Tension-shear Failure Research Articles

Study on failure mechanism of cracked coal rock and law of gas migration

China possesses abundant coal resources and has extensive potential for exploitation. Nevertheless, the coal rock exhibits low strength, and the coal seam fractures due to mining activities, leading to an increased rate of gas emission from the coal seam. This poses significant obstacles to the exploration and development of the coal seam. This paper focuses on studying the failure mechanism of fractured coal rock by conducting uniaxial and triaxial compression experiments on the coal rock found at the Wangpo coal mine site. Simultaneously, in conjunction with the findings from the field experiment, a gas migration model of the mining fracture field is constructed to elucidate the pattern of coal seam gas distribution during mining-induced disturbances. The study structure reveals that coal rock exhibits three distinct failure modes: tensile failure, shear failure, and tension-shear failure. The intricate fissure in the rock layer will intensify the unpredictability of rock collapse patterns. The compressive strength of coal rock diminishes as the confining pressure drops. The coal rock in the working face area will collapse as a result of the lack of confining pressure. In the rock strata above the mining fracture zone, the gas pressure is first higher and then significantly falls with time. After 100 days of ventilation, the low gas pressure area changes little, so to ensure the safety of the project, the ventilation time of the fully mechanized mining surface is at least 100 days. The research results will help to establish the core technology system of coal seam development and improve the competitiveness of coal seam resources in China.

Constitutive and impact response of AA7475-T7351 under different projectile shapes and velocities: An experimental and numerical investigation

Through experimental and numerical investigation, this article investigates the constitutive and impact response of the 1.6 mm thick AA7474-T7351 plate under the impact of blunt and hemispherical-nosed projectiles at different velocities. The Johnson-Cook plasticity and failure model parameters were calibrated for the target material using experimental data from the tensile experiments, which took into consideration the effects of plastic strain, strain rate, temperature and stress triaxiality. Further, JC plasticity model parameters were also optimised using a parametric optimisation process. The flow stress of AA7475-T7351 shows positive and negative sensitivity toward loading rate and temperature. It is observed that the ductility of AA7475-T7351 decreases with increases in stress triaxiality, whereas the flow stress increases. Perforation experiments on 1.6 mm thick circular AA7475-T7351 plates were carried out using a single-stage gas gun along with the high-speed Digital Image Correlation (3D-DIC) technique. The blunt nose projectile causes shear failure, whereas hemispherical nose projectile causes combined tension-shear failure; a microscopic study is performed to confirm this phenomenon. Experimental results obtained from DIC were validated using the numerical analysis in the Abaqus/Explicit platform in terms of transient out-of-plane deformation of the target plate. The quantitative error between experimental and numerical analysis was evaluated using the Russell error technique. Numerical analysis revealed that constitutive relations could predict the physical fracture mechanisms during perforation qualitatively as well as quantitatively.

Study on the dynamic fracture behavior of anisotropic CCNBD shale specimens under different impact angles

Drilling and fracturing are the key technologies for shale gas extraction, while most of the loads generated during rock drilling or fracturing are dynamic. In this study, dynamic impact experiments were conducted on the cracked chevron-notched Brazilian disc shale specimens with different chevron-notched crack (CNC) inclinations (β) and layer inclinations (α) by the split Hopkinson pressure bar. The results show that the dynamic peak load and dissipated energy increases with the increase of β, α, and strain rate, but their changing trends are different. The generation and expansion of cracks during the specimen failure process are mainly affected by β. As β increases, the failure type of the specimen can be divided into pure mode I fracture, mode I-II mixed fracture, pure mode II fracture, mixed tension-shear failure, and Brazilian splitting failure. The increase in strain rate will lead to a decrease in the time for crack initiation and propagation as well as an increase in secondary cracks. In addition, the mode I fracture toughness (KⅠC) and mode II fracture toughness (KⅡC) both grow with the increase of α and strain rate. The KⅡC predicted by the generalized maximum tangential stress criterion (GMST) exhibits more accurate.

