A criterion for the growth of cracks with bonds in the end zone

A fracture criterion which takes account of the work done in the deformation of bonds in the end zone of a crack is proposed for analysing the quasistatic growth of a crack with bonds in the end zone. The energy condition that the deformation energy release rate at the crack tip is equal to the rate of deformation energy consumption by the bonds in the end zone of the crack (the first fracture condition) corresponds to the state of limit equilibrium of the crack tip. The rupture of bonds at the trailing edge of the end zone is determined by the condition for their limiting traction (the second fracture condition). Starting from these two conditions, the processes of subcritical and quasistatic crack growth are considered for the case of a rectilinear crack at interface of materials and the two basic fracture parameters, the critical external load and the size of the end zone of the crack in the state of limit equilibrium, are determined. Analytical expressions are obtained for the deformation energy release rate at the crack tip and the rate of deformation energy consumption by the bonds and, also, the dependences of the critical external load and size of the end zone of the crack on the crack length in the case of a rectilinear crack in a homogeneous body with bond tractions which are constant and independent of the external load. The limit cases of a crack which is filled with bonds and a crack with a short end zone are considered.     

Modeling of fracture of fibrous composites with brittle components

Conclusions A numerical analysis of the stress field at the tip of a crack showed high localization, increasing with increase of anisotropy and normal and shear stresses at the crack tip, which can cause various types of fracture. The use of the J-integral for estimates of the flow of elastic energy to the crack tip, simulated by a greatly elongated elliptical notch, is apparently possible in approximate calculations, taking into account localization of the zone of nonlinear behavior of the material. A scheme of estimating the crack resistance of a fibrous material with brittle components, taking into account the contribution of various forms of microfracture to energy dissipation, is proposed. The calculated value of G^* differs from the experimental data by about 20%, which, taking into account the simplicity of the calculation method, can be considered satisfactory.Report presented at the Fourth All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, October, 1980).Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 615–619, July–August, 1981.The author thanks S. T. Mileiko for formulating the problem, advice, and discussion of the work.     

Plastic zone development in dynamic tear-type test specimens

The J-integral is a fracture criterion, which permits measurement of the fracture toughness of a specimen where fracture occurs in the elastic–plastic regime. An understanding of the ratio of plastic zone size (radius) to the crack tip blunting (stretch zone) is required to determine the upper temperature for transition curves, where elastic–plastic fracture becomes invalid and general yielding occurs. This study endeavors to acquire this ratio using finite element techniques. The development of the plastic zone in dynamic tear (DT) specimens and non-standard three-point bending fracture test specimens was the main focus of the study. The ABAQUS finite element software was used to model the elastic–plastic behaviour of the specimens. The cracks in the specimens were induced by pressing the notch followed by fatigue cracking at 30–40% of the limit loads. The shapes of these cracks were adequately modelled in the finite element analysis. The specimens were made of 350WT steel and 304 stainless steel materials and were loaded until fixed amounts of permanent deformation were recorded. Results were obtained in the form of plots, showing the progression of the plastic zone around the crack tip. For each case, mid-point plastic deflection, stretch zone width and plastic zone radius were computed.     

Similarity and dimensional analysis in the plane problem of the propagation of a vertical hydraulic fracture crack in an elastic medium

The problem of the growth of a vertical hydraulic fracture crack in an unbounded elastic medium under the pressure produced by a viscous incompressible fluid is studied qualitatively and by numerical methods. The fluid motion is described in the approximation of lubrication theory. Near the crack tip a fluid-free domain may exist. To find the crack length, Irwin’s fracture criterion is used. The symmetry groups of the equations describing the hydraulic fracture process are studied for all physically meaningful cases of the degeneration of the problem with respect to the control parameters. The condition of symmetry of the system of equations under the group of scaling and time-shift transformations enables the self-similar variables and the form of the time dependence of the quantities involved in the problem to be found. It is established that at non-zero rock pressure the well-known solution of Spence and Sharp is an asymptotic form of the initial-value problem, whereas the solution of Zheltov and Khristianovich is a limiting self-similar solution of the problem. The problem of the formation of a hydraulic fracture crack taking into account initial data is solved using numerical methods, and the problem of arriving at asymptotic mode is investigated. It is shown that the solution has a self-similar asymptotic form for any initial conditions, and the convergence of the exact solutions to the asymptotic forms is non-uniform in space and time.     

