CORRELATION BETWEEN ELASTIC AND CONDUCTIVE PROPERTIES FOR ANISOTROPIC INHOMOGENEOUS MATERIALS: THEORY AND EXPERIMENTAL VERIFICATION

摘要

Correlations between the effects of microcracks, pores and various inhomogeneities on different physical properties - elastic and conductive, for example ― constitute one of the most challenging problems in materials science. The practical needs of materials science call for the cross-property correlations that, preferably, have the explicit form and that can be applied to strongly anisotropic microstructures with high contrast between the phases. This task is quite challenging: not only the governing equations of elasticity and conductivity are different, but even the tensors that characterize the mentioned properties are of different ranks (fourth rank tensor of elastic moduli vs second rank tensor of conductivity), so that the cross-property correlations should interrelate different numbers of independent components. The explicit elastic-conductive cross-property correlations for anisotropic composites was established by Sevostianov and Kachanov. The correlations were derived in the framework of noninteraction approximation. To extend the applicability of the derived correlations to high concentrations of inclusions, we suggest and experimentally verify the following key hypothesis: interactions between inclusions affect both groups of properties ― elastic and conductive ― in a similar way, so that the cross-property correlations derived in the non-interaction approximation continue to hold (although this approximation may yield substantial errors for each of the properties separately).