Improvement of modified maximum force criterion for forming limit diagram prediction of sheet metal

Abstract

This study presents a new criterion (MMFC2) for predicting the forming limit curve (FLC) of sheet metal. The strain path evolution of a critical element examined in a uniaxial tensile test is elaborated by incorporating the results of experimental measurement, finite element simulation, and theoretical prediction via the Modified Maximum Force Criterion (MMFC). A scaling factor is introduced to mimic the theoretical evaluation with the simulated one. It is believed that the rotation of the principal axes of the theoretically considering material point, which is initially co-axial with the external load coordinate, implicates the macro track of the strain path change. Furthermore, an optimal event of the second derivative of the axial rotations is proposed to indicate the strain localization and formulate the FLC. The performance of the proposed criterion is compared with that of the original MMFC in predicting the FLC of three automotive sheet metals, of which all related data were published in the Benchmark of Numisheet 2014 conference. The use of three different hardening laws and three yield functions is examined in the analogy. The comparison reveals that the results of MMFC2 are more sensitive to the employed constitutive model than that of MMFC. Furthermore, the proposed MMFC2 presents concordant results with the experimental data. Nakajima tests are conducted for CR4 mild steel sheets to validate the capacity of the proposed criterion. Well agreement between the experimentally measured data and theoretical prediction based on the Yld2k yield function verifies its usefulness in practice.