Crack-size dependence of overall responses of fiber-reinforced composites with matrix cracking

Development of a micromechanics model capable of providing overall macroscopic responses for directionally fiber-reinforced composites undergoing matrix cracking (in terms of microgeometric features) is the principal objective of this paper. It is shown that fiber bridging plays an important role, and the effective moduli of a composite may be significantly inlluenceel by the crack size. Bridging effects are negligible for inl%itesimally small cracks (or a -+ 0), and closed-form effective moduli are obtained via standard micromechanics approach for a hybrid composite system with two distinct inclusion phases (fibers and cracks). When crack size exceeds a threshold value u* (a$ being the crack size for saturated bridging), the bridging effect is significant, and a closed-form solution for effective moduli is again possible using a self-consistent approach accommodating bridging effects within the micromechanics framework. In the transition regime (0 < a < a,), however, the effective moduli become crack-size dependent. A full three-dimensional bridging solution, involving discrete fibers and penny-shaped cracks, is developed to numerically determine the effective moduli in this regime. The procedure also allows numerical determination of the saturated crack size, 4. The important of crack-size dependence is then discussed. It is observed that the effective longitudinal modulus for a silicon carbide reinforced intermetallic may be significantly underestimated by standard micromechanics model. In the transition range (0 < u < 3, the present model also provides an avenue for estimation of crack sixes based on observations of overall macromoduli of damaged composite systems. 0 1997 Elsevier Science Ltd.