A Novel Constitutive Modelling for Spring Back Prediction in Sheet Metal Forming Processes

Abstract

The purpose of this work is to present, by the mean of a numerical study, an elastoplastic constitutive model of metals which is introduced in finite element code for predicting spring back phenomenon in sheet metal processes. A simple case study is proposed “L-bending process” which is widely used for mass production. An accurate prediction of spring back is very delicate due to non-uniform stress distribution in the sheet thickness. Knowing that, the material behaviour modelling and its incorporation into the finite element code is considered as an important step in the numerical analysis of spring back, a statistical and physically based modelling for predicting the elastic return in the sheet after a bending operation is proposed. Taking into account the material heterogeneities; on the basis that the metallic alloys are discrete and heterogeneous, the proposed model called compartmentalized model (or hybrid model) is based on the combination of mechanical behaviour law at a local level and statistical distribution of mechanical properties. By way of comparison, the advantages of the proposed model compared to classic phenomenological models were discussed. Tests have been carried out on commercially pure titanium sheets (T40 alloy), that is increasingly used in aircraft sector because of its specific properties.