Investigation on the effect of freeze–thaw cycles on damage characteristics of concrete under mixed mode I-II load conditions

In order to investigate the effect of freeze–thaw cycles on the damage characteristics of mixed mode I-II crack propagation in concrete. The three-point bending and three-point shear fracture test were carried out on specimens subjected to different freeze–thaw cycles (0, 50, 100, 150 and 200). The analytical expression of mixed mode I-II damage scale r0(I,II) and ru(I,II) was derived, and the effect of freeze–thaw cycles on damage scale was analyzed. In addition, the critical damage scale of mixed mode I-II fracture was obtained using the numerical simulation method, and the simulation results were compared with the calculation results. Finally, the accumulate energy and tension-shear failure of concrete after freeze–thaw cycles were analyzed based on acoustic emission technology.

A new approach to calculate the shear strength of high-performance reinforced concrete beams fibered with micro polypropylene (experimental and analytical study)

Micro polypropylene (PP) fibers are commonly utilized to increase concrete's durability and fire resistance in building projects. High-Performance-Fiber-Concrete (HPFC) has become increasingly popular in the sustainable buildings industry in the past two decades. Some important structures were constructed using HPFC with micro polypropylene fibers to limit corrosion and increase fire resistance. This paper presents an experimental and analytical investigation to study the effect of micro PP fibers on the shear strength of HPFC beams with and without stirrups. The experimental results were used to obtain a new and simple approach that can calculate the shear strength of HPFC beams without needing for experimental findings. Also, the effect of PP fibers was compared with that of using steel (ST) fibers only or the hybridization of both PP and ST fibers. Twelve simply supported beams were fabricated and loaded with a concentrated load up to failure and all the required data were obtained and examined. The results indicated that adding PP fibers was effective in increasing both the shear capacity and the toughness of HPFC beams, either with or without stirrups, especially for beams with 1 % PP fibers. For beams without stirrups either with or without PP fibers, the mode of failure was diagonal tension shear failure. The presence of stirrups and / or ST fibers changed the failure mode from diagonal tension shear failure to compression shear failure. Analytically, a new approach of ten equations, was proposed based on the angle of compression struts and the splitting tensile concrete strength, to calculate the shear strength of HPFC beams. The equations of the proposed approach were compared with the results of forty five experimental specimens from four different research studies to examine their validity. The results were in a very good agreement and accuracy with the experimental results.

Static mechanical properties and damage evolution characteristics of selected rocks in diversion tunnel under uniaxial loading

An in-depth understanding of the mechanical properties and damage and fracture mechanism of selected rocks in a diversion tunnel plays an important role in promoting the efficient construction and safety of rock blasting excavation in a diversion tunnel. To study the mechanical properties and damage evolution characteristics of selected rocks in diversion tunnels under uniaxial loading, the uniaxial compression and uniaxial splitting tests of granite and tuff were carried out. In terms of mechanical properties, the evolution characteristics of complete stress-strain curves, instantaneous modulus-strain curves, and input energy density-strain curves were analyzed. In the aspect of damage characteristics, the macroscopic and mesoscopic failure modes were analyzed and the damage fracture mechanism was revealed. Compression-shear failure mainly occurred in granite and tuff under uniaxial compression, showing the characteristics of elastic-brittle fracture failure. Both granite and tuff showed a failure mode of coexistence of “compression-shear failure zone at the loading ends” and “tension-shear failure zone in the middle” under uniaxial splitting. The compression-shear fracture of granite was relatively smooth, and the matrix and mineral particles produced fine particles due to friction in the process of shear slip. The compression-shear fracture of tuff was relatively rough and the characteristics of shear slip were not prominent enough. The fracture failure of granite and tuff was mainly caused by the common fracture of rock matrix and mineral particles. Based on the Lemaitre equivalent strain principle, the pre-peak-post-peak two-stage damage constitutive model established by Weibull statistical distribution theory can accurately describe the static stress-strain relationships of granite and tuff under uniaxial compression.

Influence of weak interlayer thickness on mechanical response and failure behavior of rock under true triaxial stress condition

