J积分在分层非均匀介质裂纹问题中的应用

本文对分层非均匀介质裂纹问题的J积分进行了研究,旨在把J积分方法用于焊接接头或分层复合材料的断裂分析。利用弹塑性有限元和本文给出的分层介质J的数值计算方法,在各种载荷水平下对含有软夹层的非均质中心裂纹板的J值进行了计算。软夹层中的裂纹平行于或垂直于夹层与基体的分界,分别按Rice的J积分定义和本文的适用于一般多层介质裂纹问题的J的修正定义进行分析计算。考察了软夹层相对宽度对J积分值的影响。     

脆性材料的扩展裂纹前缘形态与三维J积分

本文利用超声波断口图技术对不同类型的PMMA试件进行了测试。这些试件为承受均匀拉伸或三点弯曲变形的带单侧贯穿裂纹的PMMA板，其中拉伸试件又分为光面和带表面沟槽的两种。得到了这些试件断口上的超声波线。发现它们为平面线．其凸凹方向与试件的表面状态有关。基于有限元法，计算了试件的三维J积分，考察了杨氏模量和泊松比对其的影响．结果发现泊松比影响J积分曲线形状，而杨氏模量只影响其绝对数值，不影响其曲线形状。得到的试件在不同裂纹长度下的三维J积分与它们断口图上的超声波线的形状和凸凹方向相似。说明在脆性材料中，扩展裂纹前缘曲线形态是三维J积分的作用的结果。     

试谈J积分

自Rice于1968年给出形如:(式中,W为应变能密度;T_i,u_i为dS上的作用力矢和位移矢的积分以后至今,J积分这一名词便为整个断裂力学界所共知。J积分有许多特殊的性质,人们从各个方面对其进行了深入而广泛的研究,使J积分无论从理论和实验验证乃至实际应用上都得到了空前发展。但由于这一理论的...     

求解I型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量. 目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务. 以J积分为参量的材料断裂测试中应用最广的是I型裂纹试样的断裂韧性测试. 本文在平面应变条件下,针对断裂韧性测试中使用的6种I型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数. 分析表明,6种I型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好. 新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值. 应用新方法可便于获得各类I型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.      

求解Ⅰ型裂纹构元J积分的半解析方法

表征裂纹尖端应力应变场程度的J积分是一个定义明确、理论严密的弹塑性断裂力学基础参量.目前J积分的计算主要是依靠塑性因子法和有限元法,但对各类裂纹构元获得J积分以及载荷-位移关系的解析公式以实现材料断裂韧性理论预测和材料测试是断裂力学的重要和困难的任务.以J积分为参量的材料断裂测试中应用最广的是Ⅰ型裂纹试样的断裂韧性测试.本文在平面应变条件下,针对断裂韧性测试中使用的6种Ⅰ型裂纹构元,基于能量等效假设,提出了J积分-载荷和载荷-位移的工程半解析统一表征方法,进而结合有限元分析的少量计算获得J积分-载荷和载荷-位移关系的半解析公式待定参数.分析表明,6种Ⅰ型裂纹构元的J积分-载荷和载荷-位移统一公式的预测结果与有限元结果吻合良好.新提出的J积分-载荷工程半解析公式包含了材料的弹性模量、应力强度系数和应变硬化指数,能够广泛适应不同的材料,且运用该公式能够方便获取任意载荷点对应的J积分值.应用新方法可便于获得各类Ⅰ型裂纹构元的J积分-载荷和载荷-位移工程半解析公式.     

周边切口短圆柱试件的杆杆型冲击拉伸试验系统的弹塑性有限元分析

基于一维试验原理提出了用带有周边切口的短金属圆柱试件进行平面应变型弹塑性动态断裂韧度的测试方法；对该复杂的动力学系统进行了轴对称的弹塑性有限元分析，并计算了动态围道^J积分；根据对试件功能转换关系的分析和Rice公式的物理意义，提出了用试件两端平功载荷－两端相对位移曲线（P^-△）推广Rice公式计算试件的远场J积分，由此得到的P^-△曲线基本上消除了与裂纹运动无关的质心运动动能的影响。论证了J积分作为裂端的表征参量，且当切口深度比大于70％时，Rice公式有较高的计算精度，为平面应变型弹塑性动态断裂韧度的表征与测试提供了依据。     

三维动态裂纹问题的超奇异积分方程法

基于弹性材料的动态基本方程,结合广义Betti-Rayleigh互易等式与时域下的边界积分方程,推导得到时域下的超奇异积分方程组。引入Laplace域下的动态基本解,将经过主部分析的积分核函数分解为静态和动态部分,其中动态积分核不具有奇异性。在裂纹前沿附近单元,采用与理论分析一致的平方根位移模型。结合Lubich时间卷积实现拉氏变换,采用配置点法计算超奇异积分,获得问题的数值解。并针对椭圆裂纹算例编写Fortran程序,得到冲击荷载作用下张开型裂纹的动态应力强度因子变化规律,数值结果稳定且收敛速度快。     

