Size effect on the forming limit of sheet metal in micro-scaled plastic deformation considering free surface roughening

In micro-scaled plastic deformation, the deformation capability of sheet metals is quite different from those in macro-scale. Compared with the conventional sheets, the ratio of free surface roughness to the thickness of thin sheet metal is more obvious. The so-called free surface roughening phenomenon and size effect may affect the micro-scale forming limit curve (μ-FLC) of sheet metal. To explore how the interaction of free surface roughening and size effect affects the μ-FLC of thin sheet metal, the original M-K model was modified by introducing free surface roughening. The continuous geometrical imperfection calculated by the original M-K model was compared with the experimental surface irregularity. In addition, the effect of grain size on the μ-FLC was also analyzed. Through the comparison between the predicted μ-FLCs and the experimental ones, the modified M-K model is proven to be able to model the decrease of μ-FLCs caused by the geometry and grain size effects, which reveals that the modified M-K model is more suitable for the prediction of μ-FLCs by considering the combination of size effect and free surface roughening.