Jan Kratochvíl

The importance of being curved: bowing dislocations in a continuum description

Evolution equations for scalar density and orientation of fields of curved dislocations formulated in the framework of the continuum theory of moving dislocations serve as the starting point for development of a non-local dislocation-based constitutive relation for crystal plasticity, on the length scale intermediate between the phenomenological hardening laws of strain-gradient crystal plasticity and the explicit treatment of three-dimensional discrete dislocation dynamics. The key features of the proposed approach are the refined averaging in the continuum theory based on separation of single-valued dislocation fields, and the accounting for the line energy of the bowed dislocations which renders the theory non-local.

Model of early stage of dislocation structure formation in cyclically deformed metal crystals

Abstract The development of dislocation structure in cyclically deformed metal crystals is treated as a stability problem. The present study is restricted to single slip. The suggested system of governing equations consists of three main constituents: the ‘diffusion’-type equation for clustering of stored dislocations, the non-local relation for strain hardening, and the field equations for strain and stress. The stability analysis predicts formation of a three-dimensional dislocation pattern which corresponds to the vein structure observed in electron micrographs.

Elastic model for the sweeping of dipolar loops

Abstract The sweeping of small dipolar loops by gliding dislocations is thought to be one of the mechanisms leading to dislocation pattern formation during cyclic deformation. The individual sweeping event was calculated within the framework of isotropic linear elasticity for an infinite straight gliding segment and a rigid dipolar prismatic loop. With respect to previous estimates, the present one includes the finite size of the loop and the character of the gliding dislocation. The conditions for sweeping were quantitatively estimated as a function of the geometrical factors and the local effective and friction forces. The sweeping mechanism is found to be effective for distances between the slip planes of the two defects smaller than 9 times the height of the dipolar loop.

Finite element model of plastically deformed multicrystal

Abstract The finite element method (FEM) is a very powerful device for solving many continuum mechanics problems which can be treated neither theoretically nor experimentally. In this paper FEM is developed for the analysis of semi-microscopic effects within plastically deformed multicrystalline metals. The suggested numerical procedure is based on the model of the thermo-activated motion of dislocations which is responsible for inelastic time-dependent deformation. A comparison between numerical and experimental results for activated slip systems is presented.

Instability origin of dislocation substructure

Abstract The formation of a dislocation substructure in high-temperature deformation is treated as a stability problem. A crystal in which dislocations can glide and climb is modelled as an anisotropic viscous medium. The subgrain structure development is interpreted as a deformation-induced instability of internal bending (folding) type first described by Biot. The suggested continuum mechanics model seems to provide a rational explanation of the main observed features of the subgrain structure: misorientation, tendency to regularity and relatively uniform subgrain size.

Continuum theory of evolving dislocation fields

Continuum theory of moving dislocations is used to set up a non-local constitutive law for crystal plasticity in the form of partial differential equations for evolving dislocation fields. The concept of single-valued dislocation fields that enables us to keep track of the curvature of the continuously distributed gliding dislocations with line tension is utilized. The theory is formulated in the Eulerian as well as in the so-called dislocation-Lagrangian forms. The general theory is then specialized to a form appropriate to formulate and solve plane-strain problems of continuum mechanics. The key equation of the specialized theory is identified as a transport equation of diffusion–convection type. The numerical instabilities resulting from the dominating convection are eliminated by resorting to the dislocation-Lagrangian approach. Several examples illustrate the application of the theory.

Nonlocal versus local elastoplastic behaviour of heterogeneous materials

Abstract The scale transition methods have been developed for many years in order to obtain the overall behavior of polycrystalline materials from their microscopic behavior and their microstructure. Nevertheless, some basic aspects are absent from such formalisms. The most significant one seems to be the heterogeneization by plastic straining which involves nonlocality of hardening. In this article, a nonlocal theory based upon crystalline plasticity is developed from which a nonlocal constitutive equation at the grain level is derived. With regard to the polycrystal, in order to deduce the behavior of a local equivalent homogeneous medium, an integral equation is proposed and solved for nonlocal inhomogeneous materials by the self-consistent approximation. This scheme is developed in case of a two-phase nonlocal material representing the dislocation cell structure induced during plastic straining. Numerical simulations based on a simplified model show significant effects on the intragranular heterogeneization.

The model of formation and disintegration of vein dislocation structure

A qualitative, one dimensional model of dislocation structure evolution during cycling is treated as a process of self-organization. The main mechanisms of the dislocation structure development are a generation of dipolar loops, their sweeping by glide dislocations to high dislocation density regions and their annihilation. The model is described by the system of three equations: The balance law for the density of dipolar loops, the local yield condition governing the motion of glide dislocations and the equation controlling the local stress. The results of the numerical solution of the system simulate the formation of the dislocation vein structure, its disintegration and formation of dipolar walls in agreement with the available electron microscopic observations.

Interactions of glide dislocations in a channel of a persistent slip band

Two unlike dislocations gliding in parallel slip planes in a channel of a persistent slip band are considered. Initially they are kept apart in straight screw positions. As the dislocations are pushed by the applied stress between two walls in the opposite directions, they bow out and attract one another forming a dipole. With the increasing stress the dislocations become more and more curved, until they separate. The walls of the channel are represented by elastic fields of rigid edge dipoles. The dislocations are modelled as planar curves approximated by moving polygons. The objective of the simulations is to determine the stress in the channel needed for the dislocations to escape one another. The stress and strain controlled regimes considered provide upper and lower estimates of the escape stress. The results are compared with the studies by Mughrabi and Pschenitzka, and Brown and the recent dislocation dynamics estimates. Problems encountered in the dislocation dynamics evaluation of the escape stress are analyzed.

Self-organization model of localization of cyclic strain into PSBs and formation of dislocation wall structure

Development of dislocation structures in cubic metal crystals cyclically deformed in single slip is treated as a self-organization process. The proposed model consists of the crystal plasticity equations, the equation of motion of glide dislocations, and the balance equation for stored dislocations (dipolar loops). The model incorporates hardening by the loops, sweeping of the loops by glide dislocations, drift of the loops in the stress gradients, the mutual loop interaction, their generation and annihilation. By using analytical methods it is briefly shown that in the early stage of deformation the vein or extended wall structure is formed. In the saturation state when all newly formed dislocations are annihilated strain becomes localized. In the lamellae of concentrated slip (PSBs) the dislocation structure may be but need not to be rearranged. The criterion for rearrangement is specified. The transformation of veins to walls is a typical rearrangement in PSBs.