A crystal plasticity based estimate for forming limit diagrams from textural inhomogeneities

Abstract

An alternative method to predict forming limits for sheet metal forming is presented. Deformation instabilities are considered as the natural result of strain field fluctuations caused by textural inhomogeneities. The biaxial stretching of a sheet material configuration is analysed using the finite element method in plane stress conditions. For the description of the material behaviour at the microscopic level, a viscous crystal plasticity model is used. To accommodate the simulation of polycrystallinity, each individual integration point of the finite element mesh is assumed to be composed of a discrete number of single crystals. The single crystals are coupled according to a Taylor interaction approach. The initial texture inhomogeneity is considered as a natural microstructure imperfection, which is present in any real metal, potentially triggering deformation instabilities. The occurrence of a nonuniform deformation field is the result of the textural inhomogeneity only; no other imperfections are introduced to generate the instabilities observed. The structural instability criterion is used as an approximate localisation criterion. Proportional loading of a metal sheet with an initially random distribution of crystal lattice orientations has been analysed for different uniform strain paths. The results demonstrate the ability of the method to describe the development of strain localisation bands, from which the formability can be assessed.