Contribution of Interface Fracture Mechanism on Fracture Propagation Trajectory of Heterogeneous Asphalt Composites

: Asphalt mixture is a type of textured composite material made of aggregates and mastic part. Overall strength and failure behavior in such materials depends on the texture or heterogeneity of the mixture. In particular, the crack growth mechanism from the tip of the pre-crack is signiﬁcantly affected by the texture of the asphalt composite and environmental conditions. The crack can extend through the soft mastic, tight aggregates or interface of the mastic/aggregates. In this research, by performing some fracture tests on a typical asphalt mixture with different test specimens under mode I, mixed mode I/II and mixed mode I/III, the fracture resistance and trajectory of propagating crack is studied at two low and medium temperatures (i.e., − 15 and +15 ◦ C). The load bearing capacity and the fracture resistance of the tested asphalt samples increases by decreasing the temperature. It is also shown that a signiﬁcant part of fracture plane passes through the soft mastic and boundary of aggregates (i.e., the interface of aggregates and mastic) and only about 10–15% of the fracture surface of the propagating crack passes via the tight aggregates by breaking them. This percentage decreases for mode II and III loading conditions and higher testing temperatures. Compared to brittle and isotropic materials, the fracture path of the asphalt mixture shows more deviation, and this deviation increases for those mixtures containing coarser aggregates in the ligament and tested under medium temperature conditions.


Introduction
Cracking phenomena and the fracturing of pavements are common modes of failure in overlay structures, especially in cold regions [1][2][3][4][5]. At low temperature conditions, the probability of crack propagation from pre-existing flaws increases due to traffic loading or thermal fatigue loads induced by daily or seasonal temperature changes. A real asphalt mixture used in pavements is a multi-phase material made of some ingredients including coarse and fine aggregates, binder (or bitumen), air voids and sometimes additives in the shape of fibers or powders. Hence, the overall mechanical properties of these randomly distributed composites significantly depend on the mix-design and type of the ingredients [6][7][8]. In particular, the type of asphalt mixture can noticeably affect the load bearing capacity, fatigue life and propagation of fracture trajectory in these composites. Due to the loading type or environmental effects, the fracturing of asphalt pavements may take place in different basic modes including mode I (crack opening), mode II (crack in-plane sliding), mode III (crack out-of-plane tearing) and any combinations of these modes called mixed mode (e.g., mixed mode I/II, I/III, II/III or I/II/III) [9]. Accordingly, several researchers have investigated the fracture behavior of these composite materials using different testing methods under the mentioned loading modes [9,10]. The fracture mechanics approach and linear elastic fracture mechanics were used in the mid-1970s for studying the fracture behavior of asphalt composite materials [10]. Afterwards, some experimental testing methods and test samples including the edge cracked rectangular beam specimen subjected to four-point bend loading and the semi-circular bend (SCB) specimen were employed by Molennar et al. [11,12] for investigating the mode I fracture of the asphalt mixtures. Other test configurations such as the modified indirect tensile disc (MITD) specimen [13], disc-shape compact-tension specimen [14], single edge notch beam (SENB) subjected to three-point bend [9,15], wedge splitting disc (WSD) [16], edge notch disc bend (ENDB) [17][18][19][20][21][22][23][24], edge notch disc diametral compression (ENDC) [25][26][27], center cracked Brazilian disc subjected to diametral compression [28], semi-circular bend (SCB) specimen [29][30][31][32][33][34], and hollow disc (or ring shape) specimen containing center crack and loaded diametrically [35] are some of the test configurations employed in the literature for investigating the fracture resistance of asphalt mixtures. Any of these test samples are suitable for simulating and conducting specific modes of fracture. For example, the MITD and WSD are suitable for pure mode I testing. Other test configurations such as the SCB, three-point bend, hollow disc ring and Brazilian disc samples can be utilized for both mode I and mixed mode I/II fracture testing. On the other hand, the ENDB and ENDC test samples are capable of conducting pure mode I and mixed mode I/III fracture tests on asphalt mixtures.
