Constitutive model for thin sheet metal with one or several grains across thickness in micro-forming

Effects of four factors on thin sheet metal flow stress were considered, including grain size d, thickness t, grain number across thickness (t/d ratio) and surface property. Surface model was adopted to quantitatively describe the effect of t/d ratio on flow stress for pure copper. It is predicted that when t/d ratio is larger than a critical value, effect of t/d ratio on flow stress can be neglected. Existence of critical t/d ratio changes the Hall-Petch relationship and evolution of flow stress with thickness. A criterion was proposed to determine critical t/d ratio. Then a comprehensive constitutive model was developed to consider all the four factors, with parameters determined by fitting experimental data of high purity Ni. The predicted results show the same tendencies with experiment results. Particularly when t/d ratio decreases, Hall-Petch relationship and evolution of true stress show varied slopes with two transition points.