Non-classical thermal shock analysis of cracked functionally graded media

摘要

In this paper, the stress intensity factors (SIFs) are calculated for a crack in a functionally graded (FG) plate under transient thermal shock. In order to solve the problem and determine the displacement, temperature and stress fields, the Green-Lindsay (G-L) thermoelasticity theory is used. Extended Finite element method (XFEM) and Newmark time integration scheme are employed to model cracks and solve the governing equations. Considering the dissipated portion of internal energy in G-L theory, an interaction integral was developed for deriving the SIFs. Based on the resulting numerical data, the speed of the temperature and elastic waves has a significant effect on time variations of SIFs, especially when the thermal shock is applied. The results also show that FGM properties (the exponent P) have a great effect on the SIFs.