As a randomly distributed heterogeneous composite mixture and due to the difference in the mechanical properties of the soft mastic part and tight aggregates, it is evident that the fracture behavior of asphalt mixtures depends on the location of initial crack inside the mixture. Indeed, if the pre-crack is located inside the aggregate or in the vicinity of bigger aggregates this can result in increasing the fracture resistance. Conversely, the cracking resistance of the asphalt mixture is reduced if the initial crack tip is placed inside the binder or soft mastic or fine aggregate mixture part. In addition to the influence of heterogeneity on the fracture strength of asphalt mixtures, the texture and composition of mixture can affect the path of propagating crack. Since the material is not homogenous, random distribution of aggregates inside the matrix of binder, soft mastic or fine aggregate matrix, may affect the trajectory of fracture during the crack propagation. Indeed, the crack can grow through the tight aggregates, soft mastic or interface of aggregate/mastic parts.
For more realistic analysis of the cracked asphalt mixtures, it is better to consider the asphalt composite material as a heterogeneous mixture, and hence some research papers have focused on the failure behavior of asphalt mixtures from this viewpoint. For example, Kim et al. [36] used discrete element method (DEM) and image processing technique (IPT) for 2-D modeling of a cracked heterogeneous asphalt mixture. Zhao et al. [37] investigated the growth and propagation of cracks using the semi-circular bend (SCB) samples by means of IPT and numerical modeling. They estimated the crack propagation path using the cohesive elements. Dai et al. [38] used 2-D finite element (FE) modeling and IPT to predict the fracture behavior of asphalt mixtures. Their goal was to predict the fracture path of the asphalt mixture under indirect tension. NG and Dai [39] numerically predicted the path of crack growth for the SENB and split tensile (ST) samples. Aliha et al. [40] used the aggregate generation and packing algorithm (AGPA) and 2-D FE models to estimate the trajectory of fracture in the SCB samples. They found that heterogeneous modeling of asphalt mixtures leads to a more realistic prediction for the path of crack propagation and the mode I and mode II stress intensity factors are sensitive to the crack tip location. Using the FE modeling and AGPA method [41][42][43] Aliha and coworkers also simulated the fracture behavior of asymmetric semi-circular bend (ASCB) sample by assuming the heterogeneity for the asphalt mixtures. Li and Guo [44] employed the AGPA and FE models to estimate the trajectory of crack growth in the SCB samples. They concluded that the distribution of aggregates, gradation, and angularity of the aggregates have considerable effects on the path of fracture. Yin et al. [37,45] showed that the path of crack growth is sensitive to the aggregate distribution and cohesive strength of the aggregate/mastic interface.
However, in most of the previous works the effects of composite mixture and testing conditions have only investigated on the fracture toughness and load bearing capacity values. Indeed, very-limited studies are available for considering the influence of the mixture heterogeneity on the fracture trajectory and fracture surface of the asphalt composite mixtures at different testing and loading conditions. Therefore, in this research, using the results of experimental tests conducted on a typical asphalt mixture with different test geometries, the fracture trajectory is investigated for different loading modes and testing conditions. It is shown that the distribution of aggregates and testing temperature can significantly affect the path of mode I and the mixed mode fracture of the asphalt concrete.

