Void shape and orientation effects on anisotropic porous material formability

Abstract

This study investigates the influence of void shape and orientation on the Forming Limit Diagrams (FLDs) of porous materials with non-quadratic anisotropy. The constitutive framework integrates the Gologanu–Leblond–Devaux (GLD) damage model, which accounts for void morphology, with Barlat’s YLD-2004-18p non-quadratic yield criterion to capture metal matrix plastic anisotropy. The combined GLD-YLD model is further coupled with the Marciniak–Kuczyński (M–K) imperfection approach to predict FLDs for anisotropic sheet metals. Results demonstrate that void morphology considerably affects formability, with prolate (needle-like) voids enhancing material ductility, as compared to oblate (plate-like) voids, while spherical voids yield an intermediate behavior. Furthermore, the study highlights that the impact of material orientation on formability involves a complex interplay of several factors, which include coupled matrix-induced and void-shape-induced anisotropy, the relative angle between the rolling direction and void orientation, and void nucleation mechanism. The model predictive capabilities are assessed against experimental FLD data for two aluminum alloys. Although these alloys show only slight sensitivity to void morphology, due to low porosity, the void shape-dependent anisotropic GLD-YLD model better captures the experimental trends as compared to the undamaged isotropic von Mises model, which overly overestimates formability on the right-hand side of FLD. The role of isotropic hardening is also examined, which shows that higher hardening improves formability, and the effect is smallest for oblate voids under balanced biaxial loading. These findings underscore the importance of incorporating both damage and matrix-induced anisotropy in constitutive modeling for accurate FLD prediction.