Study on the forming limit of TA1 pure titanium foils based on digital image correlation: Experiments and predictive models

Abstract

At the micro/mesoscopic scale, traditional macroscopic methods, theories, and models used to determine the forming limit are not entirely suitable, given the impact of the size effect on mechanical response, plastic deformation, and fracture. To accurately predict the failure of metal foils during microforming processes, taking into account the size effect on the forming limit. This study constructed tension-compression forming limit diagrams (FLD) for TA1 pure titanium (Ti) foils at thicknesses of 0.08 mm, 0.1 mm, and 0.2 mm based on digital image correlation (DIC). Specifically, it implemented Holmberg uniaxial tensile testing, model prediction based on the modified Oyane ductile fracture criterion, and the fully connected neural network (FCNN). It is found that the forming limit of TA1 pure Ti foils increases with larger specimen thickness. For foils of the same thickness, the forming limit rises with the decrease in the ratio of specimen thickness to grain size (t/d). Additionally, as t/d increases, the influence of the strain rate sensitivity on the overall strain state of the material diminishes, creating similar strain states of specimens in different strain paths. By analyzing the FLD constructed in three methods, it is found that with the t/d and Hill48 yield criteria, the modified Oyane ductile fracture criterion effectively predicted the size effect. After appropriate training, the FCNN model with optimal topology also achieved a high-accuracy prediction of the forming limit.