Simplification of the Gurson model for large-scale plane stress problems

This paper discusses formulation of the constitutive model for ductile fracture prediction in large-scale metal structures that can be approximated using shell mechanics. One of the primary considerations is the issue of bridging the length scales between micromechanical phenomena governing ductile fracture (i.e. void nucleation, growth and coalescence), which occurs on the scale of several micrometers, and large scale industrial applications. A micromechanics-based shear-modified Gurson model is used as a reference for the proposed formulation. The model is simplified and implemented in generalized plane stress state, with only the most relevant phenomena considered. Bridging of the length scales is achieved through the calibration function that approximates exponential damage growth after the onset of localized neck that cannot be explicitly represented with shell elements. The resulting formulation is a phenomenological three invariant plasticity model with a scalar damage variable dependent on the volumetric plastic strain and deviatoric plastic work. The latter term is dependent on the Nahshon-Hutchinson omega function, which is based on a normalized Lode angle. The model is used to simulate a response of a hat-shaped high strength steel automotive component under three-point bending. Calibration of the model parameters is performed based on uniaxial and plane-strain tensile tests. Close correlation between experimental and analysis results are achieved validating the assumptions and proposed formulation.