Embed Size (px)
Citation preview
Research ArticleEvaluation of Fracture Resistance of Asphalt Mixtures Using theSingle-Edge Notched Beams
Biao Ding ,1 Xiaolong Zou ,2,3,4 Zixin Peng,1 and Xiang Liu5
1CCCC First Highway Consultants Co., Ltd., Xi’an, Shaanxi 710065, China2School of Architecture and Civil Engineering, Xi’an University of Science and Technology, Xi’an, Shaanxi, China3Guangxi Key Lab of Road Structure and Materials, Guangxi Transportation Research & Consulting Co., Ltd.,Nanning, Guangxi, China4Key Laboratory for Special Area Highway Engineering of Ministry of Education, Chang’an University, Xi’an, Shaanxi, China5School of Highway, Chang’an University, Xi’an, Shaanxi, China
Correspondence should be addressed to Xiaolong Zou; [email protected]
Received 25 October 2017; Accepted 20 March 2018; Published 12 April 2018
Academic Editor: Hiroshi Noguchi
Copyright © 2018 Biao Ding et al. 1is is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
To determine and compare the fracture properties of different asphalt mixtures, single-edge notched beam (SENB) tests usingthree types of asphalt mixtures were applied in this study under the conditions of different notched depths and differenttemperatures. 1e effects of notched depths and temperatures on the fracture toughness and fracture energy were analyzed. 1eresults indicate that the notch depth has no significant effects on the fracture toughness and the fracture energy, but the gradationhas relatively obvious effects on the fracture energy, which the larger contents of course aggregate leads to increase the discretenessof the fracture energy of the specimen. 1e temperature has significant effects on the ultimate loads, fracture energy, and fracturetoughness. 1e ultimate loads of the SENBs reach the peak value at 0°C, which could be resulted in that viscoelastic properties ofasphalt mixture depend with temperatures. 1e fracture toughness at −20°C of continuously graded asphalt mixtures are higherthan those of gap-graded asphalt mixtures. On the contrary, the fracture toughness of gap-graded asphalt mixtures is higher attemperatures from −10°C to 20°C. 1e fracture energy increases with temperatures, and the fracture energy of SMA-13 issignificantly larger than those of AC-13 and AC-16.
1. Introduction
1e research on the fracture characteristics of asphaltmixture is one of important topics on the properties ofasphalt mixture. 1e main research methods for analysisand evaluation of the fracture characteristics include thenumerical simulation method and fracture test method[1–3].
1e numerical simulation is usually realized by the finiteelement method (FEM) and discrete element method(DEM). Two-dimensional (2D) micromechanical modelsusing FEM and DEM have been developed to simulatemicroscale crack propagation of cemented particulatematerials, which obtained well explanations of observedcrack failures of the samples [1, 2, 4, 5]. 1e results of FEM
simulation and the results of DEM simulation are usuallycompared to evaluate the similarities and differences. 1efindings show that the results of FEM simulation and DEMsimulation have a fundamental similarity and, at the sametime, have some basic differences [4]. Furthermore, three-dimensional (3D) model development has become a trendfor the numerical simulation of fracture analysis.
1e fracture test has three typical test methods, namely,the single-edge notched beam (SENB) test, the semicircularbending (SCB) test, and the disk-shaped compact tension(DC(T)) test, which are mainly applied to obtain the fracturecharacteristics of asphalt concrete [6–9]. 1ese threemethods have different specimen geometries, applicationoccasions, and fracture models, so the results can hardly becompared directly [8, 10].
HindawiAdvances in Materials Science and EngineeringVolume 2018, Article ID 8026798, 9 pageshttps://doi.org/10.1155/2018/8026798
For asphalt mixtures, one kind of viscoelastic materials,the fracture characteristics are not only related to the initialcrack depth but also to the temperature. �erefore, the aimof this study was to determine and compare the fractureproperties of three typical surface layer asphalt mixtures,namely, two kinds of two continuously graded asphaltmixtures and a stone mastic asphalt (SMA), at di�erentconditions of the initial crack depth and the temperature.Considering as the simple and widely used model, the SENBtest was applied in this study and the SENB with di�erentnotched depths were tested at di�erent temperatures.