Test Specimens
Some test samples including ENDB, SCB, BD, and SENB were selected for conducting the fracture experiment on the asphalt concrete and investigating the related fracture trajectory. Figure 1 shows the configurations of test samples. The ENDB specimen is a disc shape sample with radius R and height t that contains an edge crack along the disc diameter. By three-point bend loading of the disc and rotating the disc direction relative to the loading rollers, different combinations of mode I and mode III are introduced by the ENDB specimen. The SCB specimen is a semi-circular specimen with radius R and thickness t containing an edge crack of length a. The specimen is loaded by three-point bending and the state of mode I and II mixity can be altered by changing the crack inclination angle, crack location or loading roller distance relative to the crack as seen from Figure 1. The center crack Brazilian disc (BD) specimen is also a circular disc with radius and thickness R and t, respectively containing a center crack of length 2a. Mode I and mixed mode I/II are obtained using this specimen by changing the crack inclination angle relative to the direction of diametral compression load applied to the disc specimen. The edge cracked beam specimen subjected to bend loading (i.e., SENB specimen) can be used for introducing pure mode I and some limited combinations of mode I and mode II (i.e., dominantly mode I case). The stress intensity factors (K I , K II and K III ) in the mentioned samples are functions of the specimen geometry and loading condition and can be written as: where P is the applied load and Y i are the geometry factors or normalized forms of the stress intensity factors that are functions of the specimen geometry and loading conditions [15,17,18,29,30,46,47]. The corresponding values of these geometry factors for any test specimen and mode mixity can be determined using the finite element analysis. For example,

Mix Design
The hot mix asphalt (HMA) of this research is composed of bitumen 60/70 with performance grade (64-22) and siliceous aggregates with the maximum nominal aggregate size (MNAS) of 12.5 mm. The physical properties of the used aggregates and also their gradations are illustrated in Tables 2 and 3, respectively.  In order to determine the optimal percentage of bitumen, some asphalt samples with percentages of 4%, 5%, 6% and 7% bitumen were prepared. After mixing bitumen and aggregates, the samples were poured into a standard Marshall cylinder with diameter and height of 100 and 62.5 mm, respectively and compacted with a Marshall compactor (75 strokes per side of the sample). Based on some mechanical and physical parameters such as specific gravity of compacted asphalt, compressive strength, relative deformation of compacted asphalt mixture and volume of air void content, the optimal bitumen percentage for each asphalt mixture is determined. In this study, 18 cylindrical samples were manufactured and tested to obtain the control parameters of the mixtures. Table 4 shows the final physical and strength characteristics of the HMA material used for manufacturing the test specimens. Using the obtained optimum bitumen percentage, the aggregate and binder were blended at 140 • C. Then for creating the disc shape samples including the ENDB, SCB and BD specimens the prepared mixture was compacted by a gyratory compactor machine (GCM) to produce cylindrical asphalt specimens with diameter of 150 mm and height of 120 mm. In addition, the beam samples were manufactured by casting the mixture inside a rectangular mold with dimensions of 400 × 50 × 50 mm 3 . Since, the air void content has noticeable influence on the mechanical and strength properties of the asphalt mixtures, the void percentage in all prepared asphalt samples was considered constant and equal to 4.7% for the sake of comparison of the experimental results. The manufactured cylindrical samples were then sliced by a specific designed fixture and by means of a high-speed rotary diamond saw blade to obtain circular discs of height approximately 35 and 50 mm. A very thin rotary diamond saw blade with thickness of 0.5 mm was used to introduce an initial artificial straight edge crack in the ENDB, SCB and SENB samples; but the center crack in the BD specimen was created using water jet cutting machine. The prepared test samples with different geometries were tested using a test machine at two test temperatures of −15 and 15 • C (room temperature). The loading rate in all experiments was constant and equal to 3 mm/min. Figure 2 shows the testing setup for some of the samples.   