Lode Parameter Dependence and Quasi-Unilateral Effects in Continuum Damage Mechanics: Models and Applications in Metal Forming

Abstract

This work concerns with two successive modifications of the Lemaitre’s damage model to meet the requirements of formability prediction for today’s modern steels. The first one is the quasiunilateral damage evolution which modifies the damage driving force by scaling the elastic energy release rate due to compressive principal stress components. The second one is the shear modification by which the damage rate is multiplied by a normalized maximum shear stress dependent factor. With the assumption of non-rotating principal axes of deformation, proportional strain paths and rigid plasticity, closed form expressions for the isochronous fracture surfaces are derived for each model variant and resulting surface plots at various spaces are compared. The findings show that the former modification not only remedies the pathological reflective symmetry of the fracture surface across the plane with vanishing stress triaxiality ratio, but also allows hindering fracture under uniaxial compression. The latter modification by adding a direct Lode parameter dependence to the damage evolution function allows prediction of premature fracture at generalized shear stress states, a condition observed for certain advanced high strength metallic sheets. Parameter calibration is realized for each model variant using the experimental data from the literature. It is shown that the fracture model with both the shear modification and the quasi-unilateral enhancement shows the best fitting quality. Finally, the models are implemented as user subroutines for ABAQUS/EXPLICIT and used in prediction of initiation and propagation of cracks for a series of deep-drawing punch tests. A good agreement with the outputs reported in the literature is observed in terms of the shear damage occurrence zones as well as corresponding punch force-displacement diagrams.