A Lattice Model for Stress Wave Propagation in Composite Materials

Abstract

Geometric dispersion, observed in a wide variety of composite materials, is believed to result mainly from the relatively periodic arrangement of the reinforcing elements in the matrix rather than from the precise shape of each reinforcing element. On the basis of this observation, a lattice model for composite materials which ignores the shape of the reinforcing elements but preserves their periodicity has been developed. For a wide range of engineering applications, this model can be used to predict the behavior of actual engineering composites. In the application of the lattice model to a specific material, consideration of the dispersive characteristics of the composite are set aside, initially, and the composite is treated as a nondispersive homogeneous mixture. The effective or average properties of the mixture are determined either by steady-wave analysis or appropriate experiments. A lattice is then formed by redistributing the mass within the mixture to form a periodic structure of laminated plates. This mass redistribution is carried out in a manner which yields a lattice with theoretical dispersive characteristics that match the measured dispersive characteristics of the composite. The model was applied to composites consisting of a regular array of tungsten fibers in an aluminum matrix and composed of 2.2 and 22.1 percent by volume of tungsten. Two flyer-plate experiments were performed in the plastic range of the composite. The agreement between experiment and calculation for the arrival time and rise time of the wave front and for the frequency of the ringing behind the wave front is good.