Variants of Lemaitre’s damage model and their use in formability prediction of metallic materials

Abstract

Taking Lemaitre’s damage model (Lemaitre, 1996) as the point of departure, we present two successive enhancements to meet the requirements of formability prediction for today’s modern steels. The first extension is a quasi-unilateral damage evolution which, after a spectral decomposition of the stress tensor, scales the elastic energy release rate due to compressive principal stress components. The second one is inspired by a recent multiplicative modification of triaxiality dependent Oyane’s fracture criterion with a shear stress dependent term, following (Lou et al., 2012)]. For plane stress states, the former modification allows, besides correcting the pathological symmetry of the fracture strain with respect to vanishing stress triaxiality ratio, i.e. η=0,hindering fracture under uniaxial compression since the altered fracture strain curve shows an asymptotic behavior at η=−1/3. Depending on the selected parameters, the latter modification permits one to further modify this curve to give account for two local minima in the vicinity of generalized shear points within the triaxiality interval [−1/3,2/3]. From a formability prediction perspective, as a consequence of the former modification, premature failure prediction of the conventional Lemaitre’s damage model in many compression dominated metal forming operations is remedied. The latter modification permits modeling shear dominated fracture. Moreover, for each variant, closed form expressions for the isochronous fracture surfaces associated with linear strain paths are derived and resulting surface plots at various spaces are compared. It is shown that only shear modification together with quasi-unilateral enhancement lets model show enough flexibility during parameter calibration for the experimental data. Finally, handled calibrations are compared with those of the existing fracture criteria frequently used in the literature to highlight relative strengths of the current proposal.