Papers by Author: M. Bigerelle

Abstract: There are few articles that mention fractal dimension in grain growth mechanism. Some authors build a simplified analytic model showing that initial fractal dimension of grain boundary has an influence on interface modification velocity. Nevertheless they postulate the relation where L is the grain length, c is a constant, s is grain size and the fractal dimension. The aims of this paper is to experimentally analyze by image analysis the fractal dimension of A5 aluminum sheet grain boundaries during heating and to simulate their evolution by a Monte Carlo method to validate experimental data.. It is shown by Monte-Carlo simulation and confirmed experimentally that the grain growth process decreases the fractal dimension of grain border. It can be concluded that it is very hazardous to build a model of grain growth without including the effect of grains morphology. The macroscopic fractal morphology of the grain structure could then be used to validate microscopic relation between Monte Carlo Steps time and real time.

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, R_a, 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.