Читать книгу Properties for Design of Composite Structures - Neil McCartney - Страница 59

The methodology developed by Maxwell when estimating the effective electrical conductivity of an isotropic particulate composite is used to estimate many of the effective thermoelastic properties of a fibre-reinforced composite. A detailed description is first given of Maxwell’s methodology applied to the thermal conduction problem, extending the approach to deal with multiphase fibres having different sizes and properties, and assuming perfect thermal contact at the fibre/matrix interfaces. It is noted that a published result, based on Maxwell’s methodology, for two-phase systems having fibres of the same size, but including interfacial thermal resistance, is in error. A stress and displacement formulation that is radial in nature is used in conjunction with Maxwell’s methodology to estimate values for many of the effective properties of a unidirectional fibre-reinforced composite. A method of applying Maxwell’s methodology to the estimation of the effective shear modulus of a unidirectional fibre-reinforced composite is also given. A key aspect of the results obtained, when using Maxwell’s methodology to estimate some of the thermoelastic properties of a unidirectional composite is that they correspond to those derived from the composite cylinders assemblage model, which, in turn, correspond to one of the bounds obtained when using variational methods. This correspondence indicates that the results obtained using Maxwell’s methodology are not restricted to low fibre volume fractions. For each effective property, it is shown that the resulting formulae for the case of just two phases, having fibre reinforcements of the same size, may be expressed as a mixtures estimate plus a correction term that is used to derive the conditions that determine whether the extreme values of properties obtained by variational methods are upper or lower bounds. These conditions differ in some cases from those that have been given in the literature.