Developments of the Marciniak-Kuczynski model for sheet metal formability: A review

This paper presents a historical perspective on the development of the model that was initially proposed by Prof. Marciniak in 1965 for calculating the Forming Limit Curves (FLC's) of metallic sheets. Based on a pre-existing geometric and/or structural non-homogeneity of the metallic sheet, it is at present the most widely used framework for the theoretical prediction of FLC's. This is a consequence of the fact that this modelling approach is well funded from the mechanical and intuitive points of view. By consulting lesser known papers (in English and Polish), the authors revisit the origins of this model that has become commonly known as the Marciniak-Kuczynski (M-K) model in the literature. To put these developments in historical context, the first experimental test for assessing the formability of metallic sheets, the evolution of the Forming Limit Diagram (FLD) concept and the first models for evaluating limit strains (Swift and Hill's models) are summarized as an introduction. The model, initially published in 1965 by Marciniak as sole author, was further developed by Marciniak, Kuczynski and co-workers as explained next in this review. Since then, the following lines of development of the M-K model have been identified and are systematically addressed in this review: implementation of new constitutive equations, polycrystalline and ductile damage models, extending the models to take into account new material or process parameters, taking into account of non-planar stress states and non-linear strain-paths.