Simulation of Two‐Phase Steels based on Statistically Similar Representative Volume Elements

Abstract

An increasing number of engineering structures in the fields of light weight constructions or automotive applications makes use of advanced high-strength steels. To optimize the overall mechanical behavior computer simulations taking into account the micro-heterogeneity of these materials have been becoming the major tool. Direct micro-macro-transition procedures, also known as the FE 2 -method, provide a suitable numerical framework. The main problem of these methods applied to large random microstructures turns out to be the high computational cost with respect to both, the amount of memory and the computation time. In this context the definition of a representative volume element (RVE) plays an important role. Therefore, we focus on the construction of statistically similar RVEs (SSRVEs), which are characterized by a much less complexity than usual random RVEs and which represent still the mechanical response of the real material. For the construction of these SSRVEs we select several statistical measures of the microstructure of a two-phase steel and assume them to be as similar as possible to the ones computed for the SSRVE. These measures are included in a least-square functional, which has to be minimized. The accuracy of this method is presented by some representative numerical simulations, where the response of the real microstructure of the considered two-phase steel and the SSRVEs is compared to each other.