含微缺陷各向异性复合材料中的J<sub>k</sub>积分和M积分

李群; 王芳文

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含微缺陷各向异性复合材料中的J_k积分和M积分

专题研究 | 更新时间：2025-12-08

- 含微缺陷各向异性复合材料中的J_k积分和M积分
- J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects
- 西安交通大学学报 2008年42卷第1期页码：60-64
- 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：
  
  : 2007-05-13. 作者简介: 李群(1980-),男,博士生;王芳文(联系人),男,副教授. 基金项目: 国家自然科学基金资助项目(10572110)
- DOI：
  中图分类号： O346.1
- 网络首发：2008-01-10，
  
  纸质出版：2008
- 稿件说明：
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李群, 王芳文. 含微缺陷各向异性复合材料中的J_k积分和M积分[J]. 西安交通大学学报, 2008,42(1):60-64.

李群, 王芳文. J_k-Integral and M-Integral in Anisotropic Composite Materials Containing Multiple Defects[J]. 2008, 42(1): 60-64.
李群, 王芳文. 含微缺陷各向异性复合材料中的J_k积分和M积分[J]. 西安交通大学学报, 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.

关键词

Keywords

references

RICE J R. A path-independent integral and the approximation analysis of strain concentration by notches and cracks [J]. ASME J Appl Mech, 1968, 35(2): 297-320.

KNOWLES J K, STERMBERG E. On a class of conservation laws in linearized and finite electrostatics [J]. Arch Ration Mech Anal, 1972, 44(3):187-211.

BUDIANSKY B, RICE J R. Conservation laws and energy release rates [J]ASME J Appl Mech, 1973,40(1): 201-203.

HERRMANN G A, HERRMANN G. On energy release rates for a plane cracks [J]. ASME J Appl Mech, 1981,48(3): 525-530.

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.

CHEN Yiheng, SHI Junping. On the relation between the 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.

CHEN Yiheng, SHI Junping. On the relation between the tegral and the Bueckner work conjugate integral [J]. Acta Mechanica Sinica, 1998, 30(4):495-502.

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BUECKNER H F. Singularities and related integral expressions [M]∥Sih G C. Mechanics of Fracture: I. Leyden: Noordhoff International Pub., 1973: 239-314.

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CHEN Y H, HASEBE N. A consistency check for strongly interacting multiple crack problems in isotropic, bimaterial and orthotropic bodies [J]. Int J Fract, 1998, 89(4): 333-353.

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含微缺陷各向异性复合材料中的Jk积分和M积分

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

DOI：

摘要

Abstract

关键词

Keywords

references

含微缺陷各向异性复合材料中的J_k积分和M积分

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