arXiv subjects

Michael Zaiser

Publications and source records attributed to Michael Zaiser.

At least 55 records · Page 3Linked to original sources

arXiv2018

Graph theoretical approaches for the characterization of damage in hierarchical materials

We discuss the relevance of methods of graph theory for the study of damage in simple model materials described by the random fuse model. While such methods are not commonly used when dealing with regular random lattices, which mimic disordered but statistically homogeneous materials, they become relevant in materials with microstructures that exhibit complex multi-scale patterns. We specifically address the case of hierarchical materials, whose failure, due to an uncommon fracture mode, is not well described in terms of either damage percolation or crack nucleation-and-growth. We show that in these systems, incipient failure is accompanied by an increase in eigenvector localization and a drop in topological dimension. We propose these two novel indicators as possible candidates to monitor a system in the approach to failure. As such, they provide alternatives to monitoring changes in the precursory avalanche activity, which is often invoked as a candidate for failure prediction in materials which exhibit critical-like behavior at failure, but may not work in the context of hierarchical materials which exhibit scale-free avalanche statistics even very far from the critical load.

cond-mat.dis-nn↗

arXiv2018

Cyclic-loading microstructure-property relations from a mesoscale perspective: An example of single crystal Nickel-based superalloys

Past models of stress-strain response under cyclic loading mainly rely on macroscopic equations which consider microstructure evolution indirectly or simply discard microstructure information. Modern materials science, on the other hand, seeks quantitive descriptions for the relations between microstrucutre and loading response. In the present work, we show a promising mesoscale phase-field framework which can describe co-evolution of phase/grain and defect microstructures, reveal microstructure mechanisms and simultaneously predict deformation properties as a natural outcome of microstrucuture interactions. The energy functionals for phase/grain and defect microstructures are constructed, followed by functional variation which leads to governing equations. Applying the developed framework to high temperature cyclic loading of single crystal Nickel-based superalloys, the simulated results show that cyclic loading-microstructure-property relations can be principally revealed. In the short term perspective (in one cycle), dislocations move back and forth, leading to cyclic loops consistent with characteristics observed in experiments. The plastic strains are one order of magnitude smaller than total strains, which explains why the cyclic loops are very "thin". In the long term perspective, all $γγ'$ microstructures exhibit directional coarsening similar to creep under zero cyclic loading ratio, with the extent of rafting slight dependent on cyclic waveform, period, etc. The plastic strains are sensitive to cyclic loading conditions both in terms of curve shape and in terms of magnitude.

cond-mat.mtrl-sci↗

arXiv2018

Properties of dislocation lines in crystals with strong atomic-scale disorder

We use a discrete dislocation dynamics (DDD) approach to study the motion of a dislocation under strong stochastic forces that may cause bending and roughening of the dislocation line on scales that are comparable to the dislocation core radius. In such situations, which may be relevant in high entropy alloys (HEA) exhibiting strong atomic scale disorder, standard scaling arguments based upon a line tension approximation may be no longer adequate and corrections to scaling need to be considered. We first study the wandering of the dislocation under thermal Langevin forces. This leads to a linear stochastic differential equation which can be exactly solved. From the Fourier modes of the thermalized dislocation line we can directly deduce the scale dependent effective line tension. We then use this information to investigate the wandering of a dislocation in a crystal with spatial, time-independent ('quenched') disorder. We establish the pinning length and show how this length can be used as a predictor of the flow stress. Implications for the determination of flow stresses in HEA from molecular dynamics simulations are discussed.

cond-mat.mtrl-sci↗

arXiv2018

Avalanche behavior in creep failure of disordered materials

We present a mesoscale elastoplastic model of creep in disordered materials which considers temperature-dependent stochastic activation of localized deformation events which are mutually coupled by internal stresses, leading to collective avalanche dynamics. We generalize this stochastic plasticity model by introducing damage in terms of a local strength that decreases, on statistical average, with increasing local plastic strain. As a consequence the model captures failure in terms of strain localization in a catastrophic shear band concomitant with a finite-time singularity of the creep rate. The statistics of avalanches in the run-up to failure is characterized by a decreasing avalanche exponent $τ$ that, at failure, approaches the value $τ= 1.5$ typical of a critical branching process. The average avalanche rate exhibits an inverse Omori law as a function of the time-to-failure, whereas the distribution of inter-avalanche times turns out to be consistent with the ETAS model of earthquake statistics.

cond-mat.mtrl-sci↗

arXiv2018

Annihilation and sources in continuum dislocation dynamics (CDD)

