Design criteria for pseudoductile fiber-reinforced composites

The toughness of brittle materials can be significantly improved by the incorporation of fibers. Moreover, both theoretical and experimental investigations have shown that properly designed fiber composites can exhibit pseudoductile tensile behavior with multiple cracking rather than brittle failure with the formation of one single crack. To attain pseudoductile behavior, two criteria have to be satisfied: (1) the steady-state cracking criterion; and (2) the further cracking criterion. In the literature, criteria for steady-state cracking are usually obtained numerically or derived approximately with assumed profiles of the bridged crack. In this paper, a general analytical approach for the determination of an exact condition for steady-state cracking is presented. The steady-stare cracking criteria for several. important cases are then derived and compared with available numerical or approximate solutions. Then, an approximate but conservative criterion for further cracking is also developed. Since the two criteria involve the microparameters of the composite (such as properties of fiber, matrix, interface, fiber size, and volume fraction), they can be used as guidelines for the choice of microparameters in composite design.