Transition from small crack to large crack for composite materials (BEM analysis on transversely reinforced composite plate with a Mode I center crack in matrix)

Stress analysis is conducted for a traversely reinforced composite with a Model I crack in plane strain condition using the boundary element method (BEM). The crack is introduced in the matrix at the center of the layered composite plate. The results obtained are summarized as follows. (1) When the normalized crack length, a* = a/d, (a: crack length, d: thickness of matrix layer) is much smaller than unity, the high stress region near the crack tip is confined to the matrix. The magnitude of stress intensity factor (SIF), K, is close to K₀ for a homogeneous body composed of a single matrix material. The crack is called a small crack for composite materials. (2) As a* becomes longer, the normalized SIF, K* = K/K₀, decreases due to the constraint by the adjacent fibers. K* shows a minimum near a* = 1 and increases when a* increases. (3) K* tends to be saturated as a* exceeds 5. The energy release rate calculated by the asymptotic magnitude of K* coincides with that of the homogeneous orthotropic body where the elastic constants are determined by a mixture of those in the matrix and fibers. The crack is called a large crack for composite materials.