Bifurcation of collinear crack system under dynamic compression

The evolution pattern of collinear crack array plays a very important role in the final failure pattern of rock and predicting earthquake. Crack interactions lead to the nonhomogeneous pseudo-traction, then result in bifurcation of crack growth pattern. Bifurcation condition of crack growth pattern can be expressed by the crack growth length/spacing ratio. For collinear cracks loaded by dynamic compressive loads, uniform crack growth pattern yields to non-uniform crack growth pattern when the crack growth length/spacing ratio is larger than a critical value. In this paper, crack interactions are studied using stress superposition principle and the Chebyshev polynomials expansion of the pseudo-traction. The analytical solution of the critical value for two collinear cracks and infinite collinear cracks is given out. The critical value is sensitive to pre-existing crack length, the friction coefficient, the orientation of pre-existing crack, crack growth velocity.     

Nano-ductile crack propagation in glasses under stress corrosion: spatiotemporal evolution of damage in the vicinity of the crack tip

Recent experiments have evidenced the existence of a ductile fracture mode at the nanometer scale in Aluminosilicate glass. The present study is designed to check whether such a ductile mode is inherent to the amorphous nature of glass. Therefore, the slow crack advance is observed in real time via an Atomic Force Microscope in a minimal glass, amorphous Silica, under stress corrosion. In this case, the Crack propagation proceeds by the nucleation, growth and coalescence of damage cavities as in the Aluminosilicate glass, but the cavity size is significantly larger. We focus here on the kinematics of crack propagation by looking at the spatio-temporal evolution of both the tip of the main crack and the cavity ahead. It is shown that the velocity of the main crack tip is significantly lower than the one of the cavity edge toward the main crack tip, like in metallic alloys. Moreover, the velocities of the different fronts (main crack, frontward and backward cavity tips) at these nanometric scales is one order of magnitude smaller than the crack tip velocity at the continuum scale. This has important consequences for the modelling of stress corrosion, especially at ultra-slow crack propagation.     

A MOVING CRACK IN A NONHOMOGENEOUS MATERIAL STRIP

This paper considers an anti-plane moving crack in a nonhomogeneous material strip of finite thickness. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. The problem is solved by means of the singular integral equation technique. The stress field near the crack tip is obtained. The results are plotted to show the effect of the material non-homogeneity and crack moving velocity on the crack tip field. Crack bifurcation behaviour is also discussed. The paper points out that use of an appropriate fracture criterion is essential for studying the stability of a moving crack in nonhomogeneous materials. The prediction whether the unstable crack growth will be enhanced or retarded is strongly dependent on the type of the fracture criterion used. Based on the analysis, it seems that the maximum 'anti-plane shear' stress around the crack tip is a suitable failure criterion for moving cracks in nonhomogeneous materials.     

Scaling behavior of thermal shock crack patterns and tunneling cracks driven by cooling or drying

Cracks driven by shrinkage due to cooling or drying arrange themselves via mutual interaction. For parallel straight crack arrays driven by idealized transient shrinkage fields the scaling behavior in an infinite half-space is derived analytically by means of fracture mechanics bifurcation analysis with two plausible scaling assumptions. Crack spacing in thermal shock crack patterns has been found to be approximately proportional to the crack length and inversely proportional to the crack velocity. The spacing of tunneling cracks formed in a drying layer between plates scales as the 2/3rd power of layer thickness as a consequence of the specific interaction between the tunneling cracks. The difference in scaling behavior in the two cases is explained by the dimensionality of the geometrical setup determined by the boundary condition rather than by different physical processes. In either case, good agreement between theory and experiments is found.     

Simulation of glass cutting with an impinging hot air jet

Thermal cutting of glass sheet due to an impinging hot air jet is simulated and analyzed. Induced thermal stresses due to the moving heat source can be used to stably initiate and attract a crack toward the jet axis. Relative motion between the jet and glass sheet then can be used to cut the glass sheet. This paper presents a theoretical study of this process for straight cuts. Process simulation is accomplished by analyzing the coupled temperature and stress fields together with the fracture mechanics criteria for the crack growth.A finite element remeshing technique is employed for the analysis and singular elements are used around the crack tip for a more precise computing of the stress intensity factor. It is shown that a certain minimum air jet temperature for a given nozzle velocity and a certain maximum air jet velocity for a given temperature are required for continuous cutting. The results of the simulation show a good agreement with the published results in the literature. However a variating nature is detected for the distance between the crack tip and the air jet nozzle from a starting value to the steady-state one.     