Figure 3 shows some of the load-displacement curves obtained for the tested ENDB, SCB, BD and SENB samples at low and medium temperature conditions. For the low temperature tests, it can be seen that the loading curves are linear and asphalt mixture exhibits as a brittle material. Therefore, the framework of linear elastic fracture mechanics (LEFM) is valid for this testing condition. However, some evidences of non-linearity in the load-displacement curves are seen for the medium temperature condition due to viscosity of bitumen material. However, the onset of fracture takes place for both temperature conditions at a critical level of loading applied to each sample. This situation is known by the peak load value in the load-displacement curve. Therefore, the critical value of stress intensity factor for each specimen can be determined by replacing the peak loads into Equations (1)-(4) and using the geometry factors given in Table 1. The results of critical stress intensity factors (K If , K IIf and K IIIf ) that are representative values for the resistance of tested asphalt mixtures at the onset of fracture initiation under different fracture modes and temperatures are presented in Table 5. The results illustrated in this Table, demonstrate the sensitivity of critical stress intensity factor value a same asphalt mixture to the geometry of test specimen (disc, semi disc and rectangular beam), loading mode (i.e., modes I, II, III or tensile, shear or tear type), loading type (compression, bending) and temperature (low and medium temperature). For example, for pure mode I loading and low temperature conditions in which the LEFM is valid, as shown in this research and explained in many previous works e.g., [1][2][3][4][5][6][7][8][9][10], where it can be seen that the K If value of a same asphalt mixture depends on the test specimen utilized for testing. The value of mode I fracture toughness increases from 0.66 MPam 0.5 (obtained from the BD specimen) to 0.82 MPam 0.5 (obtained from the SCB specimen). According to recent works published by Aliha and co-workers [25,26,48], the mode I fracture toughness of asphalt mixtures depends on the geometry and loading conditions of the employed test specimen. Based on their finding (that is confirmed in this research as well), the mode I fracture toughness value obtained from the diametral compression test is lower than the value obtained by bending type specimen. They also proposed a theoretical model for considering the influence of geometry and loading condition on the mode I fracture toughness value of asphalt mixtures. Comparison of presented results in Table 5 also demonstrates that the fracture and cracking resistance of an asphalt mixture reduces generally under application of shear type loads (i.e., mode II and mode III) relative to opening mode failure. Furthermore, according to Table 5, the cracking resistance of the asphalt mixture decreases significantly by moving from the low temperature condition to the medium temperature condition. This could be due to reducing the stiffness of mastic or bitumen part at higher temperatures.    Figure 4 shows the fracture trajectories of the tested SCB, ENDB, BD and SENB specimens under mode I. For the pure mode I case, it is expected to see a self-similar and straight fracture path. The overall mode I fracture trajectory for the broken asphaltic samples is straight, but some deviations and local zig-zag type path is observed. The amount of deviation depends on some parameters such as the size of the aggregate, the distribution of the coarse aggregate inside the asphalt mixture and also the testing temperature. Indeed, the propagating crack rounds the aggregates located in the ligament and in these regions an interface fracture between the boundary of the aggregates and the mastic part can control the mechanism of the asphalt fracture. However, if a coarse aggregate is lo-   Figure 4 shows the fracture trajectories of the tested SCB, ENDB, BD and SENB specimens under mode I. For the pure mode I case, it is expected to see a self-similar and straight fracture path. The overall mode I fracture trajectory for the broken asphaltic samples is straight, but some deviations and local zig-zag type path is observed. The amount of deviation depends on some parameters such as the size of the aggregate, the distribution of the coarse aggregate inside the asphalt mixture and also the testing temperature. Indeed, the propagating crack rounds the aggregates located in the ligament and in these regions an interface fracture between the boundary of the aggregates and the mastic part can control the mechanism of the asphalt fracture. However, if a coarse aggregate is located exactly in front of the crack tip or in the middle of the ligament and is oriented normal to the crack propagation path, the fracture can grow through such aggregates. This is probably because breaking the aggregate needs lesser energy than moving along the longer path of the aggregate's boundary (i.e., interface of aggregate and mastic) to round the aggregate. For those situations in which there is no aggregate in the route of fracture, the crack growth can occur with less energy and with the driving force through the mastic part. The path of fracture in such regions is straight with no significant kinking.     