by Böhlke, Thomas, Haus, Utz-Uwe, Schulze, Volker.
Series: 2005-20, Preprints
This paper considers the problem of approximating a given crystallite orientation distribution function (codf) by a set of texture components. Problems of this type are of importance if the crystallographic texture has to be taken into account in finite element simulations of metal forming operations. The equivalence of this task to a Mixed Integer Quadratic Programming problem (MIQP) is shown. Special emphasis is given to the generation of a class of approximations with an increasing number of texture components. Furthermore, the constraints resulting from the nonnegativity, the normalization, and the symmetry of the codf are analyzed. Finally, a set of approximations of three different experimental textures determined with this solution scheme is presented and discussed. Based on these hierarchic solutions, the engineer can decide how detailed the microstructure is considered.
texture components, crystallite orientation distribution function, mixed-integer quadratic programming