The causal differential scattering approach to calculating the effective properties of random composite materials with a particle size distribution
An implementation of the Causal Differential Method (CDM) for modelling the effective properties of a random two-phase composite material is presented. Such materials are commonly used as ultrasonic transducer matching layers or backing layers. The method is extended to incorporate a particle size distribution in the inclusion phase. Numerical issues regarding the implementation and convergence of the method are discussed. It is found that, for a given frequency of excitation, the calculated velocity for the composite has a distribution whose variance increases as the volume fraction of inclusions increases. The model predictions would suggest that to reliably and repeatedly manufacture these composites, with a desired mechanical impedance, a low volume fraction of inclusions should be used.
KeywordsPhase Velocity Effective Property Mechanical Impedance Tungsten Particle Match Layer
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