Crack‐Wake Debonding and Toughness in Fiber‐ or Whisker‐Reinforced Brittle‐Matrix Composites

Abstract

Solutions are obtained for the mechanics of debonding in the crack wake in fiber‐ or whisker‐reinforced composites for the case where a finite shear traction exists at the fiber/matrix interface in the debonded zone. These solutions are then applied to derive expressions for the steady‐state toughness increases obtained in bonded composites wherein the toughness contribution is provided by crack‐wake fiber/matrix debonding and crack bridging. The solutions for an unbonded composite containing a frictional fiber/matrix interface can be obtained from the derived equations in the limit of the fiber/matrix interface toughness equal to zero. In this limit, the debond crack length reduces to the slip length and the expressions for the crack opening and the predicted toughness increase reduce to previously derived expressions for unbonded composites. The steady‐state toughness is found to depend sensitively on the interface toughness, the fiber fracture strength, and the shear tractions in the debonded zone including other material parameters, such as fiber radius and volume fraction and the moduli of the constituent phases. It is shown that in order to obtain finite toughness increases, the fiber/matrix interface toughness must be less than a critical value dependent on the fiber fracture strength, fiber radius and volume fraction, and fiber and matrix moduli. The predictions of the model are applied to published experimental results from a detailed and complete study of toughness increases in a bonded whisker‐reinforced composite.