Fracture Analysis For Two-dimensional Problems Of Interface Crack Between Two Dissimilar Magnetoelectroelastic Materials

As a sort of new multifunctional materials, magnetoelectroelastic materials havebeen extensively used in electronic technology, ultrasound technology, intelligenceproject, as well as other advanced smart structures, owing to their specialmagneto-electric coupling effect. In the design of magnetoelectroelastic structures, itis important to take into account the defects/imperfections. As common defects,cracks are often pre-existing or are generated by external loads during the service life.Therefore, in recent years, research on fracture mechanics of magnetoelectroelasticmaterials has drawn a lot of interest. On the basis of previous achivements, two kindsof crack models, namely, classical model and contact zone model, are adopted toanalyze the fracture behaviors and make prediction of the growth and propagation ofinterface cracks in this dissertation. Work of the author is as follows:Two-dimensional fracture problem of interfacial cracks between piezoelectric andpiezomagnetic layers is investigated by using integral transform method and singularintegral equation technique. On the interface, both electric potential for piezoelectricmaterial and magnetic potential for piezomagnetic material are assumed to be zero.On the boundaries of the bounded piezoelectric and piezomagnetic layers, bothmechanical and elecrical loads are applied to the surface of piezoelectric ceramics;both mechanical and magnetical loads are applied to the surface of piezomagneticmaterial. The stress intensity factors as well as mechanical energy release rates(MERRs) are derived. The MERRs are further calculated and discussed. Thenumerical results show that the interfacial crack between piezoelectric andpiezomagnetic bimaterials is more difficult to initiate and propagate than the onebetween corresponding elastic bimaterials under the same mechanical loadings, andthat for a central interfacial crack, increasing the height of the layers generally canimpede the crack propagation and growth. The results presented here may havepotential applications to the design of multilayered magnetoelectroelastic structure.An interface crack with a frictionless contact zone at the right crack tip between two dissimilar magnetoelectroelastic materials under the action of remote anduniform magnetoelectromechanical loads is considered. The open part of the crack isassumed to be electrically impermeable and magnetically permeable. Both theDirichlet–Riemann boundary value problem and Hilbert problem have beenformulated and solved exactly. Stress, electrical displacement and magnetic inductionintensity factors as well as energy release rate are found in analytical forms.Transcendental equations and a closed form analytical formula for the determinationof the real contact zone length have been derived and analyzed. Some numericalresults are plotted to show the effects of the applied loads on the contact zone length,stress intensity factor and energy release rate.Based on the earlier part, an interface crack under the action of a thermal flux andremote and uniform magnetoelectromechanical loads is further considered. The crackface is assumed to be heat insulted. The inhomogeneous combinedDirichlet–Riemann and Hilbert boundary value problems are, respectively, formulatedand solved analytically. Stress, electrical displacement intensity factors as well asenergy release rate are found in analytical forms, and analytical expressions for thecontact zone length have been obtained for both the general case and the case of smallcontact zone length. Some typical numerical results are presented, which show clearlythe effects of thermal and magnetoelectromechanical loads on the contact zone length,stress intensity factor and energy release rate.An interface crack with a frictionless contact zone at the right crack-tip betweentwo dissimilar magnetoelectroelastic materials under the action of concentratedmagnetoelectromechanical loads on the crack faces is considered. The open part ofthe crack is assumed to be magnetically impermeable and electrically permeable. TheDirichlet–Riemann boundary value problem is formulated and solved analytically.Stress, magnetic induction and electrical displacement intensity factors as well asenergy release rate are thus found in analytical forms. Analytical expressions for thecontact zone length have been derived. Some numerical results are presented andcompared to those based on the other crack surface conditions. It is shown clearly thatthe location and magnitude of the applied loads could significantly affect the contactzone length, stress intensity factor and energy release rate.