Physically Based Constitutive Modeling of Dynamic Strain Aging in C45 Steel

Dynamic strain aging (DSA) is a sudden increase in the strength of a material under certain combinations of temperatures and strain rates. Despite the phenomenon being reported in several other studies, the literature still lacks a specific constitutive model that can physically interpret its effect. Therefore, this work proposes a modification based on physical parameters to the Voyiadjis and Abed (VA) model to account for the effect of DSA in C45 steel. The resulting modified model is then coupled with an energy-based damage model to further capture the effect of material softening. Previously, in VA model, it was assumed that the total activation energy for overcoming the obstacles without external work remains the same which works well in the absence of DSA. However, during DSA, the mobile dislocations are pinned by the diffusing solute atoms. This results in an increase in the total activation free energy needed by the dislocations to overcome the obstacle. Thus, an increase in strength is observed. It is shown in the current work that utilizing the concept of increased solute concentrations at local obstacles, in conjunction with the physical description that the VA model is based upon, successfully captures the phenomenon of DSA in C45 steel. In addition, the metal experiencing softening after reaching its ultimate strength is due to the significant growth of voids and cracks within the microstructure. To capture this behavior, an energy-based damage parameter is incorporated into the proposed model. The coupled plasticity-damage model shows a good comparison with the experimental results.