Grain Size Effect of Commercial Pure Titanium Foils on Mechanical Properties, Fracture Behaviors and Constitutive Models

The constitutive models based on grain size effect are crucial for analyzing the deformation of metal foils. Previous investigations on the constitutive models concentrate on the foils whose thickness/average grain diameter (T/D) ratios are more than 3. In this study, the commercial pure titanium foils with thickness of 0.1 and 0.2 mm were employed as the experimental materials. The mechanical properties of foils with dimensions of nine different T/D ratios categorized into three ranges (T/D < 1, 1 ≤ T/D < 3, T/D ≥ 3)were tested. Meanwhile, the fracture behaviors and fracture mechanisms of the samples with different T/D ratios were compared and analyzed. Besides, three constitutive models incorporating the surface layer effect and grain boundary strengthening effect were established for the three T/D ratio ranges correspondingly. In these models, the thickness of the surface layers is set T for T/D < 1 foils, D for T/D > 3, and increases with D linearly in 1 ≤ T/D < 3. The results calculated by the three models were compared. The experiments indicate that those models are all in good agreement.