Contact Problems Of Quasicrystalline Materials

The discovery of quasicrystals is one of the major advances for condensed matter state physics in 1980s. Owing to its unique arrangement of atoms, quasicrystals have many desirable properties, such as high hardness, low density, corrosion resistance, wear resistance and oxidation resistance, which enable quasicrystals to become a new type of functional materials and structural materials and to be widely used in engineering and other fields. Contact problems exist in modern industrial production processes everywhere. The theoretical and experimental analysis of contact problems can not only offer suggestions to security and reliability design but also provide theoretical basis and technical support for research, design, preparation and experiment of high quality quasicrystalline materials, then guide their development. Based on these facts and potentials, the dissertation presents the modeling and solving of some contact problems of quasicrystals with the aid of the classical elastic theory. The solutions of the stated problems are given. Examples are used to illustrate interesting results with some practical valuable conclusions obtained.Chapter 1 of the dissertation briefly introduces background and significance of the research, in which the history of quasicrystal linear elasticity theory, the boundary conditions and research status of contact problems are given. Further, the main research contents and the innovative points of the dissertation are presented.By applying the Green’s function of one-dimensional hexagonal piezoelectric quasicrystals and the potential theory, Chapter 2 discusses the frictionless contact problem of one-dimensional hexagonal piezoelectric quasicrystals. Analytic solutions of fields variations in terms of elementary functions for the phonon field, phason field and electric field are derived for three different types of rigid, insulated punches (flat-ended cylindrical, conical and spherical punch), which are convenient for results analysis. Examples display the influence of coupling coefficient on the relation between the exterior loading and the penetration depth. In addition,3D figures and distrubution nephograms for dimentionless normal field variables distribution are plotted in three physical fields.Based on the complex variable method and the procedures of solving Riemann-Hilbert boundary value problems, the frictional and the adhesive contact problems of one-dimensional hexagonal, two-dimensional dodecagonal and three-dimensional icosahedral quasicrystals are discussed in Chapter 3. The expressions of stress functions and contact stress are obtained in explicit form for the flat-ended punch. Examples are presented to analysis the impact of friction coefficient and material parameters on magnitude and distribution of the contact stress.Besides the single punch case in the practical application, there appears the contact phenomenon with multiple punches. If the multiple punches are in periodic array, the contact problem is called periodic contact problem. By considering the method of solving periodic contact problem for anisotropic material in elasticity theory, Chapter 4 concerns two kinds of periodic contact problems in one-dimensional monoclinic, two-dimensional decagonal and three-dimensional icosahedral quasicrystals. By using half-plane Hilbert kernel integral formula, the stress functions and contact stress are determined in closed forms. As an application, for the frictional periodic contact problem, the explicit expressions of the contact stress are given under the action of periodic straight-flat basement, periodic straight-inclined basement and periodic cylinder basement punches; for the half-plane adhesive periodic contact problem, the expression are deduced in case of the wedge shaped periodic displacement on the boundary of quasicrystals; Results analyses are conducted reveal the effect of friction coefficient and elastic parameters on the distribution of contact stress.The unique properties of quasicrystals make cracks, holes and other structure defects inevitably within them. Stress intensity factors are important parameters in evaluating the crack growth, fatigue life, and residual strength of the cracked structures. In order to use quasicrystalline materials in a safer, steadier and more efficient way, accurate determination of stress intensity factors for cracked quasicrystals has theoretical and practical significance. Hence, the frictionless contact problems for quasicrystals with arbitrary cracks are studied in Chapter 5 by employing plane elastic complex variable method. Through the reasonable partition of the stress function and elimination method, the stress functions are given in closed forms. The stress intensity factors and the distribution of contact stress under a punch are also derived. From the expressions of contact stress, it can be seen that contact stress has order -1/2 in the edge of contact zone.Finally, conclusions of this dissertation can be used to analyze the coupling property of phonon field and phason field in experiments. It also offers an important mechanics parameter for contact deformation of quasicrystals, and provides reliable theoretical basis for the application of materials in practical engineering.