裂纹扩展过程中线性内聚力模型计算的半解析有限元法

提出了求解基于线性内聚力模型的平面裂纹扩展问题的半解析有限元法,利用弹性平面扇形域哈密顿体系的方程,通过分离变量法及共轭辛本征函数向量展开法,推导了一个环形和一个圆形奇异超级解析单元列式,组装这两个超级单元能准确地描述裂纹表面作用有双线性内聚力的平面裂纹尖端场。将该解析元与有限元相结合,构成半解析的有限元法,可求解任意几何形状和载荷的基于线性内聚力模型的平面裂纹扩展问题。典型算例的计算结果表明本文方法简单有效,具有令人满意的精度。     

The simulation of dynamic crack propagation using the cohesive segments method

The cohesive segments method is a finite element framework that allows for the simulation of the nucleation, growth and coalescence of multiple cracks in solids. In this framework, cracks are introduced as jumps in the displacement field by employing the partition of unity property of finite element shape functions. The magnitude of these jumps are governed by cohesive constitutive relations. In this paper, the cohesive segments method is extended for the simulation of fast crack propagation in brittle solids. The performance of the method is demonstrated in several examples involving crack growth in linear elastic solids under plane stress conditions: tensile loading of a block; shear loading of a block and crack growth along and near a bi-material interface.     

Subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone

A recent experimental study has demonstrated the attainability of intersonic shear crack growth along weak planes in otherwise homogeneous, isotropic, linear elastic solids subjected to remote loading conditions (Rosakis et al., Science 284 (5418) (1999) 1337). The relevant experimental observations are summarized briefly here and the conditions governing the attainment of intersonic crack speeds are examined. Motivated by experimental observations, subsonic and intersonic mode II crack propagation with a rate-dependent cohesive zone is subsequently analyzed. A cohesive law is assumed, wherein the cohesive shear traction is either a constant or varies linearly with the local sliding rate. Complete decohesion is assumed to occur when the crack tip sliding displacement reaches a material-specific critical value. Closed form expressions are obtained for the near-tip fields. With a cohesive zone of finite size, it is found that the dynamic energy release rate is finite through out the intersonic regime. Crack tip stability issues are addressed and favorable speed regimes are identified. The influence of shear strength of the crack plane and of a rate parameter on crack propagation behavior is also investigated. The isochromatic fringe patterns predicted by the analytical solution are compared with the experimental observations of Rosakis et al. (1999) and comments are made on the validity of the proposed model.     

数学网格和物理网格分离的有限单元法(II):粘聚裂纹扩展问题中的应用

强化有限单元法将物理网格与数学网格分离开来,可以方便地描述非连续变形;粘聚区域模型是模拟断裂过程区作用最简单有效的方法,且可以避免裂纹尖端的应力奇异性.本文以平面问题为例,将强化有限单元法与粘聚区域模型相结合,利用富集数学节点描述任意粘聚裂纹扩展过程中的非连续变形问题,提出了裂纹扩展过程中数学节点富集和数学单元定义的方法.本文还导出了与平面4～8节点平面等参单元对应的8～16节点粘聚裂纹单元列武.最后,通过三点弯梁的裂纹扩展过程模拟验证了本文提出的粘聚裂纹扩展模拟方法的有效性.     

Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials

An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode Ⅲ dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.     

Crack propagation in the power-law nonlinear viscoelastic material

I.IntroductionCrazingdamageisacommonphenon1enonoffractureofpolymericmaterials.Theformationofcrazezoneisamid-stateinthefractureprocessofthematerialsfromperfectstatetofaiIurc.Microscopically,inthisregionthereexistssomefibrilslinkingthetwocracksurfacesandres…     

Inverse parameter identification of cohesive zone model for simulating mixed-mode crack propagation

Inverse analysis is widely applied to the identification of material properties or model parameters. In order to improve the computational efficiency of the inverse method based on the genetic algorithm, an interpolation scheme upon the response surface constructed by the finite element simulation has been adopted in this paper. Meanwhile, a gradual homogenization treatment scheme has also been presented to improve the convergence of the inverse method based on the Kalman filter algorithm. Both methods are proven effective in dealing with the single-objective inverse problem. However, literature studies show that the adoption of multiple types of experimental information is useful to improve the accuracy of inverse analysis. In this case, it turns into a multiple-objective inverse problem. Our practice proved that the above-mentioned two methods might not yield a proper result if the sensitivity issue of different types of information is not considered. Therefore, another multi-objective inverse method, in combination of the above two optimization algorithms and a weight-estimating scheme that can consider such sensitivity, has been further presented. Finally, by using a mixed-mode crack propagation simulation and two types of experimental information (loading-displacement response curve and crack path profile), the parameters of the cohesive zone model were inversely identified and its simulation results are in good agreement with the experiment.     

