fracture tests where large aggregates lead to a highcoefficient of variation (COV) in experiments [4].
Several researchers have investigated the fracture resistance ofasphalt mixtures [1–18]. The semi-circular bending (SCB) test is acommon fracture test for HMAs due to the simplicity of specimenpreparation and testing [5]. Saha and Biligiri conducted a review ofthe state-of-the-art concerning SCB testing of asphalt mixtures [6].Current standards recommend a specimen thickness of 50 mm[7,8]. Both the fracture toughness, Kc and fracture energy, Gf
parameters were evaluated. Fracture toughness, Kc was found tobe independent of thickness between 25 and 75 mm at tempera-tures below 15 �C; however, as temperature increases the magni-tude of Kc decreases and the COV increases. Fracture energy, Gf
was determined to be dependent on asphalt grade and tempera-ture; however, the effect of thickness was not discussed. In theory,Gf of homogeneous linear-elastic materials is insensitive to size;however, since HMAs are heterogeneous viscoelastic-plastic mate-rials this may not hold true. In a follow-on study, Saha and Biligiri[9] evaluated the homothetic fracture resistance behavior of densegrade HMA materials (i.e. the dependence on asphalt content, airvoids, temperature, and thickness) using the SCB test. Tests wereperformed at temperatures of 5–25 �C with thicknesses from 30to 50 mm. Increasing the thickness from 30 to 40 mm increasedthe Kc; however, thicknesses from 40 to 50 mm exhibit no changein Kc . A major advantage of the SCB configuration is the ability tomeasure the mixed-mode fracture resistance of HMAs [10,11].Aliha and colleagues performed a series of experiments on themode I, II, III and mixed cracking of HMAs in the SCB configuration[11–15]. It was determined that SCB is an extremely versatile con-figuration for examining the mixed-mode cracking observed intransportation materials under multiaxial states of stress.
Specimen geometry plays a key role in the average Kc and COV.The Texas A&M Transportation Institute evaluated the perfor-mance of several fracture test configurations including the disk-shaped compact tension (DCT), semi-circular bending (SCB), indi-rect tension (IDT), thermal stress-restrained specimen test or uni-axial thermal stress and strain test (TRSST/UTSST), texas overlay(Texas OT), bend beam fatigue (BBFT), simplified viscoelastic con-tinuum damage (S-VCD), and the repeated direct tension (DT) test[16]. The tests were compared with regards to test complexity, cor-relation to field performance, test variability, test sensitive to mixdesign parameters, and cost. The DCT, SCB, and Texas OT werefound to have the lowest cost and exhibit good correlation to fieldperformance; however, DCT was observed to produce the lowestCOV. To further examine these conclusions, Stewart et al. [1] per-formed a comparative analysis of the SCB and DCT mode I fractureenergy test standards on a dense-graded Superpave HMA. The SCBand DCT tests were conducted according to AASHTO TP105-13 andASTM D7313-13 at the thickness of 50 mm (recommended inASTM D7313) and a temperature of 27 �C [7,8]. The SCB tests pro-duced a low Gf with a high COV when compared to DCT. The DCTgeometry offers more fracture area for cracking propagation mak-ing it a more repeatable test.
Wagoner et al. [17] performed DCT fracture energy tests on fourasphalt mixtures ranging from typical Illinois to polymer-modifiedinterlayer mixtures. For a single mixture at �10 �C, the thicknesswas profiled from 25 to 75 mm. Fracture energy, Gf was found toincrease with thickness while the COV also increased from 13 to19%. Kim et al. [18] found that increasing the diameter of a speci-men from 100 to 450 mm led to an increase in Gf while the COVremained relatively constant near 15%.
According to linear-elastic fracture mechanics (LEFM) theory,the fracture toughness of a homogeneous material is thickness
dependent up to the plane-strain condition where the valuebecomes a constant material property [19–21]. The size or thick-ness dependence is associated with the transition from plane-stress to plane strain as illustrated in Fig. 1. The fracture toughness,Kc is called the ‘‘apparent” fracture toughness when it is thickness-dependent and is called the ‘‘plane-strain” fracture toughness, KIc
when it becomes an intrinsic material property that is notthickness-dependent. In plane-stress, the direction of maximumshear stress is in the anti-plane direction (±45�) leading to the for-mation of a slant crack or shear lips. Under plane-stress,microstructural defects play a significant role in fracture toughnessresulting in a high COV. As thickness increases, the specimen tran-sitions from plane-stress to a plane-strain condition. In plane-strain, the direction of the maximum shear stress is in-plane lead-ing to a flat fracture surface. The field of defects in the materialhomogenize such that the fracture toughness resolves to a horizon-tal asymptote with a low COV. By reviewing LEFM theory, it can beconcluded that
� the plane-strain fracture toughness, KIc is a conservative mea-sure of fracture resistance.
