1,323 research outputs found
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
The solid angle and the Burgers formula in the theory of gradient elasticity: line integral representation
A representation of the solid angle and the Burgers formula as line integral
is derived in the framework of the theory of gradient elasticity of Helmholtz
type. The gradient version of the Eshelby-deWit representation of the Burgers
formula of a closed dislocation loop is given. Such a form is suitable for the
numerical implementation in 3D dislocation dynamics (DD).Comment: 11 pages, to appear in: Physics Letters
Diffuse-interface polycrystal plasticity: Expressing grain boundaries as geometrically necessary dislocations
The standard way of modeling plasticity in polycrystals is by using the
crystal plasticity model for single crystals in each grain, and imposing
suitable traction and slip boundary conditions across grain boundaries. In this
fashion, the system is modeled as a collection of boundary-value problems with
matching boundary conditions. In this paper, we develop a diffuse-interface
crystal plasticity model for polycrystalline materials that results in a single
boundary-value problem with a single crystal as the reference configuration.
Using a multiplicative decomposition of the deformation gradient into lattice
and plastic parts, i.e. F(X,t) = F^L(X,t) F^P(X,t), an initial stress-free
polycrystal is constructed by imposing F^L to be a piecewise constant rotation
field R^0(X), and F^P = R^0(X)^T, thereby having F(X,0) = I, and zero elastic
strain. This model serves as a precursor to higher order crystal plasticity
models with grain boundary energy and evolution.Comment: 18 pages, 7 figure
The Green tensor of Mindlin's anisotropic first strain gradient elasticity
We derive the Green tensor of Mindlin's anisotropic first strain gradient
elasticity. The Green tensor is valid for arbitrary anisotropic materials, with
up to 21 elastic constants and 171 gradient elastic constants in the general
case of triclinic media. In contrast to its classical counterpart, the Green
tensor is non-singular at the origin, and it converges to the classical tensor
a few characteristic lengths away from the origin. Therefore, the Green tensor
of Mindlin's first strain gradient elasticity can be regarded as a physical
regularization of the classical anisotropic Green tensor. The isotropic Green
tensor and other special cases are recovered as particular instances of the
general anisotropic result. The Green tensor is implemented numerically and
applied to the Kelvin problem with elastic constants determined from
interatomic potentials. Results are compared to molecular statics calculations
carried out with the same potentials
The -invariant and topological pathways to influence sub-micron strength and crystal plasticity
In small volumes, sample dimensions are known to strongly influence
mechanical behavior, especially strength and crystal plasticity. This
correlation fades away at the so-called mesoscale, loosely defined at several
micrometers in both experiments and simulations. However, this picture depends
on the entanglement of the initial defect configuration. In this paper, we
study the effect of sample dimensions with a full control on dislocation
topology, through the use of a novel observable for dislocation ensembles, the
-invariant, that depends only on mutual dislocation linking: It is
built on the natural vortex character of dislocations and it has a
continuum/discrete correspondence that may assist multiscale modeling
descriptions. We investigate arbitrarily complex initial dislocation
microstructures in sub-micron-sized pillars, using three-dimensional discrete
dislocation dynamics simulations for finite volumes. We demonstrate how to
engineer nanoscale dislocation ensembles that appear virtually independent from
sample dimensions, either by biased-random dislocation loop deposition or by
sequential mechanical loads of compression and torsion.Comment: 4 figures, 3 Appendice
Plasticity without phenomenology: a first step
A novel, concurrent multiscale approach to meso/macroscale plasticity is
demonstrated. It utilizes a carefully designed coupling of a partial
differential equation (pde) based theory of dislocation mediated crystal
plasticity with time-averaged inputs from microscopic Dislocation Dynamics
(DD), adapting a state-of-the-art mathematical coarse-graining scheme. The
stress-strain response of mesoscopic samples at realistic, slow, loading rates
up to appreciable values of strain is obtained, with significant speed-up in
compute time compared to conventional DD. Effects of crystal orientation,
loading rate, and the ratio of the initial mobile to sessile dislocation
density on the macroscopic response, for both load and displacement controlled
simulations are demonstrated. These results are obtained without using any
phenomenological constitutive assumption, except for thermal activation which
is not a part of microscopic DD. The results also demonstrate the effect of the
internal stresses on the collective behavior of dislocations, manifesting, in a
set of examples, as a Stage I to Stage II hardening transition
Atomistically enabled nonsingular anisotropic elastic representation of near-core dislocation stress fields in -iron
The stress fields of dislocations predicted by classical elasticity are known
to be unrealistically large approaching the dislocation core, due to the
singular nature of the theory. While in many cases this is remedied with the
approximation of an effective core radius, inside which ad hoc regularizations
are implemented, such approximations lead to a compromise in the accuracy of
the calculations. In this work, an anisotropic non-singular elastic
representation of dislocation fields is developed to accurately represent the
near-core stresses of dislocations in -iron. The regularized stress
field is enabled through the use of a non-singular Green's tensor function of
Helmholtz-type gradient anisotropic elasticity, which requires only a single
characteristic length parameter in addition to the material's elastic
constants. Using a novel magnetic bond-order potential to model atomic
interactions in iron, molecular statics calculations are performed, and an
optimization procedure is developed to extract the required length parameter.
Results show the method can accurately replicate the magnitude and decay of the
near-core dislocation stresses even for atoms belonging to the core itself.
Comparisons with the singular isotropic and anisotropic theories show the
non-singular anisotropic theory leads to a substantially more accurate
representation of the stresses of both screw and edge dislocations near the
core, in some cases showing improvements in accuracy of up to an order of
magnitude. The spatial extent of the region in which the singular and
non-singular stress differ substantially is also discussed. The general
procedure we describe may in principle be applied to accurately model the
near-core dislocation stresses of any arbitrarily shaped dislocation in
anisotropic cubic media.Comment: Appearing in Phys. Rev.
A discrete dislocation dynamics study of precipitate bypass mechanisms in nickel-based superalloys
Order strengthening in nickel-based superalloys is associated with the extra
stress required for dislocations to bypass the precipitates
distributed in the matrix. A rich variety of bypass mechanism has been
identified, with various shearing and Orowan looping processes giving way to
climb bypass as the operating conditions change from the low/intermediate
temperatures and high stress regime, to the high temperature and low stress
regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms
operate, the bypass mechanism changes from shearing to looping with increased
particle size and within a broad coexistence size window. Another possibility,
supported by indirect experimental evidence, is that a third "hybrid"
transition mechanism may operate. In this paper we use discrete dislocation
dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based
superalloys. We develop a new method to compute generalized stacking fault
forces in DDD simulations. We use this method to study the mechanisms of bypass
of a square lattice of spherical precipitates by
edge dislocations, as a function of the
precipitates volume fraction and size. We show that the hybrid mechanism is
possible and it operates as a transition mechanism between the shearing and
looping regimes over a large range of precipitates volume fraction and radii.
We also consider the effects of a lattice misfit on the bypass
mechanisms, which we approximate by an additional precipitate stress computed
according to Eshelby's inclusion theory. We show that in the shearing and
hybrid looping-shearing regimes, a lattice misfit generally results in an
increased bypass stress. For sufficiently high lattice misfit, the bypass
stress is controlled by the pinning of the trailing dislocation on the exit
side of the precipitates.Comment: Submitted to International Journal of Plasticit
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