基于有限变形理论的能量释放率和J积分增率形式

上海大学学报(自然科学版) ›› 2011, Vol. 17 ›› Issue (2): 153-157.

基于有限变形理论的能量释放率和J积分增率形式

宋彦琦1,吕艳伟2

1.中国矿业大学（北京）理学院，北京 100083； 2.普利茅斯大学科技学院，英国 PL4 8AA

收稿日期:2010-03-02 出版日期:2011-04-30 发布日期:2011-04-30
基金资助:
国家重点基础研究发展计划（973计划）资助项目（2007CB209402，2010CB732002）；国家自然科学基金资助项目（10302030）；中央高校基本科研业务费资助项目（2009QS01）

Forms of Energy Release Rate and J Internal Increase Rate Based on Finite Deformation Theory

SONG Yan-Qi-1, LV Yan-Wei-2

1. School of Science, China University of Mining and Technology（Beijing）, Beijing 100083, China; 2. Faculty of Science and Technology, University of Plymouth, PL4 8AA, UK

Received:2010-03-02 Online:2011-04-30 Published:2011-04-30

摘要/Abstract

摘要：

以有裂纹的瞬时位形为参考，建立的增量变形引起的裂纹扩展方程能够更真实地描述裂纹尖端的扩展机制.而真实地描述当前裂纹状态下的增量变形的困难在于，带裂纹尖端的瞬时位形相对于初始位形应满足有关的力学平衡方程.在解决裂纹扩展问题时，基于能量方法的裂纹能量释放率G和J积分是一种有效的研究方法.由于经典的微小变形理论引入的裂纹尖端模型解决问题的方法是相对于初始位形的，为得到当前裂纹状态下的增量变形的有关方程，采用能量原理和变分原理，使用有限变形的随体张量表达方式，在瞬时位形基础上，推导裂纹体的能量释放率G和J积分的增率?和?，建立增量变形的有关方程，从而为研究裂纹尖端的扩展问题提供了新的理论思路.

关键词: 增量变形；有限变形；能量释放率；J积分；增率形式

Abstract:

To study the crack propagation problem, a model in terms of incremental deformation represents the real propagation mechanism by taking instantaneous configuration as a reference. It requires an accurate definition of incremental deformation on a fresh crack. However, it is difficult to make the instantaneous configuration including zones around the crack tip satisfy the relevant equilibrium equations with regards to the initial configuration. Generally, energy methods such as crack tip energy release rate G and J-integral are powerful in analyzing and solving crack problems. Therefore the focus is on the determination of the form of the increase rate of energy release rate, ?, and that of J-integral, ?, regarding instantaneous configuration. Because the classical theory of small deformation takes initial configuration as a reference, the formulae for ? and ? are derived by using the energy principle and variational principle in the finite deformation theory in the present study. This work provides a new theoretical line for studying crack propagation.

Key words: incremental deformation； finite deformation； energy release rate; J-integral; increase rate form

中图分类号:

O 331

宋彦琦1,吕艳伟2. 基于有限变形理论的能量释放率和J积分增率形式[J]. 上海大学学报(自然科学版), 2011, 17(2): 153-157.

SONG Yan-Qi-1, LV Yan-Wei-2. Forms of Energy Release Rate and J Internal Increase Rate Based on Finite Deformation Theory[J]. Journal of Shanghai University（Natural Science Edition）, 2011, 17(2): 153-157.