� for design it would be advantageous to determine the thicknesswhere the apparent fracture toughness, Kc is maximized andthe COV is reasonable [19–21].
Since HMAs are heterogeneous composites, and the theorydescribed above may not hold true, there is a need to investigatethe thickness-dependence of the fracture resistance of HMAs.
It is important to check the ASTM requirements for the plane-strain condition. ASTM developed two standards to support themeasurement of the KIc in metallic and homogeneous materials:ASTM E399-12e3 [22] and ASTM E1820-16 [23], respectively. Akey requirement of these two standards is that the width-to-thickness ratio, W=B, shall remain between 2 and 4. The standardratio is W=B ¼ 2. Another requirement is that the followinginequality be enforced
a;B � 2:5KIc
rYS
� �2
ð1Þ
where KIc is the approximate plane-strain fracture toughness, rYS isthe yield strength, a is the crack length, and B is the thickness. Thefracture toughness cannot be considered plane-strain, KIc , when thiscondition is violated, and it must be defined as the apparent frac-ture toughness, Kc , reported everywhere with respect to thickness[6].
In this study, the effect of specimen thickness on the Kc and Gf
of a dense-graded HMA is investigated using DCT specimens at atemperature of 27 �C. The DCT configuration was selected due tothe availability of an ASTM test standard [7] and the low COVexpected in this configuration [1,16]. The tests are performed atwidth-to-thickness ratios ranging from 1.46 to 4.4. Statistical anal-ysis is performed to investigate how Kc and Gf evolve as a functionof thickness. Photos of cracked specimens and 3D surface scans areemployed to determine how the crack path and fracture surfacechange with thickness.
2. Material and test methods
2.1. Hot mix asphalt
The material in this study is a dense-graded HMA (designated asType-C by Texas Department of Transportation) used in WestTexas. The properties of the mix are summarized in Table 1. The
Specimen Thickness, B
Frac
ture
Tou
ghne
ss, K
cIcK
Plane Stress Transitional
Plane Strain
Plane Stress Transitional Plane
Strain
B
Fig. 1. Fracture toughness and fracture surface versus thickness in homogeneous linear-elastic materials.
Table 1Summary of HMA properties.
Properties Type-C
NMAS (mm) 19Asphalt performance grade PG 70-22Binder substitution PG 64-22Optimal asphalt content (%) 4.6Specific gravity 1.001Binder percent (%) 4.6VMA (%) at optimum AC 15.2
Table 2Gradation chart of Type-C mix.
Sieve size Type-C (Percentage)
100 100.03/400 99.33/800 82.4No. 4 52.7No. 8 36.9No. 30 18.6No. 50 14.0No. 200 5.6
C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496 489
gradation is listed in Table 2. The relevant aggregates and binderwere sampled and transported to the Center for TransportationInfrastructure Systems at The University of Texas at El Paso (UTEP)where specimens were prepared and tested.
2.2. Specimen preparation
The HMA mixture is heated to 132 ± 3 �C to liquefy the binderand improve mold-ability. Standard 150 mm diameter by 114mm thick briquettes are compacted with a superpave gyratorycompactor according to AASHTO T312-15 and ASTM D6925-15[24,25]. After the briquette reaches room temperature, a disk shapespecimen is excised from the middle using a masonry saw to thedesired thickness. The disk is quality checked for an air-void per-centage (AV%) target of 7 ± 1.0%. Disks with the proper AV% aremachined into DCT specimen according to ATSM D7313-13 [7].One DCT specimen can be extracted from each disk with thedimensions illustrated in Fig. 2. Specimen were prepared withthicknesses of 25, 40, 50, and 75 mm. The width-to-thickness rangeis 1:46 � W=B � 4:4.
