Study On Fracture Of Magnetoelectroelastic Solid

Piezoelectric/piezomagnetic materials process mechanical-electric, mechanical-magnetic and magneto-electric coupling effects, and thus, they have widely potential applications in manufacturing intelligent devices. However, because of their brittleness, cracks and flaws are inevitably presented in such magnetoelectroelastic materials under the utilizing and manufacturing procedures of intelligent structures and devices. Afterwards, many mechanical researchers have fixed their attentions at the bad-distributed magnetic, electric and elastic fields of magnetoelectroelastic material weakened by a flaw recently. Up to now, two kinds of ideal crack-face magnetoelectrical boundary conditions prevail for cracked magnetoelectroelastic solid, that is, electrically and magnetically permeable, and, electrically and magnetically impermeable. The former case simply treats the crack surfaces in both electrical and magnetic contact, although the crack is opened. Evidently, this assumption neglects the presence of the opened crack interior such as vacuum or air. As for the latter case, the electric displacement and magnetic induction are simply assumed to vanish, equivalent to the assumption that the crack interior is not permeable for electric and magnetic fields. This is also contradictory to a realistic case, since a realistic crack is full of certain medium (usually air or vacuum) inside with nonvanishing electric permittivity and magnetic permeability, which should not be neglected although they may be small enough. In order to simulate the real crack, it is necessary to propose new crack-face magnetoelectric boundary conditions and investigate crack problems for cracked magnetoelectroelastic material under static and dynamic loadings.Firstly, in the chapter two, the analysis of magnetoelectroelastic boundary conditions, especial for crack-face magnetoelectric ones is made. For the anti-plane deformation problems, we assume that the electric and magnetic boundary conditions on the crack surfaces depend on two auxiliary parameters associated with the electric displacement and magnetic induction derived from a fully permeable crack. For the mode-I loading deformation problems, we propose and use the magnetoelectrical crack-face boundary conditions dependent on the crack opening displacement, which is the expansion of half-permeable electric boundary condition for cracked piezoelectric material. It is further found that the cases of fully magnetoelectric permeable, fully magnetoelec- tric impermeable, electrically permeable and magnetically impermeable, electrically impermeable and magnetically permeable are the limiting ones of the above-stated two magnetoelectrical crack-face boundary conditions, respectively.Secondly, under the assumption of anti-plane static deformation, the problem of an anti-plane eccentric shear crack embedded in a magnetoelectroelastic strip is investigated in the chapter three. By applying the finite Fourier transform, the field intensity factors and energy release rates at the crack tips can be determined in explicit form. The influences of applied electric and magnetic loadings on the normalized energy release rate and mechanical strain energy release rate are presented graphically. Obtained results reveal that applied electric and magnetic loadings affect crack growth, depending on their directions and adopted fracture criteria. Based on the proposed crack-face magnetoelectric boundary conditions, chapter four is concerned with the static problem with in-plane mechanical, electric and magnetic loadings. A full magnetoelectroelastic field in the entire plane induced by a crack is obtained explicitly, and field intensity factors and energy release rate are given. The influences of applied electric and magnetic loadings on the energy release rate, the strain intensity factor, and the stress distribution are presented graphically. On the other hand, it is considered that the stress intensity factor is independent of applied electric and magnetic loadings, and the stress distribution near the crack tip is associated with applied electromagnetic field. Then the T-stress for a cracked magnetoelectric material is investigated. Obtained results reveal that in addition to applied mechanical loading, the T-stress is dependent on electric and magnetic loadings for a vacuum crack. In the fifth chapter, a three-dimensional magnetoelectroelastic solid containing a penny-shaped crack normal to the poling axis is dealt with. Applying the Hankel transform technique, an entire magnetoelectroealstic field is obtained in simple and explicit form. Numerical results for a cracked magnetoelectroelastic material reveal the relations of the electric displacement and magnetic induction on the crack surfaces with applied mechanical loading. The influences of applied electric and magnetic loadings on the normalized fracture parameters are illustrated graphically for a vacuum circular crack.Thirdly, considering the dynamic working situations of devices, it is of significance to analyze the dynamic response of cracked magnetoelectroelastic. Along this line, the dynamic problem of an anti-plane shear crack of finite length moving with a constant velocity along the interface of two dissimilar magnetoelectroelastic materials is considered in the sixth chapter. Applying the Fourier transform method, Explicit-form solutions for the entire-plane dynamic magnetoelectroelastic field and the dynamic field intensity factors at the crack tip are determined. Based on the maximum of the hoop stress, the crack branch or kinking angle is analyzed. Numerical examples demonstrate the influences of the properties of materials, applied electric loading, applied magnetic loading and the crack running velocity on crack propagation orientation. In the seventh chapter, dynamic analysis of a Griffith crack embedded in a magnetoelectroelastic solid subjected to in-plane mechanical, electric and magnetic impacts is made. The Laplace and Fourier transforms are applied to obtain the dynamic field intensity factors and energy release rate near the crack tip. For full impermeable crack mode, numerical results reveal the variations of the dynamic intensity factors of stress and COD, and dynamic energy release rate on the normalized time, and show the effects of applied magnetic and electric impact loadings on crack growth.Finally, the scattering problem of anti-plane shear waves by an interfacial crack between a magnetoelectroelastic solid and an elastic material is studied. For fully permeable and impermeable electromagnetic crack-face boundary conditions, the dynamic intensity factors of stress, electric displacement and magnetic induction, center crack-tearing displacement and energy release rate are given by utilizing integral transform technique. Numerical results present the influences of the normalized frequency and incident angle on the normalized stress intensity factors and energy release rates for three pairs of material combinations and two cases of crack-face electromagnetic boundary conditions, respectively.