Volume fraction effect of magnetoelectroelastic composite on enhancement and impediment of crack growth

Abstract

Uniaxial or multi-axial strength test results are not adequate for the design of composites for they lack of predictive capability in terms of damage that change with load direction and type. The same applies to fracture toughness, a concept that is in general not valid for materials that possess inhomogeneity and anisotropy. Recent findings related to the behavior of crack initiation and growth for piezoelectric materials have further shown that seemingly innocent fracture initiation criterion such as the energy release rate could lead to conclusions contrary to physics. Because of the wide usage of materials with electric and magnetic properties in the electronic industry, it might be premature to assume that material characterization methods established for simple materials and loadings could be extended on an ad hoc basis to multi-functional materials involving the interaction of elastic, electric and magnetic effects as they are damaged by defect initiation and growth, not to mention how these effects would appear to be different at the various scale levels. Assume that the basic constituents of the analytical model is sufficiently small such that continuum mechanics remains valid while the crystal lattice effects may still be reflected by the material parameters of the analytical model. Analyzed in particular is the crack initiation and growth behavior of a line crack in a magnetoelectroelastic composite that is made of BaTiO 3 and CoFe 2O 4. The former represents the inclusions and the latter the matrix. Interaction of the elastic, electric and magnetic effects with the line crack can be exhibited explicitly by the form of the local strain energy density function. This includes the ways with which crack growth could be affected by altering the directions of poling for the electric and magnetic field with respect to those for the applied electric and magnetic field. Presumably, the various material, geometric and loading parameters could be selected to suppress crack extension provided that a suitable fracture criterion could be found. The strain energy density function criterion being positive definite is tested and applied as a possible candidate. The results reveal several previously undiscovered phenomena of crack initiation and growth behavior. A series of new experiments are recommended for future work.