用三维有限元模型计算复合材料粘接修补裂纹板的J积分

用复合材料单边粘接修补带裂纹金属板是三维应力问题,而采用简化的二维有限元分析模型计算则有一定近似性。本文建立了三维有限元模型,并计算了其断裂参数J积分。计算分析结果表明,厚度方向上J积分值是变化的,并且修补边比未修补边的J积分值有明显减小;修补前后裂纹面的张开位移明显不同;裂纹板模型的J积分值与裂纹长度在修补前为二次关系,修补后,变成线性关系;粘胶和补片的厚度、粘胶的模量对J积分的影响比较显著。为了提高修补性能,需要对粘胶和补片的几何尺寸和材料性能进行优化。     

杆式冲击装置测定材料动态J积分

本文介绍了一种研究材料动态断裂韧度的实验技术。该方法采用冲击杆对常规三点弯曲试件进行动态加载。由于长杆条件下存在荷载、位移及冲击速度之间的定量关系,试验中只需对荷载的时间历程进行测定,就能间接地计算出位移和J积分值。与目前广泛使用的示波摆锤(落锤)冲击法相比,不仅测试过程明显简化,而且力学分析的基础也更为可靠。     

J积分的三维理论及其在线性断裂力学中的初步应用

根据Eshelby积分的守恒性,把二维问题里Rice定义的J积分推广到三维问题。定义了三维问题的J积分,叙述并证明其主要性质和在线性断裂力学三维问题中的初步应用。     

OnJ-integrals in the plane fracture of composite materials

By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of J-integral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.     

ON J-INTEGRALS IN THE PLANE FRACTURE OF COMPOSITE MATERIALS

By using a complex function method in this paper, the complex form of J-integral of mixed mode crack tip for unidirectional plate of linear-elastic orthotropic composites is obtained first by substituting crack tip stresses and displacements into general formula of Jintegral. And then, the path-independence of this J-integral is proved. Finally, the computing formula of this J-integral is derived. As special examples, the complex forms, path-independence and computing formulae of J-integrals of mode Ⅰ and mode Ⅱ crack tips for unidirectional plate of linear-elastic orthotropic composites are given.     

Method to evaluate the invariant J-integral in finite-element models of prismatic bodies

A new method to evaluate the J-integral in finite-element models is developed and implemented. It is shown that in contrast to well-known approaches, this method ensures the invariance of the J-integral in finite-element solution of linear and nonlinear problems Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 70–82, December 2008.     

A conservative integral independent of the constitutive relation

J-integral defined by Rice depends on the constitutive relation of mediums. In the present paper, a conservative integral independent of the constitutive relation of mediums is defined in order to extend Rice’s definition of the J-integral which depends on the constitutive relation. Its main properties which are similar to those of the prevailing J-integral are proved. In the case of the elastic mediums, the extensive conservative integral is the same with Rice’s J-integral.     

A NEW CYCLIC J-INTEGRAL FOR LOW-CYCLE FATIGUE CRACK GROWTH

The constitutive equation under the low-cycle fatigue (LCF) was discussed, and a two-dimensional (2-D) model for simulating fatigue crack extension was put forward in order to propose a new cyclic J-integral. The definition, primary characteristics, physical interpretations and numerical evaluation of the new parameter were investigated in detail. Moreover, the new cyclic J-integral for LCF behaviors was validated by the compact tension (CT) specimens. Results show that the calculated values of the new parameter can correlate well with LCF crack growth rate, during constant-amplitude loading. In addition, the phenomenon of fatigue retardation was explained through the viewpoint of energy based on the concept of the new parameter.     

The derivation of J-integral conservation law from the principle of virtual work

The general form of J-integral conservation law in three di-mensions has been derived from the principle of virtual work.The necessary conditions for J-integral conservation are alsogiven.     

On J-integrals near models I,II crack tips in the plate of orthotropic composite material

In this paper, we prove the independence of the path of the J-integrals near models I, II crack tips in the plate of the orthotropic composite material. Then we derive the computing formulae of the J-integrals in the cases of <0and >0 by using a complex variable method and reducing J-integrals to complex form. The J-integral computational formulae derived in this paper have certain reference value for the theoretical researches and the experimental verifications in the plane fracture for composite material.Here the authors are particularly indebted to professor Li Hao of Huazhong university of science and technology who has gone over this paper.     

An extension of the J-integral to piezoelectric materials

This paper provides an analysis of the crack propagation criterion for a thin piezoelectric plate with a symmetry of order six. On the basis of Gol’denveizer’s asymptotic integration method or Destuynder’s unidirectional zoom technique, we obtain an extension of the purely mechanical J-integral to piezoelectric materials, with a dependence of the gradient of energy of the plate only on zeroth order terms of asymptotic expansions.