Continuum dislocation dynamics (CDD) aims at representing the evolution of systems of curved and connected dislocation lines in terms of density-like field variables. Here we discuss how the processes of dislocation multiplication and annihilation can be described within such a framework. We show that both processes are associated with changes in the volume density of dislocation loops: dislocation annihilation needs to be envisaged in terms of the merging of dislocation loops, while conversely dislocation multiplication is associated with the generation of new loops. Both findings point towards the importance of including the volume density of loops (or 'curvature density') as an additional field variable into continuum models of dislocation density evolution. We explicitly show how this density is affected by loop mergers and loop generation. The equations which result for the lowest order CDD theory allow us, after spatial averaging and under the assumption of unidirectional deformation, to recover the classical theory of Kocks and Mecking for the early stages of work hardening.

cond-mat.mes-hall↗

arXiv2018

Size and Disorder Effects in Elasticity of Cellular Structures: From Discrete Models to Continuum Representations

Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small systems. Furthermore, these structures are often irregular, which not only affects the size dependent behaviour but also leads to significant property variations among different microstructure realizations. The computational model for cellular microstructures is based on networks of Timoshenko beams. It is a computationally efficient approach allowing to obtain statistically representative averages from computing large numbers of realizations. For detailed analysis of the underlying deformation mechanisms an energetically consistent continuization method was developed which links the forces and displacements of discrete beam networks to equivalent spatially continuous stress and strain fields. This method is not only useful for evaluation and visualization purposes but also allows to perform ensemble averages of, e.g., continuous stress patterns - an analysis approach which is highly beneficial for comparisons and statistical analysis of microstructures with respect to different degrees of structural disorder.

cond-mat.mtrl-sci↗

arXiv2017

Avalanche precursors of failure in hierarchical fuse networks

We study precursors of failure in hierarchical random fuse network models which can be considered as idealizations of hierarchical (bio)materials where fibrous assemblies are held together by multi-level (hierarchical) cross-links. When such structures are loaded towards failure, the patterns of precursory avalanche activity exhibit generic scale invariance: Irrespective of load, precursor activity is characterized by power-law avalanche size distributions without apparent cut-off, with power-law exponents that decrease continuously with increasing load. This failure behavior and the ensuing super-rough crack morphology differ significantly from the findings in non-hierarchical structures.

cond-mat.dis-nn↗

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↗

arXiv2017

Determining Cosserat constants of 2D cellular solids from beam models

We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence.

cond-mat.mtrl-sci↗

arXiv2017

A continuum approach to combined $γ/γ'$ evolution and dislocation plasticity in Nickel-based superalloys

Creep in single crystal Nickel-based superalloys has been a topic of interest since decades, and nowadays simulations are more and more able to complement experiments. In these alloys, the $γ/γ'$ phase microstructure co-evolves with the system of dislocations under load, and understanding the mutual interactions is essential for understanding the resulting creep properties. Predictive modeling thus requires multiphysics frameworks capable of modeling and simulating both the phase and defect microstructures. To do so, we formulate a coupled model of phase-field evolution and continuum dislocation dynamics which adequately accounts for both statistically stored and geometrically necessary dislocations. The simulated $γ/γ'$ phase microstructure with four $γ'$ variants and co-evolving dislocation microstructure is found to be in good agreement with experimental observations. The creep strain curve is obtained as a natural by-product of the microstructure evolution equations without the need for additional parameter fitting. We perform simulations of $γ/γ'$ evolution for different dislocation densities and establish the driving forces for microstructure evolution by analyzing in detail the changes in different contributions to the elastic and chemical energy density. Together with comparisons between simulated and experimental creep curves this investigation reveals the mechanisms controlling the process of directional coarsening (rafting) and demonstrates that the kinetics of rafting significantly depends on characteristics of the dislocation microstructure. In addition to rafting under constant load, we investigate the effect of changes in loading conditions and explore the possibility of improving creep properties by pre-rafting along a different loading path.