2.3. Mechanical test equipment
The mechanical tests were conducted using an INSTRON 5969Table-Top Universal Test System. The test frame is equipped withan Instron 3119-609 Environmental Chamber capable of regulatingtemperature from �100 to +350 �C. Load and displacement limits
f ðai=WÞ ¼ fð2� ai=WÞ½ð0:76þ 4:8ðai=WÞ � 11:58ðai=WÞ2 þ 11:43ðai=WÞ3 � 4:08ðai=WÞ4�gð1þ ai=WÞ3=2
ð3Þ
were set for the load cell, crosshead displacement, and extensome-ters to avoid equipment damage. The specimens were set to an
isothermal temperature of 27 �C for the duration of each test.The data captured during each test includes time, load, and linedisplacement.
2.4. Test method
2.4.1. DCT fracture toughness (Modified from ASTM E1820-16)Fracture toughness tests are performed according to ASTM
E1820-16 the ‘‘Standard Test Method for Measurement of FractureToughness” [23]. The standard provides a procedure for calculatingthe fracture toughness, Kc (MPa-m0.5) of DCT specimens. The frac-ture toughness Kc is defined as the stress intensity factor, Ki corre-sponding to the initiation of a crack in a homogenous, linear-elasticbody. Fracture toughness, Kc , is typically measured at the peakload, Pc depicted in Fig. 3 [1]. For the DCT geometry, the stressintensity factor, Ki is computed as follows
Ki ¼ Pi
ðBBNWÞ1=2f ðai=WÞ ð2Þ
where i is the data point, Pi is the load at the ith data point (N), W isthe width (mm), f is the dimensionless geometry factor, ai is thecrack length at the ith data point (mm), BN is the net thickness(mm), and B ¼ BN if no side grooves are present.
The dimensionless geometry factor, f for the DCT geometry iscalculated as
The plane-strain fracture toughness, KIc is obtained by profilingthe apparent fracture toughness, Kc as a function of thickness and
Da
φ
d
CWB
B = 50 ± 5 mmC = 35 ± 2.5 mmD = 150 ± 10 mmW = 110 ± 2.5 mm
a = 27.5 ± 2.5 mmd = 25 ± 2.5 mm
= 25 ± 1 mmφ
(a) (b)Fig. 2. Disk-shaped compact tension (a) dimensions and (b) specimen.
Displacement, u
Load
, F
f tailU U U= +
U
tailU
cP
Fig. 3. Load versus load-line displacement [1].
490 C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496
finding the horizontal asymptote where Kc ¼ KIc is insensitive tothickness.
Before testing, the specimens were fatigue pre-cracked until thenotch grew by Da > 0:2B beyond the initial notch length. The max-imum stress intensity factor, Kmax during pre-cracking did notexceed 60% of the estimated plane-strain fracture toughness KIc .
2.4.2. DCT fracture energy (According to ASTM D7313-13)Fracture energy tests are performed according to ASTM D7313-
13 the ‘‘Standard for determining the fracture energy of asphalt-aggregate mixtures” [7]. The standard calculates the fractureenergy, Gf using a single-specimen solution. Tests are performedwith a constant crack mouth opening displacement, CMOD of0.017 mm/s. The standard does not call for pre-cracking so it wasnot preformed. The fracture energy, Gf is calculated as follows
Gf ¼ Uf
B � ðW � aÞ ð4Þ
where Uf is the work of fracture (J), B is the thickness (mm), andðW � aÞ is the initial ligament length (mm). The work of fracture,Uf is calculated as the area under the load-CMOD curve depictedin Fig. 3 using the quadrangle rule as follows
Uf ¼Xni¼1
ðuiþ1 � uiÞ � ðPiÞ þ 0:5 � ðuiþ1 � uiÞ � ðPiþ1 � PiÞ ð5Þ
where n is the number of data points, u is the CMOD, and P is theload.
2. 5 D Surface scanning
The fractured specimens are 3D scanned to produce a 3D CADreplication of the fracture surface using a MakerBot Digitizer 3DScanner. The scanner has a nominal dimensional accuracy of ± 2mm and detail resolution of 0.5 mm. The device uses two lasersand a rotating platform to generate a 3D dimensional replicationof the surface of 3D objects. The Makerware software, exports astereo lithography format file (.STL). The AutoDesk MeshMixersoftware is employed to analyze the physical features of the 3-D.STL files.