Numerical crack path prediction considering orthotropic effects and experimental verification

For a reliable prediction of crack paths, on the one hand the accurate calculation of crack tip loading quantities is inevitable, on the other hand orthotropic features of the fracture toughness need to be taken into account. The interplay of crack tip loading and material response due to fracture is still unclear and seems to have a crucial effect on crack path predictions. Numerical tools for the accurate calculation of crack tip loading quantities using path-invariant J-integrals and interaction integrals (I-integral) are presented. Here, global approaches are beneficial when considering crack tips approaching other crack faces or internal boundaries. Curved crack faces have to be taken into account and special treatment regarding crack face integrals is necessary. Experimental investigations are carried out at standard CT-specimens of rolled aluminum alloy Al-7075 exhibiting a directional orthotropy of the fracture toughness. Considering that property, the numerically predicted crack paths based on FE calculations show very good agreement with subcritically grown paths obtained from experiments. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Application of configurational forces in the context of a kinked crack

The application of the configurational force approach in crack problems is often used in order to establish fracture criteria that are adapted to a specific material behaviour. The tangential component of the calculated vectorial quantity that acts at the crack tip is a generalisation of the conventional J-integral and can be interpreted as the energy release rate when the crack extends in this direction. However, the interpretation of nontangential components in the same way, and hence the interpretation of this vectorial quantity as the crack driving force, is not consistent with established kink criteria in the special case of linear elastic fracture mechanics. As a classical example, an in-plane loaded crack in a homogeneous isotropic linear elastic material is considered under the small strain assumption. Using the expansion of stress intensity factors at the extended crack tip, nontangential components of the configurational force can be interpreted as sensitivities to crack deflection. This perspective has the potential of generalisation which can be applied to more complex situations in order to study the interplay between mechanical fields in the vicinity of the crack tip and the microstructural influence within the process zone. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

线性硬化材料中稳恒扩展裂纹尖端场的粘塑性解

采用弹粘塑性力学模型,对线性硬化材料中平面应变扩展裂纹尖端场进行了渐近分析．假设人工粘性系数与等效塑性应变率的幂次成反比,通过量级匹配表明应力和应变均具有幂奇异性,奇异性指数由粘性系数中等效塑性应变率的幂指数唯一确定．通过数值计算讨论了Ⅱ型动态扩展裂纹尖端场的分区构造随各材料参数的变化规律．结果表明裂尖场构造由硬化系数所控制而与粘性系数基本无关．弱硬化材料的二次塑性区可以忽略,而较强硬化材料的二次塑性区和二次弹性区对裂尖场均有重要影响．当裂纹扩展速度趋于零时,动态解趋于相应的准静态解;当硬化系数为零时便退化为HR(Hui-Riedel)解．     

Evolution of the Stress–Strain State of a Three-Dimensional Plate Weakened by a Central Crack under Impulsive Tension

A method is developed to describe the formation of the stress–strain state in the vicinity of the tip of a stationary crack in a three-dimensional plate under dynamic loading. The energy model used to describe the formation of the stress concentration zone around the crack tip is modified to take into account the transient character of the loading process and the influence of the free surfaces of the plate on the stress–strain state of the central part of the sample. The method is useful for describing static and dynamic brittle fracture from a unified point of view.     

Interlaminar Crack Propagation Analysis of ENF Specimens Based on the Cohesive Zone Model北大核心CSCD

Based on the classical laminated plate theory and the cohesive zone model, a theoretical model for general delamination cracked laminates was established for crack propagation of pure mode Ⅱ ENF specimens. Compared with the conventional beam theory, the proposed model fully considered the softening process of the cohesive zone and introduced the nonlinear behavior of ENF specimens before failure. The predicted failure load is smaller than that under the beam theory and closer to the experimental data in literatures. Compared with the beam theory with only fracture toughness considered, the proposed model can simultaneously analyze the influences of the interface strength, the fracture toughness and the initial interface stiffness on the load-displacement curves in ENF tests. The results show that, the interface strength mainly affects the mechanical behavior of specimens before failure, but has no influence on crack propagation. The fracture toughness is the main parameter affecting crack propagation, and the initial interface stiffness only affects the linear elastic loading stage. The cohesive zone length increases with the fracture toughness and decreases with the interface strength. The effect of the interface strength on the cohesive zone length is more obvious than that of the fracture toughness. When the adhesive zone tip reaches the half length of the specimen, the adhesive zone length will decrease to a certain extent. Copyright ©2022 Applied Mathematics and Mechanics. All rights reserved.     

