Numerical thermal shock analysis of functionally graded and layered materials

Severe thermal shocks may cause critical thermal stresses and failure in refractory materials. Because of durability, carbon based ceramics are often used in steel industry, which have negative side effects on steel quality and environment. Layered or functionally graded ceramics allow to reduce the carbon content in refractories. In order to optimize properties of these alternative structures, thermo-mechanical simulations are required. In this study, a finite difference method (FDM) is developed for solving the partial differential equation of heat conduction with spatially varying parameters. The transient temperature and thermal stresses are exemplarily presented for a three-layered strip subjected to constant temperature jump on the top surface. Results are also given for a strip of functionally graded material (FGM). The comparison of the temperature and thermal stress solutions of the presented FDM with the finite element method (FEM) and a known asymptotic solution shows its high performance. In view of implementing FGM in the finite element program Abaqus, improved techniques are outlined to avoid the often used simple approximation by layering.

► We used a FDM to simulate the transient 1D-heat conduction problem for FGM.
► Temperature and thermal stresses are calculated for three-layered and FGM strips.
► Improved techniques are outlined for Abaqus to avoid FGM-approximation by layering.
► FDM shows high performance in comparison with FEM and a known asymptotic solution.