Damage and size effect during superplastic deformation

Superplastic forming is a valuable metal working technique because of the extreme ductility that can be achieved. However, it is limited in application due to the presence of small voids that grow and coalesce during the forming process, often causing premature failure. In order to understand and control this phenomenon accurate constitutive models must be developed which account for void parameters that affect the macroscopic behavior of the material. This paper looks specifically at the effect of void size and spacing on the ductility and flow stress of viscoplastic materials. Based on the gradient-dependent theory of plasticity, a model is proposed that accounts for size effects by incorporating strain gradient terms into a continuum based constitutive equation. Both experimental testing and finite element (FE) modeling were performed on Pb–Sn, tensile specimens with small holes drilled in them in random patterns. The experimental tests indicate that a decrease in void size results in an increase in ductility. The FE results demonstrate that the gradient terms strengthen the material by diffusing the strain in areas of high strain concentration and delay failure by slowing void growth. In addition, the model predicted an increase in ductility and flow stress with decreasing void size.