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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参考文献(28)

[1]	Griffith A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London, 1921,221: 163-198.
[2]	Rice J R. A path independent integral and the approximate analysis of strain concentration by notches and cracks[J]. Journal of Applied Mechanics,1968,35(2): 379-386.
[3]	Sun C T, Wu X X. On the J-integral in periodically layered composites[J]. International Journal of Fracture,1996,78(1): 89-100.
[4]	Simha N K, Fischer F D, Shan G X, et al. J-integral and crack driving force in elastic-plastic materials[J]. Journal of the Mechanics and Physics of Solids,2008,56(9): 2876-2895.
[5]	Simha N K, Fischer F D, Kolednik O, et al. Inhomogeneity effects on the crack driving force in elastic and elastic-plastic materials[J]. Journal of the Mechanics and Physics of Solids,2003,51(1): 219-240.
[6]	Fischer F D, Predan J, Kolednik O, et al. Application of material forces to fracture of inhomogeneous materials: illustrative examples[J]. Archive of Applied Mechanics,2007,77(2): 95-112.
[7]	Fischer F D, Simha N K, Predan J, et al. On configurational forces at boundaries in fracture mechanics[J]. International Journal of Fracture,2012,174(1): 61-74.
[8]	Fischer F D, Predan J, Muller R, et al. On problems with the determination of the fracture resistance for materials with spatial variations of the Young’s modulus[J]. International Journal of Fracture,2014,190(1): 23-38.
[9]	Kolednik O, Predan J, Gubeljak N, et al. Modeling fatigue crack growth in biomaterial specimen with the configurational force concept[J]. Materials Science and Engineering A,2009,519(1/2): 172-183.
[10]	Riemelmoser O, Pippan R. The J-integral at Dugdale cracks perpendicular to interfaces of materials with dissimilar yield stresses[J]. International Journal of Fracture,2000,103(4): 397-418.
[11]	陈昌荣. 层状陶瓷的材料力和裂纹力评估方法[J]. 应用数学和力学, 2016,37(7): 748-755.(CHEN Chang-rong. A method for evaluating material forces and crack forces in ceramic laminates[J]. Applied Mathematics and Mechanics,2016,37(7): 748-755.(in Chinese))
[12]	Shi W, Kuang Z B. J-integral of dissimilar anisotropic media[J]. International Journal of Fracture,1999,96(4): 37-42.
[13]	王利民，陈浩然，徐世烺. J积分在多层介质中的守恒性和其利用[J]. 应用数学和力学, 2001,22(10): 1097-1104.(WANG Li-min, CHEN Hao-ran, XU Shi-lang. Conservation law and application of J-integral in multi-materials[J]. Applied Mathematics and Mechanics,2001,22(10): 1097-1104.(in Chinese))
[14]	Rask M, Sorensen B F. Determination of the J integral for laminated double cantilever beam specimens: the curvature approach[J]. Engineering Fracture Mechanics,2012,96(1): 37-48.
[15]	Eshelby J D. The elastic energy-momentum tensor[J]. Journal of Elasticity,1975,5(3): 321-335.
[16]	Eshelby J D. Energy relations and the energy-momentum tensor in continuum mechanics[C]// Fundamental Contributions to the Continuum Theory of Evolving Phase Interfaces in Solids . Berlin, Heidelbergs: Springer-Verlag, 1999: 82-119.
[17]	陈昌荣. 适合裂尖穿越界面行为分析的断裂模拟方法研究[J]. 应用数学和力学， 2014,35(9): 979-985.(CHEN Chang-rong. On the fracture modeling method for crack tips penetrating elastic interfaces[J]. Applied Mathematics and Mechanics,2014,35(9): 979-985.(in Chinese))
[18]	Markenscoff X. Driving forces on phase boundaries: the Eshelby principle for an interface[J]. International Journal of Fracture,2010,165(2): 223-227.
[19]	Bermejo R, Torres Y, Sanchez-Herencia A J, et al. Residual stresses, strength and toughness of laminates with different layer thickness[J]. Acta Materialia, 2006,54(18): 4745-4757.
[20]	Chen C R, Pascual J, Fischer F D, et al. Prediction of the fracture toughness of a ceramic multilayer composite: modeling and experiments[J]. Acta Materialia,2007,55(2): 409-421.
[21]	Chen C R, Bermejo R, Kolednik O. Numerical analysis on special cracking phenomena of residual compressive inter-layer in ceramic laminates[J]. Engineering Fracture Mechanics,2010,77(13): 2567-2576.
[22]	钟万勰. 力学与对称——离散: 祖冲之方法论[J]. 应用数学和力学，2016,37(1): i-ii.(ZHONG Wan-xie. Mechanics and symmetry—discretization: Zu-type methodology[J]. Applied Mathematics and Mechanics,2016,37(1): i-ii.(in Chinese))
[23]	范镜泓, 陈海波. 非均质材料力学研究进展: 热点、焦点和生长点[J]. 力学进展, 2011,41(5): 615-636.(FAN Jing-hong, CHEN Hai-bo. Advances in heterogeneous material mechanics: cutting-edge and growing points[J]. Advances in Mechanics,2011,41(5): 615-636.(in Chinese))
[24]	张金钰, 刘刚, 孙军. 纳米金属多层膜的变形与断裂行为及其尺寸效应[J]. 金属学报, 2014,50(2): 169-182.(ZHANG Jin-yu, LIU Gang, SUN Jun. Size effects on deformation and fracture behavior of nanostructured metallic multilayers[J]. Acta Metallurgica Sinica,2014,50(2): 169-182.(in Chinese))
[25]	孙军, 张金钰, 吴凯, 等. Cu系纳米金属多层膜微柱体的变形与损伤及其尺寸效应[J]. 金属学报, 2016,52(10): 1249-1258.(SUN Jun, ZHANG Jin-yu, WU Kai, et al. Size effects on the deformation and damage of Cu-based metallic nanolayered micro-pillars[J]. Acta Metallurgica Sinica,2016,52(10): 1249-1258.(in Chinese))
[26]	Beyerlein I J, Demkowicz M J, Misra A, et al. Defect-interface interactions[J]. Progress in Materials Science,2015,74: 125-210.
[27]	Guo L C, Kitamura T, Yan Y B, et al. Fracture mechanics investigation on crack propagation in the nano-multilayered materials[J]. International Journal of Solids and Structures,2015,64/65: 208-220.
[28]	Huang K, Guo L C, Yan Y B, et al. Investigation on the competitive fracture behavior in nano-multilayered structures[J]. International Journal of Solids and Structures,2016,92/93: 45-53.