Implementing a modified Marciniak–Kuczynski model using the finite element method for the simulation of sheet metal deep drawing

Sheet metal forming processes have an important role amongst the mechanical manufacturing processes, since they are characterised by high productivity and reliability at low cost, low material waste and near net shapes from design. This is achieved by controlling the design and process parameters according to initial constraints. This scenario is common at aeronautic and at automotive productions, and motivated many studies such as necking and formability in sheet metals, the use of forming limit diagrams (FLD) and the finite element method (FEM) to predict design parameters. This work reviews these concepts and introduces a modification of the Marciniak–Kuczynski (M–K) method by using FEM and a modified homogeneity factor f0 which is defined as the ratio of the strength constants in the material constitutive equation, for the two zones A and B of the M–K model. Then, a set of FLDs is predicted in conformity to the local necking criterion. Further on, a methodology for application in designing sheet metal forming tools is also developed, focused on the visualisation of the strains paths in the critical regions of the FLD. Finally, two cases of deep drawing are presented and discussed: the round and square cups.