The finite deformation field surrounding a mode I plane strain crack in a hyperelastic incompressible material under small-scale nonlinearity

A finite deformation analysis of a plane strain mode I crack in a hyperelastic incompressible material is presented. The nonlinear crack tip field was characterized in terms of its region of dominance under the assumptions of small-scale nonlinearity and compared to the theoretical dominant asymptotic solution for this problem. The influence of the material law (linear vs. third order) on the nonlinear crack tip field was also discussed. The finite element results for the third order material law determined that the maximum stress in the load direction was found along the deformed crack flank behind the crack tip. A local cavitation surface surrounding the crack tip was identified using the linear material law, enabling prediction of potential sites of cavitation.     

Dynamic asymptotic mode III crack tip field in rate dependent materials

The asymptotic field at a dynamically growing crack tip in strain-rate sensitive elastic-plastic materials is investigated under anti-plane shear loading conditions. In the conventional viscoplasticity theory, the rate sensitivity is included only in the flow stress. However, it is often found that the yield strength is also affected by previous strain rates. The strain rate history effects in metallic solids are observed in strain rate change tests in which the flow stress decreases gradually after a rapid drop in strain rate. This material behavior may be explained by introducing the rate sensitivity in the hardening rule in addition to the flow rule. The strain-rate history effect is pronounced near the propagating crack where the change of strain rates take place. Effects of the rate dependency in the flow rule and the hardening rule on the crack propagation are analyzed. The order of the stress singularity in the asymptotic field is determined in terms of material parameters which characterize the rate sensitivity of the material. The results show that an elastic sector is present in the wake zone when the rate-dependency is considered only in the hardening rule. Terminal crack propagation speed is determined by applying the critical stress fracture criterion and the critical strain criterion to the asymptotic fields under the small scale yielding condition.     

Simulation of the shear-tensile mode transition on dynamic crack propagations

We propose an approach to the simulation of the shear-tensile transition in dynamic crack growth based on two points: a new crack propagation criterion which is suitable for shear, and an algorithm which is capable of handling the transition from shear mode to tensile mode and back in the same simulation. The new crack propagation criterion for brittle crack growth is based on the maximum shear stress rather than the maximum hoop stress. The shear stress direction becomes the new crack??s direction in which propagation is initiated for shear-type failure. The stress state at the crack??s tip is obtained through a local approach which can be used even in the case of extensive plasticity. Additionally, we propose to control the transition from shear mode to tensile mode during the simulation of crack propagation using an equivalent strain estimated at the crack??s tip. Depending on a threshold strain, the propagation direction is predicted using the maximum shear stress (in the shear case) or the maximum hoop stress (in the tensile case).     

An implicit adaptive node‐splitting algorithm to assess the failure mechanism of inelastic elastomeric continua

This contribution presents a mesh adaptive crack propagation scheme for the evaluation of the viscoelastic fracture response of elastomers at large strains and up to high loading rates. The approach accounts for micromechanical based features of both elastic and viscoelastic bulk responses of idealized polymer networks. To this end, the Bergstörm–Boyce model is considered to introduce hyperelastic and nonlinear finite viscoelastic responses. Moreover, the crack driving force and the crack driving direction are predicted by the material force approach. A consistent thermodynamic framework for the combined configurational motion in viscoelastic continua at finite strain regime is discussed. The fracture toughness of non‐strain‐crystallizing elastomers shows strong rate dependency and the energy release rate versus the rate of tearing to be a fundamental material property. Therefore, in this contribution, a dynamic fracture criterion, which is a function of the rate of crack growth, is shown to be adequate in numerical simulations. The use of the presented method enables to study fracture behaviour of any material nonlinearity within the implicit time integration. Main feature of the proposed algorithm is restructuring the overall discrete system by duplication of crack front DOFs based on minimization of the overall energy via the Griffith criterion. Copyright © 2014 John Wiley & Sons, Ltd.     

NUMERICAL ANALYSIS OF CRACK PROPAGATION IN PIEZOELECTRIC CERAMICS

The formulation of an isoparametric displacement – electric potential finite element method that accounts for the electro-mechanical coupling effect of piezoelectric materials is briefly presented in this paper. The crack propagation behaviour and the elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and mechanical – electrical mixed loads are investigated using this electro-mechanical finite element method. From the numerical results, it can be seen that crack propagation along the crack plane direction will be impeded and the crack will tend to propagate at an angle of about 84° to the crack plane under a negative electric field on the basis of the maximum stress criterion. The physical explanation of the phenomena is presented in this paper and it is shown that the mechanical strain energy release rate is not a good criterion for predicting crack propagation in the case where the ratio of the electric field to the mechanical load becomes large.     

