利用有裂纹与无裂纹J积分之差分析裂纹扩展能量释放率

陈昌荣

doi:10.21656/1000-0887.380191

利用有裂纹与无裂纹J积分之差分析裂纹扩展能量释放率

doi: 10.21656/1000-0887.380191

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: O346.1
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- 被引次数: 0
出版历程
- 收稿日期: 2017-07-05
- 修回日期: 2018-03-07
- 刊出日期: 2018-10-01

Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack

CHEN Changrong

School of Air Transportation, Shanghai University of Engineering Science, Shanghai 201620, P.R.China

Funds: The National Natural Science Foundation of China（51175321）

摘要

摘要: 用有裂纹与无裂纹时的远场J积分之差分析了无限大平面中心裂纹的能量释放率,材料形式分别为均匀和层状材料，裂纹垂直于拉伸方向，层状材料界面平行于拉伸方向.有裂纹与无裂纹J积分之差表示载荷作用下的无裂纹材料引入裂纹所导致的J积分变化.对于均匀材料无限大平面中心裂纹，能量释放率等于对称轴处应变能密度释放量沿对称轴的积分，其值等于无裂纹时的应变能密度乘以一个以裂纹半长为半径的圆周长.对于层状材料无限大平面中心裂纹，能量释放率等于对称轴处应变能密度释放量沿对称轴的积分减去界面J积分的改变量.
- 能量释放率 /
- J积分 /
- 材料非均匀性 /
- 材料界面 /
- Eshelby张量J
Abstract: The difference between the J-integrals with and without a crack along a far-field contour was considered to analyze the energy release rate of the crack extension in an infinite plane. Two material cases were studied: a homogeneous material and a layered material. The constant displacement load was applied far from the crack, the crack was assumed to be perpendicular to the load, and the interfaces of the layered material were parallel to the load. The difference between the J-integrals with and without a crack represents the change of the far-field J-integral when a crack is introduced into the loaded material. For the central crack in a homogeneous infinite plane with a unit thickness, the energy release rate is the integral of the released strain energy density along the symmetry axis, and equals the product of the strain energy density without a crack and the perimeter of a circle, where the diameter of the circle is the crack length. For the central crack in an infinite plane of the layered material with a unit thickness, the energy release rate of crack extension equals the integral of the released strain energy density along the symmetry axis minus the change of the interface J-integral.
- energy release rate /
- J-integral /
- material inhomogeneity /
- material interface /
- Eshelby tensor

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参考文献(18)

[1]	嵇醒. 断裂力学判据的评述[J]. 力学学报, 2016,48(4): 741-753.(JI Xing. A critical review on criteria of fracture mechanics[J]. Chinese Journal of Theoretical and Applied Mechanics,2016,〖STHZ〗 48(4): 741-753.(in Chinese))
[2]	WILLIAMS J G. The Griffith medal lecture: the fracture mechanics of soft solids[J]. Engineering Fracture Mechanics,2015,149: 192-198.
[3]	GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London,1921,221(2): 163-198.
[4]	IRWIN G R.Analysis of stresses and strains near the end of a crack traversing a plate[J]. Journal of Applied Mechanics,1957,24: 361-364.
[5]	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 Wanxie. Mechanics and symmetry-discretization: Zu-type methodology[J]. Applied Mathematics and Mechanics,2016,37(1): i-ii.(in Chinese))
[6]	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.
[7]	YU H J, SUMIGAWA T, WU L Z, et al. Generalized domain-independent interaction integral for solving the stress intensity factors of nonhomogeneous materials[J]. International Journal of Solids and Structures,2015,67/68: 151-168.
[8]	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 Changrong. A method for evaluating material forces and crack forces in ceramic laminates[J]. Applied Mathematics and Mechanics,2016,37(7): 748-755.(in Chinese))
[9]	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.
[10]	陈昌荣. 层状弹性材料界面J积分的产生和特征[J]. 应用数学和力学, 2017,38(10): 1155-1165.(CHEN Changrong. Characteristics and generation of interface J-integrals in the layered elastic materials[J]. Applied Mathematics and Mechanics,2017,38(10): 1155-1165.(in Chinese))
[11]	李群. 材料构型力学及其在复杂缺陷系统中的应用[J]. 力学学报, 2015,47(2): 197-214.(LI Qun. Material configurational mechanics with application to complex defects[J]. Chinese Journal of Theoretical and Applied Mechanics,2015,〖STHZ〗 47(2): 197-214.(in Chinese))
[12]	胡义锋, 胡翔, 师俊平. 含缺陷的弹塑性材料中构型体积力的研究[J]. 应用力学学报, 2015,32(4): 537-542.(HU Yifeng, HU Xiang, SHI Junping. Study on configurational volume force in defected elasto-plastic materials[J]. Chinese Journal of Applied Mechanics,2015,32(4): 537-542.(in Chinese))
[13]	于宁宇, 李群. 基于数字散斑相关实验测量的材料构型力的计算方法[J]. 实验力学, 2014,29(5): 579-588.(YU Ningyu, LI Qun. On the algorithm of material configurational force based on digital image correlation measurement[J]. Journal of Experimental Mechanics,2014,29(5): 579-588.(in Chinese))
[14]	古斌, 郭宇立, 李群. 基于构型力断裂准则的裂纹与夹杂干涉问题[J]. 力学学报, 2017,49(6): 1312-1321.(GU Bin, GUO Yuli, LI Qun. Crack interacting with an individual inclusion by the fracture criterion of configurational force[J]. Chinese Journal of Theoretical and Applied Mechanics,2017,49(6): 1312-1321.(in Chinese))
[15]	KUHN C, MULLER R. A discussion of fracture mechanism in heterogeneous materials by means of configurational forces in a phase field fracture model[J].Computer Methods in Applied Mechanics and Engineering,2016,〖STHZ〗 312(1): 95-116.
[16]	ESHELBY J D. The force on an elastic singularity[J]. Philosophical Transactions of the Royal Society of London,1951,244(877): 87-112.
[17]	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.
[18]	ESHELBY J D. The elastic energy-momentum tensor[J]. Journal of Elasticity,1975,5(3/4): 321-335.