Three-dimensional stress analysis of textile composites. Part II: Asymptotic analysis

Abstract

An asymptotic singular stress analysis was performed in the unit-cell of the plain–woven composite in the vicinity of the yarn–yarn–matrix interface intersection with and without the inter-yarn delamination. The problem was reduced to a three-material wedge singularity type by introducing several curvilinear coordinate systems and systematic expansions in power series of the distance from the contour of the stress singularity. The power of stress singularity at the inter-yarn and yarn–matrix interface junction was investigated as a function of crimp angle and matrix-to-yarn stiffness ratio. In the case of perfect bonding between the yarns and the matrix with small crimp angles near 9°, the power of singularity is weak (∼0.02) and insensitive to the stiffness ratio of the axial yarn to the matrix material. For increased crimp angles, however, small variations in the stiffness of the matrix material can significantly affect the power of singularity. In the case of the inter-yarn delamination, two singular roots––one crack type (∼0.5) and one weak (∼0.01)––were obtained for all crimp angles and delamination opening modes. Coefficients of the asymptotic expansion were obtained by comparing the full-field three-dimensional numerical solution based on B-spline displacement approximation method with multi-term asymptotic expansions in the vicinity of the singular point. Good agreement between the two solutions was observed in all examples considered.