Effects of non-quadratic anisotropy and through-thickness normal stress on formability and porosity evolution in ductile materials

The accurate prediction of forming limit diagram (FLD) is crucial in sheet metal forming to prevent localized necking. This study investigates the effects of non-quadratic anisotropy and through-thickness normal (TTN) stress on the prediction of FLD and porosity evolution in ductile porous materials, such as Al-2090 and Al-3104 aluminum alloys. Various non-quadratic anisotropic yield functions (Barlat's yield surfaces YLD-1991, YLD-2004-18p, YLD-2004-27p, YLD-2011-18p, and YLD-2011-27p) are compared with isotropic and quadratic anisotropic (Hill-1948) yield functions. Gurson–Tvergaard–Needleman model is considered for modeling ductile porous materials. FLDs are predicted using both the bifurcation theory and Marciniak and Kuczyński (M − K) imperfection approach. It is found that Barlat's YLD-1991 shows better agreement with FLD experimental data for Al-2090, while Barlat's YLD-2011-27p accurately predicts the FLD for Al-3104. The prediction results also reveal that the presence of TTN stress increases the forming limit strains, especially on the right-hand side of FLD. For the undamaged material model, the FLD predictions show unrealistic sensitivity to TTN stress. By contrast, for the damaged material model, higher TTN stress delays porosity evolution, thus increasing the forming limits. Moreover, it is shown that TTN stress strongly influences void growth, while void nucleation remains unaffected. This study emphasizes the significance of considering non-quadratic anisotropy and damage (porosity), particularly in relation to TTN stress, for accurate FLD prediction in various ductile materials. © 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.