E5 Effective Thermal Properties

Topic

The effective thermal expansion coefficient and thermal conductivity of this composite are strongly anisotropic; this anisotropy stems from the disparity between the thermal properties of the reinforcement and the matrix. When the reinforcement and matrix possess vastly different thermal expansion coefficients and thermal conductivities, the resulting composite no longer behaves uniformly in all directions. A greater disparity between the thermal properties of the reinforcement and the matrix leads to a correspondingly more pronounced thermal anisotropy in the composite.

Specifically, the longitudinal thermal expansion coefficient of this composite is calculated using Schapery's rule, weighted by the stiffness of each phase rather than solely by volume fraction. The stiffer phase—typically the reinforcement—restrains the natural thermal expansion of the softer phase (the matrix) to a greater extent than a simple volume-weighted average would suggest. Because the reinforcement is significantly stiffer than the matrix, the composite's longitudinal thermal expansion coefficient aligns more closely with that of the reinforcement than with that of the matrix, even when the reinforcement occupies a smaller fraction of the total volume.

In contrast, the thermal conductivity of this same composite is calculated differently depending on the direction. In the direction parallel to the reinforcement fibers, it is determined using a rule of mixtures—summing the contributions of each phase weighted by their volume fractions—much like the Voigt bound combines the elastic moduli of each phase in the longitudinal direction. Conversely, in the direction perpendicular to the fibers, the calculation follows the logic of the Reuss bound, combining the thermal resistance of each phase rather than their direct conductivity. Because the thermal conductivity is calculated using a different rule for each direction, the composite's thermal conductivity—like its thermal expansion coefficient—exhibits strong anisotropy. For this reason, this model—characterized by the effective thermal anisotropy with which it was introduced—serves as the physical basis for another model in this set: the one describing thermal microcracking caused by a mismatch in the coefficient of thermal expansion. The fact that the longitudinal coefficients of thermal expansion for the reinforcement and the matrix—calculated here using Schapery's rule—differ from one another creates precisely the mismatch that the other model uses to explain the residual stress generated in the matrix during cooling after curing.

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