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

• 来源期刊: 力学学报（英文版）
• 年，卷（期）: 2005,（6）
• 页码范围: 601-607
• 页数: 7页
• 语种: 英文

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.