Analytical and numerical instability analysis of functionally graded low-carbon steel

The instability point of a material is one of the most important factors when choosing a material, as it could be a good representation of its formability. In this study, the instability of functionally graded materials (FGM) was investigated. An algorithm is proposed for predicting the instability of functionally graded low-carbon steel with gradient work hardening exponent (n) and strength coefficient (K). The investigated work hardening exponent and strength coefficient of the FGM vary through the cross-section as a function of radius. Numerical methods like the Simpson rule of integration were utilized to solve the equations. The mathematical and experimental results are compared, and it can be seen that the algorithm has a reliable consistency with the experimental results. The presented analysis shows that the instability of the functionally graded low-carbon steel can be predicted using the calculation of the average strain hardening exponent. The calculated average work hardening exponent (n ̅) was 0.1095 and 0.1657 for the 550 °C and 650 °C annealed samples, respectively. The instability of more complicated FGMs can be predicted with the present algorithm.