Crack initiation behavior in magnetoelectroelastic composite under in-plane deformation

Abstract

While the method of solution for crack problems in anisotropic elasticity and magnetoelectroelasticity is nearly identical, the prediction of crack initiation and/or growth behavior based on the asymptotic stress fields can differ widely depending on the chosen failure criterion. The latter has no haven to hide. Avoidance of contraction and satisfaction of the first law of thermodynamics are the rules that need to be observed. A negative crack tip energy release rate would infer the creation of energy and a negative strain energy density would imply the non-uniqueness of solution in classical linear continuum mechanics theories. Under these conditions, the crack initiation and growth behavior in a magnetoelectroelastic material will be examined. For the sake of notation and continuity, this work gives a brief account of the well-known solution for a line crack in a magnetoelectroelastic medium. Not to be underestimated is the derivation of the asymptotic form of the strain energy density function that was first given for the piezoelectroelastic crack problem. The equivalent expression for the magnetoelectroelastic case is given here. This sets the stage for a physical interpretation of how a crack would behave in a composite possessing the mixed properties of piezoelectric and piezomagnetic materials. The individual terms in the strain energy density function shows how the applied electric and magnetic field would affect the critical applied mechanical normal and shear stress to trigger crack initiation, respectively. When both normal and shear action prevail, the direction of crack initiation is no longer obvious and it needs to be determined since the energy stored ahead of the crack depends on the direction of prospective crack initiation. Numerical results are given for a BaTiO 3–CoFe 2O 4 composite. The inclusion is the piezoelectric BaTiO 3 material and the matrix is the magnetostrictive CoFe 2O 4 material. The proportion of the two phases can be varied by adjusting the volume fraction of the inclusions upon which the fluctuation of the energy density field near the crack depends and the material properties of the constituents. Directions of the applied electric and magnetic field can also be changed; their effects on crack initiation are discussed using the strain energy density criterion. Indeed, the additional magnetostrictive effect can have an influence on crack initiation as the applied field directions are altered. Possible behavior of crack initiation can be made for design-specific magnetoelectroelastic composites.