Necking and fracture limit analyses of different pre-strained sheet materials in polar effective plastic strain locus using Yld2000-2d yield model

Abstract

This paper aims to estimate and analyze both the necking and fracture based path-independent forming limit criteria during two-stage forming of anisotropic sheet materials. In this context, in-house experimental setups were fabricated to impart pre-strain along three distinct strain paths viz. equi-biaxial, plane strain and uniaxial in different automotive grade sheet materials namely EDD, AA5052 and DP600. Uniaxial tensile and stack compression tests were conducted, and the test results were used to evaluate the eight anisotropic coefficients of Yld2000-2d yield model. The predicted evolutions of the yield loci and both the strength and plastic strain ratio (r-value) directionalities of the pre-strained materials were calibrated with experimental data. In the second stage of deformation, all pre-strained sheet materials were stretch formed up to the onset of necking and further until the initiation of fracture. Correspondingly, the forming limit diagram (ε-FLD) and fracture forming limit diagram (ε-FFLD) were experimentally evaluated. The necking and fracture limit of as-received materials was theoretically predicted incorporating calibrated Yld2000-2d yield model in the geometrical imperfection based Marciniak-Kuczynski (MK) model and ductile fracture based Bao-Wierzbicki (BW) damage model, respectively. It is noteworthy that the dynamic shifting of pre-strained ε-FLDs and ε-FFLDs has been recorded in principal strain space (ε1, ε2) depending on the type and amount of pre-strain. Hence, the polar effective plastic strain (PEPS) based necking (PEPS-FLD) and fracture (PEPS-FFLD) limits were estimated using Yld2000-2d anisotropy plasticity theory, and it was observed that the shift of the limiting strains was restricted successfully. It was found that the maximum absolute error during necking and fracture dome height prediction of pre-strained materials was restricted up to 5% and 6%, respectively, when PEPS based failure limits were used as damage model in FE simulation.