2. Materials and Methods
2.1. Materials. �ree asphalt mixtures used in this studyincluded two continuously graded asphalt mixtures withnominal maximum aggregate size (NMAS) of 13.2mm and16mm (AC-13 and AC-16) and a gap-graded stone masticasphalt with NMAS of 13.2mm (SMA-13).�e experimentalgradation curves of those three asphalt mixtures are shownin Figure 1. A base asphalt SK90 was used in AC-13 and AC-16, and a styrene-butadiene-styrene- (SBS-) modi�ed as-phalt binder produced by Shanxi Guolin Huatai AsphalticProducts Co., Ltd. was used in SMA-13.�e properties of thebase asphalt and the SBS-modi�ed asphalt binder are shownin Tables 1 and 2, respectively.
�e coarse aggregate and �ne aggregate used in thosethree mixtures are basalt, and the properties are listed inTables 3 and 4. �e mineral �ller used in this study islimestone powder, and the properties are listed in Table 5.Besides, lignin �bers were used as the stabilizer in SMAmixture. Table 6 lists the properties of �bers. Design asphaltcontents were 5.0% for AC-13, 4.6% for AC-16, and 6.0% forSMA-13, which had 3.9%, 4.3%, and 4.1% void content,respectively. In addition, 0.3% of �ber was used in SMA-13.
2.2. Fabrication of Single-Edge Notched Beam. �e slabspecimens (300mm× 300mm× 50mm) were fabricatedusing a rolling wheel compactor. �e slab specimens weresawed into beams with the diameters of 250mm (length)×35mm (height)× 30mm (width).
A notch of designed depth, approximately 4mm wide,with a square end, was sawed at the middle point of eachbeam, and single-edge notched beams (SENB) were ob-tained. A group of single-edge notched beams are shown inFigure 2.
2.3. �ree-Point Bending Tests. Di�erent notch depths anddi�erent test temperatures were considered in this study. �eSENB with notch depth of 0mm (without initial notch),4mm, 8mm, 12mm, and 16mm was applied for three-point
0
0.6
1.18
2.36
4.75 9.
5
13.2 16 19
0.07
50.
15 0.3
0
20
40
60
80
100
SMA-13
AC-13
Sieve size (mm)
AC-16
Pass
ing
perc
ent (
%)
Figure 1: Experimental gradation curves for 0.45 power gradation graph.
Table 1: Properties of base asphalt.
Test item Unit Test result Test methodPenetration (25°C, 5 s, 100 g) 0.1mm 87.9 T0604-2011Ductility (5°C, 5 cm/min) cm >150 T0605-2011Softening point (R&B) °C 48.8 T0606-2011
Residue after TFOTQuality change % 0.15 T0610-2011
T0609-2011Penetration ratio (25°C) % 69.0 T0604-2011Ductility (15°C) cm 34.8 T0605-2011
2 Advances in Materials Science and Engineering
bending tests at −10°C. 1e SENB with notch depth of 4mmwas applied for three-point bending tests at −20°C, −10°C,0°C, 10°C, and 20°C.
A material test system (MTS-810) with an environ-mental chamber was used to perform the three-pointbending tests. 1e configuration of the three-point bend-ing test on a SENB is shown in Figure 3. 1e loading span is200mm. In a three-point bending test, the load usinga constant displacement rate of 0.05mm/min was directlyapplied at the point right above the notch on the uppersurface. 1e midspan displacement δ was recorded at asampling frequency of 10Hz during the whole loadingprocess until failure. 1e load-displacement curve can bedrawn to obtain the peak loads.
Table 4: Properties of fine aggregate.
Test item Unit Testresult
Testmethod
Apparent relative density / 2.726 T0329Bulk density / 2.696 T0329Sturdiness (>0.3mm) % 4 T0340Particle content of less than 0.075mm % 9.9 T0340Sand equivalent % 82 T0334Methylene blue value g/kg 1.5 T0349Angularity s 38.6 T0345
Table 5: Properties of mineral filler.
Property Unit ResultApparent specific gravity — 2.693Water content % 0.34Hydrophilic coefficient — 0.58Plasticity index % 2.5
Table 6: Properties of lignin fibers.
Property Unit ResultLength mm <6Ash content % 19.64pH — 7.6Hygroscopicity % 6.57Water content (by weight) % 0.85
Figure 2: Single-edge notch beams.
