arXiv subjects

Péter Dusán Ispánovity

Publications and source records attributed to Péter Dusán Ispánovity.

34 records · Page 2Linked to original sources

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↗

arXiv2018

Strain distribution in polycrystals: Theory and Application for Diffraction Experiments

Randomly textured polycrystalline materials of constituents with highly anisotropic nature of grains can be considered globally isotropic. In order to determine the isotropic properties, like elasticity or conductivity, we propose a theory for averaging the coefficients of the corresponding tensors unifying Voigt's, Reuss' or other self-consistent homogenization theories. We apply the method to determine elastic moduli of untextured polycrystals with arbitrary crystal structures, recovering experimental data with high precision for cubic materials. We show that the average moduli can be used to predict analytically stress and strain states inside individual grains as proven by the comparison with neutron diffraction measurements. Finally, we discuss a few possible generalizations for textured materials for further applications.

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

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↗

arXiv2016

Disorder is good for you: The influence of local disorder on strain localization and ductility of strain softening materials

We formulate a generic concept model for the deformation of a locally disordered, macroscopically homogeneous material which undergoes irreversible strain softening during plastic deformation. We investigate the influence of the degree of microstructural heterogeneity and disorder on the concomitant strain localization process (formation of a macroscopic shear band). It is shown that increased microstructural heterogeneity delays strain localization and leads to an increase of the plastic regime in the macroscopic stress-strain curves. The evolving strain localization patterns are characterized and compared to models of shear band formation published in the literature.

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

Critical behavior in dislocation systems: power-law relaxation below the yield stress

Plasticity of two-dimensional discrete dislocation systems is studied. It is shown, that at some threshold stress level the response becomes stress-rate dependent. Below this stress level the stress-plastic strain relation exhibits power-law type behavior. In this regime the plastic strain rate induced by a constant external stress decays to zero as a power-law, which stems from the scaling of the dislocation velocity distribution. The scaling is cut-off at a time only dependent on the system size and the scaling exponent depends on the external stress and on the initial correlations present in the system. These results show, that the dislocation system is in a critical state everywhere we studied below the threshold stress.

cond-mat.stat-mech↗

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

Impact of gamma' particle coarsening on the critical resolved shear stress of nickel-base superalloys with low aluminium and/or titanium content

In Ni-base superalloys with low Al and/or Ti content the precipitation and subsequent coarsening of gamma' particles at intermediate temperatures contribute to the degradation of the mechanical properties of the alloy. In the present paper the coarsening process is modelled and the change of the critical resolved shear stress of the alloy due to coarsening of the gamma' particles is calculated by means of statistical analysis of the depinning of a single gliding edge dislocation. It is found that the contribution of gamma' hardening to the critical resolved shear stress at 973 K reduces to more than half of its original value in less than one year.

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↗

arXiv2009

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 Hooke's law the variational framework gives the same field equations as Kröner's theory. However, the variational method proposed allows to study many other problems like dislocation core regularisation, role of elastic anharmonicity and dislocation--solute atom interaction. The aim of the paper is to demonstrate that these problems can be handled on a systematic manner.

cond-mat.mtrl-sci↗

arXiv2009

Role of density fluctuations in the relaxation of random dislocation systems

We study the relaxation dynamics of systems of straight, parallel crystal dislocations, starting from initially random and uncorrelated positions of the individual dislocations. A scaling model of the relaxation process is constructed by considering the gradual extinction of the initial density fluctuations present in the system. The model is validated by ensemble simulations of the discrete dynamics of dislocations. Convincing agreement is found for systems of edge dislocations in single slip irrespective of the net Burgers vector of the dislocation system. It is also demonstrated that the model does not work in multiple slip geometries.

cond-mat.mtrl-sci↗

arXiv2008

The probability distribution of internal stresses in externally loaded 2D dislocation systems

The distribution of internal shear stresses in a 2D dislocation system is investigated when external shear stress is applied. This problem serves as a natural continuation of the previous work of Csikor and Groma (Csikor F F and Groma I 2004 Phys. Rev. B 58 2969), where analytical result was given for the stress distribution function at zero applied stress. First, the internal stress distribution generated by a set of randomly positioned ideal dislocation dipoles is studied. Analytical calculations are carried out for this case. The theoretical predictions are checked by numerical simulations showing perfect agreement. It is found that for real relaxed dislocation configurations the role of dislocation multipoles cannot be neglected, but the theory presented can still be applied.

cond-mat.stat-mech↗

arXiv2008

Evolution of the correlation functions in 2D dislocation systems

In this paper spatial correlations of parallel edge dislocations are studied. After closing a hierarchy of equations for the many-particle density functions by the Kirkwood superposition approximation, we derive evolution equations for the correlation functions. It is found that these resulting equations and those governing the evolution of density fields of total as well as geometrically necessary dislocations around a single edge dislocation are formally the same. The second case corresponds to the already described phenomenon of Debye screening of an individual dislocation. This equivalence of the correlation functions and screened densities is demonstrated also by discrete dislocation dynamics simulation results, which confirm the physical correctness of the applied Kirkwood superposition approximation. Relation of this finding and the linear response theory in thermal systems is also discussed.

cond-mat.stat-mech↗