CRACK-SIZE DEPENDENCE OF OVERALL RESPONSES OF FIBER-REINFORCED COMPOSITES WITH MATRIX CRACKING

Development of a micromechanics model capable of providing overall mac roscopic responses for directionally fiber-reinforced composites under going matrix cracking (in terms of microgeometric features) is the pri ncipal objective of this paper. It is shown that fiber bridging plays an important role, and the effective moduli of a composite may be sign ificantly influenced by the crack size. Bridging effects are negligibl e for infinitesimally small cracks (or a --> 0), and closed-form effec tive moduli are obtained via standard micromechanics approach for a hy brid composite system. with two distinct inclusion phases (fibers and cracks). When crack size exceeds a threshold value a(s) (a(s) being th e crack size for saturated bridging), the bridging effect is significa nt, 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(s)) , however, the effective moduli become crack-size dependent. A full th ree-dimensional bridging solution, involving discrete fibers and penny -shaped cracks, is developed to numerically determine the effective mo duli in this regime. The procedure-also allows numerical determination of the; saturated crack size, a(s). The important of crack-size depen dence is then discussed. It is observed that the effective longitudina l modulus for a silicon carbide reinforced intermetallic may be signif icantly underestimated by standard micromechanics model. In the transi tion range (0 < a < a(s)), the present model also provides an avenue f or estimation of crack sizes based on observations of overall macro-mo duli of damaged composite systems. (C) 1997 Elsevier Science Ltd.