Transient temperature distribution in a composite with periodic microstructure

Abstract

An approach based on the assumption of periodicity of the composite structure is utilized to develop a method for the calculation of transient temperature profiles in layered, fibrous or particulate composites. The periodic microstructure gives rise to a temperature perturbation, which is represented by an implicit integral equation in the Fourier transform space. Fiber-matrix and fiber-fiber interactions at high volume fractions are accounted for by Laue interference integrals calculated in closed form. The effective material properties are found to be time dependent. For one-dimensional problems the transient effective thermal composite properties are shown to undergo a transition from the rule-of-mixtures value (Voigt average) at time zero to the steady-state value (rule-of-harmonic-means or Reuss average) at time infinity.