求解Ⅰ型裂纹构元J积分的半解析方法  

A SEMI ANALYTICAL METHOD TO SOLVE J-INTEGRAL FOR MODE-Ⅰ CRACK COMPONENTS

作　　者：贺屹 蔡力勋 陈辉 彭云强 He Yi;Cai Lixun;Chen Hui;Peng Yunqiang(Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province,School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学力学与工程学院应用力学与结构安全四川省重点实验室,成都610031

出　　处：《力学学报》2018年第3期579-588,共10页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金资助项目(11472228).

摘　　要：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.The J-integral to characterize the singular level of the stress and strain field at the crack tip is definite and rigorous and is a basic parameter of elastoplastic fracture mechanics. The calculation of J-integral mainly depends on the plastic factor method and the finite element method at present. For theoretical predicting and testing of material fracture toughness, it is important and dicult to obtain analytical expressions about J-integral-load and load-displacement relations of cracked components. The most widely used test for structure integrity evaluation with J-integral is the ductile fracture toughness of type-I cracked specimens. Here, based on the Chen-Cai energy equivalence hypothesis, a unified characterization method of J-integral-load and load-displacement relation is proposed for six Mode-I cracked components which are commonly used in fracture toughness test under the plane strain condition. Then, the undetermined parameters of the engineering semi-analytical formulas of the J-integral-load and the load-displacement relations are obtained by a small amount of finite element analysis. The results show that the J-integral-load and load-displacement relation predicted by the unified semi-analytical formulas are in good agreement with those from finite element method. The engineering semi-analytical J-integral-load formula, which contains the elastic modulus, stress strength coecient and strain hardening exponent of materials, can be widely adapted for diff erent materials. And the J-integral value corresponding to arbitrary load points can be easily obtained by the formula. The presented novel method is convenient to establish the engineering semi-analytical formulas of J-integral-load and load-displacement relations for various type-I cracked components or specimens.

关 键 词：J积分 塑性断裂 半解析公式 能量等效假设 I型裂纹 

分 类 号：O346.1[理学—固体力学]