On Springback Prediction With Special Reference To Constitutive Modeling

The springback phenomenon that occur in thin metal sheets after forming is mainly a stress driven problem, and the magnitude is roughly proportional to the ratio between the magnitude of the residual stresses after forming and Young's modulus. An accurate prediction of residual stresses puts, however, high demands on the material modeling. A phenomenological plasticity model is made up of several ingredients, such as a yield criterion, a plastic hardening curve, a hardening law, and a model for the degradation of elastic stiffness due to plastic straining. The authors have recently, Ref. [1], showed the importance of a correct modeling of a cyclic stress-strain behavior via a phenomenological hardening law, in order to obtain an accurate stress prediction. The main purposes of the present study are to study the influence of two other constitutive ingredients: The yield criterion and the material behavior during unloading. The material behavior during unloading is evaluated by loading/unloading/reloading tension tests, where the material is unloaded/reloaded at specific plastic strain levels. The slope of the unloading curve is measured and a relation between the "unloading modulus" and the plastic strains is established. In the current study, results for four different materials are accounted for. The springback of a simple U-bend is calculated for all the materials in the rolling-, transverse- and diagonal directions. From the results of these simulations, some conclusions regarding constitutive modeling for springback simulations are drawn

A comprehenisve analysis of benchmark 4: Pre-strain effect on springback of 2D draw bending

In order to be able to form high strength steels with low ductility, multi-step forming processes are becoming more common. Benchmark 4 of the NUMISHEET 2011 conference is an attempt to imitate such a process. A DP780 steel sheet with 1.4 mm thickness is considered. In order to understand the pre-strain effect on subsequent forming and springback, a 2D draw-bending is considered. Two cases are studied: one without pre-strain and one with 8% pre-stretching. The draw-bending model is identical to the "U-bend" problem of the NUMISHEET'93 conference. The purpose of the benchmark problem is to evaluate the capability of modern FE-methods to simulate the forming and springback of these kinds of problems. The authors of this article have previously made exhaustive studies on material modeling in applications to sheet metal forming and springback problems, [1],[2],[3]. Models for kinematic hardening, anisotropic yield conditions, and elastic stiffness reduction have been investigated. Also procedures for material characterization have been studied. The material model that mainly has been used in the current study is based on the Banabic BBC2005 yield criterion, and a modified version of the Yoshida-Uemori model for cyclic hardening. This model, like a number of other models, has been implemented as User Subroutines in LS-DYNA. The effects of various aspects of material modeling will be demonstrated in connection to the current benchmark problems. The provided material data for the current benchmark problem are not complete in all respects. In order to be able to perform the current simulations, the authors have been forced to introduce a few additional assumptions. The effects of these assumptions will also be discussed