On the modelling of plastic anisotropy, asymmetry and directional hardening of commercially pure titanium: A planar Fourier series based approach

Uni-axial tension and compression tests were conducted on commercially pure titanium sheet. Strong anisotropy and tension-compression asymmetry was observed. The work hardening behaviour was found to be strongly dependent on the direction and sign of the acting stress. Specifically, twinning occurred and lead to a dynamic Hall-Petch effect, but only under uni-axial compression in transverse direction. A novel approach to define a very flexible, three-dimensional yield criterion is proposed. Deviatoric stresses are mapped from five-dimensional space into a reduced three-dimensional space (the material is assumed to show an isotropic response under shear loading) and transformed to spherical coordinates. A two-dimensional Fourier series of the angular coordinates is used to define an equivalent stress. It was possible to find a smooth yield surface that could accurately capture all experimental data (yield stresses and Lankford parameters). Directional twinning and the related distortional hardening is modelled by a modified Hall-Petch relation and a dynamic internal variable representing the twin volume fraction. The models were implemented in an explicit FE code and a cup drawing test was simulated. The results of the proposed models showed a clear improvement of accuracy compared to those of two established models, while calculation time was even reduced. (C) 2017 Elsevier Ltd. All rights reserved.