Modeling the Forming Limit Curve of Steel Sheets Using GTN Model Parameters and Swift Hardening Equation Variables

مهندسی متالورژی و مواد

Article 4, Volume 35, Issue 4 - Serial Number 36, December 2024, Pages 79-96   

Document Type: Original Articles

DOI: 10.22067/jmme.2024.87801.1147

Authors

Mahdi Chelovian; Abdolvahed Kami^*

Faculty of Mechanical Engineering, Semnan University, Semnan, Iran.

Abstract

The precise prediction of forming limit curves (FLCs) is vital for improving the formability of steel sheets, significantly impacting industries like automotive and aerospace manufacturing. Despite its significance, current approaches for determining FLCs are complex and necessitate more reliable prediction models. This paper aims to introduce theoretical relationships for accurately predicting limit strains and constructing the FLC of steel sheets. By selecting four specific points on the FLC, the corresponding maximum and minimum limit strains were determined using analytical models based on finite element simulations of the M-K model. Two sets of parameters were considered: GTN damage model parameters (micro-scale) and Swift's equation variables (macro-scale). The seven studied parameters, including void volume fractions, adjustment parameter (q2), critical void volume fraction, nucleation void volume fraction, coefficient of strength, initial strain, and hardening exponent, were used as inputs for a central composite design of experiments. Each experiment represented a combination of the parameters and was simulated in four forming paths, providing coordinates for the FLC points. Interpolation of data from the finite element simulations led to the development of practical analytical functions for predicting the FLC of steel sheets. The functions' validity was demonstrated by computing multiple FLCs with randomly chosen parameter values and comparing them to FLCs obtained from the M-K model's simulations. The findings indicated that the formulated equations precisely determine the FLC of steel sheets. The predicted limit strain in the AISI304’s plane strain zone was 0.3647, exhibiting an error of 0.44% relative to the experimental value of 0.370.

Keywords

GTN model; Forming limit curve; M-K model; Steel sheet; AISI304

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