Table 2: Properties of SBS-modified asphalt.
Test item Unit Test result Test methodPenetration (25°C, 5 s, 100 g) 0.1mm 66.5 T0604-2011Ductility (5°C, 5 cm/min) cm 38 T0605-2011Softening point (R&B) °C 77.4 T0606-2011Kinematic viscosity (135°C) Pa·s 2.0 T0625-2011Flash point °C 263 T0611-2011Solubility % 99.58 T0607-2011Elastic recovery (25°C) % 97 T0662-2000
Residue after TFOTQuality change % 0.09 T0610-2011
T0609-2011Penetration ratio (25°C) % 73 T0604-2011Ductility (5°C) cm 23 T0605-2011
Table 3: Properties of coarse aggregate.
Test item Unit Test result Test methodApparent relative density / 2.953 T0304Bulk density / 2.886 T0304Acicular content % 3.95 T0312Particle content of less than 0.075mm % 0.2 T0310Soft stone content % 1.0 T0320Crushing value % 12.9 T0316Crushing value (200°C for 5 hours) % 13.6 T0316Firmness % 2.0 T0314Water absorption rate % 0.78 T0314Los Angeles wear value loss % 13.7 T0317Los Angeles wear value loss (200°C for 5 hours) % 14.4 T0317Polished value PSV 44 T0321Adhesion Grade 5 T0305
Advances in Materials Science and Engineering 3
3. Theoretical Background
3.1. Fracture Toughness. �e SENB specimen loaded ina three-point bending con�guration and notched at themidpoint, as shown in Figure 3, is under the mode oftension, so the fracture toughness for a SENB specimen isgiven as follows [11, 12]:
KI � σ0YI���πa
√, (1)
where a is the notch depth, σ0 is the applied stress, and YI isthe normalized fracture toughness. �e applied stress isgiven as follows:
σ0 �3Ps2h2w
, (2)
whereP is the applied load, s is the loading span, and h andware the specimen height and width, respectively, as seen inFigure 3. �e normalized fracture toughness, YI, is given bythe following analytical expression [3, 13–15]:
YI �1.99−(a/W)(1−(a/W)) 2.15−(3.93a/W) + 2.7a2/W2( )( )
��π
√(1 +(2a/W))(1−(a/W))3/2
. (3)
3.2. Fracture Energy. Fracture energy, GF, is de�ned as thearea under the load-displacement curve divided by theligament area, which could be expressed as follows [16]:
GF �W
Alig, (4)
where W is the work of fracture for an entire crack prop-agation period and Alig is the area of the ligament.
Figure 4 shows the work of fracture W for crackpropagation, which can be expressed as (5), considering thee�ects of the self-weight of the beam [17, 18].
W �W0 +W1 +W2 +W3, (5)
where W0 is the work performed by the external force P forcrack propagation and W1, W2, and W3 are the additionalworks caused by the self-weight of the beam. Based on special
wL
h
d
S
Roller
Roller Roller
P
L = 250 mmw = 30 mmh = 35 mms = 200 mms/L = 0.8d = 0, 4, 8, 12, and 16 mm
Figure 3: A schematic illustration of the three-point bending test on a single-edge notched beam.
12mg
Pmax
P0
PP′
O′ Displacement
W1
W3
W2
Load
O δ0 δ
δ′
W0
Figure 4: A load-displacement curve for a stable three-point bend test on a single-edge notched beam.W0 de�nes the area under the load-displacement curve if there is no compensation for the energy supplied by the weight of the beam,m is the weight of the beam (between thesupports), and g� 9.81m/s2 [17].
4 Advances in Materials Science and Engineering
hypothetic situation, W2 and W3 can be calculated as follows[12, 17]:
W2 �W3 �12mgδ0. (6)
According to (4)–(6), fracture energy,GF, can be expressedas (7) [16], so that the fracture energy of asphalt mixture couldbe calculated from a load-displacement curve recorded [19].
GF �W
Alig�∫δ0
0p(δ) dδ +mgδ0[ ]
Alig,
(7)
where GF � the fracture energy (N/m), m � m1 +m2 (kg),m1 �Ms/L (weight of the beam between the supports),
M�weight of the specimen, m2 �weight of the part of theloading arrangement which is not attached to the machinebut follows the beam until failure, δ0 � the midspan dis-placement of the specimen at failure (m), δ �midspandisplacement (m), g� 9.81 (m/s2), and Alig � area of theligament. P, s, and L are shown in Figure 3.
