Analysis of differential work hardening behavior of pure titanium sheet using spline function

A new method to analyze the shape variation of equal work contours in principal stress space with increasing plastic work (differential work hardening behavior) is introduced. This method uses the spline function of Bezier curves which approximates a work contour, inspired by the methodology proposed by Vegter and Boogaard (Int. J. Plasticity 22 (2006) 557–580). The procedure for determining the spline function is described in detail. As an example, we have applied this method to the experimental results of the pure titanium sheet (Proc. 7th Numisheet (2008) 211–214). The work contours of the pure titanium measured in small plastic range exhibited significant strength differential (SD) between tension and compression and strong asymmetry about the line σx=σy . In addition, the shapes of the work contours changed significantly with increasing plastic work. The approximation curve based on the proposed method is capable of reproducing both the work contours and the directions of plastic strain rates. Also, it reveals the details of the differential work hardening behavior of the pure titanium.