Calculation of macroscopic elasto-plastic anisotropy based on an analytical expression of the Orientation Distribution Function in the case of fibre textures

The aim of current research is to quantify the transversally isotropic mechanical behaviour in cubic materials with 〈1 0 0〉 fibre textures. It is shown that in this case, it is possible to introduce an analytical expression for the Orientation Distribution Function (ODF), depending on the second Euler angle only, when the Euler angles are restricted to the fundamental zone for crystal symmetry. Hereby the decomposition of the ODF in spherical harmonics has been avoided. Elastic parameters have been calculated based on a Voigt–Reuss–Hill modelling scheme. Therefore, a method has been used to calculate the single crystal elastic constants from the given macroscopic elastic constants of an isotropic bulk material. The initial anisotropic yield locus is determined using a visco-plastic self consistent model, with a discrete texture file generated based on the analytical expression of the ODF as input. The results show a high elastic and plastic anisotropy in the fusion zone of the weld. It has been shown how to use these results to define an anisotropic material law in a commercial Finite Element code.

► An analytical expression for the ODF is proposed for fibre textures.
► Elastic constants have been calculated.
► Anisotropic yield surface has been calculated.