Prediction of complete forming limit diagram from tensile properties of various steel sheets by a nonlinear regression based approach

Abstract

Experimental Forming Limit Curve (FLC) and tensile properties of various steel grades are collected from literatures to validate the proposed model. The experimental results show that the ultimate tensile stress (σUTS), total elongation (ɛt), coefficient of normal anisotropy (r), tensile strain hardening exponent (n) and sheet thickness (t) are strongly related to the plane strain forming limit (FLC0) values for steel sheets. A nonlinear regression equation is proposed to predict FLC0 from uniaxial tensile properties like σUTS, ɛt, r, n and t. To verify the predictive capability of the proposed equation, predicted FLC0 values for fifty six steel grades in various thickness and strength ranges are compared with experimentally measured FLC0 values. It is observed that the newly developed nonlinear regression equation predicts well the FLC0 values. Left side of the strain-based FLC is calculated from a criterion (a line with slope of –1) which is normally well matched with experimental observation. Right side of the strain-based FLC is calculated from modified Keeler–Brazier power equation. In the original Keeler–Brazier power equation for the right side of the FLC the exponent is considered as 0.5, while experimental finding revels that it varies systematically with FLC0. Complete strain-based FLCs calculated from proposed method are matched well with experimental FLCs for various automotive steel grades like IF, IF 340, DP 780, TRIP 780 and TWIP 940 steels.