arXiv subjects

Stefan Sandfeld

Publications and source records attributed to Stefan Sandfeld.

47 records · Page 3Linked to original sources

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

Insights from a minimal model of dislocation-assisted rafting in single crystal Nickel-based superalloys

Nickel-based superalloys play a major role in many technologically relevant high temperature applications. Understanding and predicting the evolution of the phase microstructure during high temperature creep together with the evolution of the dislocation microstructure is a challenge that up to date has not yet been fully accomplished. Our two-dimensional coupled phase-field/continuum dislocation dynamics model explains microstructural mechanisms which are important during the early stage of rafting in a single crystal system. It shows how $γ/γ'$ phases and dislocations interact giving rise to realistic creep behavior; no phenomenological fit parameters are required.

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

A Universal Approach Towards Computational Characterization of Dislocation Microstructure

Dislocations - linear defects within the crystal lattice of, e.g., metals - already have been directly observed and analyzed for nearly a century. While experimental characterization methods can nowadays reconstruct three-dimensional pictures of complex dislocation networks, simulation methods are at the same time more and more able to predict the evolution of such systems in great detail. Concise methods for analyzing and comparing dislocation microstructure, however, are still lagging behind. We introduce a universal microstructure "language" which could be used for direct comparisons and detailed analysis of very different experimental and simulation methods.

cond-mat.mtrl-sci↗

arXiv2016

Microstructural Comparison of the Kinematics of Discrete and Continuum Dislocations Models

The Continuum Dislocation Dynamics (CDD) theory and the Discrete Dislocation Dynamics (DDD) method are compared based on concise mathematical formulations of the coarse graining of discrete data. A numerical tool for converting from a discrete to a continuum representation of a given dislocation configuration is developed, which allows to directly compare both simulation approaches based on continuum quantities (e.g. scalar density, geometrically necessary densities, mean curvature). Investigating the evolution of selected dislocation configurations within analytically given velocity fields for both DDD and CDD reveals that CDD contains a surprising number of important microstructural details.

cond-mat.mtrl-sci↗

arXiv2015

A link between microstructure evolution and macroscopic response in elasto-plasticity: formulation and numerical approximation of the higher-dimensional Continuum Dislocation Dynamics theory

Micro-plasticity theories and models are suitable to explain and predict mechanical response of devices on length scales where the influence of the carrier of plastic deformation - the dislocations - cannot be neglected or completely averaged out. To consider these effects without resolving each single dislocation a large variety of continuum descriptions has been developed, amongst which the higher-dimensional continuum dislocation dynamics (hdCDD) theory by Hochrainer et al. (Phil. Mag. 87, pp. 1261-1282) takes a different, statistical approach and contains information that are usually only contained in discrete dislocation models. We present a concise formulation of hdCDD in a general single-crystal plasticity context together with a discontinuous Galerkin scheme for the numerical implementation which we evaluate by numerical examples: a thin film under tensile and shear loads. We study the influence of different realistic boundary conditions and demonstrate that dislocation fluxes and their lines' curvature are key features in small-scale plasticity.

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

Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model

Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear lattice defects is not applicable - still are lagging behind. We introduce an eigenstrain-based finite element lattice model for simulations of shear band formation and strain avalanches. Our model allows us to study the influence of surfaces and finite size effects on the statistics of avalanches. We find that even with relatively complex loading conditions and open boundary conditions, critical exponents describing avalanche statistics are unchanged, which validates the use of simpler scalar lattice-based models to study these phenomena.

cond-mat.soft↗

arXiv2014

Scalar model for frictional precursors dynamics

Recent experiments indicate that frictional sliding occurs by the nucleation of detachment fronts at the contact interface that may appear well before the onset of global sliding. This intriguing precursory activity is not accounted for by traditional friction theories but is extremely important for friction dominated geophysical phenomena such as earthquakes, landslides or avalanches. Here we simulate the onset of slip of a three dimensional elastic body resting on a surface and show that experimentally observed frictional precursors depend in a complex non-universal way on the sample geometry and the loading conditions. Our model satisfies Archard's law and Amontons' first and second laws, reproducing with remarkable precision the real contact area dynamics, the precursors' envelope dynamics prior to the transition to sliding, and the normal and shear internal stress distributions close to the slider-substrate interface. Moreover, it allows to assess which experimental features can be attributed to the elastic equilibrium, and which are attributed to the out-of-equilibrium dynamics, suggesting that precursory activity is an intrinsically quasi-static physical process. A direct calculation of the evolution of the Coulomb stress before and during precursors nucleation shows large variations across the sample, which helps to explain why earthquake forecasting methods based only on accumulated slip and Coulomb stress monitoring are often ineffective.

cond-mat.soft↗

arXiv2014

Scaling Properties of Dislocation Simulations in the Similitude Regime

Dislocation systems exhibit well known scaling properties such as the Taylor relationship between flow stress and dislocation density, and the "law of similitude" linking the flow stress to the characteristic wavelength of dislocation patterns. Here we discuss the origin of these properties, which can be related to generic invariance properties of the equations of evolution of discrete dislocation systems, and their implications for a wide class of models of dislocation microstructure evolution. We demonstrate that under certain conditions dislocation simulations carried out at different stress, dislocation density, and strain rate can be considered as equivalent, and we study the range of deformation conditions ("similitude regime") over which this equivalence can be expected to hold. In addition, we discuss the restrictions imposed by the formulated invariance properties for density-based, nonlocal or stochastic models of dislocation microstructure evolution, and for dislocation patterns and size effects.

cond-mat.mtrl-sci↗

arXiv2014

Deformation Patterns and Surface Morphology in a Minimal Model of Amorphous Plasticity

We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the local yield stresses. Using a finite element implementation of this simple model, we simulate the plane-strain deformation of long thin rods loaded in tension. The resulting strain patterns are statistically characterized in terms of their spatial correlation functions. Studies of the corresponding surface morphology reveal a non-trivial Hurst exponent of approx. 0.8, indicating the presence of long range correlations in the deformation patterns. The simulated deformation patterns and surface morphology exhibit persistent features which emerge already at the very onset of plastic deformation, while subsequent evolution is characterized by growth in amplitude without major morphology changes. The findings are compared to experimental observations.

cond-mat.mtrl-sci↗