arXiv subjects

István Groma

Publications and source records attributed to István Groma.

At least 19 recordsLinked to original sources

arXiv2026

Variational approach to determine the properties of dislocations at finite deformation

A generalised version of the continuum theory of curved dislocations describing the spatial and temporal evolution of the fields: statistically stored dislocation density, geometrically necessary dislocation density, and curvature has recently been proposed. The dynamics of the system are derived from a scalar functional of the relevant fields that cannot increase during the evolution of the system. However, the framework was established only for small deformations. The aim of the present paper is to discuss the fundamentals of the elasticity theory of finite deformation in cases where individual dislocations are present in the system. The equilibrium equations are derived within a variational formalism. It is shown that introducing dislocations into the finite deformation framework is a nontrivial task. Moreover, if the deformation is large, the force acting on a dislocation segment is not the well-known Peach-Koehler force. In a forthcoming paper, the results obtained will be applied to the generalisation of the dislocation continuum theory of curved dislocations.

cond-mat.mtrl-sci↗

arXiv2026

Dislocation distribution near a wall within the framework of the continuum theory of curved dislocations

A recently proposed generalised continuum theory of curved dislocations describes the spatial and temporal evolution of statistically stored and geometrically necessary dislocation densities as well as the curvature. The dynamics follow from a scalar plastic potential that constrains the allowed velocity fields and leads to a phase field like formulation with a nontrivial mobility function. Although conceptually related to strain gradient plasticity, the theory differs by introducing an intrinsic, evolving length scale given by the dislocation spacing. In this paper, we determine three key material independent parameters of this continuum theory by quantitatively comparing its predictions with discrete dislocation dynamics (DDD) simulations. To achieve this, we impose a narrow impenetrable wall inside the simulation volume, which blocks dislocation motion and generates characteristic spatial variations of the dislocation density fields under external loading. We show that for this geometry, the continuum equations reduce to a form that can be solved efficiently via direct numerical integration. The resulting stationary distributions of total and geometrically necessary dislocation densities are then compared to extensive 2D and 3D DDD simulations. This comparison allows us to extract the parameters that govern the back stress, the density gradient coupling, and the flow stress relation. Our results demonstrate that the continuum theory quantitatively captures the DDD observed structure of the dislocation pile up near the wall and therefore provides a reliable mesoscale description. The wall loading setup further serves as a benchmark problem to validate numerical implementations of the continuum theory in more general geometries.

cond-mat.mtrl-sci↗

arXiv2023

Irreversible evolution of dislocation pile-ups during cyclic microcantilever bending

In metals geometrically necessary dislocations (GNDs) are generated primarily to accommodate strain gradients and they play a key role in the Bauschinger effect, strain hardening, micron-scale size effects and fatigue. During bending large strain gradients naturally emerge which makes this deformation mode exceptionally suitable to study the evolution of GNDs. Here we present bi-directional bending experiment of a Cu single crystalline microcantilever with in situ characterisation of the dislocation microstructure in terms of high-resolution electron backscatter diffraction (HR-EBSD). The experiments are complemented with dislocation density modelling to provide physical understanding of the collective dislocation phenomena. We find that dislocation pile-ups form around the neutral zone during initial bending, however, these do not dissolve upon reversed loading, rather they contribute to the development of a much more complex GND dominated microstructure. This irreversible process is analysed in detail in terms of the involved Burgers vectors and slip systems to provide an in-depth explanation of the Bauschinger-effect and strain hardening at this scale. We conclude that the most dominant role in this behaviour is played by short-range dislocation interactions.

cond-mat.mtrl-sci↗

arXiv2022

Statistical analysis of dislocation cells in uniaxially deformed copper single crystals

The dislocation microstructure developing during plastic deformation strongly influences the stress-strain properties of crystalline materials. The novel method of high resolution electron backscatter diffraction (HR-EBSD) offers a new perspective to study dislocation patterning. In this work copper single crystals deformed in uniaxial compression were investigated by HR-EBSD, X-ray line profile analysis, and transmission electron microscopy (TEM). With these methods the maps of the internal stress, the Nye tensor, and the geometrically necessary dislocation (GND) density were determined at different load levels. In agreement with the composite model long-range internal stress was directly observed in the cell interiors. Moreover, it is found from the fractal analysis of the GND maps that the fractal dimension of the cell structure is decreasing with increasing average spatial dislocation density fluctuation. It is shown that the evolution of different types of dislocations can be successfully monitored with this scanning electron microscopy based technique.

