Dislocation patterns and the similitude principle: 2.5D mesoscale simulations

During plastic flow of crystalline solids, dislocations self-organize in the form of patterns, with a wavelength that is inversely proportional to stress. After four decades of investigations, the origin of this property is still under discussion. We show that dislocation patterns verifying the principle of similitude can be obtained from dynamics simulations of double slip. These patterns are formed in the presence of long- and short-range interactions, but they are not significantly modified when only short-range interactions are present. This new insight into dislocation patterning phenomena has important implications regarding current models

Equation of motion for dislocations with inertial effects

An approximate equation of motion is proposed for screw and edge dislocations, which accounts for retardation and for relativistic effects in the subsonic range. Good quantitative agreement is found, in accelerated or in decelerated regimes, with numerical results of a more fundamental nature.Comment: 6 pages, 4 figures, LaTe

Micro-plasticity and intermittent dislocation activity in a simplified micro structural model

Here we present a model to study the micro-plastic regime of a stress-strain curve. In this model an explicit dislocation population represents the mobile dislocation content and an internal shear-stress field represents a mean-field description of the immobile dislocation content. The mobile dislocations are constrained to a simple dipolar mat geometry and modelled via a dislocation dynamics algorithm, whilst the shear-stress field is chosen to be a sinusoidal function of distance along the mat direction. The latter, defined by a periodic length and a shear-stress amplitude, represents a pre-existing micro-structure. These model parameters, along with the mobile dislocation density, are found to admit a diversity of micro-plastic behaviour involving intermittent plasticity in the form of a scale-free avalanche phenomenon, with an exponent for the strain burst magnitude distribution similar to those seen in experiment and more complex dislocation dynamics simulations.Comment: 30 pages, 12 figures, to appear in "Modelling and Simulation in Materials Science and Engineering

Plastic Flow in Two-Dimensional Solids

A time-dependent Ginzburg-Landau model of plastic deformation in two-dimensional solids is presented. The fundamental dynamic variables are the displacement field \bi u and the lattice velocity {\bi v}=\p {\bi u}/\p t. Damping is assumed to arise from the shear viscosity in the momentum equation. The elastic energy density is a periodic function of the shear and tetragonal strains, which enables formation of slips at large strains. In this work we neglect defects such as vacancies, interstitials, or grain boundaries. The simplest slip consists of two edge dislocations with opposite Burgers vectors. The formation energy of a slip is minimized if its orientation is parallel or perpendicular to the flow in simple shear deformation and if it makes angles of $\pm \pi/4$ with respect to the stretched direction in uniaxial stretching. High-density dislocations produced in plastic flow do not disappear even if the flow is stopped. Thus large applied strains give rise to metastable, structurally disordered states. We divide the elastic energy into an elastic part due to affine deformation and a defect part. The latter represents degree of disorder and is nearly constant in plastic flow under cyclic straining.Comment: 16pages, Figures can be obtained at http://stat.scphys.kyoto-u.ac.jp/index-e.htm

Analytical integration of the forces induced by dislocations on a surface element

An analytical formulation of the nodal forces induced by a dislocation segment on a surface element is presented. The determination of such nodal forces is a critical step when associating dislocation dynamics simulations with continuum approaches to simulate the plastic behaviour of finite domains. The nodal force calculation starts from the infinite-domain stress field of a dislocation and involves a triple integration over the dislocation ensemble and over the surface element at the domain boundary. In the case of arbitrary oriented straight segments of dislocations and a linear rectangular surface element, the solution is derived by means of a sequence of integrations by parts that present specific recurrence relations. The use of the non-singular expression for the infinite-domain stress field ensures that the traction field is finite everywhere even at the dislocation core. A specific solution is provided for virtual semi-infinite segments that can be used to enforce global mechanical equilibrium in the infinite domain. The proposed model for nodal forces is fully analytical, exact and very efficient computationally. A discussion on how to adapt the proposed methodology to more complex shape functions and surface element geometry is presented at the end of the paper. © 2014 IOP Publishing Ltd

Cast aluminium single crystals cross the threshold from bulk to size-dependent stochastic plasticity

Metals are known to exhibit mechanical behaviour at the nanoscale different to bulk samples. This transition typically initiates at the micrometre scale, yet existing techniques to produce micrometre-sized samples often introduce artefacts that can influence deformation mechanisms. Here, we demonstrate the casting of micrometre-scale aluminium single-crystal wires by infiltration of a salt mould. Samples have millimetre lengths, smooth surfaces, a range of crystallographic orientations, and a diameter D as small as 6 μm. The wires deform in bursts, at a stress that increases with decreasing D. Bursts greater than 200 nm account for roughly 50% of wire deformation and have exponentially distributed intensities. Dislocation dynamics simulations show that single-arm sources that produce large displacement bursts halted by stochastic cross-slip and lock formation explain microcast wire behaviour. This microcasting technique may be extended to several other metals or alloys and offers the possibility of exploring mechanical behaviour spanning the micrometre scale

Multiscale modelling for fusion and fission materials: the M4F project

The M4F project brings together the fusion and fission materials communities working on the prediction of radiation damage production and evolution and its effects on the mechanical behaviour of irradiated ferritic/martensitic (F/M) steels. It is a multidisciplinary project in which several different experimental and computational materials science tools are integrated to understand and model the complex phenomena associated with the formation and evolution of irradiation induced defects and their effects on the macroscopic behaviour of the target materials. In particular the project focuses on two specific aspects: (1) To develop physical understanding and predictive models of the origin and consequences of localised deformation under irradiation in F/M steels; (2) To develop good practices and possibly advance towards the definition of protocols for the use of ion irradiation as a tool to evaluate radiation effects on materials. Nineteen modelling codes across different scales are being used and developed and an experimental validation programme based on the examination of materials irradiated with neutrons and ions is being carried out. The project enters now its 4th year and is close to delivering high-quality results. This paper overviews the work performed so far within the project, highlighting its impact for fission and fusion materials science.This work has received funding from the Euratom research and training programme 2014-2018 under grant agreement No. 755039 (M4F project)