The test temperature also plays a significant role in the trajectory of propagating the crack in the asphalt mixtures. This is mainly due to the visco-elastic nature of bitumen used in the mixture of asphalt concrete materials. At low temperature conditions, the bitumen behaves as a brittle and linear elastic material. The higher stiffness of bitumen at low temperatures will result in a brittle-type fracture for the whole asphalt mixture with higher load bearing capacity as shown in Figure 3 and Table 5. In this temperature condition, the fracture propagation shows less deviation from the straight line. However, under higher temperatures (such as room or medium temperature conditions) the fracture trajectory grows only through the mastic part or passes along the boundary of aggregate/soft mastic part. Indeed, for even small size aggregates located in front of the propagating crack, fracture dose not grow through or inside the aggregate and due to lower stiffness of mastic, it tends to round the aggregate and grow from the interface of aggregate/mastic. Figure 6 shows typical test samples tested at low and intermediate temperatures. As a conclusion, the heterogeneity and visco-elastic behavior of the asphalt mixtures can affect the cracking behavior of the asphalt mixtures. Increasing the amount of nonhomogeneity and the size of aggregates and increasing the temperature results in greater deviation of fracture trajectory from the straight line. Figure 7 compares the mode I fracture trajectory of the investigated asphalt samples with the cracking path of an isotropic The test temperature also plays a significant role in the trajectory of propagating the crack in the asphalt mixtures. This is mainly due to the visco-elastic nature of bitumen used in the mixture of asphalt concrete materials. At low temperature conditions, the bitumen behaves as a brittle and linear elastic material. The higher stiffness of bitumen at low temperatures will result in a brittle-type fracture for the whole asphalt mixture with higher load bearing capacity as shown in Figure 3 and Table 5. In this temperature condition, the fracture propagation shows less deviation from the straight line. However, under higher temperatures (such as room or medium temperature conditions) the fracture trajectory grows only through the mastic part or passes along the boundary of aggregate/soft mastic part. Indeed, for even small size aggregates located in front of the propagating crack, fracture dose not grow through or inside the aggregate and due to lower stiffness of mastic, it tends to round the aggregate and grow from the interface of aggregate/mastic. Figure 6 shows typical test samples tested at low and intermediate temperatures. The test temperature also plays a significant role in the trajectory of propagating the crack in the asphalt mixtures. This is mainly due to the visco-elastic nature of bitumen used in the mixture of asphalt concrete materials. At low temperature conditions, the bitumen behaves as a brittle and linear elastic material. The higher stiffness of bitumen at low temperatures will result in a brittle-type fracture for the whole asphalt mixture with higher load bearing capacity as shown in Figure 3 and Table 5. In this temperature condition, the fracture propagation shows less deviation from the straight line. However, under higher temperatures (such as room or medium temperature conditions) the fracture trajectory grows only through the mastic part or passes along the boundary of aggregate/soft mastic part. Indeed, for even small size aggregates located in front of the propagating crack, fracture dose not grow through or inside the aggregate and due to lower stiffness of mastic, it tends to round the aggregate and grow from the interface of aggregate/mastic. Figure 6 shows typical test samples tested at low and intermediate temperatures. As a conclusion, the heterogeneity and visco-elastic behavior of the asphalt mixtures can affect the cracking behavior of the asphalt mixtures. Increasing the amount of nonhomogeneity and the size of aggregates and increasing the temperature results in greater deviation of fracture trajectory from the straight line. Figure 7 compares the mode I fracture trajectory of the investigated asphalt samples with the cracking path of an isotropic As a conclusion, the heterogeneity and visco-elastic behavior of the asphalt mixtures can affect the cracking behavior of the asphalt mixtures. Increasing the amount of nonhomogeneity and the size of aggregates and increasing the temperature results in greater deviation of fracture trajectory from the straight line. Figure 7 compares the mode I fracture trajectory of the investigated asphalt samples with the cracking path of an isotropic and brittle model material (e.g., Perspex or Polymethylmethacrylate that is known as PMMA). This figure obviously shows the difference of the fracture trajectory in these two materials.

Mode I Fracture
. 2021, 11, x FOR PEER REVIEW 12 of 19 and brittle model material (e.g., Perspex or Polymethylmethacrylate that is known as PMMA). This figure obviously shows the difference of the fracture trajectory in these two materials.