预制裂纹角度对橡胶拉伸断裂影响的有限元分析

初始裂纹的形态影响着裂纹尖端的应力场和扩展方向,进而决定着橡胶材料的使用寿命。目前人们关于预制裂纹试样拉伸断裂的研究主要集中在直裂纹,很少涉及预制裂纹角度的改变对橡胶拉伸断裂的影响。文中应用ANSYS有限元分析软件计算拉伸状态下含不同裂纹角度橡胶试样裂纹尖端的等效应力值和撕裂能的大小,判断裂纹是否扩展及扩展方向,并对橡胶试样进行拉伸验证试验测试。结果表明,在拉伸断裂过程中,裂纹尖端的应力值和撕裂能随着初始预制裂纹角度的增大而增大,裂纹尖端形状均由初始的尖点变成圆弧状;含不同裂纹角度橡胶试样的拉伸断裂形貌与裂纹预测扩展方向基本一致,验证了有限元分析的正确性。     

Finite-element simulation of interfacial crack propagation: Methods and tools for the complete failure process under large scale yielding

Interface crack propagation is described with an advanced finite element model on the basis of a non-linear material law with large plastic deformation and a global energy release rate criterion. The simulation covers the whole failure process in one model, starting from small loads, development of a large plastic zone, onset of cracking and crack propagation until complete rupture.The model implements an elastic-plastic material law including hardening. Numerical stability and reliability strongly depend on the correct implementation of the material law. The central part is the realization of a moving crack. Due to the discrete nature of a finite element model, the crack can only propagate in finite steps resulting in sudden changes of boundary conditions. Smoothing these changes is essential for numerical stability and reasonable computation time.Simulated crack propagation bases on a criterion to decide between further increase of load or further advance of crack. A global energy release criterion is used here and was found to be independent of the specific discretisation.     

Analysis of the stress intensity factor dependence with the crack velocity using a lattice model

In this work, the influence of crack propagation velocity in the stress intensity factor has been studied. The analysis is performed with a lattice method and a linear elastic constitutive model. Numerous researchers determined the relationship between the dynamic stress intensity factor and crack propagation velocity with experimental and analytical results. They showed that toughness increases asymptotically when the crack tip velocity is near to a critical. However, these methods are very complex and computationally expensive; furthermore, the model requires the use of several parameters that are not easily obtained. Moreover, its practical implementation is not always feasible. Hence, it is usually omitted. This paper aims to capture the physics of this complex problem with a simple fracture criterion. The selected criterion is based on the maximum principal strain implemented in a lattice model. The method used to calculate the stress intensity factor is validated with other numerical methods. The selected example is a finite 2D notched under mode I fracture and different loads rates. Results show that the proposed model captures the asymptotic behaviour of the SIF in function of crack speed, as reported in the aforementioned models.     

高压水射流破碎胎面胶的脆化效应与胶粉形成

采用霍布金森压杆试验模拟子午线轮胎胎面胶的破碎回收过程,分析高压水射流冲击下胎面胶材料受力及响应状态,试验表明材料存在韧脆转变现象,进而发生脆性断裂。橡胶断口与胶粉微观形貌表明,裂纹扩展区呈现典型的放射状脆性断面形貌,并形成大量与胶粉尺寸匹配的平整光滑区域,直接验证了脆性断裂的存在并阐述其发生过程。然后利用应力波传播判据和脆断力学分析解释了胎面胶材料出现脆化效应的原因。对材料韧脆转变的影响因素进行分析后可知,高压水射流冲击过程中,材料质点变形速度远大于韧脆转变临界速度,在力学性能上表现为断裂应力小于屈服应力,致使材料发生脆性断裂并形成精细胶粉。     

Numerical analysis of dynamic crack propagation in rubber

In the present paper, dynamic crack propagation in rubber is analyzed numerically using the finite element method. The problem of a suddenly initiated crack at the center of stretched sheet is studied under plane stress conditions. A nonlinear finite element analysis using implicit time integration scheme is used. The bulk material behavior is described by finite-viscoelasticity theory and the fracture separation process is characterized using a cohesive zone model with a bilinear traction-separation law. Hence, the numerical model is able to model and predict the different contributions to the fracture toughness, i.e. the surface energy, viscoelastic dissipation, and inertia effects. The separation work per unit area and the strength of the cohesive zone have been parameterized, and their influence on the separation process has been investigated. A steadily propagating crack is obtained and the corresponding crack tip position and velocity history as well as the steady crack propagation velocity are evaluated and compared with experimental data. A minimum threshold stretch of 3.0 is required for crack propagation. The numerical model is able to predict the dynamic crack growth. It appears that the strength and the surface energy vary with the crack speed. Finally, the maximum principal stretch and stress distribution around steadily propagation crack tip suggest that crystallization and cavity formation may take place.     