Simulation of domain structures in cracked ferroelectric materials

The domain structure around a crack tip plays a significant role in the fracture behavior of ferroelectrics. A continuum phase field model is used to investigate the microstructure at the crack front. The concept of the Eshelby momentum tensor and configurational forces is then generalized to account for the contributions of the polarization term. Implementation of the generalized configurational force in the Finite Element code enables us to numerically obtain the driving force at the crack tip, which corresponds to the crack-tip energy release rate. Calculations show that additional positive electric fields tend to prohibit crack growth, whereas additional negative electric fields tend to promote crack growth. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of cracks on different scales in ferroelectric materials

In this work we study contributions to the effective fracture toughness of ferroelectric materials arising from effects on macroscopic and mesoscopic scales of the system. On the macroscopic scale, the crack in a ferroelectric material is modeled taking into account an extended theory of stresses at interfaces in dielectric solids [1-3]. We predict several new effects, such as the “poling effect”, “collinear effect” and the coupling of a Mode-II shear loading and the Mode-I SIF. Further, on the mesoscopic scale, we study the influence of polarization switching limited to the fracture process zone (small scale switching) on the fracture toughness. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Investigation of the prefracture zone at the tip of a mode I crack reaching a nonsmooth interface of an elastic media

We perform calculation of the initial prefracture zone at the tip of a mode I crack that reaches a nonsmooth interface of two dissimilar elastic media at its corner point by the Wiener–Hopf method. The zone is modeled by a line of normal displacement fracture on a crack continuation. Expressions for the length of the prefracture zone and the potential energy accumulated in it are obtained. Their numerical values are compared with the corresponding values for the prefracture zone in a bonding material on the interface of the media, on the basis of which we draw a conclusion on the possible direction of development of the zone.     

Revisiting Energy Release Rates in Brittle Fracture

We revisit in a 2d setting the notion of energy release rate, which plays a pivotal role in brittle fracture. Through a blow-up method, we extend that notion to crack patterns which are merely closed sets connected to the crack tip. As an application, we demonstrate that, modulo a simple meta-stability principle, a moving crack cannot generically kink while growing continuously in time. This last result potentially renders obsolete in our opinion a longstanding debate in fracture mechanics on the correct criterion for kinking.     

Experimental study about nano-deformation field near quasi-cleavage crack tip

Using the nano-moiré method, we measure the near tip nanoscopic deformation on the [111] plane of single crystal silicon with a loaded quasi-cleavage crack running in the [110] direction. The measured strain distribution ahead of the crack tip agrees with the linear elastic fracture mechanics prediction up to 10 nm from the crack tip. Dislocations of Peierls type are detected and they extend from the crack tip over a length of hundreds of Burgers vectors.     

基于裂纹尖端二阶弹性解的断裂过程区尺度

基于Westergaard应力函数裂纹尖端二阶弹性解,推导了裂纹尖端微裂区的轮廓线和特征尺寸的解析表达式;采用幂函数模型描述的拉应变软化模型,确定了在最大拉应力强度理论和最大拉应变强度理论下断裂过程区（FPZ）临界值的解析表达式;将基于Westergaard应力函数一阶弹性解及二阶弹性解、Muskhelishvili应力函数和Duan-Nakagawa模型确定的FPZ临界值进行了比较．结果表明裂纹尖端微裂区和FPZ临界值随着Poisson比的减小而增加并逐渐趋近于应用最大拉应力强度理论确定的结果;二阶弹性解确定的裂纹尖端微裂区和FPZ临界值大于一阶弹性解的值;FPZ临界值随着拉应变软化指数的增加而增加;二阶弹性解确定的FPZ临界值的精度远高于一阶弹性解确定的值.     

幂律非线性粘弹性材料中的裂纹扩展*

对蠕变不可压幂律非线性粘弹性材料中裂纹的蠕变扩展进行了分析,为描述银纹带中的力学行为,假设在裂纹尖端邻域中断裂过程区中分布着阻抗裂纹张开的粘聚应力б_f,.通过对均匀应力参考状态平凡解的摄动,将非线性粘弹性问题化成线性问题处理.对于幂指数.n≌1的弱非线性情况得到了应力与位移表达式.提出断裂过程区局域能量判据,导出了裂纹孕育时间t*与蠕变扩展率a的预测公式.     

裂纹尖端场弹塑性分析的加权残数法及塑性应力强度因子的计算

本文以幂强化材料,平面应变情形为例,系统地提出了裂纹尖端场弹塑性分析的加权残数法,并根据此法,得出了裂纹尖端场的解析式弹塑性近似解.在此基础上.对整个裂纹区域,构造了弹塑性解叠加非线性有限元计算塑性应力强度因子的方法,从而为裂纹尖端场和整个裂纹体的分析和计算,提供了一个方法.