摘要
层状弹性材料的裂纹方向垂直于界面时,沿围绕裂尖的任意一条封闭路径Γ的J积分(J_Г)由两部分组成,J_Г=J_(tip)+J_(int),这里J_(tip)表示裂尖产生的J积分,J_(int)表示Γ所包围的界面产生的J积分.裂尖产生的J积分不随Γ变化,物理含义是裂纹扩展能量释放率;界面产生的J积分随Γ变化,物理含义与裂纹扩展能量释放率无关.界面J积分的产生使J_Г失去了路径无关特性,也失去了实际物理意义.为了有助于理解非均匀材料J积分的含义和局限性,分析了层状弹性材料界面J积分的产生原因和特点.由不同均匀弹性材料组成的层状材料中,应变能密度的跳跃是界面J积分产生的原因,而弹性模量和残余应力在界面处的跳跃可使应变能密度在界面处产生跳跃.层状弹性材料的界面J积分之间具有相互抵消的作用.
When a crack in a layered elastic material is perpendicular to the interface,the J-integral along path Г surrounding the crack tip can be separated into 2 parts： JГ = Jtip ＋ Jint,where Jtip means the J-integral generated by the crack tip,and Jint the J-integral generated by the interface enclosed by Г. The J-integral generated by the crack tip is path-independent,and its physical meaning is the energy release rate of crack growth; the J-integral generated by the interface is path-dependent,and has no relation to the energy release rate of crack growth. Due to the existence of the interface J-integral,JГ loses the pathindependent property and has no real physical meaning. To better understand the physical meaning and limitations of the J-integrals in inhomogeneous materials,the generation and characteristics of the interface J-integrals in layered elastic materials were analyzed. The results show that,for a layered elastic material composed of different homogeneous materials,the interface J-integrals are generated by the jumps of the strain energy density at the interfaces,and the jumps of the residual stresses and Young＇s moduli at the interfaces would result in the jump of the elastic strain energy density. Moreover,offset effects exist between interface J-integrals.
作者
陈昌荣
CHEN Chang-rong(School of Flight Technology, Shanghai University of Engineering Science, Shanghai 201520, P.R.China)
出处
《应用数学和力学》
CSCD
北大核心
2017年第10期1155-1165,共11页
Applied Mathematics and Mechanics
基金
国家自然科学基金(51175321)~~
关键词
J积分
界面
层状弹性材料
材料非均匀性
J-integral
interface
layered elastic material
material inhomogeneity
