Crack propagation in an elastic solid subjected to general loading—III. Stress wave loading

The stress intensity factor of a half-plane crack extending non-uniformly in an isotropic elastic solid subjected to stress wave loading is determined. A plane stress pulse strikes the crack at time t = 0, the wavefront being parallel to the plane of the crack. At some arbitrary later time t = τ, the crack begins to extend at a non-uniform rate. It is found that the stress intensity factor is a universal function of instantaneous crack-tip velocity times the stress intensity factor for an equivalent stationary crack. An energy rate balance fracture criterion is applied to obtain an equation of motion for the crack tip. The delay time between the arrival of the incident pulse and the onset of fracture is also calculated for this fracture criterion.     

Effect of yield surface vertex on crack-tip fields in mode III

An asymptotic crack-tip analysis of stress and strain fields is carried out for an antiplane shear crack (Mode III) based on a corner theory of plasticity. Because of the nonproportional loading history experienced by a material element near the crack tip in stable crack growth, classical flow theory may predict an overly stiff response of the elastic plastic solid, as is the case in plastic buckling problems. The corner theory used here accounts for this anomalous behavior. The results are compared with those of a similar analysis based on the J₂ flow theory of plasticity.     

Effects of pre-stress on crack-tip fields in elastic,incompressible solids

A closed-form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre-stressed configuration of a nonlinear elastic, incompressible material. In particular, a biaxial pre-stress is assumed with stress axes parallel and orthogonal to the crack faces. Two boundary conditions are considered on the crack faces, namely a constant pressure or a constant dead loading, both preserving an homogeneous ground state. Starting from this configuration, small superimposed Mode I or Mode II deformations are solved, in the framework of Biot's incremental theory of elasticity. In this way a definition of an incremental stress intensity factor is introduced, slightly different for pressure or dead loading conditions on crack faces. Specific examples are finally developed for various hyperelastic materials, including the J₂-deformation theory of plasticity. The presence of pre-stress is shown to strongly influence the angular variation of the asymptotic crack-tip fields, even if the nominal stress rate displays a square root singularity as in the infinitesimal theory. Relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence.     

Effect of constraint induced by crack depth on creep crack-tip stress field in CT specimens

In this paper, the effect of constraint induced by the crack depth on creep crack-tip stress field in compact tension (CT) specimens is examined by finite element analysis, and the effect of creep deformation and damage on the Hutchinson–Rice–Rosengren (HRR) singularity stress field are discussed. The results show the constraint induced by crack depth causes the difference in crack-tip opening stress distributions between the specimens with different crack depth at the same C*. The maximum opening stress appears at a distance from crack tips, and the stress singularity near the crack tips does not exist due to the crack-tip blunting caused by the large creep deformation in the vicinity of the crack tips. The actual stress calculated by the finite element method (FEM) in front of crack tip is significantly lower than that predicted by the HRR field. Based on the reference stress field in the deep crack CT specimen with high constraint, a new constraint parameter R is defined and the constraint effect in the shallow crack specimen is examined at different distances ahead of the crack tip from transient to steady-state creep conditions. During the early stages of creep constraint increases with time, and then approaches a steady state value as time increases. With increasing the distance from crack tips and applied load, the negative R increases and the constraint decreases.     

Steady crack growth in elastic–plastic fluid-saturated porous media

An asymptotic solution is obtained for stress and pore pressure fields near the tip of a crack steadily propagating in an elastic–plastic fluid-saturated porous material displaying linear isotropic hardening. Quasi-static crack growth is considered under plane strain and Mode I loading conditions. In particular, the effective stress is assumed to obey the Drucker–Prager yield condition with associative or non-associative flow-rule and linear isotropic hardening is adopted. Both permeable and impermeable crack faces are considered. As for the problem of crack propagation in poroelastic media, the behavior is asymptotically drained at the crack-tip. Plastic dilatancy is observed to have a strong effect on the distribution and intensity of pore water pressure and to increase its flux towards the crack-tip.     

