Calculation of strain gradient in flow formulation using strain surface function and its applications to micro rolling

Using flow formulation-based finite element analysis, we compute the strain components of material of copper during micro rolling that material size in thickness is 1.25–12.5 μm. To examine whether the computed strain component is the component of Cartesian tensor, we also calculate the strain components using deformation kinematics of each element and we compare the results obtained from both methods. To illustrate application capability of the proposed method, we link the strain gradient plasticity theory with flow formulation-based finite element analysis. We set up a least square function composed of strain components and compute its derivatives and finally obtain information of strain gradient distribution in the material during rolling. It shows when the material thickness is less than the intrinsic material length, its deformation behavior is quite different compared with that computed from the conventional plasticity theory.