Crack tip field in functionally gradient material with exponential variation of elastic constants in two directions

作     者：Tianhu Hao 

作者机构：College of Science Donghua University EO. Box 220 Shanghai 200051 China 

出 版 物：《Acta Mechanica Sinica》 (力学学报（英文版）)

年 卷 期：2005年第21卷第6期

页      面：601-607页

核心收录：

学科分类：08[工学] 080104[工学-工程力学] 080102[工学-固体力学] 0801[工学-力学（可授工学、理学学位）] 

主　　题：Crack Plane case Functional gradient material Exponential variation 

摘      要：This paper presents an exact solution of the crack tip field in functionally gradient material with exponential variation of elastic constants. The dimensionless Poisson＇s ratios v0 of the engineering materials （iron, glass …… ） are far less than one; therefore, neglecting them, one can simplify the basic equation and the exact solution is easy to obtain. Although the exact solution for the case v0 ≠ 0 is also obtained, it is very complicated and the main result is the same with the case v0 = 0 （it will be dealt with in Appendix VII）. It has been found that the exponential term exp（ax ＋ by） in the constitutive equations becomes exp（ ax /2 ＋ by/2- kr /2 ） in the exact solution.