Algorithm to determine orientation distribution function from microscopic images of fibrous networks: Validation with X-ray microtomography.

Quantitative analysis of fibre orientation in a random fibrous network (RFN) is important to understand their microstructure, properties and performance. 2D fibre orientation distribution presents an in-plane fibre orientation without any information on fibre orientation in thickness direction. This research introduces a fully parametric algorithm for computing 3D fibre orientation as thickness is important for high-density or thick fibrous networks. The algorithm is tested for 3 major classes of nonwoven fabrics called low- (L), medium- (M) and high-density (H) ones. H fabric density is 6-8 times larger than the L fabric density. M fabric density (traditional intermediate fabric density) is 3-4 times larger than the L fabric density. Voxel models of experimental nonwoven webs were generated by an X-ray micro-CT (µCT) system and evaluated with the algorithm. Statistical results showed that a fraction of fibres orientated along the thickness direction increases as fibre density grows. To validate the accuracy of findings, deterministic voxelated virtual fibrous structures, created using mathematical functions were used. This novel algorithm is able to produce a 3D orientation distribution function (ODF) for any RFN including, models of nonwovens produced with various manufacturing parameters, experimentally verified and validated with X-ray µCT. Also, it can compute 2D ODFs of various types of RFNs to evaluate 2D behaviour of fibrous structures. The obtained results are useful for applications in many fields including finite element analysis, computational fluid dynamics, additive manufacturing, etc.