Strength failure and crack coalescence behavior of brittle sandstone samples containing a single fissure under uniaxial compression

Uniaxial compression experiments were performed for brittle sandstone samples containing a single fissure by a rock mechanics servo-controlled testing system. Based on the experimental results of axial stress-axial strain curves, the influence of single fissure geometry on the strength and deformation behavior of sandstone samples is analyzed in detail. Compared with the intact sandstone sample, the sandstone samples containing a single fissure show the localization deformation failure. The uniaxial compressive strength, Young’s modulus and peak axial strain of sandstone samples with pre-existing single fissure are all lower than that of intact sandstone sample, which is closely related to the fissure length and fissure angle. The crack coalescence was observed and characterized from tips of pre-existing single fissure in brittle sandstone sample. Nine different crack types are identified based on their geometry and crack propagation mechanism (tensile, shear, lateral crack, far-field crack and surface spalling) for single fissure, which can be used to analyze the failure mode and cracking process of sandstone sample containing a single fissure under uniaxial compression. To confirm the subsequence of crack coalescence in sandstone sample, the photographic monitoring and acoustic emission (AE) technique were adopted for uniaxial compression test. The real-time crack coalescence process of sandstone containing a single fissure was recorded during the whole loading. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle sandstone sample containing a single fissure is analyzed under uniaxial compression. The present research is helpful to understand the failure behavior and fracture mechanism of engineering rock mass (such as slope instability and underground rock burst).     

Experimental study on mechanical behavior of brittle marble samples containing different flaws under uniaxial compression

Uniaxial compression experiments were carried out for the marble samples (located in the eastern ground of China) with different pre-existing flaws in non-overlapping geometry by the rock mechanics servo-controlled testing system. Based on the experimental results of complete axial stress-axial strain curves, the effect of flaw geometry on the strength and deformation behavior of marble samples is made a detailed analysis. Compared with the intact marble sample, the marble samples with different pre-existing flaws show the localization deformation failure. The uniaxial compressive strength (UCS), elastic modulus and peak axial strain of marble samples with pre-existing flaws are all lower than that of intact marble sample, and the reduction extent is closely related to the geometry of pre-existing flaws. The crack coalescence were observed and characterized from internal tips of different pre-existing flaws in brittle marble sample. Eight different crack types were identified based on their geometry and crack propagation mechanism (tensile, shear and compressive) for two pre-existing flaws, which can be used to analyze the failure mode and cracking process of marble sample containing different flaws in uniaxial compression. In the end, the influence of the crack coalescence on the strength and deformation failure behavior of brittle marble sample is analyzed under uniaxial compression. The present research provides increased understanding of the fundamental nature of rock failure under uniaxial compression.     

混凝土单轴压缩CT观测及三维变形场计算分析

利用微焦点工业CT对混凝土试件单轴压缩过程分阶段进行原位扫描,获得相应的系列CT图像。由数字体散斑法（Digital Volumetric Speckle Photography,DVSP）获得了试件内部三维位移场与应变场。混凝土内部非均匀细观结构可以作为散斑结构成为变形信息的载体用于试件内部变形的测量;通过位移场和应变场的分析,揭示了试件内部变形局部化区域的演化及破坏过程,局部化区域与试件最终破坏面位置相一致。根据试件的体积应变随轴向应力的变化曲线分别定义了小于CT尺度微裂隙和CT尺度裂隙的发育点,分别为峰值应力的54.7 %和82.0 %,这两点同时对应着试件扩容的起始点及塑性变形的起始点。结果表明,DVSP与CT技术相结合能够直观地揭示混凝土试件内部变形局部化产生及发展过程,为三维变形的精细测量及可视化提供了方法。     

Insight into the fracture evolution behavior of pre-flawed hollow-cylinder granite under multi-stage increasing-amplitude cyclic loads: A lab-scale testing

The structural deterioration and associated fracture evolution behavior of pre-flawed hollow-cylinder granite subjected to multi-stage increasing-amplitude (MSIA) cyclic loads are studied herein. The influences of rock structure on volumetric deformation, damage accumulation, energy dissipation, and failure pattern were investigated. It is shown that the volumetric deformation is relatively large for rock having high flaw angle, and it is the minimum and maximum for rock having a 10° and 70° flaw angle. A damage evolution model that can describe a first fast and then steady damage propagation was proposed based on the irreversible axial strain. Much energy needs to be consumed to drive crack propagation and hole collapse for rock having high angle flaws. A series of 2D computed tomography (CT) images reveal the different crack network pattern and how it is affected by the rock structure. A more complicated crack network is found for rock having a high flaw angle.     

