Plane stress state of FGM thick plate under thermal loading

A Ganczarski,D Szubartowski

doi:10.1007/s00419-015-1105-5

Abstract

This paper demonstrates the plane stress state of FGM thick plate under thermal loading. First, the Sneddon–Lockett theorem on the plane stress state in an isotropic infinite thick plate is generalized for a case of FGM problem in which all thermomechanical properties are optional functions of depth coordinate. Next, an example of application to an engineering problem is presented.

Highlights

Graded materials (FGMs) provide thermal insulation and mechanical toughness at high temperature by varying the composition of thermal conductivity coefficient, thermal expansion coefficient and Young’s modulus from high-temperature side to low-temperature side continuously and simultaneously by removing the discontinuity of layered plate
∂r and accompanying plane stress components satisfying Eq (18) for a semi-infinite axially symmetric three-layer thick plate made of Functionally graded materials (FGMs) composite Al/ZrO2 stabilized by Y2O3
Thermal loading applied to the structure results in the plane stress state if only force-type boundary conditions are homogeneous and there are no body forces

Summary

Introduction

Graded materials (FGMs) provide thermal insulation and mechanical toughness at high temperature by varying the composition of thermal conductivity coefficient, thermal expansion coefficient and Young’s modulus from high-temperature side to low-temperature side continuously and simultaneously by removing the discontinuity of layered plate. Authors use Laplace’s transformation technique to reduce uncoupled quasi-static equations of linear thermoelasticity to an ordinary differential equations containing the powerlaw-type functions of effective thermomechanical constants Magnitudes of these constants (bulk and shear moduli, coefficients of thermal conductivity and expansion) at a point are determined according to either the Mori–Tanaka or self-consistent scheme and directly depend on from volume fraction of constituents (Al/SiC). Kulikov and Plotnikova [11] present a new method of sampling surfaces (SaS) applied to 3D steady-state problem of laminated FGM plates subjected to thermomechanical loading. This method is based on choosing inside each laminate layer the sampling surfaces such that temperature and displacements of these surfaces are basic plate variables. Two exemplary solutions are demonstrated: temperature, heat flux and displacements for metal/ceramic (Al/SiC) square plate and temperature, heat flux, displacements and stresses for graphite/epoxy square plate covered with metal/ceramic barrier on its top surface

The general solution of FGM thermoelastic problem

Findings

Conclusions