3. Results and discussion
3.1. ASTM requirements
Preliminary experiments were performed to check the ASTMplane-strain condition [Eq. (1)]. The AASHTO TP 105, ASTM E399,and ASTM E1820 standards recommend at least triplicate testsfor each material condition [8,22,23]. Three indirect tensile tests(IDT) were performed recording an average yield strength, rYS of849 kPa. Three DCT tests were performed at a specimen thicknessof 50 mm measuring an average fracture toughness of 0.265MPa
ffiffiffiffiffim
p. Taking these properties and evaluating [Eq. (1)], it is esti-
mated that a specimen thickness of 244 mm or greater is requiredto achieve the plane-strain condition. To maintain a width-to-thickness ratio within the recommended range of 2 � W=B � 4;the specimen width must be between 488 mm � W � 976 mm.A specimen with the above dimensions is not practical to testand exceeds the typical thickness of laid HMA. In summary, fordense-graded HMA at 27 �C, the fracture toughness measuredusing the standard DCT dimensions is the ‘‘apparent” fracturetoughness, Kc and must be reported with specimen thickness.
3.2. Fracture toughness
Fracture toughness tests were performed on triplicate speci-mens prepared at four thicknesses. The test results are presentedin Table 3 with the load-displacement curves shown in Fig. 4. Onaverage, the peak load increases with thickness. At a given thick-ness, the peak load varies. The peak load variation is linked tothe different initial notch length measured for each specimen afterpre-cracking. The critical crack length was optically measured (atthe instant of fracture) using a three-dimensional digital image
Table 3Fracture toughness of dense-graded HMA.
Specimen name* Thickness, B Air voids, AV Critical crack length, ac Peak load, Pc Apparent fracture toughness, Kc
– Avg. Std. Dev. COV(mm) (%) (mm) (N) (MPa
ffiffiffiffiffim
p) (MPa
ffiffiffiffiffim
p) (MPa
ffiffiffiffiffim
p) (%)
K25-1 26.5 6.9 37.1 236.5 0.171 0.197 ±0.035 17.5K25-2 27.0 6.3 43.0 223.6 0.184K25-3 25.1 6.4 54.5 190.4 0.236K40-1 41.4 7.1 39.2 463.7 0.228 0.235 ±0.014 6.0K40-2 39.9 7.1 44.0 377.7 0.227K40-3 41.2 7.1 54.9 332.5 0.252K50-1 50.4 6.8 38.5 678.3 0.277 0.265 ±0.029 11.1K50-2 57.8 6.3 40.3 645.5 0.232K50-3 48.9 7.5 47.8 548.4 0.288K75-1 73.2 7.3 47.8 695.8 0.248 0.289 ±0.035 12.2K75-2 73.4 6.6 59.2 625.3 0.307K75-3 73.6 6.8 71.1 393.7 0.311
*KXX-Y: K – fracture toughness test, XX – specimen thickness in mm, Y – test number at XX.
Displacement, u (mm)0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
K25-1K25-2K25-3
Displacement, u (mm)0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
K40-1K40-2K40-3
Displacement, u (mm)0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
K50-1K50-2K50-3
Displacement, u (mm)0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
K75-1K75-2K75-3
(a) (b)
(c) (d)
Fig. 4. Load-displacement of fracture toughness tests at thicknesses (a) 25 to (d) 75 mm.
C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496 491
correlation (3D-DIC) system. The 3D-DIC system consists of a set ofcameras that capture images of the surface of the specimen. Theseimages are synchronized with load cell data and the image corre-spond to the peak load is used to measure the critical crack length.The critical crack length is plotted with respect to peak load inFig. 5. Peak load versus critical crack length exhibits a linearrelationship with a negative-slope. As the critical crack lengthincreases the peak load decreases. The trend follows LEFM theorywhere when the fracture area decreases the force needed for frac-ture decreases. The dimensions, peak load, and critical crack lengthare applied to calculate the fracture toughness, Kc. Fracture tough-ness is plotted against thickness in Fig. 6a. When compared to theLEFM theory in Fig. 1, the HMA is under plane-stress at the given
thicknesses. Theory states there exists a maximum fracture tough-ness in the transition from plane-stress to plane-strain. A quadraticfunction is fitted to the fracture toughness versus thickness data asfollows KcðBÞ ¼ �2:547E� 05 � B2 þ 4:485E� 03 � Bþ 9:807E� 02.Taking the derivative of the function and setting it equal to zero,the maximum fracture toughness is approximately 0.295 MPa
ffiffiffiffiffim
pat a thickness of 88 mm. It is important to note that the thicknesswhere fracture toughness is maximized is specific to the crackingmode (mode I), composition (dense-grade HMA used in WestTexas), temperature, and geometry (DCT). The COV of Kc is plottedversus thickness in Fig. 6b. The COV is of acceptable magnitude forHMAs (below 15% acceptable, below 5% excellent) but is inconsis-tent at the given thicknesses with an unexplained drop at 40 mm.