cond-mat.mtrl-sci↗

arXiv2022

Irradiation-induced strain localization and strain burst suppression investigated by microcompression and concurrent acoustic emission experiments

Plastic deformation of microsamples is characterised by large intermittent strain bursts caused by dislocation avalanches. Here we investigate how ion irradiation affects this phenomenon during single slip single crystal plasticity. To this end, in situ compression of Zn micropillars oriented for basal slip was carried out in a SEM. The unique experimental setup also allowed the concurrent recording of the acoustic emission (AE) signals emitted from the sample during deformation. It was shown that irradiation introduced a homogeneous distribution of basal dislocation loops that lead to hardening of the sample as well as strain softening due to dislocation channeling at larger strains. With the used deformation protocol strain burst sizes were found to be decreased due to channeling. The concurrently recorded AE events were correlated with the strain bursts and their analysis provided additional information of the details of collective dislocation dynamics. It was found that the rate of AE events decreased significantly upon irradiation, however, other statistical properties did not change. This was attributed to the appearance of a new type of plastic events dominated by short-range dislocation-obstacle interactions that cannot be detected by AE sensors.

cond-mat.mtrl-sci↗

arXiv2022

Dislocation Avalanches: Earthquakes on the Micron Scale

Compression experiments on micron-scale specimens and acoustic emission (AE) measurements on bulk samples revealed that the dislocation motion resembles a stick-slip process - a series of unpredictable local strain bursts with a scale-free size distribution. Here we present a unique experimental set-up, which detects weak AE waves of dislocation slip during the compression of Zn micropillars. Profound correlation is observed between the energies of deformation events and the emitted AE signals that, as we conclude, are induced by the collective dissipative motion of dislocations. The AE data also reveal a surprising two-level structure of plastic events, which otherwise appear as a single stress drop. Hence, our experiments and simulations unravel the missing relationship between the properties of acoustic signals and the corresponding local deformation events. We further show by statistical analyses that despite fundamental differences in deformation mechanism and involved length- and time-scales, dislocation avalanches and earthquakes are essentially alike.

cond-mat.mtrl-sci↗

arXiv2020

On the dynamics of curved dislocation ensembles

To develop a dislocation-based statistical continuum theory of crystal plasticity is a major challenge of materials science.During the last two decades such a theory has been developed for the time evolution of a system of parallel edge dislocations. The evolution equations were derived by a systematic coarse-graining of the equations of motion of the individual dislocations and later retrieved from a functional of the dislocation densities and the stress potential by applying the standard formalism of phase field theories. It is, however, a long standing issue if a similar procedure can be established for curved dislocation systems. An important prerequisite for such a theory has recently been established through a density-based kinematic theory of moving curves. In this paper, an approach is presented for a systematic derivation of the dynamics of systems of curved dislocations in a single slip situation. In order to reduce the complexity of the problem a dipole like approximation for the orientation dependent density variables is applied. This leads to a closed set of kinematic evolution equations of total dislocation density, the GND densities, and the so-called curvature density. The analogy of the resulting equations with the edge dislocation model allows one to generalize the phase field formalism and to obtain a closed set of dynamic evolution equations.

cond-mat.mtrl-sci↗

arXiv2019

Investigation of geometrically necessary dislocation structures in compressed Cu micropillars by 3-dimensional HR-EBSD

Mechanical testing of micropillars is a field that involves new physics, as the behaviour of materials is non-deterministic at this scale. To better understand their deformation mechanisms we applied 3-dimensional high angular resolution electron backscatter diffraction (3D HR-EBSD) to reveal the dislocation distribution in deformed single crystal copper micropillars. Identical micropillars (6 um x 6 um x 18 um in size) were fabricated by focused ion beam (FIB) and compressed at room temperature. The deformation process was stopped at different strain levels (~1%, 4% and 10%) to study the evolution of geometrically necessary dislocations (GNDs). Serial slicing with FIB and consecutive HR-EBSD mapping on the (100) side was used to create and compare 3-dimensional maps of the deformed volumes. Average GND densities were calculated for each deformation step. Total dislocation density calculation based on X-ray synchrotron measurements were conducted on the $4\%$ pillar to compare dislocation densities determined by the two complementary methods. Scanning transmission electron microscopy (STEM) and transmission electron microscopy (TEM) images were captured on the 10% pillar to visualize the actual dislocation structure. With the 3D HR-EBSD technique we have studied the geometrically necessary dislocations evolving during the deformation of micropillars. An intermediate behaviour was found at the studied sample size between bulk and nanoscale plasticity: A well-developed dislocation cell structure built up upon deformation but with significantly lower GND density than in bulk. This explains the simultaneous observation of strain hardening and size effect at this scale.