Analysis of the energy and damage evolution rule for sandstone based on the particle flow method

We use the particle flow code PFC3D to simulate the triaxial compression of sandstone under various radial stresses and loading strain rates to determine the triaxial stress-strain curves, crack propagation path, and contact forces to investigate the failure process of sandstone. We analyze the energy and damage evolution during triaxial compression. The results indicate that the tension and shear-induced cracks increase with the increase of radial stress under the same loading strain rate. Both normal and tangential contact forces exhibit strong anisotropy and increase with radial stress and strain rate. The normal contact force has an approximately symmetrical distribution with respect to the horizontal plane, whereas the tangential contact force has an approximately symmetrical distribution with respect to the axis. For the characteristics of the energy evolution, the boundary energy density, strain energy density, and dissipated energy density all increase linearly with the radial stress, and the boundary energy density increases at the fastest rate, followed by the strain energy density and dissipated energy density. In the post-peak stage the primary energy consumption is the dissipated energy. After that, in the remaining stage the strain energy decreases gradually. By analyzing the evolution of the damage variables in the prepeak area we observed that the damage variable followed an exponential relationship with the axial strain. When the loading strain rate is constant, the damage variable corresponding to the same strain value decreases with increase of radial stress. The results indicate that the increase in radial stress delays the damage acceleration. In contrast, the effect of the loading strain rate on the damage variable is small. The findings reveal the internal structural evolution of rocks during deformation and failure.

     

循环荷载下大孔隙红砂岩的动力响应及损伤研究

为探究循环荷载下不同孔隙率红砂岩的动力特性和损伤规律,采用SHPB冲击实验系统,选取了2组不同孔隙率的红砂岩进行循环冲击实验,分析大孔隙率红砂岩的动力波形,本构曲线及损伤度,得到不同孔隙率红砂岩的变形模量、峰值应力、峰值应变及损伤度的变化规律。结果表明:不同孔隙率的红砂岩试件在循环荷载下的应力时程基本一致,随着循环次数的增加,岩石经历了孔隙闭合-裂隙开展-应力硬化-应变软化直至破坏的阶段,其变形模量和峰值应变呈现出先减小,再增大,再减小的趋势,峰值应力与速度呈正相关的关系。随着循环次数的递增,孔隙率大的岩石的峰值应力下降趋势大于孔隙率小的岩石,并且损伤累积使岩石在冲击破坏前表现出了较明显的塑性特征,不同孔隙率红砂岩的损伤度变化趋势基本是先增大后减小,孔隙率大的岩石累计损伤度大于孔隙率小的岩石,其损伤裂纹基本都是从透射杆端部开始,随着裂纹的产生扩展直至破坏。     

循环荷载下大孔隙红砂岩的动力响应及损伤研究

为探究循环荷载下不同孔隙率红砂岩的动力特性和损伤规律,采用SHPB冲击实验系统,选取了2组不同孔隙率的红砂岩进行循环冲击实验,分析大孔隙率红砂岩的动力波形,本构曲线及损伤度,得到不同孔隙率红砂岩的变形模量、峰值应力、峰值应变及损伤度的变化规律。结果表明:不同孔隙率的红砂岩试件在循环荷载下的应力时程基本一致,随着循环次数的增加,岩石经历了孔隙闭合-裂隙开展-应力硬化-应变软化直至破坏的阶段,其变形模量和峰值应变呈现出先减小,再增大,再减小的趋势,峰值应力与速度呈正相关的关系。随着循环次数的递增,孔隙率大的岩石的峰值应力下降趋势大于孔隙率小的岩石,并且损伤累积使岩石在冲击破坏前表现出了较明显的塑性特征,不同孔隙率红砂岩的损伤度变化趋势基本是先增大后减小,孔隙率大的岩石累计损伤度大于孔隙率小的岩石,其损伤裂纹基本都是从透射杆端部开始,随着裂纹的产生扩展直至破坏。     

