层状弹性材料界面J积分的产生和特征

陈昌荣

doi:10.21656/1000-0887.370270

层状弹性材料界面J积分的产生和特征

doi: 10.21656/1000-0887.370270

陈昌荣

上海工程技术大学飞行学院, 上海 201620

基金项目: 国家自然科学基金（51175321）

详细信息

作者简介:
陈昌荣（1964—），男，教授，博士（E-mail: 13761742152@163.com）.

中图分类号: O343
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- 被引次数: 0
出版历程
- 收稿日期: 2016-09-05
- 修回日期: 2016-12-21
- 刊出日期: 2017-10-15

Characteristics and Generation of Interface J integrals in Layered Elastic Materials

CHEN Chang-rong

School of Flight Technology, Shanghai University of Engineering Science, Shanghai 201620, P.R.China

Funds: The National Natural Science Foundation of China（51175321）

摘要

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.
- J积分 /
- 界面 /
- 层状弹性材料 /
- 材料非均匀性
Abstract: 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: J_Г=J_tip+J_int, where J_tip means the J integral generated by the crack tip, and J_int 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, J_Г loses the path-independent 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.
- J integral /
- interface /
- layered elastic material /
- material inhomogeneity

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