(a) (b) The fracture surface of the tested asphalt samples with different geometries are also presented in Figure 8a. According to this figure although the overall fracture surface is flat but there is a rough surface due to propagation of fracture mainly from the boundary of the aggregates. However, the fracture surface shows some evidences for breakage of the tight aggregates, demonstrating that the fracture can either grow through the coarse aggregates. Using image processing technique, the observed fracture surface was divided into three parts: (i) passed through the aggregates, (ii) passed through the mastic and (iii) passed through the interface of aggregate and mastic. For example, these three regions are shown in Figure 8b with white, green and black colors, respectively for mode I fracture surface of SCB, ENDB and SENB samples tested at low temperature conditions. Using the utilized image processing method, the contribution of different regions or cracking mechanisms can be studied better for the asphalt mixtures. For example, for the SENB specimen tested under low temperature, it was observed that approximately 15% of the fracture surface belongs to the broken aggregates. In addition, it was seen from the observations of the fracture surface that typically about 20% of the fracture surface grows along the interface of aggregate/mastic or boundary of coarse aggregates. However, a significant part of the fracture surface in the tested mode I samples (i.e., approximately 65%) passes via the inside of soft mastic part. The fracture surface of the tested asphalt samples with different geometries are also presented in Figure 8a. According to this figure although the overall fracture surface is flat but there is a rough surface due to propagation of fracture mainly from the boundary of the aggregates. However, the fracture surface shows some evidences for breakage of the tight aggregates, demonstrating that the fracture can either grow through the coarse aggregates. Using image processing technique, the observed fracture surface was divided into three parts: (i) passed through the aggregates, (ii) passed through the mastic and (iii) passed through the interface of aggregate and mastic. For example, these three regions are shown in Figure 8b with white, green and black colors, respectively for mode I fracture surface of SCB, ENDB and SENB samples tested at low temperature conditions. Using the utilized image processing method, the contribution of different regions or cracking mechanisms can be studied better for the asphalt mixtures. For example, for the SENB specimen tested under low temperature, it was observed that approximately 15% of the fracture surface belongs to the broken aggregates. In addition, it was seen from the observations of the fracture surface that typically about 20% of the fracture surface grows along the interface of aggregate/mastic or boundary of coarse aggregates. However, a significant part of the fracture surface in the tested mode I samples (i.e., approximately 65%) passes via the inside of soft mastic part. and brittle model material (e.g., Perspex or Polymethylmethacrylate that is known as PMMA). This figure obviously shows the difference of the fracture trajectory in these two materials.
(a) (b) The fracture surface of the tested asphalt samples with different geometries are also presented in Figure 8a. According to this figure although the overall fracture surface is flat but there is a rough surface due to propagation of fracture mainly from the boundary of the aggregates. However, the fracture surface shows some evidences for breakage of the tight aggregates, demonstrating that the fracture can either grow through the coarse aggregates. Using image processing technique, the observed fracture surface was divided into three parts: (i) passed through the aggregates, (ii) passed through the mastic and (iii) passed through the interface of aggregate and mastic. For example, these three regions are shown in Figure 8b with white, green and black colors, respectively for mode I fracture surface of SCB, ENDB and SENB samples tested at low temperature conditions. Using the utilized image processing method, the contribution of different regions or cracking mechanisms can be studied better for the asphalt mixtures. For example, for the SENB specimen tested under low temperature, it was observed that approximately 15% of the fracture surface belongs to the broken aggregates. In addition, it was seen from the observations of the fracture surface that typically about 20% of the fracture surface grows along the interface of aggregate/mastic or boundary of coarse aggregates. However, a significant part of the fracture surface in the tested mode I samples (i.e., approximately 65%) passes via the inside of soft mastic part. SENB:

Mixed Mode Fracture Trajectory
As expected, the trajectory of the asphalt fracture under mixed mode loading is not self-similar and a curved in-plane and out-of-plane fracture path is often seen for the tested mixed mode I/II and I/III, respectively. Figure 9 presents some of the observed fracture paths for the mixed mode I/II of the tested asphalt specimens. Again, according to this figure, the propagating curve crack may alter its route to round the coarse aggregates located in front of the crack. The fracture trajectory deviation depends on the mode mixity, distribution of aggregates and also the test temperature. Compared to the mode I case, mixed mode I/II fracture grows mostly through the interface and soft mastic parts and the propagating crack rarely breaks the aggregates.

Mixed Mode Fracture Trajectory
As expected, the trajectory of the asphalt fracture under mixed mode loading is not self-similar and a curved in-plane and out-of-plane fracture path is often seen for the tested mixed mode I/II and I/III, respectively. Figure 9 presents some of the observed fracture paths for the mixed mode I/II of the tested asphalt specimens. Again, according to this figure, the propagating curve crack may alter its route to round the coarse aggregates located in front of the crack. The fracture trajectory deviation depends on the mode mixity, distribution of aggregates and also the test temperature. Compared to the mode I case, mixed mode I/II fracture grows mostly through the interface and soft mastic parts and the propagating crack rarely breaks the aggregates.