Fracturing behaviour of sandstone specimens with a cavity formed by intersecting excavations under compression: Experimental study and numerical modelling

To investigate the mechanical properties, damage characteristics, and fracturing behaviour of specimens with a cavity formed by intersecting excavations, a series of uniaxial compression tests were conducted incorporating digital image correlation (DIC) and acoustic emission (AE) techniques. PFC^2D modelling was conducted to further study the failure modes and crack evolution under biaxial loading. The results showed that the mechanical properties are significantly weakened by the cavity and influenced by its shape. The failure of the specimens containing a cavity under uniaxial compression can be considered as a progressive process of crack initiation, propagation, and coalescence of different cracks with each other, leading to forming macrofractures, which can be visually displayed by the DIC technique. A new method for determining the crack closure stress is proposed, and the crack initiation stress and the crack damage stress of specimens are also obtained by the AE measurements. The failure mode of the intact specimen changed from the tensile–shear failure mode under the uniaxial compression to the shear‐dominated failure mode under the biaxial compression. Failure of the specimens with a cavity is dominated by shear cracks rather than tensile cracks. Under high confining stresses, almost no macrotensile cracks appeared on the roof or floor of the cavity; instead, several spalling fractures were visible on the two sides of the cavity. The fracturing mechanism is well explained by the evolution of the internal stresses in the specimens.     

Failure of AA 6061 and 2099 aluminum alloys under dynamic shock loading

Microstructural aspects of the deformation and failure of AA 6061 and AA 2099 aluminum alloys under dynamic impact loading are investigated and compared with their responses to quasi-static mechanical loading in compression. Cylindrical specimens of the alloys, heat-treated to T4, T6 and T8 tempers, were subjected to dynamic compressive loading at strain rates of between 2800 and 9200 s⁻¹ and quasi-static compressive loading at a strain rate of 0.0032 s⁻¹. Plastic deformation under the dynamic impact loading is dominated by thermal softening leading to formation of adiabatic shear bands. Both deformed and transformed shear bands were observed in the two alloys. The shear bands offer preferential crack initiation site and crack propagation path in the alloys during impact loading leading to ductile shear fracture. While cracks propagate along the central region of transformed bands in AA 6061 alloy, the AA 2099 alloy failed by cracks that propagate preferentially along the boundary region between the transformed shear bands and the bulk material. Whereas the AA 2099 alloy shows the greatest propensity for adiabatic shear banding and failure in the T8 temper condition, AA 6061 alloy is most susceptible to formation of adiabatic shear bands and failure in the T4 temper. Deformation under quasi-static loading is dominated by strain hardening in the two alloys. Rate of strain hardening is higher for naturally aged AA 6061 than the artificially aged alloy, while the strain hardening rate for the AA 2099 alloy is independent of the temper condition. The AA 2099 alloy shows a superior mechanical behaviour under quasi-static compressive loading whereas the AA 6061 shows a higher resistance to impact damage.     

Experimental and numerical investigations on fracture process zone of rock–concrete interface

A crack propagation criterion for a rock–concrete interface is employed to investigate the evolution of the fracture process zone (FPZ) in rock–concrete composite beams under three‐point bending (TPB). According to the criterion, cracking initiates along the interface when the difference between the mode I stress intensity factor at the crack tip caused by external loading and the one caused by the cohesive stress acting on the fictitious crack surfaces reaches the initial fracture toughness of a rock–concrete interface. From the experimental results of the composite beams with various initial crack lengths but equal depths under TPB, the interface fracture parameters are determined. In addition, the FPZ evolution in a TPB specimen is investigated by using a digital image correlation technique. Thus, the fracture processes of the rock–concrete composite beams can be simulated by introducing the initial fracture criterion to determine the crack propagation. By comparing the load versus crack mouth opening displacement curves and FPZ evolution, the numerical and experimental results show a reasonable agreement, which verifies the numerical method developed in this study for analysing the crack propagation along the rock–concrete interface. Finally, based on the numerical results, the effect of ligament length on the FPZ evolution and the variations of the fracture model during crack propagation are discussed for the rock–concrete interface fracture under TPB. The results indicate that ligament length significantly affects the FPZ evolution at the rock–concrete interface under TPB and the stress intensity factor ratio of modes II to I is influenced by the specimen size during the propagation of the interfacial crack.     

