Numerical analysis of shear stiffness of an entangled cross-linked fibrous material

International audienceThe objective of this paper is to understand and study the effect of morphological parameters on the shear stiffness of an entangled cross-linked fibrous material made with carbon fibres where some of the contacts are bonded by the epoxy resin. This current work presents a 3D finite element model using ABAQUS/Standard in order to characterize the mechanical behaviour of different carbon fibre networks rigidified by epoxy cross-links. Numerical simulations are achieved on a representative volume element (RVE) with the orientation distribution of the fibres based on a tested sample. Since not all the strands are perfectly separated, an equivalent diameter of fibre is determined to obtain the rigidity experimen- tally measured in shear. Then, an investigation of the influence of morphological descriptors, such as the distance between cross-links, distribution fibre orientations and junction properties, is carried out. For the entangled cross-linked fibrous material with a small fibre volume fraction, the relationship between the shear stiffness and the fibre volume fraction is a linear function whereas the relation between the shear stiffness and the distance between junctions is a power law with exponent of −3/2. The shear stiff- ness depends slightly on the twisting joint stiffness, and its relationship with the tension joint stiffness is a logarithmic function. The effect of fibre stiffness is also investigated by taking Young’s modulus values corresponding to those of glass fibres, inox fibres or aramid fibres. A linear function is obtained between the shear stiffness and the Young’s modulus. These results are consistent with the analytical models in the literature for a cross-linked fibrous material