M积分与夹杂/缺陷弹性模量的显式关系

于宁宇; 李群

doi:10.6052/0459-1879-13-097

M积分与夹杂/缺陷弹性模量的显式关系

doi: 10.6052/0459-1879-13-097

于宁宇,
李群

西安交通大学航天航空学院机械结构强度与振动国家重点实验室, 西安710049

基金项目: 国家自然科学基金青年项目（11202156）；国家自然科学基金重点项目（10932007）和国家自然科学基金创新团体（11021202）资助项目.

详细信息

作者简介:
李群，副教授，主要研究方向：断裂与损伤力学.E-mail：qunli@mail.xjtu.edu.cn

中图分类号: O346
计量
- 文章访问数: 1060
- HTML全文浏览量: 24
- PDF下载量: 900
- 被引次数: 0
出版历程
- 收稿日期: 2013-04-01
- 修回日期: 2013-05-28
- 刊出日期: 2014-01-18

THE EXPLICIT RELATION BETWEEN THE M-INTEGRAL AND THE ELASTIC MODULI OF INCLUSION/DAMAGES

Yu Ningyu,
Li Qun

State Key Laboratory for Strength and Vibration of Mechanical Structures, School of Aerospace, Xi'an Jiaotong University, Xi'an 710049, China

Funds: The project was supported by the National Natural Science Foundation of China (11202156, 10932007, 11021202).

摘要

摘要: M积分在材料构型力学中表征着缺陷自相似扩展的能量释放率，而有效弹性模量下降量在传统损伤力学中是一个具有内变量属性的损伤参数. 探讨了两者之间的特定关系，以此为材料构型力学与损伤力学搭建桥梁.借助穆斯海里什维利（Muskhelishvili）复势函数方法获取无限大弹性平面含圆形夹杂的弹性场解，根据M 积分的复势函数解析表达式得到M 积分与夹杂弹性模量的显式表达式. 随后通过有限元分析，对含复杂缺陷群的弹塑性材料进行数值模拟，结果表明内部缺陷区域的有效弹性模量下降与M 积分存在着特定关系. 基于此，提出利用材料构型力学中的外变量参数（M 积分）来替代损伤力学中的内变量参数（弹性模量下降量）描述材料的缺陷演化.
- M积分 /
- 损伤力学 /
- 复杂缺陷 /
- 有效弹性模量
Abstract: The M-integral represents the energy release rate due to the self-similar expansion of defects in material configurational mechanics while the reduction of effective elastic moduli is an inner damage parameter in traditional damage mechanics. This study will focus on the inherent relation between them in order to build the bridge of material configurational mechanics and damage mechanics. The explicit expression of M-integral is derived by using Muskhelishvili complex potential for the infinite plane with a circle inclusion. And the explicit expression of M-integral reveals the explicit relation between M-integral and the elastic moduli of the inclusion. A finite element method analysis is then performed to simulate the complex defects embedded in an elastic-plastic plane. The results reveal the inherent relation between the reduction of the effective elastic moduli for damaged area and the M-integral. In conclusion, the M-integral as an outer variable is believed to be capable of replacing the inner variable (reduction of the effective moduli) to describe the defects evolution in damaged material.
- M-integral /
- damage /
- mechanics /
- complex

HTML全文

参考文献(20)

Chen YZ. A technique for evaluating the stress intensity factors by means of the M-integral. Engineering Fracture Mechanics, 1986, 23: 777-780

Choi NY, Earmme YY. Evaluation of stress intensity factors in circular arc-shaped interfacial crack using L integral. Mechanics of Materials, 1992, 14: 141-153

Chen YZ, Lee KY. Analysis of the M-integral in plane elasticity. Journal of Applied Mechanics, 2004, 71: 572-574

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. 西安交通大学学报, 2008, 42(1): 60-64 (Li Qun, Wang Fangwen. J_k-integral and M-integral in anisotropic composite material containing multiple defects. Journal of Xi'an Jiaotong University, 2008, 42(1): 60-64 (in Chinese))

郭树祥, 许希武. 任意多椭圆孔多裂纹无限大板的应力强度因子与M积分. 固体力学学报, 2006, 27(1): 7-14 (Guo Shuxiang, Xu Xiwu. The SIFS and M-integral of the infinite plane with multiple elliptical holes and cracks. Acta Mechanica Solida Sinica, 2006, 27(1): 7-14 (in Chinese))

王德法, 高小云, 师俊平. 三维固体问题中M积分与总势能变化关系的研究. 水利与建筑工程学报, 2009, 7(1): 36-38 (Wang Defa, Gao Xiaoyun, Shi Junping. Study on relation between M-integral and change of total potential energy in three-dimensional Solids. Journal of Water Resources and Architectural Engineering, 2009, 7(1): 36-38 (in Chinese))

Chen YH, Hasebe N. A consistency check for strongly interacting multiple crack problems in isotropic, bimaterial and orthotropic bodies. International Journal of Fracture, 1998, 89: 333-353

Chen YH. M-integral analysis for two-dimensional solids with strongly interacting cracks, Part I: In an infinite brittle solids. International Journal of Solids and Structures, 2001, 38: 3193-3212

Chang JH, Chien AJ. Evaluation of M-integral for anisotropic elastic media with multiple defects. International Journal of Fracture, 2002, 114: 267-289

Chang JH, Wu WH. Using M-integral for multi-cracked problems subjected to nonconservative and nonuniform crack surface tractions. International Journal of Solids and Structures, 2011, 48: 2605-2613

Hu YF, Chen YH. M-integral description for a strip with two microcracks before and after coalescence. Journal of Applied Mechanics, 2009, 76: 061017

Wang FW, Chen YH. Fatigue damage driving force based on the M-integral concept. Procedia Engineering, 2010, 2: 231-239

Hui T, Chen YH. The M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. Journal of Applied Mechanics, 2010, 77: 021019

Hu YF, Li Q, Shi JP, et al. Surface/interface effect and size/configuration dependence on the energy release in nanoporous membrane. Journal of Applied Physics, 2012, 112: 034302

Muskhelishvili NI, Some basic problems of the mathematical theory of elasticity. Leyden: Noordhoff, 1953

Sendeckyj GP. Elastic Inclusion Problems in Plane Elastostatics. Int J Solids Struct, 1970, 6: 1535-1543

Ru CQ. A new method for an inhomogeneity with stepwise graded interphase under thermomechanical loadings. J Elasticity, 1999, 56: 107-127

Banerjee B, Adams DO. On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method. International Journal of Solids and Structures, 2004, 41: 481-509

Carka D, Landis CM. On the path-dependence of the J-integral near a stationary crack in an elastic-plastic material. Journal of Applied Mechanics, 2011, 78: 011006

Li Q, Hu YF, Chen YH. On the physical interpretation of the M-integral in nonlinear elastic defect mechanics. International Journal of Damage Mechanics, 2012, doi: 10.1177/1056789512456860

施引文献

资源附件(0)

访问统计