4. Results and Discussions
4.1. E�ects of Notch Depth
4.1.1. Displacement. �e load-displacement curves wererecorded by three-point bending tests. Figure 5 are shown theload-displacement curves of the three mixtures of SENBspecimens with di�erent notch depths. According to Figure 5,
0
200
400
600
800
1000
1200
0.2 0.4 0.6 0.8 1.0 1.20Displacement (mm)
16 mm12 mm8 mm
4 mm0 mm
Load
(N)
(a)
0
200
400
600
800
1000
1200
1400
0.5 1.0 1.5 2.0 2.50Displacement (mm)
Load
(N)
16 mm12 mm8 mm
4 mm0 mm
(b)
0
200
400
600
800
1000
1200
1400
1600
0.2 0.4 0.6 0.8 1.0 1.2 1.40Displacement (mm)
Load
(N)
16 mm12 mm8 mm
4 mm0 mm
(c)
Figure 5: Load-displacement curves for di�erent notch depths: (a) AC-13, (b) AC-16, and (c) SMA-13.
Advances in Materials Science and Engineering 5
the load-displacement curves of the mixtures present typicalthree stages. At the �rst stage, the load increases linearly withthe displacement up to the peak. At the second stage, after thepeak, the load decreases largely with the displacement and, atthe same time, the fracture develops rapidly. At the third stage,the load decreases steadily until the specimen fracture failure.
4.1.2. Ultimate Load. �e ultimate loads of the three-pointbending tests can be obtained through the load-displacementcurves. Figure 6 shows the ultimate loads for the SENBspecimens of the three mixtures with di�erent notch depthsat 10°C. From Figure 6, with the increase of notch depth, theultimate loads of three kinds of asphalt mixture show a lineardownward trend. In addition, under the same conditions of
notch depth, the ultimate load of the AC-13 specimen isminimum, AC-16 is moderate, and SMA-13 is maximumamong the three asphalt mixtures. It is analyzed that thehigher ultimate load of the SMA-13 specimen is attributed tothe material composition, which the utilization of the SBS-modi�ed asphalt and the �ber can contribute to improvingthe tensile strength and the ultimate load.
4.1.3. Fracture Toughness. Fracture toughness, KI, for SENBspecimens with di�erent notch depths can be determined by(1)–(3). �e calculations of fracture toughness for di�erentnotch depths are shown in Figure 7. With the increase ofnotch depth, for the three asphalt mixtures, the fracturetoughness increases moderately. It is notable that thefracture toughness for SMA-13 is largest among the threeasphalt mixtures at the same conditions of notch depth.
4.1.4. Fracture Energy. From load-displacement curves, thefracture energy of mixtures was calculated by using (7).Fracture energy of the three-point bending test on SENBspecimens with di�erent notch depths is shown in Figure 8.From Figure 8, it can be seen that the notch depth has nosigni�cant e�ects on the fracture energy of AC-13 speci-mens. For AC-16 and SMA-13, there is no obvious regularityof the notch depth versus the fracture energy. �e contentsof �ne aggregate (less than 2.36mm) of AC-16 and SMA-13are relatively small, and the contents of course aggregate arerelatively large, which results in increasing the discretenessof the fracture energy of the specimen.
4.2. E�ects of Temperature
4.2.1. Displacement. �e load-displacement curves wererecorded by three-point bending tests. Figure 9 shows the
0
10
20
30
40
50
60
28.6
29.8
31.9
31.7
36.4
35.6
38.3
41.9
40.4
42.9
42.3
45.7
AC-13AC-16SMA-13
dS
P
h
d = 4 d = 8 d = 12 d = 16d/h = 0.114 d/h = 0.229 d/h = 0.343 d/h = 0.457
Notch depth, d (mm)
Frac
ture
toug
hnes
s, K I
(N·m
m3/
2 )
Figure 7: Fracture toughness for di�erent notch depths.
271.
0
275.
2
281.
7
266.
1
276.
6
398.
3
565.
2
268.
4
371.
1
488.
0
448.
9
290.
0
328.
5
320.
9388.
