Abstract
In this paper, the initial values of damage parameters in the Gurson–Tvergaard–Needleman (GTN) model are determined by a microscopic test combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration. The original void volume fraction (f0), the volume fraction of potential nucleated voids (fN), the critical void volume fraction (fc), the void volume fraction at the final failure (fF) of material are assigned as 0.006, 0.001, 0.03, 0.06 according to the simulation results, respectively. The hemispherical punch stretching test of commercially pure titanium (TA1) sheet is simulated by a plastic constitutive formula derived from the GTN model. The stress and strain are obtained at the last loading step before crack. The forming limit diagram (FLD) and the forming limit stress diagram (FLSD) of the TA1 sheet under plastic forming conditions are plotted, which are in good agreement with the FLD obtained by the hemispherical punch stretching test and the FLSD obtained by the conversion between stress and strain during the sheet forming process. The results show that the GTN model determined by the finite element reverse calibration method can be used to predict the forming limit of the TA1 sheet metal.
Highlights
Titanium alloy sheets have gained extensive applications in the aviation and aerospace fields due to its superior mechanical and physical properties, such as high specific strength, superior thermal stability and good corrosion resistance [1,2,3,4,5]
The initial values of damage parameters in the GTN model are determined by SEM combined with empirical formulas, and the final accurate values are determined by finite element reverse calibration
Compared with the forming limit diagram (FLD) obtained by the hemispherical punch stretching test and the forming limit stress diagram (FLSD) obtained by the transformation between stress and strain, the results show a good agreement
Summary
Titanium alloy sheets have gained extensive applications in the aviation and aerospace fields due to its superior mechanical and physical properties, such as high specific strength, superior thermal stability and good corrosion resistance [1,2,3,4,5]. The forming limit is an important performance index in the sheet metal forming process, which can reflect the maximum degree of deformation before the plastic instability of the sheet. It is the main basis for the development of the sheet metal forming process and die design [6]. The experimental studies on forming limit have been carried out widely. Kleemola and Pekkikangas [8] studied the forming limits of deep drawing quality steel, copper and brass, which followed uniaxial and equibiaxial pre-strain, and noticed the dependence of FLD on the magnitude and type of pre-strain. FLD has been considered to be accurate for proportional loading, where the ratio
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