Genetic Algorithm-based Optimization Procedures to Find the Constants of Johnson-Cook Constitutive Equation

Johnson-Cook constitutive equation is one of the most famous constitutive equations that have ever been developed to model the hot deformation flow curves of different materials. This equation is a predefined model in the traditional finite element codes to describe the material behavior in applications such as simulating the manufacturing processes. In this work, two different genetic algorithm-based (GA) optimization procedures, referred to as free and constrained optimization procedures, were proposed to find the constants of the Johnson-Cook constitutive equation. The proposed procedures were applied to fit the Johnson-Cook constitutive equation on the experimental flow curves of API X65 pipeline steel. According to the obtained constants, the modeling performances of the proposed procedures were compared with each other and with the modeling performance of the conventional procedure of finding the constants of the Johnson-Cook equation. Root mean square error (RMSE) criterion was used to asses and to compare the performances of the examined procedures. According to the obtained results, it was determined that the proposed free GA based optimization procedure with the RMSE value of 7.2 MPa had the best performance, while the performance of the conventional procedure was the worst.