Biaxial stress tests and in-plane tension/compression tests of pure titanium sheet (JIS #1) have been carried out in order to elucidate its anisotropic plastic deformation behavior under linear stress paths. Contours of plastic work and the directions of plastic strain rates at different levels of plastic work have been precisely measured in the stress space. The measured work contours bulged significantly toward the equibiaxial direction and showed strong asymmetry, and moreover, changed its shapes significantly with increasing plastic work (differential work hardening). Using the data of the measured work contours, the applicability of selected anisotropic yield functions, i.e., Hill's quadratic, the Yld2000-2d and Cazacu's yield functions, to the accurate prediction of the plastic deformation behavior of the pure titanium has been discussed. It was found that these yield functions were not able to reproduce the measured data. A new method for analyzing the differential work hardening behavior of the pure titanium sheet has been developed. 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. The calculated results have been in good agreement with the differential work hardening behavior of the pure titanium sheet.

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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 x y σ σ = . 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.

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