Analysis of a compressive shear test for adhesion between elastomeric polymers and rigid substrates

A compressive shear test for investigating adhesion between an elastomeric polymer and a rigid substrate has been studied. The test consists of loading a specimen comprising of a 3-ply laminate: substrate/polymer/ substrate, in compression and shear at a specified angle to the loading direction. Under displacement control and when adhesion is sufficiently low, an interfacial crack nucleates at one interface early during loading and propagates stably up to a critical load at which unstable propagation with an associated load drop ensues. The case of an isothennal hyperelastic material has been analyzed by computing the energy release rate for an interfacial crack as a function of crack length. The analysis shows that for a range of initial crack size interfacial crack propagation is stable until crack length reaches a critical size at which unstable propagation ensues. The energy release rate at this instability is relatively insensitive to angle of loading, strain, and hyperelastic parameters, which allows one to extract an interfacial toughness, ₀, from overall measurement of stress and strain. The analysis has been extended to consider combined hyperelasticity and viscoelasticity by using a cohesive zone model for crack propagation implemented as a cohesive finite element. The energy release rate and cohesive zone analyses give identical results for an hyperelastic material. For a viscoelastic-hyperelastic material, the cohesive zone approach allows the viscous losses in the bulk polymer to be estimated separately from the value of interfacial fracture toughness. Both analyses have been applied to experiments on glass/polyvinyl butyral (Butacite®)/glass laminate specimens. The intrinsic interfacial toughness, consisting of contributions from bond rupture and a near-tip process zone, is found to be rate-dependent and lies in the range 50–200 J m^–2.     

Application of viscoelastic fracture criteria to progressive crack propagation in polymer matrix composites

With the view of comparing local and global viscoelastic fracture criteria, an extension of Christensen's criterion to composite materials with stiff elastic fibers is proposed. Several versions of this criterion are compared with Schapery's local approach of the same phenomenon. The asymptotic version of Christensen's criterion for rapid crack propagation is found suitable for the material investigated, at room temperature. Dissipation in the specimen has two main sources: the undamaged material on one hand, and the damaged material inside the `failure zone' close to the crack tip on the other. The respective roles of these two kinds of dissipation are assessed.     

Study of crack growth in solid propellants

The stress and displacement fields in an edge-cracked sheet specimen made of a solid propellant and subjected to a uniform displacement along its upper and lower faces was studied. The solid propellant was simulated as a hyperelastic material with constitutive behaviour described by the Ogden strain energy potential. A non-linear finite deformation analysis was performed based on the finite element code ABAQUS. A detailed analysis of the stress field in the vicinity of the crack tip was undertaken. The deformed profiles of the crack faces near the crack tip were determined. The results of stress analysis were coupled with the strain energy density theory to predict the crack growth behaviour including crack initiation, stable crack growth and final termination for two specimens with different dimensions. Crack growth resistance curves representing the variation of crack growth increment versus applied displacement were drawn.     

Numerical simulations of dynamic crack growth along an interface

Dynamic crack growth is analyzed numerically for a plane strain bimaterial block with an initial central crack. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to crack initiation and the crack speed history are predicted without invoking any ad hoc failure criterion. Full finite strain transient analyses are carried out, with two types of loading considered; tensile loading on one side of the specimen and crack face loading. The crack speed history and the evolution of the crack tip stress state are investigated for parameters characterizing a PMMA/Al bimaterial. Additionally, the separate effects of elastic modulus mismatch and elastic wave speed mismatch on interface crack growth are explored for various PMMA-artificial material combinations. The mode mixity of the near tip fields is found to increase with increasing crack speed and in some cases large scale contact occurs in the vicinity of the crack tip. Crack speeds that exceed the smaller of the two Rayleigh wave speeds are also found.     

