Randomly Oriented Glass Fibre Reinforced Dough and Sheet Moulding Compounds: Testing for Dispersion and Determination of Average Effective Lengths of Fibre Strands in Transversely and longitudinally Vibrating Beams

Amongst the various methods used to characterise the elastic properties of materials are the transverse and longitudinal vibration tests. The two methods rely on the transmission of elastic waves in a material to induce vibrations in it, whose characteristics yield the required elastic properties. The methods assume heterogeneity and homogeneity of the tested materials and therefore elastic properties that are also heterogeneous and homogenous. The presence of discontinuities in materials that are significant in size relative to the wavelength of the transmitted elastic waves distorts the waves in what is referred to as dispersion. Therefore, the need to determine the significance of dispersion in materials, in this case, short randomly oriented fibre reinforced composites. This is achieved in this chapter for Dough and Sheet Moulding Compounds, by developing analytical formulae and using these together with known dimensions of test specimens for the two composites, to test for dispersion in the first three modes of vibration. The obtained results show dispersion not to be an issue for the first three modes of transverse vibrations and all orientations of the reinforcing fibre strands. However, this is not the case for all orientations of the reinforcing fibres for longitudinal vibrations and the first three modes. This underscores the importance of such theoretical analysis prior to building and testing such specimens. The formulae developed here give rise to average effective lengths of reinforcing fibre strands within the scale the fibre strand widths and are significantly shorter than the fibre strand lengths, for both Dough and Sheet Moulding compounds, respectively. The results obtained here clearly show that dispersion is best based on the characteristic effective scale of reinforcing fibre strand inhomogeneities (dvar), while providing values of average effective fibre strand lengths (laverage) that can be used to determine mechanical properties of the composites such as strength, stiffness and coefficient of thermal expansion.