CTS试件中复合型疲劳裂纹扩展

针对复合型循环载荷作用下的金属构件中的裂纹扩展问题进行了实验分析和理论建模. 首先 采用紧凑拉剪试件(CTS)和 Richard研制的复合型载荷加载装置，对承受复合型循环载荷的裂纹进行了实验研究. 实验选择了两种金属材料试件，分别承受3种形式的复合型循环载荷的作用，在裂纹尖端具 有相同的初始应力场强度的条件下考察复合型循环载荷对裂纹扩展规律的影响. 实验结果表明，疲劳裂纹的扩展速率与加载角度有关. 对于同样金属材料的试件，当裂尖处 初始应力场强度相等时，载荷越接近于II型，裂纹增长速率越快. 采用等效应力强度 因子(I型和II型应力强度因子的组合)、裂纹扩展速率及复合强度等参数，以实验数据为 基础，建立了一个疲劳裂纹扩展模型，用来预测裂纹在不同模式疲劳载荷作用下的扩展速率. 为验证其有效性，该模型被应用于钢制试件的数值模拟计算中. 实验结果与模拟计算曲线保 持一致，表明该模型可以用来估算带裂纹金属构件的寿命.     

Stress pulses emitted during fracture in tension

This paper is concerned with the stress pulses which are emitted during the tensile fracture of glass rods of rectangular cross-section. Both a longitudinal and a flexural pulse were observed. The experimentally recorded pulse shapes are found to be in close agreement with those predicted by using a theoretical model proposed by Phillips and Kolsky. It is shown that the deviations noted in the earlier work with circular glass rods are due, primarily, to the effect of crack bifurcation and not to the geometry of the cross-section. Further, the phenomenon of crack bifunction is found to depend upon the magnitude of the applied stress required to initiate fracture, and to be essentially independent of the section geometry.     

Effects of humidity and temperature on subcritical crack growth in sandstone

In order to ensure long-term stability of structures in a rock mass, the study of time-dependent fracturing is essential. The influences of the surrounding environmental conditions and rock fabric on subcritical crack growth in sedimentary rocks in air are yet to be clarified, while the nature of subcritical crack growth in igneous rocks has been studied well. In this study, the influences of temperature and relative humidity on subcritical crack growth in Berea sandstone, Shirahama sandstone and Kushiro sandstone were investigated in air. The load relaxation method of Double Torsion (DT) testing method was used to measure both crack velocity and stress intensity factor under a controlled temperature and relative humidity.Results show that the change of the crack velocity at a given stress intensity factor was unclear when the temperature increased under a constant relative humidity in air. On the other hand, we show that the crack velocity increased by several orders of magnitude when the relative humidity increased threefold or fourfold under a constant temperature at a given stress intensity factor. This increase is much larger than that expected from the conventional concept based on the theory of stress corrosion. It is therefore necessary to consider the additional mechanisms for subcritical crack growth in sandstone. The increase of the crack velocity was larger for sandstone which contained larger amount of clays. We conclude that subcritical crack growth in sandstone in air is affected remarkably by the relative humidity and the amount of clays in rock.     

Effect of orthotropy on crack propagation

The tendency of moving cracks to spread along the preferred directions of material anisotropy is treated. Depending on the velocity of crack propagation, the change of material properties in orthogonal planes is shown to affect the bifurcation characteristics. The problem is reduced to a system of dual integral equations that can be solved in a standard fashion. Of particular interest is the dynamic stress field near the tip of a moving crack in an orthotropic material. Although the 1√r stress singularity is preserved with r being the radial distance measured from the crack tip, the angular variations of the stresses are dependent on crack speed and material anisotropy. The possibility of crack bifurcation is examined by application of the strain energy density criterion for several composite systems. Crack branching is found to be enhanced by material anisotropy, a phenomenon that is not uncommon in composite materials.     

On the temperature rise at the tip of a fast running crack2

The high energy concentration at the tip of a running crack leads to irreversible deformations, and a great amount of the deformation energy is set free as heat. Assuming that this moving heat source is of circular shape, the temperature distribution around the crack tip has been calculated. The temperatures are dependent on the radius of the heat source and the crack velocity. Some examples for the material glass are given. The very high temperatures computed lead to the supposition that the observed light emission during fast fracture is of thermal origin.     

Automated Control of Stable Crack Growth for R-Curve Measurements in Brittle Materials

Stable crack advance is required for a reliable crack growth resistance (R-Curve) measurement. In bending experiments, manual control of the mechanical load and observation of the growing crack is still being done by the operator. This work presents an approach to partly and fully automated R-curve measurements, where stable crack growth is achieved solely via computer control. The experimental setup in conjunction with an intelligent control algorithm leads to reliable results, even for brittle materials like alumina ceramics, silicon nitride, and glass. Furthermore, it allows for a novel type of measurement, because the device detects any kind of energy release in the specimen, actually also without visible crack extension. The setup has been used successfully for about 3 years. The operating principle is explained and some of the results are presented exemplarily. The method is realized in 4-point-bending, but can be implemented also for other types of specimen and loading to automatically achieve stable crack growth.     

Dynamic crack growth under stress wave loading

The crack growth process has been analysed on the basis of a fracture criterion of a dynamic stress intensity factor when a crack in an infinite plate was subjected to a pulse type of stress wave. The crack velocity and the amount of crack extension were related to the constant amplitude and the duration of the stress pulse. The calculated amount of crack extension was well in agreement with the experimental one for the polymer material Acrylite (which is similar to polymethylmethacrylate) found by the authors, thus indicating the validity of the present approach.     

