The effect of approximation accuracy of the orientation distribution function on the elastic properties of short fibre reinforced composites

In present paper the authors are focusing on the features of the orientation distribution function (ODF), used to give a probabilistic assessment to the orientation of fibres in fibre reinforced composites. The ODF can be approximated using experimental data and used to evaluate the anisotropic effect of fibres in considered directions. The hardened orthotropic elastic properties of steel fibre reinforced concrete (SFRC), evaluated based on the approximated ODF with different orders of accuracy are used as a case study. Input data for the approximation of the ODF are individual orientations of fibres measured by X-ray micro-tomography method. The study outcomes revealed that the orthotropic elastic properties of SFRC may not be estimated accurately enough by using only the second order terms in the reconstruction of the ODF. The accuracy of the stiffness matrix components is sensitive for the orientation distribution type and the approximation of the ODF, and this should be considered in all FE applications using the ODF approach. Besides, within the study the relation between the values of the scalar-order parameter S, evaluating how well the fibres are aligned with each other, and the approximation orders of the ODF is established.