Analytical Model for Springback Prediction of CuZn20 Foil Considering Size Effects: Weakening versus Strengthening

The prediction of springback angle for ultra-thin metallic sheets becomes extremely difficult with the existence of size effects. In this study, size effects on the springback behavior of CuZn20 foils are investigated by experiments and analytical methods. The experimental results reveal that the springback angle first decreases gradually and then increases markedly with the decrease of foil thickness, which cannot be analyzed by current theoretical models. Then, an analytical model based on the Taylor-based nonlocal theory of plasticity is developed, in which the drastic increases of both the proportion of surface grains and the strain gradient are taken into account. Moreover, the influence of strain gradient is modified by the grain-boundary blocking factor. The calculation results show that the springback angle of foils is determined by the intrinsic competition between the decrement angle caused by surface grains and the increment angle caused by the strain gradient. Besides, the relative error of predicted springback angle by the model is less than 15%, which means that the developed model is very useful for improving the quality of micro sheet parts with high accuracy of springback prediction.