ADVANCED MODELLING OF FAILURE MECHANISMS IN ALUMINIUM SHEET FORMING SIMULATION Holger Aretz * , Stefan Keller, Rolf Vogt, Olaf Engler Hydro Aluminium Deutschland GmbH, R&D Center Bonn, Germany ABSTRACT: In this paper novel and efficient approaches to model localized necking and ductile fracture in sheet forming simulation using the finite element method are presented. The stress-based forming limit curve is used to detect localized necking. Post-necking is captured using a new concept called accelerated plastic thinning. A simple ductile fracture model was developed. Various application examples demonstrate the capabilities of the modelling framework. KEYWORDS: Forming limits, Necking, Fracture, Sheet forming 1 INTRODUCTION Nowadays, the analysis of sheet metal forming processes is strongly supported by numerical simulation based on the finite element method (FEM). By means of FEM stresses, strains, reaction forces etc. can be predicted with high accuracy. However, a physically sound concept to account for localized necking, post-necking and fracture is not available yet. In the present work an approach is presented that aims at closing this gap. 2 THEORETICAL BASIS 2.1 CONSTITUTIVE MODEL In the present work a co-rotational rate-independent elastic-plastic constitutive framework is used. Details can be found in the references [1, 2]. The constitu- tive model was linked to the commercial FEM codes ABAQUS/Standard and ABAQUS/Explicit via the user material subroutines UMAT and VUMAT, respectively. In the present work only the dynamic explicit code is consid- ered. The constitutive model consists of isotropic elastic- ity combined with orthotropic plasticity. The plane-stress yield function ‘Yld2003’ [1] is considered in the present work, but many other yield functions have been imple- mented as well. Isotropic hardening is assumed. Rate- dependent yielding can be accounted for, but is not being used in the present work. 2.2 MODELLING OF LOCALIZED NECKING The forming limit curve (FLC) discriminates strain (or stress) states that are safe or lead to necking. In the present work the stress-based FLC is used. Compared to the strain-based variant the stress-based one has the ad- vantage of being less sensitive to strain-path changes, see e.g. [3]. In the present work the FLC is computed using a stand-alone software implementation of the Hill/M-K * Corresponding author: holger.aretz@hydro.com model as described in detail in [2]. The computed FLC is transferred to the FEM simulation in form of sampling points that are stored in a look-up table. In the FEM anal- ysis these sampling points are linearly interpolated on de- mand. This concept is very efficient as the FLC is com- puted only once and prior to the FEM analysis rather than during the analysis. Localized necking occurs when the FLC is reached or exceeded. 2.3 MODELLING OF POST-NECKING The concept of the FLC allows the detection of onset of lo- calized necking, but no information is provided regarding the post-necking behavior of the material. For this purpose a dedicated model was developed which is inspired by the following essential features of a localized neck: 1. A neck is very similar to a groove whose width is of the order of the sheet thickness. 2. After the localized necking has set in accelerated plastic thinning of the necked region occurs, i.e. the primary mechanism is geometrical rather than mate- rial softening. 3. Neck formation is practically irreversible, i.e. upon formation of a neck it is practically impossible to re- move it by subsequent re-thickening of the material. In elastic-plastic plane-stress analysis the total thickness strain increment, Δε 33 , is given by Δε 33 = Δε e 33 + Δε p 33 (1) with the elastic and the plastic portions Δε e 33 and Δε p 33 , respectively. Inspired by the phenomenological aspects of localized necking summarized above the key element of the developed post-necking approach is the acceleration of the plastic portion of the thickness strain increment once necking has set in. Thus, (1) is modified as follows: Δ ¯ ε ← κ · Δ ¯ ε , Δε 33 ← Δε e 33 + κ · Δε p 33 (2)