4
0 4 8 12 160
100
200
300
400
500
600
700
800
Notch depth (mm)
AC-13
AC-16
SMA-13Fr
actu
re en
ergy
(N/m
)Figure 8: Fracture energy for di�erent notch depths.
0 4 8 12 16
400
600
800
1000
1200
1400
1600
SMA-13
AC-16
Notch depth (mm)
AC-13
12mg
Pmax
P0
PP′
O′ Displacement
W1
W3
W2
Load
O δ0 δ
δ′
W0
Ulti
mat
e loa
d (N
)
Pmax = ultimate load
Figure 6: Ultimate loads for di�erent notch depths.
6 Advances in Materials Science and Engineering
load-displacement curves at di�erent temperatures.According to Figure 9, AC-13, AC-16, and SMA-13 havesimilar load-displacement curves at di�erent temperatures.At −20°C, the loads rise rapidly, and there are no peak valuesuntil fracture failure which indicates that the SENB speci-mens are brittle failure in the three-point bending tests at−20°C. When the temperature increases (from −10°C to10°C), the specimens present a certain toughness, the load ofthe beam increases �rst and then decreases with the dis-placement. In particular, when the temperature increases to20°C, it is obvious that the load-displacement curves at 20°Care noticeably di�erent from the curves at the lower tem-peratures. At 20°C, the linearly increase stage of the loadreduces and the load rises steadily with the displacement and
the load decreases when the fracture grows to a certainextent and the specimen fracture failure occurs until thedisplacement reaches a relatively large value compared withthat at lower temperatures.
4.2.2. Loading. Figure 10 shows the ultimate loads for theSENB specimens of the three mixtures at di�erent tem-peratures. �e ultimate loads increase at �rst and thendecrease and reach the maximum at 0°C, which could beresulted in that asphalt mixture is a viscoelastic material thatthe mechanical properties depend with temperatures. �eSENB specimens are brittle fracture at −20°C, and the ul-timate load is small, and toughness of the SENB specimens
0 1 2 3 4 50
200
400
600
800
1000
1200
Displacement (mm)
–20°C–10°C0°C
10°C20°C
Load
(N)
(a)
0 1 2 3 4 5Displacement (mm)
0
200
400
600
800
1000
1200
Load
(N)
–20°C–10°C0°C
10°C20°C
(b)
0 1 2 3 4 5 6 7Displacement (mm)
0
200
400
600
800
1000
1200
1400
Load
(N)
–20°C–10°C0°C
10°C20°C
(c)
Figure 9: Load-displacement curves at di�erent temperatures: (a) AC-13, (b) AC-16, and (c) SMA-13.
Advances in Materials Science and Engineering 7
increases with temperatures which contributes to the ulti-mate load increase. �e tensile strength of the SENBspecimens decreases with temperatures after the criticaltemperature, and the ultimate load decreases.
4.2.3. Fracture Toughness. Figure 11 shows the fracturetoughness at di�erent temperatures for SENB specimensusing the three asphalt mixtures. It can be found that thefracture toughness at −20°C of AC-13 and AC-16 is higherthan that of SMA-13. However, it can be seen that SMA-13has higher fracture toughness than AC-13 or AC-16 has at
temperatures from −10°C to 20°C, indicating its better re-sistance to fracture generally.
4.2.4. Fracture Energy. �e fracture energy at di�erenttemperatures for SENB specimens using the three asphaltmixtures is shown in Figure 12. It can be seen from Figure 12that the fracture energy increases with temperatures. At thelower temperatures, −20°C and −10°C, the asphalt mixturespresent relatively notable elasticity and SENB specimens trendto brittle crack, consequently the three asphalt mixtures havesimilar fracture energy. At the higher temperatures, 0°C to20°C, the asphalt mixtures present relatively notable viscosityespecially at moderate temperatures, 10°C to 20°C, which thefracture energy greatly di�ers among the three asphalt mix-tures. From Figure 12, the fracture energy of SMA-13 issigni�cantly larger than those of AC-13 and AC-16.
5. Conclusions
�is study adopted the SENB test to evaluate the fractureproperties of three typical surface layer asphalt mixtures,AC-13, AC-16, and SMA-13, changing with variations ofnotched depths and temperatures. �e following conclusionscan be drawn:
(1) �e notch depth has no signi�cant e�ects on thefracture toughness and the fracture energy, butthe gradation has relatively obvious e�ects on thefracture energy, which the larger contents of courseaggregate results to increase the discreteness of thefracture energy of the specimen.
