A constitutive model for thin sheet metal in micro-forming considering first order size effects

Abstract

Size effects in the minimization make most know-how of traditional macro-forming not suitable for the micro-forming process. Material behaviours greatly vary in micro-forming process with different thickness and grain size. The influence of the first order size effects (size effects I) on flow stress has been studied quantitatively using the surface layer model and a new presented internal grain boundary model. It was discovered that the flow stress of micro-forming can be expressed as a function of t/ d (thickness/average grain size) ratio. Then, a new constitutive model considering the size effects I for thin sheet-based micro-forming has been developed combining the Hollomon equation and Hall–Petch relation. The model has also been validated with the experimental results in the literature. A good coincidence is obtained when t/ d > 1. However, it has great offset when t/ d < 1 due to the orientations of the local individual grains have great influence on flow stress, which can be ignored by the new constitutive model because it only considers the influence of grain size. This investigation gives the support for theoretical and numerical study of micro-forming.