Role of elasticity in elastic–plastic fracture: Analytical bi-linear crack-tip fields and finite element analysis

A solution for Model-I plane strain crack tip fields in a bi-linear elastic–plastic material is presented. The elastic–plastic Poisson's ratio is introduced to characterize the influence of elastic deformation on the near tip constraint. Attention is focused on the distribution of elastic/plastic strain energy in the sensitive region of the forward sector ahead of a crack tip. The present study shows that the elastic strain energy can be higher than the plastic strain energy in this sensitive sector while large amount of the plastic strain energy develops outside this sector around the crack tip. The effect of elastic deformation in this sensitive region on the structure of crack-tip fields is considerable and the assumption in some important solutions for crack-tip fields reported in literature that the elastic deformation is small and can be ignored is therefore not physically reasonable. Besides, finite element analysis is carried out to validate the analytical solution and good agreement between them is found. It is seen that the present solution with T-stress can properly describe the crack-tip fields under various constraints for different specimens and an analytical relation is established between the critical value of J-integral, J_c, and T-stress for elastic–plastic fracture.     

ASYMPTOTIC ANALYSIS OF MODE Ⅱ STATIONARY GROWTHCRACK ON ELASTIC-ELASTIC POWER LAWCREEPING BIMATERIAL INTERFACE

A mechanical model was established for mode Ⅱ interfacial crack static growingalong an elastic-elastic power law creeping bimaterial interface. For two kinds of boundaryconditions on crack faces, traction free and frictional contact, asymptotic solutions of thestress and strain near tip-crack were given. Results derived indicate that the stress andstrain have the same singularity, there is not the oscillatory singularity in the field; thecreep power-hardening index n and the ratio of Young‘s module notably influence the crack-tip field in region of elastic power law creeping material and n only influences distribution ofstresses and strains in region of elastic material. When n is bigger, the creepingdeformation is dominant and stress fields become steady, which does not change with n.Poisson‘s ratio does not affect the distributing of the crack-tip field.     

高温结构蠕变裂尖拘束效应

如何对蠕变裂纹扩展寿命进行准确预测和评价是高温结构完整性评定、寿命设计和运行维护中需要解决的核心问题.基于宏观单参数C?的蠕变断裂行为的评价方法,未有效纳入裂尖拘束效应的影响,因而其评价结果过于保守或非保守.目前国内外还未建立起有效纳入裂尖拘束效应的高温结构蠕变寿命评价的理论体系和技术方法,还没有纳入蠕变拘束效应的高温结构完整性评定规范.本文综述了作者近年来在高温蠕变断裂拘束效应方面的研究工作.主要包括:裂尖拘束对材料蠕变裂纹扩展行为的影响及机理;蠕变裂尖场和拘束参数R的定义和影响因素;载荷无关的蠕变拘束参数R? 的提出及其应用基础;承压管道表面裂纹的拘束参数R? 解及纳入裂尖拘束的蠕变寿命评价方法;试样与管道轴向裂纹蠕变裂尖拘束的关联;基于裂尖等效蠕变应变的面内与面外蠕变裂尖拘束的统一表征参数Ac的研究;材料拘束相关的蠕变裂纹扩展速率的建立;宽范围C? 区蠕变裂纹扩展速率及其拘束效应的数值预测;材料拘束对焊接接头蠕变裂纹扩展行为的影响及机理等.这些研究为建立纳入裂尖拘束效应的高温部件的蠕变裂纹扩展寿命评价方法奠定了理论和技术基础.论文对后续拟开展的工作也进行了展望.     

Asymptotic fields in steady crack growth with linear strain-hardening

The asymptotic stress and velocity fields of a crack propagating steadily and quasi-statically into an elastic-plastic material are presented. The material is characterized by J₂-flow theory with linear strain- hardening. The possibility of reloading on the crack flanks is taken into account. The cases of anti-plane strain (mode III), plane strain (modes I and II), and plane stress (modes I and II) are considered. Numerical results are given for the strength of the singularity and for the distribution of the stress and velocity fields in the plastic loading, elastic unloading and plastic reloading regions, as functions of the strain-hardening parameter. An attempt is made to make a connection with the perfectly-plastic solutions in the limit of vanishing strain-hardening.     

Dynamic crack-tip fields in rate-sensitive solids

The asymptotic stress and strain fields near the tip of a crack which propagates dynamically in a rate-sensitive solid are obtained under anti-plane shear and plane strain conditions. The problem is formulated within the context of a small-strain theory for a solid whose mechanical behavior under high strain rates is described by an elastic-viscoplastic constitutive relation. It is shown that, if the stresses are singular at the crack-tip, the viscoplastic relation is equivalent asymptotically to an elastic-non-linear viscous relation. Furthermore, for a certain range of the material parameter which characterizes the rate-sensitivity of the material, the elastic strain-rates near the propagating crack tip are shown to have the same asymptotic radial dependence near the propagating crack-tip as the inelastic strain-rates. This determines the order of the stress singularity uniquely. The governing equations for anti-plane shear and plane strain are then derived. The numerical results for the stress and strain fields are presented for anti-plane shear and plane strain. For the present model, the results suggest that under small-scale yielding conditions, there exists a minimum velocity for stable steady crack propagation. The implication that a terminal velocity for a running crack may exist is also discussed.     

