István Groma

Mesoscopic scale simulation of dislocation dynamics in fcc metals: Principles and applications

This paper reviews the methods and techniques developed to simulate dislocation dynamics on a mesoscopic scale. Attention is given to techniques of acceleration and to the implementation of special boundary conditions. Typical results concerning the deformation of a bulk crystal, the effect of image forces and the combination with a finite-element code to simulate the indentation test are presented. The limits and future development of each application are discussed.

Submicron Plasticity: Yield Stress, Dislocation Avalanches, and Velocity Distribution

The existence of a well-defined yield stress, where a macroscopic crystal begins to plastically flow, has been a basic observation in materials science. In contrast with macroscopic samples, in microcrystals the strain accumulates in random bursts, which makes controlled plastic formation difficult. Here we study by 2D and 3D simulations the plastic deformation of submicron objects under increasing stress. We show that, while the stress-strain relation of individual samples exhibits jumps, its average and mean deviation still specify a well-defined critical stress. The statistical background of this phenomenon is analyzed through the velocity distribution of dislocations, revealing a universal cubic decay and the appearance of a shoulder due to dislocation avalanches.

Dynamics of coarse grained dislocation densities from an effective free energy

A continuum description of the time evolution of an ensemble of parallel straight dislocations has recently been derived from the equations of motion of individual dislocations. The predictions of the continuum model were compared to the results of discrete dislocation dynamics (DDD) simulations for several different boundary conditions. It was found that it is able to reproduce all the features of the dislocation ensembles obtained by DDD simulations. The continuum model, however, is systematically established only for single slip. Due to the complicated structure of the equations extending the derivation procedure for multiple slip is not straightforward. In this paper an alternative approach based on a thermodynamics-like principle is proposed to derive continuum equations for single slip. An effective free energy is introduced even for zero physical temperature, which yields equilibrium conditions giving rise to Debye-like screening; furthermore, it generates dynamical equations along the lines of phase field theory. It is shown that this leads essentially to the same evolution equations as obtained earlier. In addition, it seems that this framework is extendable to multiple slip as well.

Thermal stability of nanocrystalline nickel electrodeposits: differential scanning calorimetry, transmission electron microscopy and magnetic studies

Abstract The grain-growth process of electrodeposited nanocrystalline Ni foils upon heating has been studied by differential scanning calorimetry (DSC), transmission electron microscopy (TEM) and X-ray diffraction (XRD). The direct structural observations have shown that the exothermic calorimetric peak detected at about 600 K corresponds to a grain growth process. Furthermore, the TEM pictures indicate that dislocation loops are formed during grain growth. An almost complete recovery of the Curie point has also been observed, although its correlation with the structural changes is still to be revealed.

Dislocation patterning in a two-dimensional continuum theory of dislocations

Understanding the spontaneous emergence of dislocation patterns during plastic deformation is a long standing challenge in dislocation theory. During the past decades several phenomenological continuum models of dislocation patterning were proposed, but few of them (if any) are derived from microscopic considerations through systematic and controlled averaging procedures. In this paper we present a two-dimensional continuum theory that is obtained by systematic averaging of the equations of motion of discrete dislocations. It is shown that in the evolution equations of the dislocation densities diffusionlike terms neglected in earlier considerations play a crucial role in the length scale selection of the dislocation density fluctuations. It is also shown that the formulated continuum theory can be derived from an averaged energy functional using the framework of phase field theories. However, in order to account for the flow stress one has in that case to introduce a nontrivial dislocation mobility function, which proves to be crucial for the instability leading to patterning.

Role of the secondary slip system in a computer simulation model of the plastic behaviour of single crystals

Abstract A computer simulation model is proposed for investigating the plastic behaviour of single crystals oriented for single slip. To match transmission electron microscopy results our model consists of a dislocation system of parallel straight edge dislocations with a maximum of two different Burgers vectors, yielding essentially a two-dimensional problem. The velocity of the dislocations is taken to be proportional to the local shear stress, and generation of new dislocations is allowed. On the basis of the continuum theory of dislocations a special equation is set up to simulate a tensile deformation experiment with constant rate. An AMT DAP computer was used for the computations. In the first simulations, dislocation motion was allowed only in one slip system. This relatively simple case is enough to reproduce the properties of stage I of the deformation of single crystals. During the deformation the dislocations tend to arrange in sheets parallel to the slip direction. There is no sign of cell formation, but a long-range fluctuation appears in the stress field of the dislocations. In a couple of simulations we introduce two slip systems with 45° and 105° angles to the tensile axis, whereupon after stage I the stress starts to increase much more rapidly as the dislocations start to form walls and cells.

Variational approach in dislocation theory

A variational approach is presented to calculate the stress field generated by a system of dislocations. It is shown that in the simplest case, when the material containing the dislocations obeys Hookes law, the variational framework gives the same field equations as Kröners theory. However, the proposed variational method allows us to study many other problems, such as dislocation core regularization, the role of elastic anharmonicity and the dislocation–solute atom interaction. The aim of this paper is to demonstrate that these problems can be handled in a systematic manner.

Dislocation glasses : Aging during relaxation and coarsening

The dynamics of dislocations is reported to exhibit a range of glassy properties. We study numerically various versions of 2D edge dislocation systems, in the absence of externally applied stress. Two types of glassy behavior are identified (i) dislocations gliding along randomly placed, but fixed, axes exhibit relaxation to their spatially disordered stable state; (ii) if both climb and annihilation are allowed, irregular cellular structures can form on a growing length scale before all dislocations annihilate. In all cases both the correlation function and the diffusion coefficient are found to exhibit aging. Relaxation in case (i) is a slow power law, furthermore, in the transient process (ii) the dynamical exponent z approximately 6, i.e., the cellular structure coarsens relatively slowly.

Scale-free phase field theory of dislocations.

According to recent experimental and numerical investigations, if a characteristic length (such as grain size) of a specimen is in the submicron size regime, several new interesting phenomena emerge during the deformation. Since in such systems boundaries play a crucial role, to model the plastic response it is crucial to determine the dislocation distribution near the boundaries. In this Letter, a phase-field-type continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near internal boundaries, is presented. Since the dislocation-dislocation interaction is scale free (1/r), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations.

Criticality of relaxation in dislocation systems.

Relaxation processes of dislocation systems are studied by two-dimensional dynamical simulations. In order to capture generic features, three physically different scenarios were studied and power-law decays found for various physical quantities. Our main finding is that all these are the consequence of the underlying scaling property of the dislocation velocity distribution. Scaling is found to break down at some cutoff time increasing with system size. The absence of intrinsic relaxation time indicates that criticality is ubiquitous in all states studied. These features are reminiscent of glassy systems and can be attributed to the inherent quenched disorder in the position of the slip planes.