Forming limit strains of interstitial free-IF steel sheet

Abstract

Present work examines mathematical models to predict the onset of localized necking in sheet metal forming of interstitial free steel, such as biaxial stretching and deep drawing. Forming Limit Curve, FLC, which is an essential material parameter necessary to numerical simulation by FEM, of IF steel sheet was assessed experimentally by Nakajima testing and ASAME software. The “Map of Principal Surface Limit Strains - MPLS”, shows the experimental FLC which is the plot of principal true strains in the sheet metal surface (ε1, ε2), occurring at critical points obtained in laboratory formability tests or in the fabrication process of parts. Two types of undesirable rupture mechanisms can occur in sheet metal forming products: localized necking and rupture by induced shear stress. Therefore, two kinds of limit strain curves can be plotted in the forming map: the local necking limit curve FLC-N and the shear stress rupture limit curve FLC-S. Localized necking is theoretically anticipated to occur by two mathematical models: Marciniak-Kuczynski modeling, hereafter named M-K approach, and D-Bressan modeling. In the M-K approach, local necking originates at an initial sheet thickness heterogeneity or defect fo = tob/toa. The strain state inside the evolving groove moves to plane strain and the limit strain ε1* is attained when the strain ε1a outside the groove or neck stop to increase. In the D-Bressan model, local necking is proposed to initiate at the instability point of maximum load, at a thickness defect (λ/μ)diffuse inside the grooved sheet thickness. The inception of visible grooving on the sheet surface evolves from instability point to localized (λ/μ)crit and final rupture, during further sheet metal straining. Work hardening law is defined for a strain and strain-rate material by the effective current stress. The average experimental hardening law curve for tensile tests at 0°, 45° and 90°, assuming normal anisotropy, was used to analyze the plasticity behavior during the biaxial stretching of sheet metals. Theoretical predicted curves of local necking limits are plotted in the positive and negative region of MPLS for different defect values fo and λ/μ parameters. Limit strains are obtained from a software developed by the authors. Experimental results of FLC obtained from experiments for IF steel sheets were compared with the theoretical predicted curves: the correlation is reasonable good in the positive quadrant, but the predicted values are above the experimental points in the negative quadrant due to punch friction, non-linear strain path and grid measurements.