Introduction to elasticity theory for crystal defects. (Q2886993)

This textbook is devoted to different types of defects (point, line, planar and volume) considered in the framework of the elasticity theory. The book is divided into sixteen chapters. The introductory Chapter 1 presents the book's content and discusses applicability of linear elasticity for the above-mentioned problems. Chapter 2 treats basic elements of anisotropic theory of elasticity and states main relationships and principles for local displacements, strains, forces and stresses used into the book. The methods of studying defect elasticity problems are presented in Chapter 3. In particular, basic differential equations for stress-strain states are considered, and the Fourier transform method and Green's function method for their solution are presented. Then, the stress function method for solving the stated problems is developed by using the Airy stress function method. Green's functions are used to the problem on defects in finite homogeneous regions bounded by interfaces. Chapter 4 states the elastic Green's functions for a unit point force in the case of three types of regions, namely, (i) an infinite homogeneous region; (ii) a half-space with a planar traction-free surface; and (iii) a half-space joined to an elastically dissimilar half-space along planar interface. Chapter 5 focuses on basic formulations of the interactions between (i) a defect source of stress and imposed internal or applied stresses; (ii) a defect source of stress and its image stress; and (iii) an inhomogeneity and an imposed stress. These interactions are expressed in terms of interaction energies and corresponding forces which are used in the next chapters for specific defects. Chapter 6 determines the elastic properties of different types of inclusions in infinite homogeneous matrix. By this, the inclusions are considered as defects produced by the introduction of transformation strains. As a coherent homogeneous inclusion, there are considered first inclusions of ellipsoidal shapes with following treating inhomogeneous inclusions by Eshelby equivalent homogeneous inclusion method. Then, elastic fields of incoherent ellipsoidal inclusions produced by the coherent-incoherent transformations are treated. Interactions of inclusions with imposed stress are considered in Chapter 7 and with this aim are defined the total field produced by the imposed stress, the inhomogeneity associated with the inclusion and the transformation strain of the inclusion by using the Eshelby equivalent homogeneous inclusion method. Chapter 8 is devoted to image stresses for inclusions in finite regions, demonstrating significant volume changes produced by them. Stress states and strain energies of inclusions near interfaces are studied by using Green's functions for point forces in homogeneous regions and adjoining interfaces. Chapter 9 considers effects of inhomogeneities, treating the perturbation of the imposed stress and the accompanying interaction energy when a uniform and ellipsoidal inhomogeneity is situated in a large body and the imposed stress field is uniform in the absence of the inhomogeneity. In the other case, both the inhomogeneity and imposed stress are non-uniform. Based on considering the symmetry of point defects, Chapter 10 studies the elastic displacement field produced in infinite homogeneous regions by point forces by using point-force Green's functions. Chapter 11 develops the force multipole models for interaction between point defects and stress state in finite bodies. The elastic behavior description of dislocations is presented in Chapter 12. Based on their geometrical features, a wide variety of dislocation configurations (from pure edge and pure screw to smoothly curved loops) are analyzed. Then, the elastic properties of segmented dislocation structures are studied and applied to the definition of the properties of the comparatively more complex dislocations in 2D and 3D. Chapter 13 is devoted to interactions between dislocations and various stress states. The forces in the cases of external or internal loading are obtained by using the Peach-Koehler force equation and the interaction ``dislocation-image stress'' is analyzed in various cases of dislocation disposition to an interface and in a finite (semi-infinite) region. Then, a set of dislocation image stress problems are solved by using the obtained solutions. Chapter 14 presents interfaces of two major classes, namely, (i) iso-elastic interfaces with effectively the same elastic properties of two crystals adjoining the interfaces; and (ii) hetero-elastic interfaces, where these properties differ significantly. The elastic fields of single dislocations in hetero-elastic interfaces are also defined independently. Chapter 15 analyzes the force arising from the elastic field difference across the interface formulated in terms of the energy-momentum tensor and the geometrical features of interfaces whose motion causes body shape changes described in terms of their interfacial dislocation content. The final chapter presents the general procedure for determining the interaction between two defects with obtaining the elastic field due to one defect at the location of the other and next determination of interaction of the latter defect with this field. The basic methods are present by using a limited number of representative interactions.NEWLINENEWLINEIn total, this comprehensive textbook brightly demonstrates the application of strict, modern mathematical methods with covering numerous interesting problems to the study of crystal defects of various types. The book includes very many exercises accompanied by solutions; it is very useful for self-education; and should be of big interest to students, graduate students and their teachers and also could be very useful for specialists working in related areas of material science and mechanics of deformable solids.