Interaction Between Screw Dislocations And Circular Inclusions With Imperfect Interfaces In Anisotropic Materials

The interaction of dislocation, inhomogeneity and interfacial defects is a greatly significant subject in the fields of solid mechanics and materials science. The elastic, viscoelastic and electroelastic interaction effects between imperfect interface and screw dislocations in anisotropic materials are investigated in this paper. The solutions for a screw dislocation interacting with imperfect interface,viscoelastic interaction between a screw dislocation and a circular inhomogeneity with Kelvin-type viscoelastic interface in cylindrically anisotropic composites; electroelastic interaction between multiple piezoelectric screw dislocations and an annular interphase layer with imperfect interfaces in transversely isotropic piezoelectric materials are presented.Using Riemann-Schwarz's symmetry principle of complex functions, the above problems are transformed into Riemann-Hilbert boundary problems. By combining the analysis of singularity of complex functions, generalized Liouville's theorem and Cauchy model integral, the explicit solutions to the complex variable functions of above problems are provided. With the aid of the Peach-Koehler formula, the image forces on dislocation are obtained respectively. The dependence of image force on materials'properties and imperfect interface parameters are calculated, plotted and discussed.As a result, analysis and discussion show that the influence of imperfect interface on the interaction between screw dislocation and inhomogeneity is significant. When the interface is imperfect, in anisotropic composites, the influence acting on the dislocation of the anisotropic properties of cylindrically composites increases with the increase of the interface imperfection degree. When the anisotropic properties parameter of matrix is less than the one of inhomogeneity, there will be a critical value of imperfect interface parameter which changes the attraction-repulsion direction of the image force of dislocation. Due to the viscoelasticity of the interface, with the process of time, the image force decreases dramatically first and then evolves toward a steady-going value, meanwhile, the influence of anisotropic properties of inhomogeneity attenuate obviously. For the annular interphase layer with imperfect interfaces in piezoelectric composites, the imperfect interface attracts dislocation which increases with the decrease of the imperfect interface parameter while the hard inclusion and the hard interphase layer repel the dislocation and the repellence increases with the increase of the relative thickness coated interphase layer.The provided results can not only offer a scientific basis for the design of composite structures but also provide basic solutions to further investigation on the strength and toughness of structures. The present solutions can be used as Green functions to obtain a series of solutions of related problems, and also contain a number of previously known results which can be shown to be special cases.