Numerical Simulation of Plastic Softening at Elevated Temperatures Using Gradient Damage Methodology

In the present work, gradient plasticity-based damage methodology has been employed to capture the plastic softening behaviour under monotonic loading at elevated temperatures. The conventional approach to capture the stress-strain curve of materials using classical elastoplasticity-based simulation often suffers from its incapability to accurately capture the softening curve. This drawback becomes more pronounced at elevated temperatures where an early onset of softening occurs. Therefore, the present work investigates the stress-strain softening behaviour of steels under tensile loads at elevated temperatures through gradient based elasto-plastic damage methodology. The framework, originally developed by Engelen et al. (2003), has been modified by using a temperature-dependent damage evolution law. The damage variable, which is incorporated in the yield function, captures the accumulation of damage through non-local strains. The gradual reduction of stiffness with increasing load captures the softening behaviour of the material. Two example problems are numerically investigated, firstly a S900 steel specimen and secondly a Q960 steel specimen. From experimental evidences, it is found that the present methodology satisfactorily captures the plastic softening upto 700˚C for both materials. The present results are also compared with classical von-Mises elastoplasticity through Ramberg-Osgood behaviour, and it is observed that the present methodology provides better agreement with the experimental data of S900 steel (Narimani et al., 2023) as well as Q960 steel (Wang et al., 2020).