A novel unified data-based approach for determining the material constants in complex unified constitutive equations
In the hot metal forming processes, materials deform viscoplastically and the microstructure of materials changes dynamically, and constitutive equations used to characterize the material flow and microstructure evolution during the deformation can be complicated. Although different types of constitutive equations have been proposed by many researchers, due to the strong non-linear relationship and interconnectivity between the variables, determining the material constants in the constitutive equations could be complex, and it lacks a unified optimization method and program for these problems. This work will develop a groundbreaking step-by-step optimization methodology to determine the material constants in constitutive equations effectively and efficiently. Relationships between the variables will be analyzed, and the computational complexity and cost will be reduced by dividing the whole optimization process into several steps and considering only one or several variables in each step. Five different sets of experimental data for different materials and forming conditions will be considered in this work for demonstration, and different constitutive equations will be used to describe the material flow behaviors and microstructure evolution, where the material constants will be determined using the proposed optimization method. Instead of taking days, weeks or even months to accurately determine the large number of material constants, the proposed unified data-based optimization method only took less than 7 minutes even for the most complex case, using a conventional personal desktop computer. This transformative optimization method will significantly improve the accuracy and efficiency of viscoplastic constitutive models’ development, enabling more complex microstructure behaviors e.g., phase transformation, void reduction, solid welding quality to be incorporated and reliably modelled.