(2) �e ultimate loads of the SENBs reach the maximum at0°C, which could be resulted in that viscoelastic prop-erties of asphalt mixture depend with temperatures.
(3) �e fracture toughness at −20°C of continuouslygraded asphalt mixtures are higher than those of
–20 –10 0 10 20200
400
600
800
1000
1200
1400
Temperature (°C)
AC-13AC-16SMA-13
Ulti
mat
e loa
d (N
)
Figure 10: Ultimate loads at di�erent temperatures.
–20 –10 0 10 200
10
20
30
40
50
60
25.4
28.3
31.2
28.6
11.8
21.2
30.3
35.2
30.5
11.5
18.2
34.0
40.5
35.4
13.2
AC-13AC-16SMA-13
Frac
ture
toug
hnes
s, K I
(N·m
m3/
2 )
Temperature (°C)
d = 4 mmd/h = 0.114dd
S
P
h
Figure 11: Fracture toughness at di�erent temperatures.
80
307 51
5 592
1635
70
272
767
785
1364
49
314
765
1631
2588
–20 –10 0 10 200
500
1000
1500
2000
2500
3000
3500
Frac
ture
ener
gy (N
/m)
Temperature (°C)
AC-13AC-16SMA-13
Figure 12: Fracture energy at di�erent temperatures.
8 Advances in Materials Science and Engineering
gap-graded asphalt mixtures. On the contrary, thefracture toughness of gap-graded asphalt mixturesis higher at temperatures from −10°C to 20°C.
(4) Temperature has significant effects on the fractureenergy, and the fracture energy increases withtemperatures. 1e fracture energy of SMA-13 issignificantly larger than those of AC-13 and AC-16.
Conflicts of Interest
1e authors declare that they have no conflicts of interest.
Acknowledgments
1is research was sponsored by the Natural Science Foun-dation of Shaanxi Province (2016JQ5115), the PhD ResearchStartup Foundation of Xi’an University of Science andTechnology (2017QDJ024), the opening fund of Guangxi KeyLab of Road Structure and Materials (2017gxjgclkf-001), theopening fund of Key Laboratory for Special Area HighwayEngineering of Ministry of Education (300102218512), and theOutstanding Youth Science Fund of Xi’an University of Sci-ence and Technology (2018YQ3-07). 1e results and opinionspresented are those of the authors and do not necessarilyreflect those of the sponsoring agencies.
References
[1] H. Kim, M. P. Wagoner, and W. G. Buttlar, “Simulation offracture behavior in asphalt concrete using a heterogeneouscohesive zone discrete element model,” Journal of Materials inCivil Engineering, vol. 20, no. 8, pp. 552–563, 2008.
[2] Q. Dai and K. Ng, “2D cohesive zone modeling of crackdevelopment in cementitious digital samples with micro-structure characterization,” Construction and Building Ma-terials, vol. 54, pp. 584–595, 2014.
[3] I. Artamendi and H. A. Khalid, “A comparison between beamand semi-circular bending fracture tests for asphalt,” RoadMaterials and Pavement Design, vol. 7, no. s1, pp. 163–180, 2011.
[4] M. H. Sadd and Q. Dai, “A comparison of micro-mechanicalmodeling of asphalt materials using finite elements anddoublet mechanics,” Mechanics of Materials, vol. 37, no. 6,pp. 641–662, 2005.
[5] W. Buttlar and Z. You, “Discrete element modeling of asphaltconcrete: Microfabric approach,” Transportation ResearchRecord: Journal of the Transportation Research Board,vol. 1757, pp. 111–118, 2001.
[6] S. J. Sulaiman and A. F. Stock, “1e use of fracture mechanicsfor the evaluation of asphalt mixes,” in Association of AsphaltPaving Technologists Technical Sessions, 1995, pp. 500–531,Portland, OR, USA, 1995.
[7] J. M. M. Molenaar and A. A. A. Molenaar, “Fracture toughnessof asphalt in the semi-circular bend test,” in Proceedings of the2nd Eurasphalt & Eurobitume Congress, pp. 509–517, Barcelona,Spain, September 2000.
