Estimating fibre direction distributions of reinforced composites from tomographic images

Fibre reinforced composites constitute a relevant class of materials used chiefly in lightweight constructions for example in fuselages or car bodies. The spatial arrangement of the fibres and in particular their direction distribution have huge impact on macroscopic properties and, thus, its determination is an important topic of material characterisation. The fibre direction distribution is defined on the unit sphere, and it is therefore preferable to work with fully three-dimensional images of the microstructure as obtained, e.g., by computed micro-tomography. A number of recent image analysis algorithms exploit local grey value variations to estimate a preferred direction in each fibre point. Averaging these local results leads estimates of the volume-weighted fibre direction distribution. We show how the thus derived fibre direction distribution is related to quantities commonly used in engineering applications. Furthermore, we discuss four algorithms for local orientation analysis, namely those based on the response of anisotropic Gaussian filters, moments and axes of inertia derived from directed distance transforms, the structure tensor, or the Hessian matrix. Finally, the feasibility of these algorithms is demonstrated for application examples and some advantages and disadvantages of the underlying methods are pointed out.