Multiscale modelling of morphological evolution of rough surface duringsuperficial, volume and evaporation-condensation diffusions

Abstract

Fractal functions are used to model a metallic interface. An analytical model described by three partial differential equations is built to model time evolution of the surface during heating including three different mechanisms of diffusion: superficial diffusion (SD), volume diffusion (VD) and diffusion by evaporation-condensation (DEC). Initial topographies are modeled by Stochastic Weierstraβ functions because of their ability to reproduce experimental roughness profiles. Applied to an aluminum alloy at 550°C, a high number of roughness parameters and their variance are calculated. A classification method shows that the best geometrical approach that discriminates heat effect is the fractal dimension. The most popular parameter, Ra, badly discriminates processes (classification number = 58). The four order spectral moments of the roughness profile are correlated with the evolution of profile. It is shown theoretically that the superficial diffusion depends directly to the fourth spectral moment of the roughness profile.