Mixed Mode Fracture Trajectory
As expected, the trajectory of the asphalt fracture under mixed mode loading is not self-similar and a curved in-plane and out-of-plane fracture path is often seen for the tested mixed mode I/II and I/III, respectively. Figure 9 presents some of the observed fracture paths for the mixed mode I/II of the tested asphalt specimens. Again, according to this figure, the propagating curve crack may alter its route to round the coarse aggregates located in front of the crack. The fracture trajectory deviation depends on the mode mixity, distribution of aggregates and also the test temperature. Compared to the mode I case, mixed mode I/II fracture grows mostly through the interface and soft mastic parts and the propagating crack rarely breaks the aggregates.  Figure 10 compares the fracture trajectories of investigated asphalt samples with a brittle homogenous material (e.g., PMMA) for mixed mode I/II. Different manners are seen for the fracture trajectory of mixed mode as seen from this figure. The heterogeneity of the asphalt mixture can affect the fracture initiation direction and even concavity or convexity of the fracture path and indeed, depending on the distribution of aggregates, the interface fracture (or rounding the aggregates) is the preferred trajectory for propagation of crack under mixed mode I/II. The difference between the fracture paths of isotropic PMMA material and heterogeneous visco-elastic asphalt material becomes more at higher temperatures and mixtures containing greater amount of large size aggregates in the ligament of tested samples.

BD SCB
Asphalt PMMA Figure 10. Comparison of fracture trajectory obtained for isotropic PMMA and heterogeneous asphalt mixture under mixed mode I/II.  Figure 10 compares the fracture trajectories of investigated asphalt samples with a brittle homogenous material (e.g., PMMA) for mixed mode I/II. Different manners are seen for the fracture trajectory of mixed mode as seen from this figure. The heterogeneity of the asphalt mixture can affect the fracture initiation direction and even concavity or convexity of the fracture path and indeed, depending on the distribution of aggregates, the interface fracture (or rounding the aggregates) is the preferred trajectory for propagation of crack under mixed mode I/II. The difference between the fracture paths of isotropic PMMA material and heterogeneous visco-elastic asphalt material becomes more at higher temperatures and mixtures containing greater amount of large size aggregates in the ligament of tested samples.
Similar to the mode I case, the fracture surface observed for the mixed mode I/II shows a rough surface passing mainly through the soft mastic and boundary of aggregates (or interface of aggregate/mastic). Observation of fracture surface under mixed mode loading indicates that more than 85% of the fracture path grows through the mastic or interface of aggregate/mastic. The roughness of fracture surface in the heterogeneous asphalt mixture is also greater than the surface of isotropic material with the same mode mixity.
of the asphalt mixture can affect the fracture initiation direction and even concavity or convexity of the fracture path and indeed, depending on the distribution of aggregates, the interface fracture (or rounding the aggregates) is the preferred trajectory for propagation of crack under mixed mode I/II. The difference between the fracture paths of isotropic PMMA material and heterogeneous visco-elastic asphalt material becomes more at higher temperatures and mixtures containing greater amount of large size aggregates in the ligament of tested samples.
Asphalt PMMA Figure 10. Comparison of fracture trajectory obtained for isotropic PMMA and heterogeneous asphalt mixture under mixed mode I/II. The mode III and mixed mode I/III fracture grows in a twisted manner and out-of the plane of the initial crack. Figure 11 shows the mode III fracture trajectory observed for the ENDB specimen made of asphalt mixture for low and medium temperatures. Close observation of the mixed mode I/III and mode III fracture surface reveals that by contributing the mode III component on the fracture behavior of the heterogeneous asphalt mixture, the fracture grows mainly through the interface of aggregate/mastic or the mastic part. In other words, the coarse aggregates are rarely broken during the propagation of mode III fracture. This can be attributed to the lower resistance of the binder and soft mastic against the tear type deformation compared to its tensile resistance. Similar to the mode I case, the fracture surface observed for the mixed mode I/II shows a rough surface passing mainly through the soft mastic and boundary of aggregates (or interface of aggregate/mastic). Observation of fracture surface under mixed mode loading indicates that more than 85% of the fracture path grows through the mastic or interface of aggregate/mastic. The roughness of fracture surface in the heterogeneous asphalt mixture is also greater than the surface of isotropic material with the same mode mixity.
