Evaluation of formability and fracture of pure titanium in incremental sheet forming

A forming limit diagram (FLD) is commonly used as a useful means for characterising the formability of sheet metal forming processes. In this study, the Nakajima test was used to construct the forming limit curve at necking (FLCN) and fracture (FLCF). The results of the FLCF are compared with incremental sheet forming (ISF) to evaluate the ability of the Nakajima test to describe the fracture in ISF. Tests were carried out to construct the forming limit diagram at necking and fracture to cover the strain states from uniaxial tension to equi-biaxial tension with different stress triaxialities—from 0.33 for uniaxial tension to 0.67 for equi-biaxial tension. Due to the fact that the Gurson–Tvergaard-Needleman (GTN) model can be used to capture fracture occurrence at high stress triaxiality, and the shear modified GTN model (Nahshon-Hutchinson’s shear mechanism) was developed to predict the fracture at zero stress or even negative stress triaxiality, the original GTN model and shear modified GTN model may be not suitable to predict the fracture in all samples of the Nakajima test as some samples are deformed under moderate stress triaxiality. In this study, the fractures are compared using the original GTN model, shear modified GTN model and the Nielsen-Tvergaard model with regard to stress triaxiality. To validate the ability of these models, and to assess which model is more accurate in predicting the fracture with different stress triaxialities, finite element (FE) simulations of the Nakajima test were compared with an experimental results to evaluate the applicability of the Nakajima test to characterise the fracture from ISF. The experimental and FE results showed that the shear modified GTN model could predict the fracture accurately with samples under uniaxial tension condition due to low stress triaxiality and that the original GTN model is suitable for an equi-biaxial strain state (high stress triaxiality), whereas the stress triaxiality modified GTN model should be considered for samples which have moderate stress triaxiality (from plain strain to biaxial strain). The numerical and experimental FLCF of pure titanium from the Nakajima test showed a good agreement between the experimental and numerical results of ISF.