Evaluation of constitutive models for formability of DP and TRIP steel sheets

Abstract

Sheet formability, as determined by the Limiting Dome Height (LDH) test, was evaluated by various plasticity constitutive models implemented in finite element analysis. Two advanced high strength steel grades, DP590 and TRIP590, were considered in the evaluation. Three yield functions, the von Mises isotropic yield function, Hill’s 1948 anisotropic yield function, and the Yld2000-2d non-quadratic anisotropic yield function, were used to examine the effect of yield criterion on the formability simulation. The parameters of the two anisotropic yield functions were determined from different experimental tests and their effect on predictions was compared. For Hill’s 1948 model, the anisotropic coefficients were obtained either by the yield stress or r-values in different material orientations. The anisotropic coefficients of the Yld2000-2d were determined from biaxial yield stress data measured by an in-plane biaxial test were used in addition to the conventional uniaxial test-based data. The stress-strain curves for the hardening law were measured in uniaxial tension and balanced biaxial tension from the hydraulic bulge test. The latter was proposed to have more reliable test data with an extended strain range without exhibiting instability. The constitutive models were implemented in the finite element program, ABAQUS with a user material subroutine, and evaluated by comparing the predicted punch load-displacement and variation of sheet thickness after forming in the LDH test. The results for this particular example showed that the non-quadratic yield function and the hardening law characterized by the biaxial stress state might improve the prediction capability of sheet formability.