A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

Abstract

This investigation focuses on the Marciniak and Kuczynski, visco-plastic, self-consistent (VPSC) prediction of the forming-limit curves for AA6061-T4 aluminum, cold-rolled steel and a Zn-Cu-Ti alloy denoted Zn20. These simulations were based on and calibrated with an extensive experimental database–stress/strain curves, measurements of Lankford coefficients and experimentally determined actual initial textures—and they were conducted with various parametric profiles: hardening laws and both VPSC affine and tangent linearization techniques. Anisotropy, as seen through stress/strain curves and Lankford coefficients, was found to dominate the left-hand side of the forming-limit diagram. After matching the simulations to the hardening curves and Lankford data, satisfying agreement for all three materials was found for the forming-limit measurements at and between plane-strain and uniaxial tension. The right-hand side of the forming-limit diagram was dominated by texture evolution. In the case of aluminum, predicted balanced-biaxial textures evolved differently for the affine and tangent linearizations and the predicted limit strains did not coincide. It was only when the simulations were forced to maintain the initial texture that the results of the two linearizations matched. The affine and tangent results were also in disagreement for the cold-rolled steel. Eliminating texture evolution alone did not resolve this inconsistency. It was necessary to also eliminate pencil glide—restricting glide to only the {110} <111> planes and directions, 12 slip systems—for the affine and tangent results to agree, The initial Zn20 texture hardly evolved from its initial state in the simulations. Thus, it was not surprising that the VPSC affine and tangent limit-strain predictions coincided without requiring restrictions. These results show the importance of accurate input data and at a minimum having balanced-biaxial limit-strain data to verify the simulation predictions. Clearly, a single parametric input recipe is insufficient when considering multiple material classes.