Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part I: Analytical Method

Abstract

In most published papers, in order to obtain the analytical solution of the crack problems in functionally graded materials (FGMs), the thermomechanical properties of FGMs are usually assumed to be very particular functions and, hence, may not be physically realizable for many actual material combinations. Very few analytical methods can be used to solve the thermal shock crack problem of an FGM cylindrical shell or plate with general thermomechanical properties. In this article, a set of analytical methods is proposed for the thermal shock crack problem of an FGM plate or cylindrical shell with general thermomechanical properties. The crack problem of a cylindrical shell is modeled by a plate on an elastic foundation. Greatly different from previous studies, a set of analytical methods using both the perturbation method and a piecewise model are developed to obtain the transient temperature field and thermal stress intensity factor (TSIF). The perturbation method is applied to deal with the general thermal properties and the piecewise model is used to deal with the general mechanical properties. In the analytical procedure, integral transform, the residue theorem, and the theory of singular integral equation are used. Several representative examples are considered to check the capability of the present method. The transient thermal shock behavior of a ZrO2/Ti-6Al-4 V FGM plate with a surface crack and a Rene 41-Zirconia FGM cylindrical shell with a circumferential crack are analyzed.