Study of a drawing-quality sheet steel. II: Forming-limit curves by experiments and micromechanical simulations

Abstract

In Part I of the current paper, we showed the results of uniaxial-tension tests, through-thickness and plane-strain compression experiments, quantitative texture – orientation distribution function – evaluations and Lankford coefficient measurements. These data were used for calibration and verification of a visco-plastic self-consistent (VPSC) polycrystal-plasticity simulation code for predicting a steel sheet’s ability to be stretched and deep drawn. Lankford coefficients are one, although incomplete, measure of a steel’s drawing quality. In order to obtain a deeper insight and better verification of the simulation code, we measured the forming-limit curve, FLC, for the same steel sheet. To make these measurements we stretched circle-gridded sheets of material with a punch and die. Samples had both a flat-sided and hourglass geometry and ranged from 20 to 80 mm in width. The 80 mm wide sample completely filled the die. With this range of sample sizes, we spanned all of the stress states applicable to a FLC, from uniaxial to biaxial tension. Our FLC curve had the classic “V” shape typical of drawing-quality steel, with a minimum safe forming strain of about 0.35 in plane-strain deformation and a safe forming strain of nearly 0.45 in balanced biaxial stretching. To model the FLC behavior, we used the same VPSC model and calibration employed in Part I. In order to obtain a necking instability in the calculation, a Marciniak defect was implemented into the VPSC model. The severity of the defect was adjusted to match the measured instability strain, 0.35, in plane-strain deformation. Both hardening laws fit in Part I were used to calculate the FLC. In the positive biaxial quadrant of the FLC, the limit strains predicted by the power law closely follow the measured uniform deformations, while the saturation law appears to over predict the limit strains. In uniaxial-tension, it was the opposite. The power-law hardening predictions seemed excessive. However, if we consider the FLC curve to be a band of finite width, both hardening laws and the VPSC formulation capture the essence of the FLC data.