Dynamic interfacial debonding initiation induced by an incident crack

When a crack propagates towards a weak interface, interface debonding may occur before the incident crack reaches the interface. This phenomenon refers to the “Cook–Gordon mechanism”. In this investigation, an equivalent dynamic Cook–Gordon mechanism is studied both experimentally and analytically. Two strength-based criteria incorporating dynamic fracture mechanics analysis are proposed to predict the initiation location of interface debonding ahead of a dynamic incident crack. As validation, a comparison is made between the analytical predictions and experimental measurements. Results show that the strength-based criteria can effectively predict the initiation of interface debonding. Meanwhile, effects of the stress intensity factor and the T stress of the incident crack, on the interfacial debonding initiation are investigated. It is concluded that high-stress intensity factors of the incident cracks will easily induce interfacial debonding initiation, and changing the T stress is an effective way to control interfacial debonding initiation. Furthermore, high-interfacial tensile strengths rather than shear strengths, tend to suppress interfacial debonding initiation induced by a mode-I incident crack.     

Dynamic crack deflection and penetration at interfaces in homogeneous materials: experimental studies and model predictions

We examine the deflection/penetration behavior of dynamic mode-I cracks propagating at various speeds towards inclined weak planes/interfaces of various strengths in otherwise homogeneous isotropic plates. A dynamic wedge-loading mechanism is used to control the incoming crack speeds, and high-speed photography and dynamic photoelasticity are used to observe, in real-time, the failure mode transition mechanism at the interfaces. Simple dynamic fracture mechanics concepts used in conjunction with a postulated energy criterion are applied to examine the crack deflection/penetration behavior and, for the case of interfacial deflection, to predict the crack tip speed of the deflected crack. It is found that if the interfacial angle and strength are such as to trap an incident dynamic mode-I crack within the interface, a failure mode transition occurs. This transition is characterized by a distinct, observable and predicted speed jump as well as a dramatic crack speed increase as the crack transitions from a purely mode-I crack to an unstable mixed-mode interfacial crack.     

A general solution method for an anti-plane shear crack dynamically accelerating along a bimaterial interface

We develop a general solution method for a dynamically accelerating crack under anti-plane shear conditions along the interface between two different homogeneous isotropic elastic materials. The crack is initially at rest, and after loading is applied the crack-tip speed which may accelerate up to the shear wave speed of the more compliant material. The analysis includes an exact, closed-form expression for the stress intensity factor for an arbitrary time-dependent crack-face traction, as well as expressions for computing the crack-face displacements and the stress in front of the crack. We also present some numerical examples for fixed loads and for loads moving with the crack tip, using a stress intensity factor fracture criterion, in order to examine the predicted effect of material mismatch on interfacial fracture.     

Brittle fracture dynamics with arbitrary paths I. Kinking of a dynamic crack in general antiplane loading

We present a new method for determining the elasto-dynamic stress fields associated with the propagation of anti-plane kinked or branched cracks. Our approach allows the exact calculation of the corresponding dynamic stress intensity factors. The latter are very important quantities in dynamic brittle fracture mechanics, since they determine the crack path and eventual branching instabilities. As a first illustration, we consider a semi-infinite anti-plane straight crack, initially propagating at a given time-dependent velocity, that changes instantaneously both its direction and its speed of propagation. We will give the explicit dependence of the stress intensity factor just after kinking as a function of the stress intensity factor just before kinking, the kinking angle and the instantaneous velocity of the crack tip.     

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.     

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.     

ANALYSIS OF A CRACK IN A FUNCTIONALLY GRADED STRIP WITH A POWER FORM SHEAR MODULUS

The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy＇s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line.     

New stress intensity factor solutions of a periodic array of cracks in residual stress field

Many important applications of crack mechanics involve self-equilibrating residual or thermal stress fields. For these types of problems, the traditional fracture mechanics approach based on the superposition principle has ignored the effect of crack surface contact when the crack-tip propagates into the residual compressive region. Contact between the crack faces and the wedging action are responsible for subsequent crack-tip reopening, which often leads to a much larger mode I stress intensity factor. In this study, an analytical approach is used to study the effect of crack face contact for a period array of collinear cracks embedded in several typical residual stress fields. It is found that the nonlinear contact between crack surfaces dominates the cracking behavior in residual/thermal stress fields, which is responsible for crack coalescence.     

Intersonic crack propagation along interfaces: Experimental observations and analysis

The isochromatic fringe patterns surrounding an intersonically propagating interface crack are developed and characterized using the recently developed stress field equations. A parametric investigation is conducted to study the influence of various parameters such as the crack-tip velocity and the contact coefficient on the isochromatic fringe patterns. It has been observed that the crack-tip velocity has a significant effect on the size and shape of isochromatic fringe patterns. The contact coefficient, on the other hand, does not affect the fringe pattern significantly. The paper also presents a numerical scheme to extract various parameters of interest such as the series coefficients of the stress field, the contact coefficient and the dissipation energy. The results show that the crack growth is highly unstable in the intersonic regime, and the energy dissipation decreases monotonically with increasing crack-tip velocity. The experimental data fit well with the recently proposed fracture criterion for intersonic interfacial fracture.     

