Modeling of Size Effect on Tensile Flow Stress of Sheet Metal in Microforming

This investigation considers the size effect on the deformation behavior of simple tension in microforming and thus proposes a simple model of the tensile flow stress of sheet metal. Experimental results reveal that the measure of the flow stress can be represented as a hyperbolic function $tanh(T/D)$⁠, which is a function of $T/D$ (sheet thickness/grain size). The predicted flow stress agrees very well with the published experiment. Notably, a specimen with smaller grains has lower normalized flow stress for a given $T/D$⁠. Since the material properties of the macroscale specimen do not pertain to the microscale, a critical condition $(T/D)c$ that distinguishes the macroscale from the microscale in the tensile flow stress is subsequently proposed, based on the “affected zone” model, the pile-up theory of dislocations, and the Hall–Petch relation. The distribution of the predicted $(T/D)c$ is similar to the experimental finding that the $(T/D)c$ decreases as the grain size increases. However, the orientation-dependent factor $β$ is sensitive to $(T/D)c$⁠. Hence, further study of the orientation-dependent factor $β$ is necessary to obtain a more accurate $(T/D)c$ and, thus, to evaluate and understand better the tensile flow stress of sheet metal in microforming.