Validation of the modified rule of mixtures using a combination of fibre orientation and fibre length measurements

Abstract

The goal of this study was to investigate the fibre orientation distribution (FOD), and subsequent mechanical properties, of an injection moulded plate with two different number averaged fibre lengths, termed in this paper medium (1.35 mm) and long (2.40 mm). Fibre orientation measurements (FOD) were made using the 2D elliptical section method and an in-house developed image analyser. The samples were injected from a pin gate located at the centre and top of the plate. Expansion flow on the divergent flow front from this pin gate resulted in a core region with circumferential alignment, while through thickness shear resulted in the usual realignment of fibres in the flow direction either side of the core, termed the shell layers. Two interesting aspects were discovered from these measurements. First, and most importantly, the FOD was found to be independent of the two fibre lengths in this study, and so predominantly controlled by the mould shape and the interaction with the flow front. Second, the fibres in the core region were found to be much closer packed than those in the shell regions. The interaction between the flow front and the mould shape resulted in a range of FOD across the moulded plate, from equal in-plane orientation at the centre of the plate, to highly aligned at the plate edge. This gave a very useful set of samples from which to test out the well known modified rule of mixtures (MROM). Often the fibre orientation distribution cannot be measured directly, but indirectly using the modified rule of mixtures model in reverse. The samples from this moulding (at two different average fibre lengths) gave an excellent opportunity to validate this often used approach.

Both the tensile modulus and strength (measured parallel to the injection direction) were found to show a strong correlation with the measured fibre orientation, with a significant increase in both measures between the centre and the edge of both plates. The increased length of the ‘long’ fibre plate was found to give only a small increase in tensile modulus but a much larger increase in tensile strength.

The tensile modulus showed a linear dependence with the measured fourth order orientation tensor average, 〈cos4 θ〉, with respect to the injection direction of the plate, as predicted by the modified rule of mixtures. Excellent agreement was found between the measured modulus and the predictions from the modified rule of mixtures, based only on measured quantities (matrix modulus, fibre fraction and average fibre length) for both plates.