数字梯度敏感方法及其在航空透明件断裂力学中的应用

本文将数字梯度敏感方法用于航空透明件断裂力学问题研究。首先,基于透明材料的弹性-光学效应,建立了透明件应力状态与光线穿过透明件后的偏转角之间的关系。在平面应力假设下,利用最小二乘拟合建立了I型裂纹尖端应力强度因子与光学偏转角的关系。其次,通过数字梯度敏感方法搭建非接触光学测试平台,开展了带单边裂纹的航空有机玻璃试件三点弯曲实验,应用数字梯度敏感方法提取了I型裂纹尖端应力强度因子。最后,通过选择不同计算子区域和步长大小,分析了数字梯度敏感方法中的子区域和步长选择对计算结果的影响。研究结果表明,数字梯度敏感方法实验所得应力强度因子与经验公式计算所得结果偏差小于10%,通过增加最小二乘拟合项数以及合理的子区域和步长选择可以减小数字梯度敏感方法计算应力强度因子误差。     

U形切口的有限断裂准则

有限断裂力学准则综合了应力和能量参数,假设裂纹或切口端部有限裂纹长度的增长．特别地,该有限裂纹的长度不是材料的基本常数,而是与构件的结构有关．基于U形切口两种形式：点方式和线方式有限断裂准则,对文献中的铝合金U形切口三点弯曲断裂实验进行了分析验证．一方面基于材料的断裂韧度和抗拉强度,预测切口件断裂载荷;另一方面根据几组不同的切口根部半径及其对应的临界切口应力强度因子,同时估算材料的断裂参数：断裂韧度和抗拉强度．将点方式和线方式两种不同形式有限断裂准则的预测结果,与平均周向应力准则、最大周向应力准则以及文献中相关结果进行了比较得出：无论是预测断裂载荷还是估算材料断裂参数,线方式有限断裂准则,与文献中相关结果比较吻合,尤其是估算的断裂韧度精度较高．     

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.     

含预制裂纹L形梁柱试件动态断裂过程

针对含预制裂纹L形梁柱试件,为研究预制裂纹动态扩展的力学特征及其对梁柱试件破坏模式的影响,采用数字动态焦散线实验系统,对距节点核心区不同距离l处含有预制裂纹的试件进行落锤冲击实验,得到预制裂纹的扩展轨迹、速度、动态应力强度因子的变化规律。结果表明,l值增大,扩展裂纹在梁下边缘的贯通点与预制裂纹的夹角逐渐增大,曲裂程度变大。裂纹扩展速度随着l的增大振荡性增强,裂纹扩展平均速度逐渐降低。l值为2 mm时,裂尖表现为Ⅰ型断裂,l值增大,裂尖受到剪应力作用增强,Ⅰ型动态应力强度因子减小,Ⅱ型动态应力强度因子增大,断裂逐渐转变为Ⅰ-Ⅱ复合型。     

断裂力学判据的评述

从Inglis 和Griffith 的著名论文到Irwin 和Rice 等的奠基性贡献,对断裂力学中的线弹性断裂力学的K判据,界面断裂力学的G判据,和弹塑性断裂力学的J 判据作了扼要的综述. 介绍了在界面断裂力学G判据的基础上提出的界面断裂力学的K判据,以说明断裂力学的判据存在改进的可能性. 在综述中归纳出断裂力学判据中目前还没有较好解决的几个问题. 在总结以往断裂力学研究经验的基础上,指出裂纹端应力奇异性的源是对断裂力学判据存在的问题作进一步研究的切入点. 探讨了裂纹端应变间断的奇点是裂纹端应力奇异性的源的问题,从而对裂纹端应力强度因子的物理意义进行了讨论. 最后,阐述了进行可靠的裂纹端应力场的弹塑性分析是改进弹塑性断裂力学判据的关键,而进行可靠的裂纹端应力场的弹塑性分析的前提是要通过裂纹端应力奇异性的源的研究来获得作用在裂纹端的造成裂纹端应变间断的有限值应力.      

