Prediction of Crack Paths in Particulate Composites Using Electrical Analog

An electrical analog technique was used to simulate crack paths in the vicinity of elastic inhomogeneities in ceramic composites. The technique makes use of the analogy that exists between electrical potential differences between clamped ends of a conducting foil with electrical inhomogeneities (second phases of different electrical conductivity) and the load-point displacements of a mechanically loaded plate with elastic inhomogeneities (second phases of different elastic modulus). In crack problems, this analogy is exact for mode III loading. The specific problems investigated were the interaction between a crack and a well-bonded second phase of higher elastic modulus (simulating a fiber or a second-phase particle) and the interaction between a crack and a pore. Crack paths were incrementally determined by maximizing the end-point potential differences (corresponding to the maximum energy release rate criterion in the mechanical system) with respect to the direction of crack growth. Comparable mechanical tests were carried out using precracked Plexiglas * plates with either circular holes or elastic inclusions. Good agreements were obtained between the electrically simulated crack paths and the crack paths observed in the mechanical tests despite the fact that the mechanical tests were carried out in mode I loading and the analogy is not exact.