Quantification of multiple softening processes occurring during multi-stage thermoforming of high-strength steel

During the multi-stage thermoforming of steel, work hardening and the stress softening processes initiated by its dynamic recovery (DRV) and dynamic recrystallisation (DRX) are mainly considered for predicting the flow stress. However, the stress softening components describing the static recovery (SRV), static recrystallisation (SRX), and metadynamic recrystallisation (MDRX) processes that occur during post-deformation annealing have not been reflected in the majority of the existing plasticity models, leading to poor prediction accuracy. To accurately predict the flow stress generated during multi-stage thermoforming, modification has been proposed to the Sellars-Tegart-Garofalo model to account for the evolution of all possible recrystallisation processes and the resultant softening effects in the present work. An integrated response of the flow stress caused by DRV-initiated softening and work hardening was characterised using the Estrin-Mecking dislocation model. Another softening process occurring during thermoforming was quantified by a modified strain-independent DRX kinetic equation. In order to quantify all softening processes occurring during multi-stage thermoforming, comprehensive relationships between the described dynamic and static processes were discussed, and the softening fraction was introduced as a global internal variable for quantifying softening equations. In addition, variations of these physical parameters with the interruption stress and holding time were discussed, and the dependency of the residual softening fraction on the former DRX process was expressed as a logarithmic function. A unified constitutive model capable of predicting the comprehensive contribution of multiple softening processes and the resultant macro-flow stress was constructed by updating internal variables. The flow stress values predicted by the unified model were consistent with the results of compression experiments involving complex loading and isothermal histories. This study proposes an efficient approach to elucidating the relationship between the flow stress of steels and the softening effect of microstructural evolution.