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

Abstract

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 ν 0 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 ν 0 = 0 is also obtained, it is very complicated and the main result is the same with the case ν 0 = 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.