Creep crack-tip constraint effect in high temperature structures

如何对蠕变裂纹扩展寿命进行准确预测和评价是高温结构完整性评定、寿命设计和运行维护中需要解决的核心问题.基于宏观单参数C^*的蠕变断裂行为的评价方法,未有效纳入裂尖拘束效应的影响,因而其评价结果过于保守或非保守.目前国内外还未建立起有效纳入裂尖拘束效应的高温结构蠕变寿命评价的理论体系和技术方法,还没有纳入蠕变拘束效应的高温结构完整性评定规范.本文综述了作者近年来在高温蠕变断裂拘束效应方面的研究工作.主要包括：裂尖拘束对材料蠕变裂纹扩展行为的影响及机理;蠕变裂尖场和拘束参数R的定义和影响因素;载荷无关的蠕变拘束参数R^*的提出及其应用基础;承压管道表面裂纹的拘束参数R^*解及纳入裂尖拘束的蠕变寿命评价方法;试样与管道轴向裂纹蠕变裂尖拘束的关联;基于裂尖等效蠕变应变的面内与面外蠕变裂尖拘束的统一表征参数A_c的研究;材料拘束相关的蠕变裂纹扩展速率的建立;宽范围C^*区蠕变裂纹扩展速率及其拘束效应的数值预测;材料拘束对焊接接头蠕变裂纹扩展行为的影响及机理等.这些研究为建立纳入裂尖拘束效应的高温部件的蠕变裂纹扩展寿命评价方法奠定了理论和技术基础.论文对后续拟开展的工作也进行了展望.     

Effects of characteristic material lengths on mode III crack propagation in couple stress elastic–plastic materials

The asymptotic fields near the tip of a crack steadily propagating in a ductile material under Mode III loading conditions are investigated by adopting an incremental version of the indeterminate theory of couple stress plasticity displaying linear and isotropic strain hardening. The adopted constitutive model is able to account for the microstructure of the material by incorporating two distinct material characteristic lengths. It can also capture the strong size effects arising at small scales, which results from the underlying microstructures. According to the asymptotic crack tip fields for a stationary crack provided by the indeterminate theory of couple stress elasticity, the effects of microstructure mainly consist in a switch in the sign of tractions and displacement and in a substantial increase in the singularity of tractions ahead of the crack-tip, with respect to the classical solution of LEFM and EPFM. The increase in the stress singularity also occurs for small values of the strain hardening coefficient and is essentially due to the skew-symmetric stress field, since the symmetric stress field turns out to be non-singular. Moreover, the obtained results show that the ratio η introduced by Koiter has a limited effect on the strength of the stress singularity. However, it displays a strong influence on the angular distribution of the asymptotic crack tip fields.     

压电圆柱形夹杂对邻近裂纹三维应力场的影响

研究了压电复合材料薄板中压电圆柱形夹杂与邻近宏观钝裂纹间的相互作用。重点分析了外加电场，裂尖与压电圆柱形夹杂间韧带长度对裂尖三维应力场的影响。计算结果表明：在不同的外加电场作用下，压电体不仅能改变裂尖张开应力的大小，还能改变其分布。所得结果对进一步探讨线弹性介质中裂纹的启裂控制有参考价值。     

Asymptotic analysis of transient curved crack in functionally graded materials

Transient mixed-mode elastodynamic crack growth along arbitrary smoothly varying paths in functionally graded materials (FGMs) is considered. The property gradation in FGMs is considered by varying shear modulus and mass density exponentially along the gradation direction. Crack tip out of plane displacement fields and their gradients are developed for propagating curved cracks of arbitrary velocity using asymptotic approach. The mode-mixity due to the inclination of curved crack with respect to property gradient is accommodated in the analysis through superposition of the opening and shear modes. The expansion of the displacement fields and their gradients around the crack-tip are derived in powers of radial coordinates with the coefficients of expansion depending on the instantaneous value of the local curvature of the crack path, time derivatives of crack-tip speed, and time derivative of mode-I and mode-II stress intensity factors. The effect of the transient terms instantaneous local curvature, crack-tip speed, time derivatives of crack-tip speed, and time derivative of mode-I and mode-II stress intensity factors on the contours of constant out of plane displacement are also discussed.     

