Transient Analysis of a Functionally Graded Ceramic/Metal Layer considering Lord-Shulman Theory

Abstract

The transient displacement, temperature, and stress fields in a functionally graded ceramic/metal layer under uniform thermal shock conditions at the upper surface are numerically studied based on the Lord-Shulman model, employing a direct finite element method. The Newmark method is employed for the time integration of the problem. A Matlab finite element code is developed for the numerical analysis of the one-dimensional problem under consideration. The Voigt model (rule of mixture) is used for the estimation of the effective properties inside the functionally graded layer and the variation of the volume fraction of the materials follows the sigmoid function in terms of the introduced parameter p. Furthermore, a parametric study with respect to the parameter p follows, where three different combinations of ceramic/metal materials are considered. It is concluded that the value p=1, which corresponds to a linear variation of the properties, minimizes the maximum (tensile) stress applied at the middle of the functionally graded layer.