Prediction of micro/meso scale forming limit for metal foils using a simple criterion

Accurately forecasting the forming limit of metal foils is essential in their micro-forming due to the appearance of necking failure easily. In order to accurately and easily forecast the forming limit of metal foils influenced by size effect, an idea for failure modeling of metal foils using the mechanism that different fracture modes of metal foils are related to shear bands is presented in this work. Based on the idea, a simple ductile failure criterion that considers the maximum shear stress and grain size effect but excludes the stress triaxiality is proposed, motivated by the demand to decrease the complexity of parameter calculation tests in micro-forming failure prediction. The proposed criterion and another criterion called as the μ-DF2022 model are applied to capture the forming limit curves of various thick copper and 304 stainless steel foils with different grain sizes to verify its advantage and performance, and the corresponding mechanisms of their prediction capabilities are also elucidated. Furthermore, the proposed and μ-DF2022 models are applied to forecast the limit drawing ratio of a 304 stainless steel foil to further show its performance and advantage in real micro-forming. The applications show that the proposed failure criterion effectively forecasts the forming limit of metal foils between equi-biaxial tension and uniaxial tension influenced by size effect. Moreover, the prediction accuracies using the proposed model and the μ-DF2022 model are comparable, whereas the proposed model does not require complex micro equi-biaxial tension tests, which are typically unavailable to many engineers and researchers, to calibrate its material parameters. Therefore, it is recommended to utilize the proposed criterion to capture the forming limit of metal foils in micro-forming. This work advances the forming limit modeling method of metal foils and provides insight into the application of uncoupled ductile failure criteria in the micro-forming of metal foils, which contributes to the development of their optimal micro-forming processes.