Damage evolution in Ti6Al4V–Al3Ti metal-intermetallic laminate composites

The crack propagation and damage evolution in metal (Ti6Al4V)-intermetallic (Al₃Ti) laminate composites were investigated. The composites (volume fractions of Ti6Al4V: 14%, 20% and 35%) were tested under different loading directions (perpendicular and parallel directions to laminate plane), to different strains (1%, 2%, 3%) and at different strain rates (0.0001 and 800–2000 s⁻¹). Crack densities and distributions were measured. The crack density increases with increasing strain, but decreases (at a constant strain) with increasing volume fraction of Ti6Al4V. Differences in crack propagation and damage evolution in MIL composites under quasi-static (10⁻⁴ s⁻¹) and dynamic (800–2000 s⁻¹) deformation were observed. The fracture stress does not exhibit significant strain-rate sensitivity; this is indicative of the dominance of microcracking processes in determining strength. Generally, the crack density after dynamic deformation is higher than that after quasi-static deformation. This is attributed to the decreased time for crack interaction in high-strain rate deformation. The effect of crack density, as quantified by a damage parameter, on elastic modulus and stress–strain relation were calculated and compared with experimental results.     

A Damage-Mode Based Three Dimensional Constitutive Model for Fibre-Reinforced Composites

This article presents a three dimensional constitutive model for anisotropic damage to describe the elastic-brittle behavior of unidirectional fibrereinforced laminated composites. The primary objective of the article focuses on the three dimensional relationship between damage of the material and the effective elastic properties for the purpose of stress analysis of composite structures, in extension to the two dimensional model in Matzenmiller, Lubliner and Taylor (1995). A homogenized continuum is adopted for the constitutive theory of anisotropic damage and elasticity. Damage initiation criteria are based on Puck failure criterion for first ply failure and progressive micro crack propagation is based on the idea of continuum damage evolution. Internal variables are introduced to describe the evolution of the damage state under loading and as a subsequence the degradation of the material stiffness. Emphasis is placed on a suitable coupling among the equations for the rates of the damage variables with respect to the different damage modes.     

CDM based modelling of damage and fracture mechanisms in concrete under tension and compression

Anisotropic damage evolution and crack propagation in the elastic–brittle materials is analysed by the concepts of continuum damage mechanics (CDM) and finite element method (FEM). The modified Murakami–Kamiya (MMK) model of elastic-damage material is used to describe damage anisotropy in concrete. The Helmholtz free energy representation is discussed. The unilateral crack opening/closure effect is incorporated in such a way that the continuity requirement during unloading holds. The incremental form of the stress–strain equations is developed. The general failure criterion is proposed by checking the positive definiteness of the Hessian matrix of the free energy function. The local approach to fracture (LAF) by FEM is applied to the pre-critical damage evolution that precedes the crack initiation, and the post-critical damage/fracture interaction. Crack is modelled as the assembly of failed finite elements in the mesh, the stiffness of which is reduced to zero when the critical points at stress–strain curves are reached. A concrete specimen with the pre-load, inclined crack is analysed in order to simulate different fracture mechanisms in tension or compression. The constitutive model is capable of predicting the kinked-type crack under tension and the wing-type crack under compression.     

Computational modeling of mixed-mode fatigue crack growth using extended finite element methods

The extended finite element method (XFEM) combined with a cyclic cohesive zone model (CCZM) is discussed and implemented for analysis of fatigue crack propagation under mixed-mode loading conditions. Fatigue damage in elastic-plastic materials is described by a damage evolution equation in the cohesive zone model. Both the computational implementation and the CCZM are investigated based on the modified boundary layer formulation under mixed-mode loading conditions. Computational results confirm that the maximum principal stress criterion gives accurate predictions of crack direction in comparison with known experiments. Further popular multi-axial fatigue criteria are compared and discussed. Computations show that the Findley criterion agrees with tensile stress dominant failure and deviates from experiments for shear failure. Furthermore, the crack propagation rate under mixed mode loading has been investigated systematically. It is confirmed that the CCZM can agree with experiments.     