[8] M. P. Wagnoner, W. G. Buttlar, and G. H. Paulino, “Disk-shaped compact tension test for asphalt concrete fracture,”Experimental Mechanics, vol. 45, no. 3, pp. 270–277, 2005.
[9] G. S. Xeidakis, I. S. Samaras, D. A. Zacharopoulos, andG. E. Papakaliatakis, “Crack growth in a mixed-mode loadingon marble beams under three point bending,” InternationalJournal of Fracture, vol. 79, no. 2, pp. 197–208, 1996.
[10] A. Braham, W. Buttlar, and F. Ni, “Laboratory mixed-modecracking of asphalt concrete using the single-edge notchbeam,” Road Materials and Pavement Design, vol. 11, no. 4,pp. 947–968, 2011.
[11] J. E. Srawley, “Wide range fracture toughness expressions forASTM E 399 standard fracture toughness specimens,” In-ternational Journal of Fracture, vol. 12, no. 3, pp. 475-476,1976.
[12] Y. Murakami and S. Aoki, Stress Intensity Factors Hand-book, vol. 2, Pergamon, Oxford, UK, 1987.
[13] J. E. Srawley and W. F. Brown Jr., Fracture Toughness Testing,National Aeronautics and Space Administration, Lewis Re-search Center, Cleveland, OH, USA, 1965.
[14] J. E. Srawley and B. Gross, Stress Intensity Factors for Crackline-Loaded Edge-Crack Specimens, National Aeronautics and SpaceAdministration, Washington, DC, USA, 1967.
[15] J. E. Srawley, M. H. Jones, and B. Gross, Experimental De-termination of the Dependence of Crack Extension Force on CrackLength for a Single-Edge-Notch Tension Specimen, NationalAeronautics and Space Administration, Washington, DC, USA,1964.
[16] RILEM, “Determination of the fracture energy of mortar andconcrete by means of three-point bend tests on notchedbeams,” Materials and Structures, vol. 18, no. 4, pp. 285–290,1985.
[17] P.-E. Petersson and L. Tekniska,Crack Growth and Developmentof Fracture Zones in Plain Concrete and Similar Materials, LundInstitute of Technology, Lund, Sweden, 1981.
[18] M. Hossain, S. Swartz, and E. Hoque, “Fracture and tensilecharacteristics of asphalt-rubber concrete,” Journal of Materialsin Civil Engineering, vol. 11, no. 4, pp. 287–294, 1999.
[19] G.-F. Peng, W.-W. Yang, J. Zhao, Y.-F. Liu, S.-H. Bian, andL.-H. Zhao, “Explosive spalling and residual mechanicalproperties of fiber-toughened high-performance concrete sub-jected to high temperatures,” Cement and Concrete Research,vol. 36, no. 4, pp. 723–727, 2006.
Advances in Materials Science and Engineering 9
CorrosionInternational Journal of
Hindawiwww.hindawi.com Volume 2018
Advances in
Materials Science and EngineeringHindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
Journal of
Chemistry
Analytical ChemistryInternational Journal of
Hindawiwww.hindawi.com Volume 2018
Scienti�caHindawiwww.hindawi.com Volume 2018
Polymer ScienceInternational Journal of
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
Advances in Condensed Matter Physics
Hindawiwww.hindawi.com Volume 2018
International Journal of
BiomaterialsHindawiwww.hindawi.com
Journal ofEngineeringVolume 2018
Applied ChemistryJournal of
Hindawiwww.hindawi.com Volume 2018
NanotechnologyHindawiwww.hindawi.com Volume 2018
Journal of
Hindawiwww.hindawi.com Volume 2018
High Energy PhysicsAdvances in
Hindawi Publishing Corporation http://www.hindawi.com Volume 2013Hindawiwww.hindawi.com
The Scientific World Journal
Volume 2018
TribologyAdvances in
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
ChemistryAdvances in
Hindawiwww.hindawi.com Volume 2018
Advances inPhysical Chemistry
Hindawiwww.hindawi.com Volume 2018
BioMed Research InternationalMaterials
Journal of
Hindawiwww.hindawi.com Volume 2018
Na
nom
ate
ria
ls
Hindawiwww.hindawi.com Volume 2018
Journal ofNanomaterials
Submit your manuscripts atwww.hindawi.com
