Characterization of the microscale forming limit for metal foils considering free surface roughening and failure mechanism transformation

Abstract

The failure behavior of metal foils is greatly influenced by size effect and surface roughness. To explore and characterize the effects induced by the two factors on the formability and failure mechanism in microscale plastic deformation, the micro-scaled forming limit of metal foils (μ-FLC) was investigated by physical experiment and theoretical modeling. A sectionalized failure criterion was proposed according to the modified Considère and Parmar-Mellor-Chakrabarty (PMC) models, which considers the coupled effects of free surface roughening and failure mechanism transformation at microscale. In detail, the modified Considère criterion coupled with the free surface roughening was proposed to predict the right-hand-side μ-FLC, while the PMC model by adjusting the surface roughness parameter was developed to construct the left-hand-side μ-FLC. The physical experiment suggests that the magnitude of surface roughness caused by free roughening can be up to 10˜20% of foil thickness until the fracture of the sample. The failure mechanism of metal foils in microscale deformation changes from localized necking to diffuse instability with the transformation of stress state from uniaxial to equi-biaxial tension. Furthermore, the increasing grain size or the decreasing foil thickness promotes the transformation of failure pattern from the localized necking to diffuse instability. The experimentally determined μ-FLC descend with the increasing grain size and the decreasing foil thickness. The original Considère criterion and Marciniak-Kuczynski (M-K) model are inappropriate for the determination of μ-FLC as they do not consider the significant effects of free surface roughening and failure mode transformation on the micro-formability of metal foils. The developed criterion was validated and corroborated by comparing the theoretically determined μ-FLC with the experimental one. All of these findings advance the insight into the ductile fracture and formability of metal foils influenced by size effect and surface roughness and help to improve the microformed product quality and facilitate the applications of microforming technologies.