Crack bifurcation in laminar ceramics having large compressive stress

Crack bifurcation is observed in laminar ceramics that contain large residual compressive stress. In such composites, alternating material layers have tensile and compressive residual stress, due to thermal expansion mismatch or other sources. The compressive stress ensures that crack growth leading to failure in the laminar system is mediated by threshold strength, but, in some cases, it also leads to bifurcation of the propagating flaw. The phenomenon of bifurcation takes place when the crack tip is propagating in the compressive layer, and occurs typically at a distance equal to a few laminate thicknesses below the free surface and beyond. The observation of this phenomenon is usually associated with the presence of edge cracking in the compressive layers of the laminar ceramic, although it can also occur in the absence of such edge cracks. In the few cases where bifurcation occurs without edge cracks, the residual stresses and layer thicknesses are close to the condition in which edge cracks will occur. In addition, in this case the bifurcation is confined to near the specimen free surface, and below the bifurcation plane, the cracks are straight. The energy release rates for the straight and bifurcated cracks are calculated from the results of finite element computations and compared. When edge cracking is ignored, the crack is simulated as a through-thickness crack in an infinite body, and the energy release rate is used to predict crack deviation and bifurcation. Based on this, the finite element model successfully predicts bifurcation in only one material combination that was investigated in experiments. However, the experimental bifurcation takes place in two additional material combinations. When the effect of edge cracking is incorporated into the finite element simulations, the energy release rate calculations successfully predict the phenomenon of bifurcation in three material combinations, as observed in the experiments. Since no edge cracks are present in the fourth material combination tested experimentally, its lack of bifurcations is automatically predicted by the model. The presence of edge cracking, or its incipience, is thus concluded to be critical to the occurrence of crack bifurcation in laminar ceramic composites.     

Some characteristics of thermal fracture in glass

Techniques for obtaining controlled fractures in sheet glass by means of thermal stress are outlined. The velocity behavior of fracture under different stress configurations is analyzed, and it is seen that the nature of crack is strongly influenced by the ambient stress field. The peak velocity of a typical free-running fracture is observed to be 1450 m/sec and the corresponding crack opening to be 4 microns.     

Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth

Background:

Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip.

Objective:

We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading.

Methods:

Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force.

Results:

The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data.

Conclusions:

The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.

     

Simulation of fatigue crack growth at plastically mismatched bi-material interfaces

The present paper reports the results of a study on fatigue crack growth in a system with an interface between two elastic–plastic solids of different yield strength. Fatigue crack growth analysis is conducted by the use of a cohesive zone model. Irreversibility of material separation processes is introduced through the load history dependent degradation of the cohesive strength. Fatigue crack growth is considered to occur along the direction perpendicular to the interface and along the interface. Crack growth rate acceleration, deceleration or arrest, as well as crack bifurcation at the interface are predicted in dependence of the plastic property mismatch of the two solids and the interface properties. The outcome of the simulations is in very good agreement with trends of published experimental data.     

Computational crack path prediction

A computer program has been developed for the numerical prediction of curved crack growth paths under proportional loading conditions. The numerical prediction is performed by the step-by-step method in cooperation with the stress analysis ahead of the crack tip and the determination of the curved increment of the crack growth. The stress analysis is performed by the method of superposition of analytical and finite-element solutions, and the results are then utilized to determine the coefficients of the analytical expression of the curved crack path obtained by the first order perturbation method.The first numerical example is given for the crack path prediction in DCB-type specimen, where we often observe abrupt crack curving. Computational prediction is performed by introducing slight and small initial branching at the original crack tip. Within few steps of numerical calculations unstable crack curving is obtained, and the predicted path shows extremely good agreement with the experimentally measured path. The second numerical prediction is made for an edge crack approaching a circular hole, which may be considered as a crack arrester. In the present case the effect of the initially introduced slight kink diminishes with increasing crack length. The crack turns back to the original direction, resulting arrest at the hole.     

Delamination of compressed thin layers at corners

An analysis of delamination for a thin elastic layer under compression, attached to a substrate at a corner is carried out. The analysis is performed by combining results from interface fracture mechanics and the theory of thin shells. In contrast with earlier results for delamination on a flat substrate, the present problem is not a bifurcation problem. Crack closure at sufficiently high stress levels are shown to occur. Results show a very strong dependency on fracture mechanical parameters of the angle of the corner including the range of parameters where crack closure occurs. Analytical results for the fracture mechanical properties have been obtained, and these are applied in a study of the effect of contacting crack faces. Special attention has been given to analyse conditions under which steady state propagation of buckling driven delamination takes place.     

对裂纹扩展规律Paris公式物理本质的探讨

首先讨论了著名力学家K.Krausz和A.S.Krausz关于Paris公式物理本质研究的成果，从材料的微观结构和裂纹尖端的应力场出发，应用位错动力学理论，热激活能理论和速率过程理论对疲劳裂纹扩展规律进行了微观到宏观的探讨。最终推导出疲劳裂纹扩展速率的一个解析表示式，该式严格地定了Paris公式的两个试验常数，赋予了Paris公式明确的物理意义，从而真实地揭示了Paris公式的物理本质，为这一经验的普遍规律奠定了理论基础。