Measurement of ductile forming limit in non-linear strain paths and anisotropic yield conditions for 11% Cr steel sheets

Abstract

The ductile forming limit in nonlinear strain paths is investigated for a 11 % Cr steel which displays a high r-value and is used practically in difficult forming applications. Experimental measurements were performed to examine the forming limit in strain paths which involve plane strain loading in first-stage loading and loading at various strain ratios in the second stage. Because the forming limit diagram (FLD) is not applicable to nonlinear loading paths, the forming limit stress diagram (FLSD) theory is investigated. In order to evaluate the stress at the forming limit from measured strain, the anisotropic yield criterion of the material is investigated by uniaxial tension testing in three directions and biaxial stretching using hydraulic bulging. Hill quadratic yield criterion gives the best approximation for biaxial tension, whereas Hosford criterion is more appropriate for uniaxial tension. Yld2000-2d is the ideal criterion for both stress states. Considering the possible effect of dependency of r-values on measured strain, the evolution of r-values is measured. Under sufficiently large strain, the r-value becomes virtually constant. Based on the preliminary investigation outlined above, it was found that the evaluated forming limit stresses in nonlinear strain paths lie on one consistent line in the principal stress field. The limit stress line is not affected by changes in the amount of strain applied in the first loading stage, demonstrating that the FLSD theory of ductile fracture is adequate for this particular material. © 2007 ISIJ.