Indentation Anaysis Of Piezoelectric Materrals And Quasicrystals

The piezoelectric material, which is one of the typical multi-field coupling materials, has been extensively used in intelligent structures or devices such as sensors and actuators. With the development of the MEMS and NEMS, piezoelectric materials in the form of thin film or layered medium have become more and more important. Quasicrystal material is also attracting increasing research interests due its quasi-periodic structure and the phonon-phason coupling property. Recently, indentation technique has been widely applied in testing piezoelectric and quasicrystal materials. Theoretical studies on indentation responses of these materials would be significant to the experimental study of indentation and quantitative analysis of the material constants. In view of the application of indentation technique in characterization of material property for multi-field coupling materials, this dissertation presents the modeling and solving procedure of relevant contact problems of piezoelectric and quasicrystal materials.By the appropriate methods for solving mixed boundary value problems in linear elasticity, this dissertation studies the axisymmetric contact problems of transversely isotropic piezoelectric material, one-dimensional hexagonal and two-dimensional hexagonal quasicrystal materials. First of all, the Green’s functions of the half-space subjected to point sources on the surface are derived by applying Hankel integral transform or using potential theory method. By substituting the Green’s function into the contact boundary conditions, the Fredholm integral equation, which serves as the final governing equation of the contact problem, is then derived. Finally, the solutions of the indentation responses are obtained by solving the Fredholm integral equation. This dissertation studies not only the frictionless contact problems of the piezoelectric film-elastic substrate system, piezoelectric layered half-space, one-dimensional and two-dimensional quasicrystal half-space, but also the adhesive (no-slip) contact problem of piezoelectric half-space. The rigid flat-ended cylindrical, conical and spherical indenters are considered in contact with the materials, and several interface models are used to characterize the interface between the film and the substrate or layers. For half-space model, the analytic solution of the contact problem is presented. However, the contact problem of layered medium is solved numerically. In the numerical examples, we analyze the influences of various parameters on the indentation responses, compare not only the solution of film-substrate system or layered medium with the solution of the half-space material, but also compare the solution of adhesive contact problem with the solution of frictionless contact problem, and plot the stress contour of the quasicrystals under indentation.The contact solutions of the film-substrate system and layered medium obtained in this dissertation could directly guide the indentation test. The solutions of half-space material can not only serve as benchmarks for numerical or approximate solutions of thin-film model or layered model, but also have important value for experimental studies. The exact and complete analytic expressions for the displacements and stresses of quasicrystals under indentation presented in terms of elementary functions in this dissertation would be very helpful to the studies and understanding of the coupling property of phonon field and phason field.