Average Strain in Fiber Bundles and Its Effect on NCF Composite Stiffness

Transverse strain in bundles governs transverse cracking in noncrimp fabric (NCF) composites. Finite element (FE) analysis shows that this strain may be significantly lower than the applied macroscopic strain component in the same direction. This feature is important for damage evolution modeling. The isostrain assumption which in different combinations is widely used in stiffness models is inadequate because the strain in different mesoelements (bundles of different orientation and matrix regions) is assumed the same. Analyzing by FEM the importance of media surrounding the bundle on average transverse strain it was found that an increasing ratio of the bundle transverse stiffness to the matrix stiffness leads to a decrease of the strain in the bundle. An increase of the stiffness in the same direction in adjacent layers leads to an increase of the transverse strain in the bundle. Higher bundle volume fraction in the layer leads to larger transverse strain in the bundle. These trends are described by a power law and used to predict the average strain in bundles. The calculated $H$ matrix which establishes the relationship between strains in the mesoelement and representative volume element strains is used to calculate the “effective stiffness” of the bundle. This effective stiffness is the main element in simple but exact expressions derived to calculate the stiffness matrix of NCF composites. Considering the three-dimensional (3D) FE model as the reference, it was found that all homogenization methods used in this study have sufficient accuracy for stiffness calculations, but only the presented method gives reliable predictions of strains in bundles.