The mode III and mixed mode I/III fracture grows in a twisted manner and out-of the plane of the initial crack. Figure 11 shows the mode III fracture trajectory observed for the ENDB specimen made of asphalt mixture for low and medium temperatures. Close observation of the mixed mode I/III and mode III fracture surface reveals that by contributing the mode III component on the fracture behavior of the heterogeneous asphalt mixture, the fracture grows mainly through the interface of aggregate/mastic or the mastic part. In other words, the coarse aggregates are rarely broken during the propagation of mode III fracture. This can be attributed to the lower resistance of the binder and soft mastic against the tear type deformation compared to its tensile resistance.
(a) (b) Figure 11. Fracture path and fracture surface of the asphalt mixture tested with the ENDB specimen under mode III (a) low temperature and (b) medium temperature.
In addition, the roughness of the fracture surface made of the asphalt samples is greater than the isotropic PMMA material tested under mode III as compared in Figure  12. The fracture tends to round the aggregates instead of breaking the aggregates and this behavior is more pronounced for the intermediate temperature condition.  In addition, the roughness of the fracture surface made of the asphalt samples is greater than the isotropic PMMA material tested under mode III as compared in Figure 12. The fracture tends to round the aggregates instead of breaking the aggregates and this behavior is more pronounced for the intermediate temperature condition.
As a conclusion, the influence of some affecting parameters such as heterogeneity, loading mode and temperature was investigated in this research for identifying the fracture mechanism of the propagating crack in the ligament of the asphalt concrete composites. Table 6 compares and summarizes the percentages and contribution of the passing fracture path through different locations (aggregates, mastic or interface of aggregate/mastic) for different test specimens, fracture modes and test temperatures. It can be seen that in general, the fraction of the aggregate breakage during the crack growth of the asphalt mixture becomes smaller for mode II and mode III loading and higher temperatures. Indeed, for such situations the fracture propagates mainly through the interface of aggregate/mastic and soft binder parts. Understanding the contribution of different cracking mechanisms (i.e., propagating the fracture surface through the tight aggregates, soft mastic or interface of tight and soft parts) can provide better knowledge for estimating the service life of asphalt pavement structures. Figure 11. Fracture path and fracture surface of the asphalt mixture tested with the ENDB specimen under mode III (a) low temperature and (b) medium temperature.
In addition, the roughness of the fracture surface made of the asphalt samples is greater than the isotropic PMMA material tested under mode III as compared in Figure  12. The fracture tends to round the aggregates instead of breaking the aggregates and this behavior is more pronounced for the intermediate temperature condition.

Conclusions
• The fracture resistance, fracture trajectory and fracture surface of the asphalt samples were investigated under different mode mixities and testing conditions using different test samples and configurations.

•
The fracture resistance values (i.e., critical stress intensity factors, K If , K IIf and K IIIf ) were dependent to the shape of test sample, applied loading type, loading mode, and temperature. Generally, the fracture resistance was decreased by increasing the test temperature and changing the loading mode from tensile type to shear type.

•
The heterogeneity of the asphalt mixture and location of the coarse aggregates in the route of fracture propagation along the ligament can noticeably affect the trajectory of fracture. The fracture path shows more deviations relative to the path observed for a model brittle and isotropic material, when the coarser aggregates are located in front of the trajectory of propagating crack. Indeed, the crack tends to round the aggregates in most of the cases and propagate through the softer mastic part or the interface of aggregate/mastic.

•
Increasing the temperature can result in more deviation in the fracture trajectory because of the reduction in the stiffness of mastic and bitumen relative to the aggregate and tendency of the crack to not grow through the aggregates by rounding them.
• Observation of fracture surface for all mode mixities revealed that a significant part of the fracture surface (i.e., greater than 80% of the fracture surface) propagates through the mastic and interface of aggregates/mastic. This percentage increases with increasing the test temperature or adding the contribution of mode II or mode III in the process of asphalt cracking.