In this study, we meticulously investigate the influence of the thickness of weak interlayer on mechanical response and failure behavior of rock mass near the free surface of tunnel, with the aid of a true triaxial test system. We simulated the true triaxial stress condition of rock mass containing weak interlayer proximate to the excavation boundary, where one face remains free, while others are subjected to loading stress and increasing tangential stress. The experimental results reveal a distinct change in the fracture morphology near the free surface of rock mass as the thickness of weak interlayer increases, concomitant with a gradual decrease in the fractal dimension. With the increase of the thickness of weak interlayer, the failure characteristics of rock mass change from a “binary” to a “unitary” feature, i.e. mixed tension-shear failure near the free surface and shear failure far away from the free surface changes to mixed tension-shear failure that only occurs near the free surface. Moreover, an inverse relationship is observed between the bearing capacity of the rock mass and the thickness of weak interlayer. Conversely, the peak strain in the tangential stress direction increases with the increase of the thickness of weak interlayer, illustrating that the slip shear strain of rock block positioned above the weak interlayer is gradually formed, and governs the strain behavior of rock mass in the tangential stress direction with the increases of the thickness of weak interlayer. By employing the finite-discrete element method (FDEM), we replicated the failure process of surrounding rocks containing weak interlayers near the free surface of tunnel, demonstrating considerable congruity with our physical test results. In light of the failure characteristics of surrounding rocks containing weak interlayers, we advocated a localized area priority reinforcement support strategy, prioritizing regions with weak interlayers. Numerical simulations verified the effectiveness of this approach in controlling fracture proliferation in surrounding rocks and inhibiting the splitting failure of surrounding rocks containing weak interlayers near the free surface of tunnel.

Mechanical response and energy evolution of interbedded shales subjected to multilevel constant/increasing-amplitude cyclic loading

This study aims to investigate the effects of fatigue loading paths and interbed structure on the mechanical properties and energy evolution characteristics of shales. In the experiments, shale specimens with five types bedded angles (0°, 30°, 45°, 60°, 90°) were prepared, and multilevel constant-amplitude fatigue loading test (MCFT) and multilevel variable-amplitude fatigue loading test (MVFT) were performed. Results indicated that shale's fatigue behaviors were highly affected by the bedding plane angles and the cyclic loading paths. Specifically, with the increasing of bedding angle, the peak strength, total dissipated energy, and total input energy of the shales showed a "U" trend, the ultimate macro-damage mode changed from mixed tension-shear failure to failure along the bedding planes, and the damping ratio firstly increased and then decreased. Test schemes of stepwise increase of the lower stress limit or keeping it constant were the differences between MCFT and MVFT, which significantly influenced the evolution of irreversible deformation of shales. Compared to MVFT, the shale in MCFT displayed reduction in peak strength in the range of 4.3% to 23.9%, greater and more drastic variations in elastic modulus and damping ratios, dissipative energy and elastic strain energy were relatively low by an order of magnitude.

Temperature effect of rockburst in granite caverns: insights from reduced-scale model true-triaxial test

To investigate the influence of thermal treatment on the rockburst in granite caverns, true-triaxial compression tests were conducted on pre-heated granite cubic samples containing a circular through-hole using a true-triaxial test system, and the micro camera was used to monitor and record the rockburst process in realtime. Test results show that the uniaxial compressive strength and elastic modulus first increase and then decrease as the temperature increases, which reach the maximums at 200 °C and sharply decrease at temperatures from 400 to 600 °C. The density and P-wave velocity decrease and the peak strain increases with increasing temperature. The main failure mode is X-shaped shear-tension failure at 25 and 200 °C, and single-slope shear failure at 400 and 600 °C. Thermal treatment exhibits slight effect on the rockburst incubation process in granite caverns. The stress required for rockburst decreases when the temperature increases or decreases from 200 °C. The higher the temperature, the lower the required stress. At 25 and 200 °C, rockburst is violent, and fine particles and large slabs are mainly produced; at 400 and 600 °C, the intensity of rockburst is relatively weak, and fine particles are mainly generated. Thermal treatment exhibits double effects on rockburst. The mechanism of thermal treatment on granite rockburst is the strengthening effect caused by water loss and the weakening effect caused by thermal expansion cracking. This study can provide theoretical guidance for the stability analysis and rockburst prevention of temperature-affected granite caverns.

