Crystal plasticity-based finite element simulations of load reversals and hat-shaped draw-bending for predicting the springback behavior of dual-phase steel sheets

Abstract

This work is concerned with predicting geometrical shape changes in sheet metal forming using a multi-level simulation framework that considers the directionality of deformation mechanisms acting at the single-crystal level and microstructural evolution. The multi-level model is an elasto-plastic self-consistent (EPSC) homogenization of single-crystal behavior giving the constitutive response at each finite element (FE) material point. Numerical solution of a boundary value problem over geometry is then obtained using continuum finite elements at the macro-level. First, a set of model parameters for the evolution of slip resistance of ferrite and martensite and backstress are established by fitting a comprehensive set of mechanical data for dual-phase (DP) steels 590, 780, and 1180 using one-element model. Next, the potential of the FE-EPSC modeling framework is illustrated by carrying out a set of hat-shaped draw-bending simulations of the steel sheets. The evolution of geometry after hat-shaped draw-bending and springback is predicted and verified with experimental measurements for as-received DP 780. In doing so, the role of accounting for backstress is revealed as critical for the accurate prediction of the part geometry. The same process simulation involving a pre-strained sheet of DP 780 is compared with a corresponding experiment to reveal the role of strain hardening and residual stress on the subsequent part shape changes after the hat-shaped draw-bending test and springback. Finally, the same process simulations involving DP 590 and DP 1180 are performed to confirm the effect of strength on the geometrical shape changes of the sheets after springback.