Unified approach for the estimate of effective magnetostriction of composites and polycrystals with particulate and columnar microstructures

A unified approach for an estimate of the effective magnetostriction of composite systems is presented. Following an idea of Levin, originally devised for the estimate of effective thermal expansion of composite materials, we show that there exists an exact connection between the effective magnetostriction and influence functions for the composite system. The influence functions are defined as the average of local stress fields in each phase versus uniform stresses applied on the boundary. The exact formula states that the effective magnetostriction is spatial and orientational averages of local magnetostriction strain in which the influence functions serve as weighting factors. Various existing micromechanical approaches can be used to approximate the influence functions and thereby to provide an estimate for the effective magnetostriction. This result complements our previous findings that the effective magnetostriction can be directly linked to the effective elastic moduli for a few selected composite systems. Here an analogous link between magnetostriction and mechanical behavior can also be established, although more complex in algebra but much wider in the scope of applicability. For illustration, various micromechanical methods, such as dilute approximation, self-consistent and Mori-Tanaka models, together with Voigt and Reuss assumptions, are employed to predict the effective saturation magnetostriction of composites. The estimates are compared with available experimental results and also with the reported theoretical estimates. The effects of particle shapes, orientations, and crystallite growth directions are illustrated for composite systems of technological interest.