Mechanical behaviours of bedded sandstone under hydromechanical coupling

The combination of the dipping effect and hydromechanical (H-M) coupling effect can easily lead to water inrush disasters in water-rich roadways with different dip angles in coal mines. Therefore, H-M coupling tests of bedded sandstones under identical osmotic pressure and various confining pressures were conducted. Then, the evolution curves of stress-strain, permeability and damage, macro- and mesoscopic failure characteristics were obtained. Subsequently, the mechanical behaviour was characterized, and finally the failure mechanism was revealed. The results showed that: (1) The failure of the sandstone with the bedding angle of 45° or 60° was the structure-dominant type, while that with the bedding angle of 0°, 30° or 90° was the force-dominant type. (2) When the bedding angle was in the range of (0°, 30°) or (45°, 90°), the confining pressure played a dominant role in influencing the peak strength. However, within β∈(30°, 45°), the bedding effect played a dominant role in the peak strength. (3) With the increase in bedding angle, the cohesion increased first, then decreased and finally increased, while the internal friction angle was the opposite. (4) When the bedding angle was 0° or 30°, the “water wedging” effect and the “bedding buckling” effect would lead to the forking or converging shear failure. When the bedding angle was 45° or 60°, the sliding friction effect would lead to the shear slipping failure. When the bedding angle was 90°, the combination of the “bedding buckling” effect and shear effect would lead to the mixed tension-shear failure. The above conclusions obtained are helpful for the prevention of water inrush disasters in water-rich roadways with different dips in coal mines.

Stress corrosion and interaction behaviour of adjacent cracks in rock-like material under hydro-mechanical Coupling: An experimental and numerical study

Under long-term hydro-mechanical coupling, the propagation of adjacent cracks present obvious time effect, and have significant influence on the progressive failure mode of rock-like materials. The creep tests were carried out based on the cement mortar specimen containing adjacent cracks, and the low-field Nuclear Magnetic Resonance (NMR) technology were used to evaluate the evolution of crack structure in the specimen. Based on the numerical simulation, the influences of the interaction behaviour between cracks on the time-dependent propagation of cracks and failure of specimens is revealed. The results show that: The specimen presents a tension-shear failure mode, and the macro fracture on its surface is Z-shaped; Crack interaction has an important role in promoting the formation and connection of microcracks, which increases the number of seepage channels and promotes the formation of the macro fracture; The propagation of adjacent cracks show significant asymmetry and non-uniformity, due to the stress superposition effects in the rock bridge area; The interaction between cracks is manifested as the inhibition of wing crack propagation in the rock bridge area at the initiation stage and then promotion effect at the later stage.

The influence of saturation and loading angle on sandstone damage characteristics after freeze-thaw cycle

The strength deterioration and fracture tendency of freeze-thaw rock determine the construction and operation safety of rock engineering. This article conducted compression-shear composite load tests on sandstones with various saturations to examine the failure law of rocks in cold climates and the contributing elements of strength degradation. It was found that with an increase in saturation and loading angle, the compressive strength and elastic modulus dropped. The concept of freeze crack threshold and saturation threshold was proposed. The peak shear stress was negatively correlated with saturation and positively correlated with loading angle. The σ CI (crack initiation stress) and σ CD (crack damage stress) in the saturated state were only 39.91% and 45.18% of those in the dry state. Serious damage occurred at high saturations, which is consistent with the scanning electron microscopy results. The σ CI and σ CD under 30°loading angle are 49.72% and 42.91% of those under uniaxial, respectively. This is mainly due to the change of the failure mode from tensile-shear failure to combined tension-shear failure, and finally to single-shear failure. A strength prediction model was established based on sandstone damage characteristics. The research results have important reference value for rock engineering design in frigid climates and complex load environments.

Study of the mechanical characteristics of coal-serial sandstone after high temperature treatment under true triaxial loading

In this study, a series of true triaxial loading tests were carried out on coal-measure sandstone after high temperature treatment by using a self-developed true triaxial test system combined with acoustic emission (AE) monitoring, and the mass loss, deformation characteristics and loss failure mode of sandstone before and after heat treatment were systematically studied. It is found that the true triaxial mechanical properties of sandstone after high temperature treatment are closely related to temperature, and the peak strength, maximum principal strain, volume strain, minimum fracture angle and elastic modulus, which all showed bimodal changes, and 800 °C is the threshold temperature of the first four parameters. The transition temperature of the elastic modulus is 400 °C. It is found that the test results of true triaxial high temperature sandstone are in good agreement with the existing true triaxial theory and test results. The failure forms of the samples at different temperatures show inverted “Y” or inverted “N” shapes. Shear failure occurs when the temperature is below 400 °C, and shear-tension failure occurs when the temperature is above 600 °C. At the same time, it is found that the AE signal has four periods, namely the quiet period, growth period, explosion period and decline period. The number of AE events corresponds to the deviatoric stress interval well. Experimental study of the mechanical properties of sandstone under the coupling effect of high temperature and true triaxial stress has guiding significance for the parameter selection and safety evaluation of roof sandstone in underground coal gasification.