cond-mat.mtrl-sci↗

arXiv2016

Universality of Avalanche Exponents in Plastic Deformation of Disordered Solids

Plastic yield of amorphous solids occurs by power law distributed slip avalanches whose universality is still debated. Determination of the power law exponents from experiments and molecular dynamics simulations is hampered by limited statistical sampling. On the other hand, while existing elasto-plastic depinning models give precise exponent values, these models to date have been limited to a scalar approximation of plasticity which is difficult to reconcile with the statistical isotropy of amorphous materials. Here we introduce for the first time a fully tensorial mesoscale model for the elasto-plasticity of disordered media that can not only reproduce a wide variety of shear band patterns observed experimentally for different deformation modes, but also captures the avalanche dynamics of plastic flow in disordered materials. Slip avalanches are characterized by universal distributions which are quantitatively different from mean field predictions, both regarding the exponents and regarding the form of the scaling functions, and which are independent of system dimensionality (2D vs 3D), boundary and loading conditions, and uni-or biaxiality of the stress state. We also measure average avalanche shapes, which are equally universal and inconsistent with mean field predictions. Our results provide strong evidence that the universality class of plastic yield in amorphous materials is distinct from that of mean field depinning.

cond-mat.mtrl-sci↗

arXiv2016

Continuum Representation of Systems of Dislocation Lines: A General Method for Deriving Closed-Form Evolution Equations

Plasticity is governed by the evolution of, in general anisotropic, systems of dislocations. We seek to faithfully represent this evolution in terms of density-like variables which average over the discrete dislocation microstructure. Starting from T. Hochrainer's continuum theory of dislocations (CDD), we introduce a methodology based on the 'Maximum Information Entropy Principle' (MIEP) for deriving closed-form evolution equations for dislocation density measures of different order. These equations provide an optimum representation of the kinematic properties of systems of curved and connected dislocation lines with the information contained in a given set of density measures. The performance of the derived equations is benchmarked against other models proposed in the literature, using discrete dislocation dynamics simulations as a reference. As a benchmark problem we study dislocations moving in a highly heterogeneous, persistent slip-band-like geometry. We demonstrate that excellent agreement with discrete simulations can be obtained in terms of a very small number of averaged dislocation fields containing information about the edge and screw components of the total and excess (geometrically necessary) dislocation densities. From these the full dislocation orientation distribution which emerges as dislocations move through a channel-wall structure can be faithfully reconstructed.

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↗

arXiv2016

Dislocation patterning in a 2D 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 2D 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 diffusion like 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.

cond-mat.mtrl-sci↗

arXiv2015

Local density approximation for the energy functional of three-dimensional dislocation systems

The elastic energy functional of a system of discrete dislocation lines is well known from dislocation theory. In this paper we demonstrate how the discrete functional can be used to systematically derive approximations which express the elastic energy in terms of dislocation density-like variables which average over the discrete dislocation configurations and represent the dislocation system on scales above the spacing of the individual dislocation lines. We study the simple case of two-dimensional systems of straight dislocation lines before we proceed to derive energy functionals for systems of three-dimensionally curved dislocation lines pertaining to a single, as well as to multiple slip systems. We then illustrate several applications of the theory including Debye screening of dislocations in two and three dimensions, and the derivation of back stress and friction stress terms entering the stress balance from the free energy functionals.

cond-mat.mtrl-sci↗

arXiv2015

Pattern formation in a minimal model of continuum dislocation plasticity

The spontaneous emergence of heterogeneous dislocation patterns is a conspicuous feature of plastic deformation and strain hardening of crystalline solids. Despite long-standing efforts in the materials science and physics of defect communities, there is no general consensus regarding the physical mechanism which leads to the formation of dislocation patterns. In order to establish the fundamental mechanism, we formulate an extremely simplified, minimal model to investigate the formation of patterns based on the continuum theory of fluxes of curved dislocations. We demonstrate that strain hardening as embodied in a Taylor-type dislocation density dependence of the flow stress, in conjunction with the structure of the kinematic equations that govern dislocation motion under the action of external stresses, is already sufficient for the formation of dislocation patterns that are consistent with the principle of similitude.

cond-mat.mtrl-sci↗

arXiv2015

Statistical Analysis and Stochastic Dislocation-Based Modelling of Microplasticity

Plastic deformation in microscale differs from the macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size (ii) the scatter of plasticity increases significantly. In this work we focus on the scatter of plasticity. We statistically characterize the deformation process of micropillars under tension using results from discrete dislocation dynamics (DDD) simulations. We then propose a stochastic microplasticity model which uses the extracted information from the above statistical characterization to make statistical predictions regarding the micropillar stress-strain curves. This model aims to map the complex dynamics of interacting dislocations onto a stochastic processes involving the continuum variables of stress and strain. Therefore, it combines a classical continuum description of the elastic-plastic problem with a stochastic description of the discrete dislocation dynamics. We compare the model predictions with the underlying DDD simulations and outline potential future applications of the same modelling approach.

cond-mat.mtrl-sci↗