Magnetoelectroelastic composite with poling parallel to plane of line crack under out-of-plane deformation

The three-dimensional field equations can in general be regarded as the sum of in-plane and out-of-plane deformation. The method for the general solution is the same for both although the boundary conditions could make a difference. If a particular solution in exact form may be found for the out-of-plane case, the same may not hold for the in-plane case. Hence, there may be a good reason for discussing the out-of-plane crack problem in certain situations that should be emphasized. Otherwise, the reason may lie in the exploration of possible application to the in-plane problem, a direct solution of which would have required a considerable effort. The contribution of this work rests on the new findings for the case of poling parallel to the crack in a magnetoelectroelastic composite made of BaTiO₃–CoFe₂O₄. The inclusions are BaTiO₃ and the matrix is CoFe₂O₄. Several new features of the solution were not expected before hand.Unlike in-plane deformation with poling normal to the crack plane, maximum crack growth enhancement is found to occur in the BaTiO₃–CoFe₂O₄ composite for a volume fraction of about 50%. Crack retardation increases as the volume fraction of the inclusions either increase or decrease. The occurrence of this same phenomenon in Mode I and II remain to be investigated. Poling direction of magnetic and electric field for line defects can have a significant effect on crack growth for magnetoelectroelastic materials. The foregoing conclusions are based on predictions made from the strain energy density criterion.