Constitutive description of distortional hardening in a TWIP steel: Addressing differential hardening under nonlinear strain paths

The present study aims to describe the in-plane differential hardening behaviour of the twinning induced plasticity sheet metal TWIP980 under various stress states, including uniaxial tension, plane strain tension, and pure shear, particularly focusing on non-proportional loading conditions. The true stress–strain curves for each stress states were inversely obtained from their corresponding load–displacement curves and modeled using a differential hardening model that can accommodate all three stress states simultaneously on plastic work (density) contours. For non-proportional loading tests, oversize specimens were initially stretched under uniaxial tension up to a 10% pre-strain along the rolling, diagonal, and transverse directions, respectively. Subsequently, the three stress states were applied to subsize specimens cut from the deformed oversize specimens along the rolling direction. To describe the hardening behaviours during non-proportional loading, a homogeneous anisotropic hardening model was adopted and calibrated using two-step uniaxial tension tests. Subsequently, the differential hardening model was successfully incorporated into the homogeneous anisotropic hardening model to describe both the differential hardening and the strain path change-induced hardening behaviours under the two-step loadings, i.e., uniaxial tension to pure shear and uniaxial tension to plane strain tension. Both experimental and simulation results underscore the necessity to consider differential hardening under non-proportional loading conditions.