A coupled kinetic-constitutive approach to the study of high temperature crack initiation in single crystal nickel-base superalloys

A rate-dependent crystallographic constitutive theory coupled with a mass diffusion model has been used to study crack initiation in single crystal nickel-base superalloys, exposed to an oxidising environment and subjected to mechanical loading. The time to crack initiation under constant load has been predicted using a strain-based failure criterion. A notched compact tension (CT) specimen containing a single casting defect, idealised as a cylindrical void close to the notch surface, has been studied. Finite element analysis of the CT specimen revealed that, due to the strong localisation of inelastic strain at the void, a microcrack will initiate in the vicinity of the void rather than at the notch surface. The numerical results have also shown that the time to crack initiation depends strongly on the void location. The coupled diffusion-deformation studies have revealed that environmental effects reduce the time to crack initiation due to the oxidation-induced material softening in the vicinity of the notch and void. The applicability of a failure assessment approach, based on the linear elastic stress intensity factor, K, to predict the crack initiation time under creep loading is examined and a probabilistic framework for prediction of component lifetime is proposed.     

A boundary element modeling of fatigue crack growth in a plane elastic plate

This paper presents an extension of a boundary element method to fatigue growth analysis of mixed-mode cracked plane elastic bodies. The method consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity element due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of non-singular displacement discontinuity elements that cover the entire crack surface and the other boundaries. Crack growth is simulated with an incremental crack extension analysis based on the modified maximum strain energy density criterion. In numerical simulation, for each increment of crack extension, remeshing of existing boundaries is not required because of an intrinsic feature of the boundary element method. Crack growth is simulated by adding new boundary elements on the incremental crack extension to the previous crack boundaries. At the same time, the element characters of some related elements are adjusted according to the manner in which the boundary element method is implemented. Some numerical results of fatigue growth in a plane elastic plate with a center-inclined crack under uniaxial cyclic loading are given.     

An integral equation method in dynamic fracture mechanics

This paper contains a study of the problems of crack propagation under static stresses and under transient stress waves. Within the assumption of linear elastic fracture mechanics, an integral-equation method has been developed for the analysis of these problems. The method has been applied to: (a) the determination of the stress intensity factor at a given loading and a crack-tip velocity and (b) the determination of the crack-tip motion under a given transient loading.     

Role of inclusion stiffness and interfacial strength on dynamic matrix crack growth: An experimental study

Experimental simulations of dynamic crack growth past inclusions of two different elastic moduli, stiff (glass) and compliant (polyurethane) relative to the matrix (epoxy), are carried out in a 2D setting. Full-field surface deformations are mapped in the crack–inclusion vicinity optically. The crack growth behavior as a function of inclusion–matrix interfacial strength and the inclusion location relative to the crack is studied under stress-wave loading conditions. An ultra high-speed rotating mirror-type digital camera is used to record random speckle patterns in the crack–inclusion vicinity to quantify in-plane displacement fields. The crack-tip deformation histories from the time of impact until complete fracture are mapped and fracture parameters are extracted. The crack front is arrested by the symmetrically located compliant inclusion for about half the duration needed for complete fracture event. The dynamically propagating crack is attracted and trapped by the weakly bonded inclusion interface for both stiff and compliant symmetrically located inclusion cases, whereas it is deflected away by the strongly bonded stiff inclusion and attracted by strongly bonded compliant inclusion when located eccentrically. The crack is arrested by a strongly bonded compliant inclusion for a significant fraction of the total dynamic event and is longer than the one for the weakly bonded counterpart. The compliant inclusion cases show higher fracture toughness than the stiff inclusion cases. Measured crack-tip mode-mixities correlate well with the observed crack attraction and repulsion mechanisms. Macroscopic examination of fracture surfaces reveals much higher surface roughness and ruggedness after crack–inclusion interaction for compliant inclusion than the stiff one. Implications of these observations on the dynamic fracture behavior of micron size A-glass and polyamide (PA6) particle filled epoxy is demonstrated. Filled-epoxy with 3% V_f of PA6 filler is shown to produce the same dynamic fracture toughness enhancement as the one due to 10% V_f glass.