Mechanical behavior and tension-shear failure mechanism of fractured rock mass under uniaxial condition

Mechanical behavior and tension-shear failure mechanism of fractured rock mass under uniaxial condition

Experimental and Numerical Study of the Strength Performance of Deep Beams with Perforated Thin Mild Steel Plates as Shear Reinforcement

This study aims to investigate a new shear reinforcement method which utilizes thin mild steel (TMS) plates as shear reinforcement in deep beams to replace conventional reinforcement. Thirteen reinforced concrete deep beam specimens with three different plate thicknesses and four varying perforated hole arrangements on the TMS plates were experimentally tested to determine the load-carrying capacity and crack pattern. The experimental results indicate that the 2.0 mm thick TMS plate has the highest load-carrying capacity. Among the four different hole arrangements on the TMS plates, the perforated plates with a three-column hole arrangement show the best performance in terms of load-carrying capacity, with a 2.9% increment against the control beam specimen. The specimens also demonstrated compatible elastic stiffness with the control beam that used conventional shear links. This shows that TMS plates have the potential to replace conventional shear links in deep beams. This proposed method also changed the failure mode from conventional diagonal shear tension failure to a combination of flexural failure and shear deformation. A numerical model was developed and was found to have a good correlation with the experimental results, demonstrating potential for use in future parametric investigations on deep beams and cost reduction in future experimental work.

Experimental study on wire and arc additively manufactured steel double-shear bolted connections

Wire and arc additive manufacturing (WAAM) has emerged as a highly promising technique for manufacturing large-scale steel structural elements. However, the distinct mechanical properties of WAAM steel could potentially lead to different performance of WAAM steel bolted connections compared to the traditional steel bolted connections. This study aims to investigate the material properties of WAAM steel and the structural behaviours of WAAM steel bolted connections, focusing on the effects of print layer orientation and connection plate geometrical dimensions. A total number of 24 WAAM steel coupon specimens with three different print layer orientations and 36 WAAM double-shear bolted connections with two print layer orientations and different geometric dimensions were designed, fabricated and tested under monotonic tension. These specimens were measured using a 3D laser scanner and Digital Image Correlation (DIC) was adopted to measure the structural response during testing. The impact of print layer orientations on WAAM material properties and the effects of WAAM material properties on bolted connections were analysed and discussed. The current design codes for traditional steel bolted connections were evaluated against the test results of WAAM steel bolted connections. The study found that the print layer orientations of WAAM steel plates initiated an anisotropic material property of the coupon specimens, demonstrated by the differences in ultimate tensile strength and strain of specimens with different print layer orientations. Five failure modes, including net section tension, shear-out, bearing, end-splitting, and block shear failure were observed for the bolted connections. The material anisotropy further affects the performance of the bolted connections, though in the same dimensions, 28% of the specimens presented different failure modes due to the different print layer orientations. The effectiveness of current steel design standards was compromised by inaccurate predictions of failure modes due to the distinct end-splitting failure mode and the effects of material anisotropy, though the predictions of the ultimate capacities of the WAAM lap shear specimens were relatively accurate.

Experimental study on uniaxial compressive properties and damage evolution of basalt fiber reinforced concrete after being subjected to high temperature

The study investigated basalt fiber reinforced concrete (BFRC) for failure characteristics after being subjected to high temperatures under uniaxial compression. Twenty-five sets of cylindrical BFRC specimens were carried out under different basalt fiber (BF) content and temperature. Based on 3D digital image correlation (3D-DIC) and acoustic emission (AE), the effects of temperature and volume content of BF on the compressive mechanical properties, damage evolution and failure mode of BFRC are analyzed. The results indicate that the proper volume content (0.26%) of BF can improve the compressive strength of concrete. Generally, the uniaxial compressive strength of BFRC decreases with increasing temperature. The internal and external damage evolution trend of BFRC is basically the same, which can be divided into pore compaction stage, stable crack growth stage and unstable crack growth stage. The proper volume content (0.26%) of BF reduces the degree of BFRC damage. The increase in the volume content of BF leads to an increase shear cracks proportion in BFRC, and the failure mode of the main crack gradually changes from tension-shear failure to shear failure. Conversely, the increase in temperature increased the degree of BFRC damage. The internal and external failure modes of BFRC are basically the same. At 20 °C, the failure of concrete without basalt fiber is mainly tensile crack. With the increase of temperature, the main failure mode is tension-shear failure.

