Application of the electrical analog technique in fiber-reinforced composites

Abstract

The electrical analog technique which has been previously used for the determination of normalized stress intensity factors in isotropic plates and in bimaterial plates is extended to the case of fiber-reinforced composites. The technique is based on the similarities between electrical and certain mechanical problems. Specifically, the fact that electric potential in a conductor as well as displacement in two dimensional elasticity problems in antiplane loading both obey the Laplace equation is made use of in determining normalized stress intensity factors ( K N ) in bimaterial plates and in fiber-reinforced composites. The K N determined by the electrical analog technique corresponds to the anti-plane problem. Since the behavior of cracks in the vicinity of interfaces is qualitatively similar in both plane and antiplane loading, the K N determined by the electrical analog technique provides useful information for the design of composites. This paper uses the electrical equivalence of the J- integral for the determination of K N . The specific problems examined include cracks in bimaterial plates, the behavior of a crack in the vicinity of fibers of higher modulus than the matrix, and the role of debonding and fiber fracture on K N . Fiber-reinforced composites and bimaterial plates were electrically simulated by electroplating copper or nickel on part of the surface of steel foils. The electroplated regions have higher electrical conductivity than the unplated regions and simulate materials of higher modulus in the corresponding mechanical problems.