Finite Difference Analysis of 2D Stress Wave Propagation in Two Dimensional Functionally Graded Ceramics - Metals Composites

Abstract

In this study, a finite difference method is presented for longitudinal stress wave propagation analysis in functionally graded 2D plane strain media. The plane material consists of two ceramics (SiC and Al2O3) and two metals (Al 1100 and Ti-6A1-4V (TC4)) with power‐law variation for mechanical properties in terms of volume fractions of the constituents. Firstly, the governing equations of wave propagation in the functionally graded plane strain media were derived in Cartesian coordinate. It’s assumed that elastic module, density and Poisson’s ratio are variable in all of the media. Secondly, finite difference method was used to discretize the equations. Time step size was obtained using von Neumann stability approach. The materials distribution effects are studied in different states and history of stress, strain and displacement. To validate the numerical simulation, stress are compared with theoretical equations in special states. Results show that the wave propagation behavior is considerably influenced by material composition variation.