Molecular-dynamics simulation-based cohesive zone representation of intergranular fracture processes in aluminum

A traction-displacement relationship that may be embedded into a cohesive zone model for microscale problems of intergranular fracture is extracted from atomistic molecular-dynamics (MD) simulations. An MD model for crack propagation under steady-state conditions is developed to analyze intergranular fracture along a flat Σ99 [1 1 0] symmetric tilt grain boundary in aluminum. Under hydrostatic tensile load, the simulation reveals asymmetric crack propagation in the two opposite directions along the grain boundary. In one direction, the crack propagates in a brittle manner by cleavage with very little or no dislocation emission, and in the other direction, the propagation is ductile through the mechanism of deformation twinning. This behavior is consistent with the Rice criterion for cleavage vs. dislocation blunting transition at the crack tip. The preference for twinning to dislocation slip is in agreement with the predictions of the Tadmor and Hai criterion. A comparison with finite element calculations shows that while the stress field around the brittle crack tip follows the expected elastic solution for the given boundary conditions of the model, the stress field around the twinning crack tip has a strong plastic contribution. Through the definition of a Cohesive-Zone-Volume-Element—an atomistic analog to a continuum cohesive zone model element—the results from the MD simulation are recast to obtain an average continuum traction-displacement relationship to represent cohesive zone interaction along a characteristic length of the grain boundary interface for the cases of ductile and brittle decohesion.     

Analysis of crack growth and crack-tip plasticity in ductile materials using cohesive zone models

Crack initiation and crack growth resistance in elastic plastic materials, dominated by crack-tip plasticity are analyzed with the crack modeled as a cohesive zone. Two different types (exponential and bilinear) of cohesive zone models (CZMs) have been used to represent the mechanical behavior of the cohesive zones. In this work, it is suggested that different forms of CZMs (e.g., exponential, bilinear) are the manifestations of different micromechanisms-based inelastic processes that participate in dissipating energy during the fracture process and each form is specific to each material system. It is postulated that the total energy release rate comprises the plastic dissipation rate in the bounding material and the separation energy rate within the fracture process zone, the latter is determined by CZMs. The total energy release rate then becomes a function of the material properties (e.g., yield strength, strain hardening exponent) and cohesive properties of the fracture process zone (e.g., cohesive strength and cohesive energy), and the form of cohesive zone model (CZM) that determines the rate of energy dissipation in the forward and wake regions of the crack. The effects of material parameters, cohesive zone parameters as well as the form/shape of CZMs in predicting the crack growth resistance and the size of plastic zone (SPZ) surrounding the crack tip are systematically examined. It is found that in addition to the cohesive strength and cohesive energy, the form (shape) of the traction–separation law of CZM plays a very critical role in determining the crack growth resistance (R-curve) of a given material. It is further observed that the shape of the CZM corresponds to inelastic processes active in the forward and wake regions of the crack, and has a profound influence on the R-curve and SPZ.     

多裂纹扩展分析的边界元方法

采用边界元数值模拟和即时等效材料常数计算相结合的办法,只需模拟一个裂纹的扩展情况便可预测裂纹体的整体响应.针对准脆性材料的特点,采用粘性裂纹模型模拟裂纹开裂行为;采用二次裂纹扩展量作为增量控制变量,避免了软化及失稳分析中用力或位移作控制变量时遇到的困难.针对二次裂纹扩展路径未知情况,给出了预测和修正裂纹开裂界面的迭代技术.分析计算了含多个规则分布裂纹石膏板受压时的响应,并与实验结果进行了比较.结果表明该文方法的可行性与有效性.     

Effect of plastic zone on the fatigue crack propagation behavior between two fatigue cracks

In this study, the fatigue crack propagation behavior in the stress interaction field between two different fatigue cracks is studied by experiment and finite element analysis. In the experiment, the offset distance between two cracks and the applied stress are varied to create different stress interaction fields. The size of the plastic zone area is used to examine the crack propagation path and rate. Three types of crack propagation in the interaction field were found by experiment, and the crack propagation behavior of two cracks was significantly changed as different stresses were applied. The size of the plastic zone obtained by finite element analysis can be used to explain crack propagation behavior qualitatively.     

