Analysis of the pre-straining effects on the limit strains of interstitial-free steel: experiments and elasto-plastic modeling of strain and stress-based forming limit curves

Abstract

In this work, the limit strains under as-received and pre-strained conditions of an interstitial-free steel sheet were investigated by mechanical tests and numerical modeling. An original testing procedure was proposed to reproduce two equivalent pre-straining amounts under equibiaxial stretching (EB-PS) and uniaxial tension (UT-PS) deformation modes. The limit strains were defined from Nakajima’s hemispherical punch tests using digital image analysis according to the ISO 12004:2 standard. The plastic behavior of the interstitial-free steel sheet was evaluated by uniaxial tensile, disk compression, and hydraulic bulge tests. Moreover, an elasto-plastic framework based on the Marciniak–Kuczynski (M–K) model is proposed to forecast both the strain-based and stress-based forming limits. The parameters of the Yld-2000-2d yield criterion were identified using the plastic anisotropy coefficients with the flow-stress values determined from two distinct amounts of plastic-work per unit volume. For both deformation modes and pre-straining levels defined by the von Mises effective plastic-strain (4.8% and 9.0% EB-PS; 5.0% and 10% UT-PS), the transformed polar effective plastic-strain (PEPS) and forming limit stress (FLSC) results shown to be more strain-path insensitive than the conventional strain-based forming limit curve (FLC). The proposed elasto-plastic M–K model successfully forecasted the linear strain-path limit strains defined using the FLC, PEPS, and FLSC representations. The M–K model also provided quite conservative predictions for the pre-strained PEPS and FLSC. The Yld-2000-2d parameters identified using the flow-stress values defined from an upper-level of the plastic-work per unit volume proved to be the best choice in the present M–K modeling framework.