Finite element modeling for ultrathin and thick steel sheets

Abstract

The present study aims to analyze the specific problems associated with the use of shell elements, which are commonly used in industry, for finite-element (FE) simulation of ultrathin and thick steel sheets. For ultrathin materials, the constitutive description of a 0.1-mm-thick ferritic stainless-steel sheet was optimized for application to springback simulations after bending. Springback simulations require the Bauschinger effects to be carefully characterized, which is a challenging task with an ultrathin sheet because of the overwhelming occurrence of buckling during compression loading. The coefficients of the homogeneous anisotropic hardening (HAH) distortional plasticity model, which accounts for reverse loading effects, were calibrated with Zang’s novel approach based on three-point bending tests conducted on pre-strained sheets [S.L. Zang, 2014]. The Hockett–Sherby isotropic hardening law and the Yld2000-2d non-quadratic yield function were considered in this study to complete the HAH framework. Moreover, the degradation of the elastic modulus was accounted for in the FE simulations. The coefficients of the HAH model were calibrated using an inverse method by minimizing the difference between the experimental and predicted specimen profiles after three-point bending and springback of pre-strained sheets. To validate the coefficients determined from three-point bending, U-draw bending tests were conducted and FE simulations were carried out. The springback predictions were found to be in good agreement with the experimental results for all three pre-strains investigated, i.e., 0% (as-received material), 7.5%, and 12.5% pre-strained ferritic stainless-steel sheets. This study clearly indicates that the use of shell elements in the FE modeling of thin sheet metal forming is not limited by the inherent plane stress assumption of the shell approach alone but also by the challenge of testing the material in question. Very thin sheets are highly vulnerable to specimen buckling and edge quality issues. As a result, test analysis is not straightforward and requires the use of advanced mechanical and computational tools to extract the suitable data and develop sets of constitutive coefficients appropriate for forming process simulations. Limits to the application of shell elements in thick sheets were investigated with three different hot-rolled steel sheet samples (about 3.0-mm thickness). Since the formulation of shell elements is based on the plane stress assumption, this approach for the simulation of thick sheet forming seems unreasonable. An in-depth level of investigation was performed by categorizing forming modes into tension and bending modes. The Swift hardening law and the Yld2004-18p yield function were considered for constitutive modeling in this study. In the tension mode, the load predicted with shell elements dramatically decreased after the maximum load, because the evolution of the hydrostatic stresses could not be fully considered. Taking the examples of uniaxial and plane strain tension tests, the lack of hydrostatic stress was compensated for by using strain hardening and strain rate sensitivity corrections. These methods successfully postponed plastic flow localization and led to load predictions that were in good agreement with solid element simulations and experiments. In the bending mode, taking the example of a stretch bending test, the behavior of the shell elements was analyzed. It was found that the predicted failure area based on the shell elements was different from that of the solid elements and the experiments. Because the flow stresses of the shell elements were overpredicted in the bending mode, a correction in the form of thickness reduction in the bend area was adopted to force plastic flow localization to occur in the bending region. This method provided a reasonable failure region and load prediction for the shell elements in the bending mode. It was shown that the methods proposed for these two modes are compatible and can be operated simultaneously. This study clearly demonstrates the limitations of using shell elements in the FE modeling of thick sheet metal forming applications owing to the inappropriate nature of the plane stress assumption, which cannot capture all physical phenomena during a boundary value problem. Nevertheless, a detailed outline of a methodology that is implemented in an FE code for general sheet metal forming process simulations to compensate for the limitation of the shell elements was developed. This methodology is expected to provide the industry with an improved framework for conducting numerical simulations with shell elements. Although not physical, such simulations are time-efficient for large practical problems.