Numerical Study Of Fracture Mechanics In Piezoelectric Materials By Boundary Element Methord

Due to their intrinsic electro-mechanical coupling behavior, piezoelectricmaterials have been widely used in information, new materials, aerospace and otherhigh-tech fields. Their inherent brittleness and low fracture toughness make themsusceptible to produce cracks in the process of polarization and application. Thepre-existing crack will continuously propagate till the failure happens in advanceunder the in-service loadings. Therefore, to the study of fracture behavior inpiezoelectric materials is of significance. So this thesis will focus on some classicalfracture problems in piezoelectric materials. Based on the numerical results of theextended stress intensity factors (ESIFs) in the vicinity of the crack tip by usingboundary element method (BEM), the problems involving the micro-cracks shieldingeffect, the comparison of the existing fracture criterions and the crack growth pathunder some specific stress/electric loadings are investigated numerically. The contentsof this paper are listed as follows:(1) Four typical approaches to evaluate the crack-tip field intensity factors in thecommon elastic media involving the displacement extrapolation, the stress method,the J-integral and the modified crack closure integral method (MCCI) are extended topiezoelectric materials. All the required mechanical and electrical variables in theseformulas are numerically determined by the boundary integral equations. Then theESIFs in some cracked piezoelectric plates are numerically evaluated using these fourapproaches and their results are compared with each other to show their accuracy.(2) The crack-tip shielding by micro-cracking in piezoelectric solids undercombined in-plane electromechanical loadings is studied by BEM. The amplificationratios of the field intensity factors and mechanical strain or electrical energy releaserate are defined to show the crack-tip amplification and shielding. Numerical resultsare compared with the analytical results for isotropic materials to verify the presentBEM. The influences of various loading conditions, the location and orientationangles of micro-cracks on the amplification ratios are investigated. The contours ofthe amplification ratios for an arbitrarily located micro-crack are also presented toshow the crack-tip amplification and shielding effects.(3) Finally, the changing rules of the five crack-tip parameters including thecircumferential stress and strain, the energy density factor, the total energy release rateand the mechanical strain energy release rate are investigated by BEM. The couplingloading effects on the crack initiating direction are further studied. The growing cracktrajectories under the three-point bending and the uniaxial tensile loading arenumerically simulated. In our computation, two fracture criteria including themaximum circumferential stress and the minimum energy density factor are adopted, respectively, to determine the crack propagating direction, and the results arecompared with the existing experimental data.