A simple damage-accumulation model for constraint effects on ductile fracture

A simple model is presented to account for the effects of void-type damage on crack initiation and propagation in ductile steels under plane strain conditions by virtue of elementary fracture mechanics solutions. Multiple primary voids from large inclusions are uniformly distributed ahead of the crack tip. The growth of these primary voids is followed by nucleation of a large population of secondary voids from second-phase particles. A critical accumulative damage based on the length ratio of the damage zone to the spacing of primary voids, is employed as a failure criterion, including contributions from two populations of voids. Damage accumulation depends much on the strain and stress states such as stress triaxilities, which are extracted from existing results instead of detailed computation. Results show the dependence of fracture toughness on the size of damage zones associated with constraints. Initiation of crack growth is insensitive to the constraints since nucleation of fine voids is determined by local deformation. The model captures the transition in mechanisms from void-by-void growth to multiple void interactions in terms of a decreasing trend in the slopes of fracture resistance curves. At high constraints and large damage zone, a steady-state crack advance is identified with constant toughness. Damage accumulation from the growth of primary voids determines subsequent crack growth resistance and the study demonstrates its dependences on the crack-tip constraints.     

AlSi10Mg(Cu)铸铝合金的热疲劳裂纹萌生及早期扩展行为

微观观察AlSi10Mg(Cu)铸铝合金在热疲劳裂纹的萌生和早期扩展过程,重点研究共晶硅粒子对热疲劳裂纹行为的影响。结果表明:热疲劳裂纹萌生于脱粘共晶硅粒子与铝基体间的开裂界面,原因是共晶硅粒子与铝基体的热膨胀系数不同,引起热循环过程中两相热应变不协调,从而在两相界面处产生循环应力而引起疲劳破坏。热疲劳裂纹的扩展在长度和宽度上同时进行,具有良好塑性的铝枝晶对疲劳裂纹的扩展起阻碍作用。对热疲劳过程中共晶硅粒子周围应力场的模拟分析进一步解释了实验现象。     

A finite element analysis of fracture initiation in ductile/brittle periodically layered composites

A near-tip plane strain finite element analysis of a crack terminating at and normal to the interface in a laminate consisting of alternate brittle and ductile layers is conducted under mode-I loading. The studies are carried out for a system representing steel/alumina composite laminate. The Gurson constitutive model, which accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence, is employed within the framework of small deformation plasticity theory. Evolution of plastic zone and damage in the ductile layer is monitored with increasing load. High plastic strain localization and microvoid damage accumulation are found to occur along the brittle/ductile interface at the crack-tip. Fracture initiation in the ductile phase is predicted and the conditions for crack renucleation in the brittle layer ahead of the crack are established for the system under consideration. Ductile fracture initiation has been found to occur before plasticity spreads in multiple ductile layers. Effects of material mismatch and yield strength on the plastic zone evolution are briefly discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Elastic–plastic cracking analysis for brittle–ductile rocks using manifold method

In this study, the formation of localized deformation band and failure processes of brittle–ductile materials (coarse and medium marbles) containing pre-existing flaws under various loading conditions are simulated numerically. By incorporating the modified Mohr–Coulomb crack initiation criterion and the crack evolution techniques, the cracking processes, such as crack initiation, propagation and coalescence are successfully modeled by the developed numerical manifold method. According to the results, the development of macro-shear cracks is preceded by the development of localized deformation bands, which are underlain by damage accumulation and material deterioration. The numerical results are comparable to the laboratory test results.     

Damage evolution and constitutive behavior of advanced composites

The aim of this paper is to present a mechanics based theory that accounts for damage evolution in advanced composites. Single-ply behavior, under various loading conditions, is studied in detail herein. It is shown that the proposed theory can capture the essential deformational characteristics of single composite material plies, subjected to external load. Emphasis is placed on the properties of the theory and its capability to predict the observed behavior; further, the present approach is compared to classical analysis procedures. The paper extends previous work by the first author; it considers loading path effects, relation of damage growth to apparent Poisson ratio, strain based distinction between tension and compression, failure criteria under different loading conditions, and thermodynamic restrictions.