Strain gradient plasticity based finite element analysis of ultra-fine wire drawing process

Abstract

Steady-state rigid-plastic finite element analysis coupled with strain gradient plasticity theory has been performed to examine the size effect of material on its plastic deformation behavior and find an optimal semi-cone angle of die which minimizes the drawing energy in the ultra-fine wire drawing process. A stream-line tracing method was adopted to calculate strain component at each element and a strain surface function was introduced to compute the equivalent strain gradient of each element. Introduction of this function enables us to use an established FE code without renewal of its main structure. Hence, the constitutive equation in FE formulation is changed to couple the strain gradient plasticity. A series of FE simulation reveals that significant differences in drawing stress are observed when material size approaches its intrinsic material length. When the strain gradient plasticity theory is reflected on the steady-state FE analysis, the optimal semi-cone angle of the die is reduced by 30%. The variation of optimal semi-cone angle is attributable to considerable increment of homogeneous deformation when the material size reaches its intrinsic material length.