Size effect affected formability of sheet metals in micro/meso scale plastic deformation: Experiment and modeling

• The setups of forming limit testing were developed for meso scale sheet metals.
• The forming limit curves (FLC) were developed for pure copper sheets.
• The FLC shifts down with the decrease of thickness-to-grain-size ratio.
• The GTN–Thomason coupled model was extended by considering the size effect.
• The FLCs predicted based on the model agree with the experimental ones.

Ductile fracture of metallic materials in micro/meso scale plastic deformation is influenced by geometry and grain sizes and the so-called size effect thus exists. To reveal how the size effect affects the formability of sheet metals in micro/meso scale plastic deformation, the forming limit of sheet metals was studied by experiment and modeling. An extended coupled damage model was first developed based on the Gurson–Tvergaard–Needleman and the Thomason models via considering the geometry and grain size effects on void evolution. In modeling process, the void nucleation was analyzed by taking account the phenomenon that the number of voids decreases with the ratio of thickness to grain size of workpiece. For the void growth, the widely used surface layer model was employed to describe the size effect on the flow stress of material. The grain size effect on void spatial arrangement was also modeled during the coalescence of micro voids. The model was then implemented into finite element simulations and the predicted forming limit curves under different scale factors were constructed. On the other hand, the forming limit experiments were conducted based on the miniaturized Holmberg and Marciniak tests to estimate the formability of sheet metals under different conditions. Both the physical experiments and finite element simulations show a significant size effect on the micro/meso scaled fracture behavior: The forming limit curve shifts down with the decreasing ratio of the thickness to grain size. The simulation results were also corroborated and verified by experiments. In addition, when the ratio is two or less than two, the very scattered limit strain results are observed in the experiments and the strain localization tends to occur at the beginning of deformation. The research conducted advances the understanding of size effect on the formability of micro/meso scaled sheet metals and thus helps the development of the successful and reliable microforming processes.