Critical Crack Length, ac (mm)
30 40 50 60 70 80
Peak
Loa
d, P
c (N
)
0
200
400
600
80025mm40mm50mm75mm
337.2 N742.8 N1201 N1344 N
Pc(ac)=m*ac+P0
m =
P0 =
-2.682 N/mm-7.636 N/mm-13.67 N/mm-13.01 N/mm
Fig. 5. Peak load versus critical crack length.
492 C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496
A high COV is expected in plane-stress since microstructural fea-tures become dominant at small thicknesses, particularly inheterogeneous materials.
In summary, for dense-graded HMA at 27 �C, Kc depends onspecimen thickness between 25 and 75 mm. It is estimated thatthe specimen is under plane-stress at B � 88 mm and plane-strain at B � 244 mm. These findings are dependent on composi-tion, temperature, and specimen. Different HMA compositionsand gradations will have different mechanical properties. Thedeformation and fracture mechanisms of HMAs change with tem-
Thickness, B (mm)20 30 40 50 60 70 80Fr
actu
re T
ough
ness
, Kic
(M
Pa-
m1/
2 )
0.16
0.18
0.20
0.22
0.24
0.26
0.28
0.30
0.32
Quadratic Fit(a)
Fig. 6. Fracture toughness versus thickness: (a)
Table 4Fracture Energy of Dense-Graded HMA.
Specimen Name* Thickness, B Air voids, AV Ligament length, W � a
(mm) (%) (mm)
G25-1 26.9 6.8 83.9G25-2 27.1 6.1 77.8G25-3 25.2 6.3 81.6
G40-1 41.5 7.5 81.3G40-2 41.8 7.0 79.8G40-3 42.3 7.3 82.5
G50-1 53.1 6.4 82.3G50-2 53.0 6.9 79.4G50-3 54.7 6.8 82.4
G75-1 74.7 7.5 81.5G75-2 75.0 7.5 80.5G75-3 76.0 7.9 82.3
*GXX-Y: G – fracture energy test, XX – specimen thickness in mm, Y – test number at X
perature. Specimen that offer large fracture areas will producelower COVs. The mode I DCT configuration does not reflect theactual multiaxial state of stress induced in the surface of flexiblepavement layers during traffic loads; however, it is a useful config-uration to consistently evaluate the basic fracture resistance ofthese materials. If a fracture toughness test can be configured toperfectly replicate the cracking mode, composition, temperature,and geometry of flexible pavement layers in-service, a design engi-neer can apply the LEFM theory demonstrated here to maximizethe fracture resistance of flexible pavement layers by derivingthe optimal thickness. The COVmust be involved in the design pro-cess such that the decision is based not only on performance butreliability.
3.3. Fracture energy
Fracture energy tests were performed on triplicate specimens atfour different thicknesses. The test results are presented in Table 4with the load-displacement curves shown in Fig. 7. The fractureenergy load-displacement curves have a tight grouping when com-pared to the fracture toughness tests in Fig. 4. At a given thickness,the peak load remains relatively constant. This trend relates to theabsence of pre-cracking. On average, the peak load and work offracture increase with thickness. The initial dimensions and workof fracture are applied to calculate the fracture energy, Gf . Fractureenergy and the COV is plotted against thickness in Fig. 8a and b
Thickness, B (mm)20 30 40 50 60 70 80 90
Coe
ffici
ent o
f Var
iatio
n, C
OV
(%)
02468
101214161820
(b)
magnitude and (b) coefficient of variation.
Work of fracture, Uf Fracture energy, Gf
– Avg. Std. Dev. COV(J) (J m�2) (J m�2) (J m�2) (%)
1.265 560.7 714.7 ±167.1 23.381.457 691.21.835 892.4
2.634 780.6 718.2 ±70.32 9.7912.141 642.02.555 732.0
2.915 667.2 645.6 ±19.98 3.0952.700 641.82.830 627.8
4.153 682.1 700.8 ±23.44 3.3454.186 693.14.548 727.1
X.