粘聚裂纹扩展的强化有限元h型网格自适应模拟

非连续变形分析和非规则节点处理是基于单元细划的粘聚裂纹扩展网格自适应模拟的关键。首先,利用强化有限单元法中数学单元和物理单元分离的特点,通过引入过渡单元,将适用于非连续变形描述的数学模式覆盖法和方便处理非规则节点的物理模式重构法结合,提出了强化有限单元法的统一关联法则,并导出了相应的单元列式。其次,基于数学裂纹尖端影响域和裂尖单元尺寸,提出了基于强化有限单元法的粘聚裂纹扩展过程模拟的h型网格自适应策略。最后,通过两个算例验证了本文方法的合理性和有效性。     

应用修正的虚裂纹模型研究混凝土结构的三维裂缝扩展

本文在虚裂纹模型中引入初裂强度因子的概念以研究混凝土结构的三维裂缝扩展。虚裂纹的扩展由裂纹尖端的初裂强度因子和虚裂纹所传递的软化应力共同控制。将软化应力分析曲线分段线性化进行模拟,这使问题得到很大程度的简化,同时又保证了解的必要精度。对所建立的有限元基本方程组建议了一次性的求解方法,可以不进行迭代,这既保持了解的稳定,又减轻了计算工作量。     

构元组集损伤断裂模型及其与内聚区模型的比较

结构的响应实质上是材料的响应,宏观结构损伤至断裂的发展过程也是材料性质不断演化的结果.构元组集模型从材料的微观物理变形机制出发,基于对泛函势理论和Cauchy-Born准则,抽象出两种构元:弹簧束构元和体积构元.在微观层次上,结构损伤和断裂的实质都是原子间键合力减弱和丧失的结果,而弹簧束构元是同一方向上的原子键的抽象,因此损伤可以通过弹簧束构元的响应曲线来反映.组集两种构元的响应,建立了材料的弹性损伤本构关系,从而能一致描述材料从弹性到损伤、破坏的发展过程.将构元组集模型的本构关系嵌入ABAQUS的用户材料单元子程序UMAT,实现对结构响应的数值模拟.论文模拟了包含中心预制裂纹三点弯曲梁的裂纹扩展过程,并与内聚区模型比较,给出了内聚区模型所假设的应力-位移关系曲线,并从材料损伤演化的角度对材料裂纹扩展过程做出了物理解释.     

Cohesive zone size of microcracks in brittle materials

Consideration of cohesive microcracks in continuum micromechanics is a challenging task since a lot of applications (such as, e.g., estimation of the stiffness of a microcracked solid) require a priori knowledge of the size of the cohesive zone. The latter, however, can be determined analytically only for the special case of Barenblatt–Dugdale cracks, i.e. for cracks with spatially constant cohesive tractions. Herein, we deal with the general case of spatially non-constant cohesive tractions: Generalizing the Barenblatt–Dugdale approach, we consider that each crack is surrounded by a plane annular cohesive zone characterized by a constitutive softening law (introduced as a power law) relating the vector of cohesive tractions to the displacement discontinuity. The size of this cohesive zone is then estimated using the theorem of minimum potential energy, based on a class of kinematically admissible displacement fields.     

Mode-3 spontaneous crack propagation along functionally graded bimaterial interfaces

The effects of combining functionally graded materials (FGMs) of different inhomogeneous property gradients on the mode-3 propagation characteristics of an interfacial crack are numerically investigated. Spontaneous interfacial crack propagation simulations were performed using the newly developed spectral scheme. The numerical scheme derived and implemented in the present work can efficiently simulate planar crack propagation along functionally graded bimaterial interfaces. The material property inhomogeneity was assumed to be in the direction normal to the interface. Various bimaterial combinations were simulated by varying the material property inhomogeneity length scale. Our parametric study showed that the inclusion of a softening type FGM in the bimaterial system leads to a reduction in the fracture resistance indicated by the increase in crack propagation velocity and power absorbed. An opposite trend of increased fracture resistance was predicted when a hardening material was included in the bimaterial system. The cohesive tractions and crack opening displacements were altered due to the material property inhomogeneity, but the stresses ahead of the cohesive zone remained unaffected.     

Analysis of electric boundary condition effects on crack propagation in piezoelectric ceramics

There are three types of cracks: impermeable crack, permeable crack and conducting crack, with different electric boundary conditions on faces of cracks in piezoelectric ceramics, which poses difficulties in the analysis of piezoelectric fracture problems. In this paper, in contrast to our previous FEM formulation, the numerical analysis is based on the used of exact electric boundary conditions at the crack faces, thus the common assumption of electric impermeability in the FEM analysis is avoided. The crack behavior and elasto-electric fields near a crack tip in a PZT-5 piezoelectric ceramic under mechanical, electrical and coupled mechanical-electrical loads with different electric boundary conditions on crack faces are investigated. It is found that the dielectric medium between the crack faces will reduce the singularity of stress and electric displacement. Furthermore, when the permittivity of the dielectric medium in the crack gap is of the same order as that of the piezoelectric ceramic, the crack becomes a conducting crack, the applied electric field has no effect on the crack propagation. The project supported by the National Natural Science Foundation of China (19672026, 19891180)