physics.app-ph↗

arXiv2019

Micron-scale deformation: a coupled in-situ study of strain bursts and acoustic emission

Plastic deformation of micron-scale crystalline materials differ considerably from bulk ones, because it is characterized by random strain bursts. To obtain a detailed picture about this stochastic phenomenon, micron sized pillars have been fabricated and compressed in the chamber of a SEM. An improved FIB fabrication method is proposed to get non-tapered micro-pillars with a maximum control over their shape. The in-situ compression device developed allows high accuracy sample positioning and force/displacement measurements with high data sampling rate. The collective avalanche-like motion of dislocations appears as stress drops on the stress-strain curve. To confirm that these stress drops are directly related to dislocation activity, and not to some other effect, an acoustic emission transducer has been mounted under the sample to record emitted acoustic activity during strain-controlled compression tests of Al-5\% Mg micro-pillars. The correlation between the stress drops and the acoustic emission signals indicates that indeed dislocation avalanches are responsible for the stochastic character of the deformation process.

cond-mat.mtrl-sci↗

arXiv2019

The Emergence and Role of Dipolar Dislocation Patterns in Discrete and Continuum Formulations of Plasticity

The plasticity transition at the yield strength of a crystal typically signifies the tendency of dislocation defects towards relatively unrestricted motion. For an isolated dislocation the motion is in the slip plane with velocity proportional to the shear stress, while due to the long range interaction dislocation ensembles move towards satisfying emergent collective elastoplastic modes. Such collective motions have been discussed in terms of the elusively defined backstress. In this paper, we develop a two-dimensional stochastic continuum dislocation dynamics theory that clarifies the role of backstress and demonstrates a precise agreement with the collective behavior of its discrete counterpart, as a function of applied load and with only three essential free parameters. The main ingredients of the continuum theory is the evolution equations of statistically stored and geometrically necessary dislocation densities, which are driven by the long-range internal stress, a stochastic flow stress term and, finally, two local diffusion-like terms. The agreement is shown primarily in terms of the patterning characteristics that include the formation of dipolar dislocation walls.

cond-mat.mtrl-sci↗

arXiv2017

Deterministic and stochastic models of dislocation patterning

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a driven system which tries to minimize an internal energy functional while subject to dynamic constraints and state dependent friction. This leads us to a novel interpretation which resolves the old 'energetic vs. dynamic' controversy regarding the physical origin of dislocation patterns. We demonstrate the robustness of the developed patterning scenario by considering the simplest possible case (plane strain, single slip) yet implementing the dynamics of the dislocation density evolution in two very different manners, namely (i) a hydrodynamic formulation which considers transport equations that are continuous in space and time while assuming a linear stress dependency of dislocation motion, and (ii) a stochastic cellular automaton implementation which assumes spatially and temporally discrete transport of discrete 'packets' of dislocation density which move according to an extremal dynamics. Despite the huge differences between both kinds of models, we find that the emergent patterns are mutually consistent and in agreement with the prediction of a linear stability analysis of the continuum model. We also show how different types of initial conditions lead to different intermediate evolution scenarios which, however, do not affect the properties of the fully developed patterns.

cond-mat.mtrl-sci↗

arXiv2016

Comparison of the dislocation density obtained by HR-EBSD and X-ray profile analysis

Based on the cross correlation analysis of the Kikuchi diffraction patterns high-resolution EBSD is a well established method to determine the internal stress in deformed crystalline materials. In many cases, however, the stress values obtained at the different scanning points have a large (in the order of GPa) scatter. As it was first demonstrated by Wilkinson and co-workers this is due to the long tail of the probability distribution of the internal stress ($P(σ)$) generated by the dislocations present in the system. According to the theoretical investigations of Groma and co-workers the tail of $P(σ)$ is inverse cubic with prefactor proportional to the total dislocation density $<ρ>$. In this paper we present a direct comparison of the X-ray line broadening and $P(σ)$ obtained by EBSD on deformed Cu single crystals. It is shown that $<ρ>$ can be determined from $P(σ)$. This opens new perspectives for the application of EBSD in determining mesoscale parameters in a heterogeneous sample.