Crack Mouth Opening Displacement, CMOD (mm)
0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
1000
1200
1400
G25-1G25-2G25-3
Crack Mouth Opening Displacement, CMOD (mm)
0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
1000
1200
1400
G40-1G40-2G40-3
Crack Mouth Opening Displacement, CMOD (mm)
0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
1000
1200
1400
G50-1G50-2G50-3
Crack Mouth Opening Displacement, CMOD (mm)
0 2 4 6 8 10 12
Load
, P (N
)
0
200
400
600
800
1000
1200
1400
G75-1G75-2G75-3
(a) (b)
(c) (d)
Fig. 7. Load-CMOD curves of fracture energy tests at thicknesses (a) 25 to (d) 75 mm.
Thickness, B (mm)
20 30 40 50 60 70 80
Frac
ture
Ene
rgy,
Gf
(J/m
2 )
500
600
700
800
900
1000
Average
Thickness, B (mm)
20 30 40 50 60 70 80 90
Coe
ffici
ent o
f Var
iatio
n, C
OV
(%)
0
5
10
15
20
25
(b)(a)
Fig. 8. Fracture energy versus thickness: (a) magnitude and (b) coefficient of variation.
C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496 493
respectively. On average, fracture energy remains approximately700J=m2 at thicknesses between 25 and 75 mm; however, thisstatistic is misleading when the COV is considered. The COV of Gf
is thickness-dependent and decreases as the thickness increasesfrom 23.4% at 25 mm to 3.3% at 75 mm. Statistically, the likelihoodof achieving a consistent fracture energy in replicate testsdecreases as thickness decreases. Thus, fracture energy is thicknessdependent. The standard 50 mm thickness (recommended byASTM D7313-13) is sufficient to obtain consistent fracture energymeasurements at a COV of 3.1%.
In summary, for dense-graded HMA at 27 �C, the COV of Gf isdependent on specimen thickness between 25 and 50 mm. Atthickness > 50 mm, the COV of Gf becomes independent of thick-
ness. Similar to fracture toughness, these findings are dependenton material, temperature, and specimen. For example, Wagoneret al. [17] found specimen size has a significant impact on the frac-ture energy of an HMA at �10 �C. Overall, the fracture toughnessand energy of a given HMA mixture must be evaluated experimen-tally at the expected service conditions (layer thicknesses, temper-ature range, strain rates) before any conclusions concerning thedependencies of a given mixture can be made.
3.4. Crack path
Photographs of the crack path for each Kc and Gf specimen arepresented in Figs. 9 and 10, respectively. In both tests and at all
25 mm
Not to scale75 mm
50 mm
40 mm
Fig. 9. Crack path observed in Kc specimen.
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thicknesses, the primary crack propagates through the bitumenbypassing most large aggregates. From specimen-to-specimen,the crack is torturous and travels uniquely through the heteroge-neous structure following a path of least resistance. The crack pathis perturbed by obstacles (such as large well-bonded aggregates)and weak zones (voids, weakly-bonded interfaces, etc.). In limitedcases, the crack bisects moderately sized aggregates. These failed
25mm 40mm
Not to Scale
Fig. 10. Crack path obser
aggregates are primarly found at long cracks near the points wherethe specimen separated in half. In summary, for dense-gradedHMA at 27 �C, there is no trend between crack path and thickness.
3. 5D surface scanning
In homogeneous linear-elastic materials, the fracture surfaceshould evolve with thickness as illustrated in Fig. 1. Under plane-stress, a slant crack should be observed. In the transition fromplane-stress to plane-strain a mixed-mode fracture surface, includ-ing both shear lips and a flat surface, should be observed. In plane-strain, the fracture surface should be flat with minimal shear lips.
3D surface scans taken of Gf specimens at different thicknessesare shown in Fig. 11. The trends for homogeneous linear-elasticmaterials do not hold for dense-graded HMA. It was previouslydetermined that dense-graded HMA is in plane stress whenB � 88 mm and plane-strain when B � 244 mm. Examining the3D scans, the fracture surfaces at all thicknesses are non-planarand reside between 0 and 45�. The crack bypasses aggregates lead-ing to a tortuous and cratered fracture surface. It is possible thatthe crack may become more planar as the specimen approachesplane-strain, B � 244 mm; however, the gradation chart for thedense-graded mix used (Table 2) suggests the fracture surfacecan remain out-of-plane by up to 19 mm (the largest aggregatessize). In summary, for dense-graded HMA at 27 �C, 3D scans ofthe fracture surface cannot reasonable predict the plane-stress orplane-strain condition.
