Hierarchical multi-scale modeling of texture induced plastic anisotropy in sheet forming

Abstract

In this paper we present a Hierarchical Multi-Scale (HMS) model of coupled evolutions of crystallographic texture and plastic anisotropy in plastic forming of polycrystalline metallic alloys. The model exploits the Finite Element formulation to describe the macroscopic deformation of the material. Anisotropy of the plastic properties is derived from a physics-based polycrystalline plasticity micro-scale model by means of virtual experiments. The homogenized micro-scale stress response given by the micro-scale model is approximated by an analytical plastic potential function. The methods to reconstruct the plastic potential upon a sufficient change of the crystallographic texture are discussed. A dedicated stress integration scheme is elaborated to utilize the hierarchy of the models. Cup drawing from circular blanks is considered as an example of sheet forming process. The results from the HMS simulations with updating of texture and anisotropy are compared to the outcomes of the FE model assuming constant anisotropy. Experimental verification of the HMS model is provided for two steel grades and one aluminum alloy. An assessment of the texture evolution calculated by the HMS model reveals very high reliability of the predictions. Macroscopic cup profiles obtained by the HMS model show good agreement with the experiment. A substantial improvement of the predicted cup profile is found for one of the investigated steels. The origin of this enhancement is discussed in the context of evolving plastic anisotropy.