A Hybrid Model for Studying the Size Effects on Flow Stress in Micro-Forming with the Consideration of Grain Hardening

Size effects extremely exist in the metal micro-forming process. When a deformation process scales down to micro scale, the appearances of geometry size and single grain size start to play a major role in deformation. Generally, the size effects are unavoidable in the experimental work and cannot be neglect in the optimization of micro-forming processes. In this paper, size effect on flow stress is investigated in the form of the coupled effect of workpiece geometry (sample thickness) and grain size, (T/D) by the micro tensile test of pure copper foil. Following the previous approaches, a new hybrid material model is projected to describe the hardening behavior of grains in polycrystalline material. Tensile tests performed on the copper foil with constant thickness and width, while to get dissimilar grain sizes, the foil annealed for different times. The ratio of thickness to grain size (T/D) is limited to larger than 1 (T/D˃1). A hybrid material model is proposed and established based on grain heterogeneity and sample thickness. The hybrid material model builds a relationship between the surface layer and sheet interior. The hybrid material model developed by the strain gradient theory in which the dislocation cell structure, cell densities (interior and wall) engaged to define the polycrystalline aggregate and calculated the dislocations in a grain (grain interior and grain wall). The results show that flow stress varies with the different values of T/D, but with an increase of the share of the grains flow stress start to decreases. After applying the hybrid material model of flow stress, the micro-tensile test of copper foil is simulated by finite element method. The simulation outcomes well matched with experimental results.