cond-mat.mtrl-sci↗

arXiv2016

The role of weakest links and system size scaling in multiscale modeling of stochastic plasticity

Plastic deformation of crystalline and amorphous matter often involves intermittent local strain burst events. To understand the physical background of the phenomenon a minimal stochastic mesoscopic model was introduced, where microstructural details are represented by a fluctuating local yielding threshold. In the present paper, we propose a method for determining this yield stress distribution by lower scale discrete dislocation dynamics simulations and using a weakest link argument. The success of scale-linking is demonstrated on the stress-strain curves obtained by the resulting mesoscopic and the discrete dislocation models. As shown by various scaling relations they are statistically equivalent and behave identically in the thermodynamic limit. The proposed technique is expected to be applicable for different microstructures and amorphous materials, too.

cond-mat.mtrl-sci↗

arXiv2013

Avalanches in 2D Dislocation Systems: Plastic Yielding is not Depinning

We study the properties of strain bursts (dislocation avalanches) occurring in two-dimensional discrete dislocation dynamics models under quasistatic stress-controlled loading. Contrary to previous suggestions, the avalanche statistics differs fundamentally from predictions obtained for the depinning of elastic manifolds in quenched random media. Instead, we find an exponent τ=1 of the power-law distribution of slip or released energy, with a cut-off that increases exponentially with the applied stress and diverges with system size at all stresses. These observations demonstrate that the avalanche dynamics of 2D dislocation systems is scale-free at every applied stress and, therefore, can not be envisaged in terms of critical behavior associated with a depinning transition.

cond-mat.mtrl-sci↗

arXiv2013

Average yielding and weakest link statistics in micron-scale plasticity

Micron-scale single crystalline materials deform plastically via large intermittent strain bursts that make the deformation process unpredictable. Here we investigate this stochastic phenomenon by analysing the plastic response of an ensemble of specimens differing only in the initial arrangement of dislocations. We apply discrete dislocation dynamics simulations and microcompression tests on identically fabricated Cu single crystalline micropillars. We find that a characteristic yield stress can be defined in the average sense for a given specimen ensemble, where the average and the variance of the plastic strain start to increase considerably. In addition, in all studied cases the stress values at a given strain follow a Weibull distribution with similar Weibull exponents, which suggests that dislocation-mediated plastic yielding is characterized by an underlying weakest-link phenomenon. These results are found not to depend on fine details of the actual set-up, rather, they represent general features of micron-scale plasticity.

cond-mat.mtrl-sci↗

arXiv2011

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 cut-off time increasing with system size. The absence of intrinsic relaxation time indicates that criticality is ubiquitous in all states studied. These features are reminiscent to glassy systems, and can be attributed to the inherent quenched disorder in the position of the slip planes.

cond-mat.mtrl-sci↗

arXiv2010

Abnormal subgrain growth in a dislocation-based model of recovery

Simulation of subgrain growth during recovery is carried out using two-dimensional discrete dislocation dynamics on a hexagonal crystal lattice having three symmetric slip planes. To account for elevated temperature (i) dislocation climb was allowed and (ii) a Langevin type thermal noise was added to the force acting on the dislocations. During the simulation, a random ensemble of dislocations develop into subgrains and power-law type growth kinetics are observed. The growth exponent is found to be independent of the climb mobility, but dependent on the temperature introduced by the thermal noise. The in-depth statistical analysis of the subgrain structure shows that the coarsening is abnormal, i.e. larger cells grow faster than the small ones, while the average misorientation between the adjacent subgrains remains nearly constant. During the coarsening Holt's relation is found not to be fulfilled, such that the average subgrain size is not proportional to the average dislocation spacing. These findings are consistent with recent high precision experiments on recovery.

cond-mat.mtrl-sci↗

arXiv2010

Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution

The existence of a well defined yield stress, where a macroscopic piece of crystal begins to plastically flow, has been one of the basic observations of materials science. In contrast to macroscopic samples, in micro- and nanocrystals the strain accumulates in distinct, unpredictable bursts, which makes controlled plastic forming rather difficult. Here we study by simulation, in two and three dimensions, 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, which we identify with the jamming-flowing transition. The statistical background of this phenomenon is analyzed through the velocity distribution of short dislocation segments, revealing a universal cubic decay and an appearance of a shoulder due to dislocation avalanches. Our results can help to understand the jamming-flowing transition exhibited by a series of various physical systems.

cond-mat.mtrl-sci↗