Accounting for mesoscale geometry and intra-yarn fiber volume fraction distribution on 3D angle-interlock fabric permeability

Abstract

Understanding resin flows within 3D interlock fabrics involves addressing a dual-scale flow problem. Indeed, the fluid can flow through inter-yarn channels, characterized by a unit cell mesoscale morphology, but also within yarns considered as homogeneous equivalent porous media. The former is assumed to follow the Stokes’ law while the latter be related to the Darcy’s law, directly linked to the microscopic intra-yarn fiber volume fraction (FVF) field. In this work, a coupled Stokes–Darcy steady-state flow within a 3D woven textile, modeled at mesoscale, is solved through a finite element monolithic approach with a mixed velocity-pressure formulation, stabilized by the Variational MultiScale Method (VMS) and implemented in the Z-set software. The fabric permeability tensor is then computed without any assumptions on its nature and analyzed both through its diagonal components, its eigenvectors and eigenvalues. The main contribution of this study lies in examining the influence of variations of the inter-yarn porous medium morphology, through textile compaction and geometrical reduction to prevent edge flows, and the intra-yarn permeability (from complete field to unique value) on the overall fabric permeability.