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.
Highlights
Ceramic materials are used as thermal barrier coatings for the thermal protection of metals in high-temperature environments
The thermomechanical properties of the functionally graded materials (FGMs) layer vary from the properties of the ceramic material to the properties of the metal material in a continuous way, eliminating the material discontinuities
In the present paper the standard Galerkin finite element method [22] is used to study the transient fields of displacement, temperature, and stress in a ceramic/metal FGM layer under uniform thermal shock loading, based on the generalized theory of Lord-Shulman
Summary
Ceramic materials are used as thermal barrier coatings for the thermal protection of metals in high-temperature environments. Combustion chambers, exhaust pipes, power generators, aircraft engines, and space shuttles are typical examples of such machines In these applications, the study of the thermomechanical response of a ceramic/metal FGM layer under thermal shock conditions using generalized thermoelasticity theories is of great importance. Bagri et al [16] studied the problem of a FGM layer under thermal shock conditions in the context of Lord-Shulman theory, where the variation of the thermomechanical properties in the FGM layer followed a power law function They used a transfinite element method to solve the coupled system of equations, where time is eliminated using the Laplace transform. In the present paper the standard Galerkin finite element method [22] is used to study the transient fields of displacement, temperature, and stress in a ceramic/metal FGM layer under uniform thermal shock loading, based on the generalized theory of Lord-Shulman. A Matlab finite element code [25] is developed for the numerical analysis of the problem under consideration
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