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Coupled Dynamical Thermoelasticity of a Functionally Graded Cracked Layer

The effect of thermal shock on a cracked FGM layer is analized using the Galerkin finite element method. The thermoelasticity equations are assumed in the classical form and the effect of thermal-mechanical coupling in the energy equation is included in the calculations. The eight node rectangular element is used and the nodes near the crack tip are replaced to introduce the crack tip singularity. The coupled dynamical system of equations obtained from the finite element discretization are solved by the Newmark method in the time domain. The domain form of the J integral is then employed to calculate the dynamical thermal stress intensity factors at each instance of time. A computer program in C+ + environment is developed to do the different stages of calculations from mesh generation to numerical calculation of the J integral. Some numerical examples are implemented to investigate the validity and accuracy of the written computer program to simulate the shock phenomena on a functionally graded cracked body.