A 3-D finite element method for non-isothermal sheet-forming processes

Abstract

In sheet forming of ductile materials, the forming limit and strain distribution are governed by plastic instability and fracture following strain localization. A number of phenomena influence the localization process, including the best-known plastic properties of strain hardening, strain-rate sensitivity and yield-surface shape. The temperature gradient caused by deformation heating, heat transfer, and friction between sheet and tools also controls strain localization. In this paper, a numerical method for analyzing the non-isothermal, rigid-viscoplastic deformation of sheets is presented. The method consists of two parts: a rigid-viscoplastic finite element model (FEM) to solve the plastic deformation, and transient heat transfer FEM to evaluate the temperature change throughout the specimen during the deformation process. Bishop's step-wise decoupled method is adopted to handle coupling between mechanical deformation and the temperature change. Using this method, the effect of temperature distribution on strain patterns was investigated. As illustrative 3-D examples, hemispherical punch-stretching and square punch-stretching operations have been analyzed, including deformation heating, frictional heating, heat transfer to tooling and air, and internal heat conduction in the workpiece. The role of temperature gradients is revealed by examination of the simulation results.