## 留言板

 引用本文: 陈昌荣. 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[J]. 应用数学和力学, 2018, 39(10): 1172-1179.
CHEN Changrong. Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1172-1179. doi: 10.21656/1000-0887.380191
 Citation: CHEN Changrong. Analysis on the Energy Release Rate Considering the Difference Between J-Integrals With and Without a Crack[J]. Applied Mathematics and Mechanics, 2018, 39(10): 1172-1179.

## 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

###### 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

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

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

##### 计量
• 文章访问数:  658
• HTML全文浏览量:  50
• PDF下载量:  540
• 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

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