On the effect of material strength on ductile failure through the extended Gurson model

The ductile failure process in steel involves micro-void nucleation, growth, and coalescence of the formed voids. Experimental evidence have shown that both the stress triaxiality (T) and the stress state characterized by the Lode parameter (L) significantly influence the ductile failure strain. Moreover, the sensitivity to L itself has been found to increase with material strength, a trend quantified by the Lode sensitivity parameter (L_S). In this study, the effect of material strength on ductile failure is investigated for six steel grades ranging from medium to high strength using the extended Gurson model. The model parameters governing damage, such as the initial void volume fraction f₀ and coefficient of shear-induced damage k_ω, are calibrated using tensile tests on round notched bar (RNB) and flat notched specimen (FNS) geometries, respectively. The calibrated model is further validated against experiments on two shear specimen configurations, showing markedly good agreement. The results confirm that the failure strain of steels is not governed by T alone, and a clear relationship between both k_ω and Lode sensitivity L_S with the material strength is established. Specifically, k_ω increases approximately linearly from 0.6 to 3.2 with the ultimate tensile strength over the range 520–1620 MPa. The analysis also shows that steels with ultimate tensile strengths exceeding 400 MPa exhibit pronounced strength-dependent Lode sensitivity, which increases from values close to unity in medium-strength steels to nearly 3 in high-strength steels. Complementary scanning electron microscopy (SEM) fractography supports these findings, showing a transition from rough, highly deformed fracture surfaces in low-strength steels to smoother surfaces with limited plastic deformation in high-strength steels, consistent with the observed increase in L_S and k_ω. This establishes a constitutive link between strength-dependent shear-driven void evolution and the increasing sensitivity of ductile failure to the Lode parameter in high-strength steels.