In large-scale industrial simulations the numerical prediction of fracture in sheet metal forming operations as well as in crash events is still a challenging task of high social and economic relevance. Among several approaches presented in literature, the authors and their colleagues developed a model which accounts each for three different mechanisms leading finally to fracture in thin sheet metals: the local instability (necking), ductile normal fracture and ductile shear fracture. The focus of this paper is to develop and validate a new approach to improve the predictive capabilities for fracture triggered by localized necking for a wide variety of steel grades. It is well known that after the onset of a local instability additional strain is still necessary to induce fracture. In a numerical simulation using shell elements this post instability strain becomes of increasing importance when the ratio of the characteristic shell element edge length to its thickness decreases. Today's shell element lengths in industrial applications can be of the same order as the width of the necking zone. Therefore, the post instability strain may contribute to a significant percentage of the shell elements total elongation up to fracture and cannot be neglected any longer.
The enhanced necking model termed Post Instability Strain Model for Shells (PIS Model) combines the model for localized necking with the model for ductile shear fracture. Guided by careful Nakajima type tests of three representative steel grades, the development of the PIS Model also focuses on minimizing the influence of varying shell element edge lengths. The model is implemented in such a way that the elongation of a shell element after onset of necking is highly independent of the element edge length.
The improvements achieved with this model are demonstrated by validation examples which include small specimens (tensile specimen with circular hole), technological sheet metal forming experiments (Nakajima tests) and finally the 3-point bending test of an automotive component.
