ANALYSIS OF A CRACK IN A FUNCTIONALLY GRADED STRIP WITH A POWER FORM SHEAR MODULUS  

作　　者：Jinju Ma Zheng Zhong Chuanzeng Zhang 

机构地区：[1]School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China [2]Department of Civil Engineering, University of Siegen, D-57068 Siegen, Germany

出　　处：《Acta Mechanica Solida Sinica》2009年第5期465-473,共9页固体力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.10872150 and 10432030);Financial supports from German Research Foundation(DFG,project No.ZH 15/13-1)

摘　　要：The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy＇s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line.The plane strain problem of a crack in a functionally graded strip with a power form shear modulus is studied. The governing equation in terms of Airy＇s stress function is solved exactly by means of Fourier transform. The mixed boundary problem is then reduced to a system of singular integral equations and is solved numerically to obtain the stress intensity factor at crack-tip. The maximum circumferential stress criterion and the strain energy density criterion are both employed to predict the direction of crack initiation. Numerical examples are given to show the influence of the material gradation models and the crack sizes on the mode-I and mode-II stress intensity factors. The dependence of the critical kink-angle on the crack size is examined and it is found that the crack kink-angle decreases with the increase of the normalized crack length, indicating that a longer crack tends to follow the original crack-line while it is much easier for a shorter crack to deviate from the original crack-line.

关 键 词：functionally graded material CRACK stress intensity factors fracture criterion 

分 类 号：O346.1[理学—固体力学] TM621.2[理学—力学]