4. Conclusions
The goal of this effort was to evaluate the effect of thickness onthe fracture resistance of HMA mixtures in the DCT configuration.For dense-grade HMA tested at 27 �C, it is determined that
� checking the requirements of ASTM E399-12 and E1820-16, [Eq.(1)], the specimens are in plane-stress when B � 88 mm andplane-strain when B � 244 mm.
� the fracture toughness is maximized at B ¼ 88 mm.
50mm 75mm
ved in Gf specimen.
40 mm
50 mm
75 mm
m
25mm
m
Note: Not to scaleFig. 11. 3D Fracture surface at specimen thicknesses from 25 to 75 mm.
C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496 495
� the Kc is thickness dependent at all thicknesses tested in thisstudy. The COV of Kc is inconsistent but acceptable (less than15%) at B � 40 mm.
� the COV of Gf is thickness dependent from 25 to 50 mm andbecomes insensitive at B � 50mm. The standard 50 mm thickspecimen is adequate when performing Gf test.
� there is no trend between crack path and thickness. 3D surfacescans do not provide enough evidence to determine the plane-stress or plane-strain condition.
This study examined the effect of thickness on fracture tough-ness at one HMA composition and temperature in the DCT config-uration. As the properties of HMA are highly dependent oncomposition, temperature, and geometry the outcomes of theresearch are limited to understanding the fracture characteristicsof this specific mixture; however, the techniques applied to iden-tify plane-stress versus the plane-strain condition and theapproach of maximizing the fracture toughness by altering the
dimensions can be applied to any HMAmixture towards improvingthe design and performance of flexible pavement layers. In futurework, fracture resistance tests will be performed under service-like conditions including the cracking mode, strain rate, tempera-ture, and geometry. Thermo-mechano-chemical fatigue tests willbe designed to simulate (in an accelerated manner) the degrada-tion of HMAs.
Acknowledgments
This research was support with funds from the Southern PlainsTransportation Center under grant No. 14.1-97. The authors wouldlike to thank the Center for Transportation Infrastructure Systems(CTIS), especially their Executive Director Dr. Imad Abdallah andDirector Dr. Soheil Nazarian, as well as the Challenger-ColumbiaMaterials Research Facility for the use of equipment and materials.
References
[1] C.M. Stewart, J.G. Reyes, V.M. Garcia, Comparison of fracture test standards fora super pave dense-graded hot mix asphalt, Eng. Fract. Mech. 169 (2017) 262–275, https://doi.org/10.1016/j.engfracmech.2016.10.016.
[2] K.W. Kim, M. El Hussein, Variation of fracture toughness of asphalt concreteunder low temperatures, Constr. Build. Mater. 11 (1997) 403–411, https://doi.org/10.1016/S0950-0618(97)00030-5.
[3] E. Zegeye, J.-L. Le, M. Turos, M. Marasteanu, Investigation of size effect inasphalt mixture fracture testing at low temperature, Road Mater. PavementDes. 13 (2012) 88–101, https://doi.org/10.1080/14680629.2012.657064.
[4] X. Li, M. Marasteanu, The fracture process zone in asphalt mixture at lowtemperature, Eng. Fract. Mech. 77 (2010) 1175–1190, https://doi.org/10.1016/j.engfracmech.2010.02.018.
[5] A.A.A. Molenaar, A. Scarpas, X. Liu, S. Erkens, Semi-circular bending test;simple but useful?, J Assoc. Asph. Paving Technol. 71 (2002) 794–815.
[6] S. Gourab, K.P. Biligiri, Fracture properties of asphalt mixtures using semi-circular bending test: a state-of-the-art review and future research, Constr.Build. Mater. 105 (2016) 103–112, https://doi.org/10.1016/j.conbuildmat.2015.12.046.
[7] ASTM D7313-13, Standard Test Method for Determining Fracture Energy ofAsphalt-Aggregate Mixtures using the Disk-Shaped Compact TensionGeometry 10.1520/D7313, ASTM International, West Conshohocken, PA, 2013.
[8] AASHTO TP105-13, Standard Method of Test for Determining the FractureEnergy of Asphalt Mixtures Using the Semi Circular Bend Geometry, AAHSTO,Washington, DC, 2013.