Dynamic stress intensity factor of a crack perpendicular to the weak-discontinuous interface in a nonhomogeneous coating–substrate structure

A mechanical model was established for the antiplane dynamic fracture problem of a functionally graded coating–substrate structure with a coating crack perpendicular to the weak-discontinuous interface. The problem was reduced to a Cauchy singular integral equation by the methods of Laplace and Fourier integral transforms. Erdogan’s collocation method and the Laplace numerical inversion proposed by Miller and Guy were used to calculate the dynamic stress intensity factors. Three conclusions were drawn through parametric studies: (a) unlike the conclusion drawn for an interfacial crack, reducing the weak discontinuity of the interface will not necessarily decrease the dynamic stress intensity factor (DSIF) of the coating crack perpendicular to the interface; (b) increasing the stiffness of the substrate when that of the coating is fixed, or decreasing the stiffness of coating when that of the substrate is fixed, will be beneficial for the reduction of the DSIF of a coating crack perpendicular to the interface; and (c) the free surface has a greater influence on the DSIF than the interface does, and the effect of the interface on the DSIF is greater than that of the material stiffness in the crack-tip region.     

Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts

Using the integral transform and the Cauchy singular integral equation methods, the problem of an interface crack between two dissimilar piezoelectric layers under mechanical impacts is investigated under the permeable electrical boundary condition on the crack surface. The dynamic stress intensity factors (DSIFs) of both mode-I and II are determined. The effects of the crack configuration and the combinations of the constitutive parameters of the piezoelectric materials on the dynamic response are examined. The numerical calculation of the mode-I plane problem indicates that the DSIFs may be retarded or accelerated by specifying different combinations of material parameters. In addition, the parameters of the crack configuration, including the ratio of the crack length to the layer width and the ratio between the widths of two layers, exert a considerable influence on the DSIFs. The results seem useful for design of the piezoelectric structures and devices of high performance.     

Comparison of finite element techniques for 2D and 3D crack analysis under impact loading

For several technical applications the dynamic aspect in fracture mechanics cannot be neglected. When the reliability of components with macroscopic cracks has to be assessed, the consideration of dynamic effects may lead to much higher stress intensity factors than under static conditions. In this paper three different methods to calculate the dynamic stress intensity factor for the mode-I loading of stationary cracks are compared. Based on two- and three-dimensional finite element simulations, the dynamic stress intensity factor is computed with the dynamic J-integral, the modified crack closure integral and the displacement interpretation method. The theoretical fundamentals of all three methods are summarized in the paper and the numerical implementation is explained briefly. Results for different models are shown and compared to findings in the literature.     

脆性断裂的非局部力学理论

本文提出一种脆性材料断裂的非局部力学理论,内容包括:Ⅰ、Ⅱ、Ⅲ型Griffith裂纹的非局部弹性应力场,裂纹尖端邻域非局部弹性应力场的渐近形式,脆性开裂的最大拉应力准则。文中给出了这种理论应用于三种基本型裂纹和Ⅰ-Ⅱ、Ⅰ-Ⅲ复合型裂纹临界开裂条件的计算结果,并把它们与一些试验资料和最小应变能密度因子理论进行了对比。     

Transient response of an insulating crack between dissimilar piezoelectric layers under mechanical and electrical impacts

Summary  The dynamic response of an interface crack between two dissimilar piezoelectric layers subjected to mechanical and electrical impacts is investigated under the boundary condition of electrical insulation on the crack surface by using the integral transform and the Cauchy singular integral equation methods. The dynamic stress intensity factors, the dynamic electrical displacement intensity factor, and the dynamic energy release rate (DERR) are determined. The numerical calculation of the mode-I plane problem indicates that the DERR is more liable to be the token of the crack growth when an electrical load is applied. The dynamic response shows a significant dependence on the loading mode, the material combination parameters as well as the crack configuration. Under a given loading mode and a specified crack configuration, the DERR of an interface crack between piezoelectric media may be decreased or increased by adjusting the material combination parameters. It is also found that the intrinsic mechanical-electrical coupling plays a more significant role in the dynamic fracture response of in-plane problems than that in anti-plane problems. Received 4 September 2001; accepted for publication 23 July 2002 The work was supported by the National Natural Science Foundation under Grant Number 19891180, the Fundamental Research Foundation of Tsinghua University, and the Education Ministry of China.     

Fracture mechanics and crack contact analyses of the active repair of multi-layered piezoelectric patches bonded on cracked structures

In this paper, two-dimensional plane strain finite element analyses of the active repair for cracked structures by using multi-layered piezoelectric patches have been studied. The reductions of stress intensity factors and strain energy density factor at the crack tips are obtained. Also, the repair voltages for various conditions are obtained for estimating the repair performances. Lower repair voltage is a better choice because it is low-energy-consuming and safer for the operation. From the results of numerical fracture mechanics, it shows the crack contact conditions must be considered in the analysis. However, the friction on the crack has few effects on the repair performances for this mode-I dominated case. The better design choices for the piezoelectric patch are as follows: increasing the layer number, increasing the patch length, and reducing the patch thickness. In additions, it is not a good idea to use higher input voltage that is larger than the repair voltage because it will enlarge the crack open near the crack tip. Too long patch length has no advantage for the active repair.