Dominance of asymptotic crack tip fields in elastic functionally graded materials

The stress field surrounding an edge crack in an elastic functionally graded plate is calculated using two dimensional finite element analysis. The property gradient direction is parallel to the crack line and loading is constrained to be symmetric such that a pure mode I situation is achieved. The extent of dominance of asymptotic fields is evaluated by comparing the stress field calculated from the finite element analysis to that calculated by asymptotic equations. Two separate forms of the asymptotic stress fields, one for homogeneous materials and another for continuously nonhomogeneous materials are used. The shape and extent of the dominance regions of each asymptotic field and their dependence on crack length and material nonhomogeneity is also presented. Under the pure mode I conditions considered here, it is seen that both asymptotic fields exist around the crack tip with the one for homogeneous materials in general being embedded in the one for continuously nonhomogeneous materials. The ligament length is seen to primarily control the extent of development of the asymptotic stress field for nonhomogeneous materials. The steepness of the material gradient affects the relationship between the two asymptotic stress fields and therefore the extent of their dominance.     

Crack propagation analysis for orthotropic non-homogeneous materials

The fracture mechanics of orthotropic non-homogenous materials like welds involves the use of a fracture criterion with the stress analysis of the specimen. A maximum energy release rate criterion is proposed in this analysis. A finite element model with special crack tip elements has been developed for this study. Two techniques have been developed to model the crack propagation. The model was then applied to a compact tension specimen with a hypothetical weldment and to a weldment with an edge crack.The maximum energy release rate criterion seems to be the most suitable for fracture prediction of non-homogeneous materials, since it gives the crack propagation direction as well as the maximum value for the energy released. The virtual displacement technique for modeling the crack propagation saves computer time and gives accurate results. The analysis indicates the effect of orthotropy on the crack propagation direction and maximum energy release rate.     

梯度复合材料裂纹扩展路径和起裂载荷的有限元分析

为了模拟功能梯度材料(FGM)在工程应用中可能会出现的断裂问题并计算相应的开裂载荷,通过编写用户自定义UEL子程序将梯度扩展单元嵌入到ABAQUS软件中模拟功能梯度材料的物理场,并编写交互能量积分后处理子程序计算裂纹尖端的混合模式应力强度因子(SIF),采用最大周向应力准则编写子程序计算裂纹的偏转角,并模拟了裂纹扩展路径,计算了裂纹的起裂载荷。讨论了材料梯度参数对裂纹扩展路径以及起裂载荷的影响规律。通过与均匀材料的对比,验证了功能梯度材料断裂性能的优越性。研究表明:外载平行于梯度方向时,垂直梯度方向的初始裂纹朝着等效弹性模量小的方向扩展,且偏转角在梯度指数线性时出现峰值,并随着组分弹性模量比的增加而变大;当外载和初始裂纹均平行于梯度方向时,材料等效弹性模量和断裂韧性的增加或者梯度指数的减小都导致起裂载荷变大。     

Strain-driven corrosion crack growth: A pilot study of intergranular stress corrosion cracking

This work proposes a model for corrosion driven crack growth. The model poses a moving boundary problem, where a chemical attack removes material from the body. The rate of the chemical attack is a function of the strain along the body surface. No crack growth criterion is needed for the analysis. A finite strain formulation is used and the material model is assumed hyperelastic. The problem is stated for a large body, containing a large crack. A low frequency cyclic loading is considered. Thus, corrosion is assumed to dissolve material with a rate approximately proportional to the strain rate. The problem is solved using finite element method based program, enhanced with a procedure handling the moving boundary. Parametric studies are performed for a series of different initial shapes of the near-tip region. Presented results show that the crack growth rate is largely dependent on the initial crack geometry. For a set of initial shapes and load levels steady-state conditions of growth are achieved, while for the others the cracks show tendency to branch.     

Strain-driven corrosion crack growth: A pilot study of intergranular stress corrosion cracking

This work proposes a model for corrosion driven crack growth. The model poses a moving boundary problem, where a chemical attack removes material from the body. The rate of the chemical attack is a function of the strain along the body surface. No crack growth criterion is needed for the analysis. A finite strain formulation is used and the material model is assumed hyperelastic. The problem is stated for a large body, containing a large crack. A low frequency cyclic loading is considered. Thus, corrosion is assumed to dissolve material with a rate approximately proportional to the strain rate. The problem is solved using finite element method based program, enhanced with a procedure handling the moving boundary. Parametric studies are performed for a series of different initial shapes of the near-tip region. Presented results show that the crack growth rate is largely dependent on the initial crack geometry. For a set of initial shapes and load levels steady-state conditions of growth are achieved, while for the others the cracks show tendency to branch.