[9] G. Saha, K.P. Biligiri, Homothetic behaviour investigation on fracture toughnessof asphalt mixtures using semicircular bending test, Constr. Build. Mater. 114(2016) 423–433, https://doi.org/10.1016/j.conbuildmat.2016.03.169.
[10] S. Im, H. Ban, Y.R. Kim, Characterization of mode-I and mode-II fractureproperties of fine aggregate matrix using a semicircular specimen geometry,Constr. Build. Mater. 52 (2014) 413–421, https://doi.org/10.1016/j.conbuildmat.2013.11.055.
[11] M.R.M. Aliha, H. Behbahani, H. Fazaeli, M.H. Rezaifar, Study of characteristicspecification on mixed mode fracture toughness of asphalt mixtures, Constr.Build. Mater. 54 (2014) 623–635, https://doi.org/10.1016/j.conbuildmat.2013.12.097.
[12] M. Ameri, A. Mansourian, S. Pirmohammad, M.R.M. Aliha, M.R. Ayatollahi,Mixed mode fracture resistance of asphalt concrete mixtures, Eng. Fract. Mech.93 (2012) 153–167, https://doi.org/10.1016/j.engfracmech.2012.06.015.
[13] M.R.M. Aliha, A. Bahmani, S. Akhondi, Determination of mode III fracturetoughness for different materials using a new designed test configuration,Mater. Des. 86 (2015) 863–871, https://doi.org/10.1016/j.matdes.2015.08.033.
[14] M.R.M. Aliha, A. Bahmani, S. Akhondi, A novel test specimen for investigatingthe mixed mode I+III fracture toughness of hot mix asphalt composites –Experimental and theoretical study, Int. J. Solids Struct. 90 (2016) 167–177,https://doi.org/10.1016/j.ijsolstr.2016.03.018.
[15] M.R.M. Aliha, A. Razmi, A. Mansourian, The influence of natural and syntheticfibers on low temperature mixed mode I+ II fracture behavior of warm mixasphalt (WMA) materials, Eng. Fract. Mech. (2017) 322–336, https://doi.org/10.1016/j.engfracmech.2017.06.003.
[16] F. Zhou, D. Newcomb, C. Gurganus, S. Banihashemrad, E.S. Park, M. Sakhaeifar,R. L. Lytton, Experimental Design for Field Validation of Laboratory Tests toAssess Cracking Resistance of Asphalt Mixtures, Project No. 9-57, NationalCooperative Highway Research Program of the Transportation Research Boardof the National Academies. Washington, DC.
[17] M. Wagoner, W. Buttlar, G. Paulino, P. Blankenship, Investigation of thefracture resistance of hot-mix asphalt concrete using a disk-shaped compacttension test, Transp. Res. Rec. 2005 (1929) 183–192, https://doi.org/10.3141/1929-22.
[18] H. Kim, M.P. Wagoner, W.G. Buttlar, Numerical fracture analysis on thespecimen size dependency of asphalt concrete using a cohesive softening
496 C.M. Stewart et al. / Construction and Building Materials 160 (2018) 487–496
model, Constr. Build. Mater. 23 (2009) 2112–2120, https://doi.org/10.1016/j.conbuildmat.2008.08.014.
[19] R.J. Sanford, Principles of Fracture Mechanics, first ed., Upper Saddle River,New Jersey, 2003.
[20] M. Janssen, J. Zuidema, R. Wanhill, Fracture Mechanics, second ed., New York,NY, 2004.
[21] T.L. Anderson, Fracture Mechanics Fundamentals and Applications, second ed.,Boca Raton, Florida, 1995.
[22] ASTM E399-12e3, Standard Test Method for Linear-Elastic Plane-StrainFracture Toughness Kic of Metallic Materials 10.1520/E399-12E03, ASTMInternational, West Conshohocken, PA, 2012.
[23] ASTM E1820-16, Standard Test Method for Measurement of FractureToughness 10.1520/E1820-16, ASTM International, West Conshohocken, PA,2016.
[24] AASHTO T312-15, Preparing and Determining Density of Hot Mix Asphalt(hma) Specimens by Means of the Superpave Gyratory Compactor, AAHSTO,Washington, DC, 2015.
[25] ASTM D6925-15, Standard Test Method for Preparation and Determination ofthe Relative Density of Asphalt Mix Specimens by Means of the SuperpaveGyratory Compactor 10.1520/D6925-15, ASTM International, WestConshohocken, PA, 2015.