Publisher Summary The chapter presents a discussion on the continuum theory of lattice defects. The continuum analog of a crystal containing imperfections is an elastic body in a state of stress not produced by surface and body forces. The appropriate tool for handling the “continuum theory of lattice defects” is thus the usual theory of elasticity modified to include internal stress. Unlike the residual stresses encountered in engineering practice, these internal stresses have to be considered as capable of moving about in the medium. Recent interest in solid state physics has stimulated further development. The discussion of this chapter emphasizes on some of the background principles and illustrates them by specific examples chosen to bring out the peculiar features involved. Naturally, the continuum theory can hardly be expected to answer questions of current interest about the more intimate behavior of lattice defects (for example, the binding energy of two adjacent point defects). On the other hand, the theory perhaps suffers from the disadvantage that its limitations are more immediately obvious than are those of other approximate methods that have to be used in dealing with the solid state, for it sometimes gives good results even in what appear to be extreme cases. The theory of elasticity is concerned with the relation between the deformation of a body and the energy content of itself and its surroundings. The chapter also discusses specification of internal stress, including the Somigliana dislocations and the incompatibility tensor.

The Continuum Theory of Lattice Defects

This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical...

Flux vortices and transport currents in type II superconductors

Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen

Publisher Summary This chapter focuses on micromechanics of crystals and polycrystals. In Section II of the chapter, a brief outline of only some of the important features of the micromechanics of crystalline plasticity is given. The discussion is confined to plastic flow caused by dislocation slip, and face-centered-cubic crystals are used in the examples of dislocation mechanisms. Particular attention is paid to kinematics and to the phenomenology of strain hardening, because these are shown to play dominant roles in macroscopic response. In Section III, constitutive laws for elastic-plastic crystals are developed. The framework draws heavily on Hill's analysis of the mechanics of elasticplastic crystals, but the theory is extended by incorporating the possibility of deviations from the Schmid rule of a critical resolved shear stress for slip. Deviations from the Schmid rule are motivated by micromechanical models for dislocation motion and are shown to lead to deviations from the “normality flow rule” of continuum plasticity. The implications of these “non-Schmid effects” regarding the stability of plastic flow are brought out via some examples of models for kinks bands and shear bands in Section IV. In Section IV some examples of analyses of elastic-plastic deformation in crystals are discussed. The chapter concludes with some suggestions for fruitful research. These involve extensions of the theory to finite-strain rate-dependent polycrystalline models.

Micromechanics of Crystals and Polycrystals

Configurational Forces within a Classical Context.- Kinematics.- Standard Forces. Working.- Migrating Control Volumes. Stationary and Time-Dependent Changes in Reference Configuration.- Configurational Forces.- Thermodynamics. Relation Between Bulk Tension and Energy. Eshelby Identity.- Inertia and Kinetic Energy. Alternative Versions of the Second Law.- Change in Reference Configuration.- Elastic and Thermoelastic Materials.- The Use of Configurational Forces to Characterize Coherent Phase Interfaces.- Interface Kinematics.- Interface Forces. Second Law.- Inertia. Basic Equations for the Interface.- An Equivalent Formulation of the Theory. Infinitesimal Deformations.- Formulation within a Classical Context.- Coherent Phase Interfaces.- Evolving Interfaces Neglecting Bulk Behavior.- Evolving Surfaces.- Configurational Force System. Working.- Second Law.- Constitutive Equations. Evolution Equation for the Interface.- Two-Dimensional Theory.- Coherent Phase Interfaces wtih Interfacial Energy and Deformation.- Theory Neglecting Standard Interfacial Stress.- General Theory with Standard and Configurational Stress within the Interface.- Two-Dimensional Theory with Standard and Configurational Stress within the Interface.- Solidification.- Solidification. The Stefan Condition as a Consequence of the Configurational Force Balance.- Solidification with Interfacial Energy and Entropy.- Fracture.- Cracked Bodies.- Motions.- Forces. Working.- The Second Law.- Basic Results for the Crack Tip.- Constitutive Theory for Growing Cracks.- Kinking and Curving of Cracks. Maximum Dissipation Criterion.- Fracture in Three Space Dimensions (Results).- Two-Dimensional Theory of Corners and Junctions Neglecting Inertia.- Preliminaries. Transport Theorems.- Thermomechanical Theory of Junctions and Corners.

http://inis.jinr.ru/sl/P_Physics/PC_Classical%20physics/PCem_Elastic%20media/Gurtin%20Configurational.pdf

M. Peach

Papers

The Forces Exerted on Dislocations and the Stress Fields Produced by Them