J<sub>k</sub>-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects

李群; 王芳文

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J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects

更新时间：2025-12-08

- J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects
- Vol. 42, Issue 1, Pages: 60-64(2008)
- 作者机构：
  
  西安交通大学航天航空学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： O346.1
- Online First：10 January 2008，
  
  Published：2008
- 稿件说明：
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李群, 王芳文. J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects[J]. 2008, 42(1): 60-64.
DOI：

李群, 王芳文. J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects[J]. 2008, 42(1): 60-64. DOI：

摘要

对于含裂纹、孔洞、夹杂等各种微缺陷的平面各向异性复合材料

通过Bueckner功共轭积分的路径无关性和渐进特性

给出了Bueckner积分在这类材料中的解析表达式

并引入不同的辅助位移应力场

证明了功共轭积分与J

积分和M积分存在简单的2倍关系

由此获得了含微缺陷各向异性材料中J

积分和M积分的显式表达式.结果表明:当各个缺陷上不受任何外力作用时

对于沿包含所有微缺陷的闭合积分路径

积分总是为0

而M积分则取决于材料常数、外加机械载荷、具体缺陷情况等所有断裂损伤因素.此项研究有望为描述微缺陷损伤的M积分方法提供理论基础.

Abstract

Anisotropic composite materials with multiple defects are investigated

where a number of arbitrarily distributed defects

such as cracks

voids and inclusions are involved. The explicit expression of the Bueckner work conjugate integral is derived following the path-independence and the asymptotic features of the Bueckner integral. It is concluded that the value of the Bueckner integral is twice of that of the J

-integral or the M-integral when the real physical field and the special complementary field are chosen to establish the Bueckner integral. The J

- and M-integrals are obtained in the explicit forms due to the universal relations between the Bueckner integrals and the above invariant integrals

especially

both components of

the J

-integral vanish along the integral contour enclosing all the defects without the resultant force on each defect. However

the M-integral is significantly influenced by all the mechanical levels in multi-defect damaged anisotropic composite materials

e.g. the material properties

the remote loading condition

and the damaged factors

etc. The M-integral is expected to serve as a description of the fracture behavior of a multi-defect mechanical system in anisotropic materials.

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Keywords

references

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陈宜亨,师俊平. 论M积分和Bueckner功共轭积分之间的关系[J]. 力学学报,1998,30(4):495-502.

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Jk-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects

DOI：

摘要

Abstract

关键词

Keywords

references

J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects