Fast calculation of average Taylor factors and Mandel spins for all possible strain modes

The average Taylor factor of the crystallites of a polycrystalline material and the average spins (‘spin’ here means rate of rotation) of the crystal lattices (Mandel spin) are functions of the strain mode to which the material is subjected. These functions can be very helpful when constructing material models to be used by elastic–plastic FE simulations of forming processes in which the anisotropy due to texture, back stress etc. is taken into account. These functions can be calculated from the crystallographic texture. It is shown in the present paper, that a calculation done for all possible strain modes can be organised in a very efficient way. This is made possible by the Fourier series expansion method used in quantitative texture analysis. The newest calculation method which uses this methodology is 400 times faster than one which would not, and this with sufficient accuracy. This makes it possible to incorporate calculations of complete yield loci in FE simulations without prohibitive increase in computer time.