Strain rockburst evolution process under true triaxial condition with single face unloading due to tunnel excavation

Based on the technology of polycrystalline modelling (generating Voronoi polycrystal) and three-dimensional discrete element theory, a three-dimensional polycrystalline discrete element nonlinear dynamic and static coupled numerical analysis method was proposed. This method can accurately simulate the initiation and evolution entire process of strain rockburst. The three-dimensional Voronoi polycrystalline discrete element model considering the mineral composition was established. The rockburst simulation of heterogeneous granite under true triaxial single face unloading was carried out. The rockburst ejection failure characteristics, strength and deformation characteristics, acoustic emission characteristics of rock samples were analyzed, as well as the characteristics of rock fragments and the evolution law of kinetic energy. The inoculation and evolution entire process of strain rockburst during true triaxial single face unloading was studied. The research results show that the failure process of rockburst ejection can be divided into four stages, including: grains ejection, rock spalling into plates, rock shearing into fragments, and rock fragments ejection. The failure modes of rockburst are pluralistic, that is, rockburst pits caused by tension-shear failure and split cracks due to tensile failure near the unloading face, and shear cracks caused by shear failure away from the unloading face. The kinetic energy is released abruptly in the post-peak stage, and the kinetic energy suddenly increases from zero to a high value when elastic energy drops sharply. The dissipation energy of rockburst fragments mainly includes shear dissipation energy and tension dissipation energy; among them, the shear dissipation energy accounts for 99.66 %. The primary conditions for rockburst ejection failure are accumulating enough elastic strain energy and reaching a large loading rate in the tangential direction.

Study on the Response of Tunnel Lining under Fault Dislocation

In order to clarify the influence of fault dislocation on tunnel lining, the FEM and single factor variable methods were used to explore the influence of the degree of fault dislocation, dip angle, width, the intersection angle between the strike and the tunnel axis, and the fault dislocation form on the lining structure response, based on which length of the lining anti-dislocation set-up for engineering design was obtained. The research shows that the maximum displacement of the lining is basically consistent with the fault displacement; with the increase of the fault width, the overall fortification range of the tunnel increases. Among the three types of fault dislocation, the axial force of the lining caused by reverse fault dislocation is the largest, the level of normal fault is the moderate, and the strike-slip fault is the smallest. With the increase of the intersection angle between the fault strike and the tunnel axis, the lining gradually changes from tension-shear failure to shear failure. It is suggested that the tunnel should cross the fault at a large angle as far as possible. If it is unavoidable to cross the fault when selecting the tunnel route in the project, the tunnel axis should be selected to cross the fault vertically as far as possible.

Fracturing evolution and strain characteristics of layered rock-like materials with rough interfaces

Layered rock-like samples containing saw-tooth interfaces of various joint roughness coefficients (JRC) and included angles were conducted uniaxial compression with the loading rate of 0.005 mm/s. The peak stress declines from 38.36–39.90 MPa to 17.35–30.67 MPa for included angle = 15°–60°, and then increases to 24.30–33.83 MPa for 60°–75°, but the peak strain decreases by 22.39%–41.30%. For JRC = 0–19.55, mechanical properties of samples are enhanced, while the anisotropy weakens. When the included angle is small (15°, 30°), the layered samples show a typical tensile splitting failure crossing the weak interlayers. For a large included angle of 45°–75°, failure modes are featured by shear sliding along weak interlayers combined with tensile splitting. As JRC increases, fracturing mechanism transition from shear sliding to mixed tension shear failure then to tensile splitting can be identified. With an increase in JRC or included angles, the global lateral strain of samples in plastic deformation stages changes from “sudden increase” to “progressive increase” to “jump increase”. For included angle = 15°, the layered sample produces dramatic lateral local strain at the weak interlayers due to tensile splitting failure. For included angle = 45°, both axial and lateral local strains at the weak interlayers show an obvious increase at the main shear failure surface. For a large included angle of 75°, the lateral local strain remarkably increases at the weak interlayers along with tensile failure of samples.