A systematic numerical study using discrete dislocation dynamics has been conducted to investigate the formation of geometrically necessary dislocation boundaries (GNBs), a fundamental component of dislocation patterning and work-hardening. The simulations presented in this paper focus on GNBs forming along the (010) plane, which are observed in the (121) [111] copper orientation on the beta-fibre of the FCC rolling texture. The results demonstrate that GNBs can emerge as a relaxation product, self-organising to satisfy low-energy theorems such as the Frank equation. Additionally, the requirements for the involved slip systems and their relative densities to form stable mobile and immobile boundaries are evaluated.

Dynamic recovery (DR) during single crystal stage III is believed to result from cross-slip or at least be triggered by this dislocation mechanism. However, the precise causal chain of events that induces a return to a low hardening value, similar to stage I, after the strong hardening of stage II, remains unclear. Unlike strain hardening, which has been the subject of numerous successful 3D Dislocation Dynamics simulations (3D-DD), DR has been sparsely studied. This is primarily because it requires achieving large strains to reach stage III, which is difficult to obtain in a sufficiently large volume to be statistically meaningful for dislocation modeling, especially under quasi-static loading. However, it is possible to conduct 3D-DD simulations with high dislocation density to approximate conditions close to stage III and attempt to identify the potential causes of recovery. This is what we aimed to do in the present study, with simulations at different dislocation densities and by testing specific dislocation mechanisms separately to determine their exact contributions. Our results, while not definitive, provide insight into the origin of DR. Firstly, we demonstrate that a previously neglected athermal mechanism, i.e. collinear annihilation, plays an important role in DR, being the only forest mechanism that induces virtually no storage. Secondly, we show that plastic instabilities favoring a reduction in the number of active systems are a highly effective way of reducing dislocation storage. Lastly, cross-slip is found to reduce dislocation storage under very specific slip conditions, suggesting that these conditions should exist during Stage III.

Strain localization mechanisms taking place in polycrystal grains are investigated using Discrete Dislocation Dynamics (DDDs) simulations. First, elastic Finite Element Method simulations are used to calculate the intragranular stress distribution linked to strain incompatibilities between grains. Many configurations are tested to evaluate the stress heterogeneity and constitute a database for DDD simulations. From the analysis of these microstructures, a criterion is proposed to identify the grains where the emergence of the localization of the deformation is the most likely. Then, DDD simulations are used to explore the plastic strain localization phenomenon at the grain scale. Those simulations show that stress concentrations close to a polycrystal quadruple node can play a fundamental role in plastic strain localization. This work paves the way for future investigations to be made thanks to DDD simulations regarding slip band initiation and strain relaxation phenomena.

DDD simulation is a numerical method that reproduces the plastic deformation of crystalline materials in a physically justified way at the scale of several tens of micrometers down to the atomic scale. This method is particularly well adapted to study the mechanical properties of superalloys as the plastic deformation of such materials is located in volumes with submicrometer dimensions. In this chapter, recent progress of the DDD technique and its important results on superalloys single crystals are reviewed.

A multiscale modeling methodology involving discrete dislocation dynamics (DDD) and crystal plasticity finite element method (CPFEM) was used to study the grain size effect in FCC polycrystalline plasticity. The developed model is based on the dislocation density storage-recovery framework and is expanded to the scale of slip systems. DDD simulations were used to establish a constitutive law incorporating the main dislocation mechanisms that are involved in the strain hardening process observed in monotonically deformed FCC polycrystals. This was achieved by calculating the key features controlling the accumulation of the forest dislocation density within the grains and the polarized dislocation density at the grain boundaries during plastic deformation. The model was then integrated with a CPFEM model at the polycrystalline aggregate scale to compute short- and long-range internal stresses within the grains. These simulations quantitatively reproduced the deformation curves of the FCC polycrystals as a function of grain size. Because of its predictive ability to reproduce the Hall–Petch effect in a physically justified approach, the proposed framework has significant potential for further applications.

The influence of the grain orientation on the long-range internal stress associated with the accumulation of geometrically necessary dislocations (GNDs) during plastic deformation is numerically investigated. GNDs stored at grain boundaries (GBs) do not systematically generate a backstress inside grains. Surprisingly, long-range anti-backstress promoting dislocation dynamics and plastic strain inside grains arises at certain GBs interfaces from the accumulation of GNDs. This discovery on one important elementary mechanism affecting the macroscopic mechanical behavior of polycrystals provides guidelines to improve the physical content of current crystal plasticity models.

The M4F project brings together the fusion and fission materials communities working on the prediction of radiation damage production and evolution and their 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.

Most of crystalline materials develop an hysteresis on their deformation curve when a mechanical loading is applied in alternating directions. This effect, also known as the Bauschinger effect, is intimately related to the reversibile part of the plastic deformation and controls the materials damage and ultimately their failure. In the present work, we associate mesoscale Dislocation Dynamics simulations and Finite Element simulations to identify two original dislocation mechanisms at the origin of the traction/compression asymmetry and quantify their impacts on the cyclic behaviour of FCC single-crystals. After demonstrating that no long-range internal stresses can be measured in the simulations, careful analysis of the dislocation network show that the Bauschinger effect is caused by an asymmetry in the stability of junctions formed from segments whose curvature is determined by the applied stress, and a significant portion of the stored dislocation segments is easily recovered during the backward motion of dislocations in previously explored regions of the crystal. These mechanisms are incorporated into a modified crystal plasticity framework with few parameters quantified from statistical analysis of Dislocation Dynamics simulations or from the literature. This strategy has a real predictive capability and the macroscale results are in good agreement with most of the experimental literature existing on the Bauschinger and cyclic deformation of FCC single-crystals. This work provides valuable mechanistic insight to assist in the interpretation of experiments and the design of structural components to consolidate their life under cyclic loading.

3D -DD simulations are performed with cubic grains ranging from 1 to 10 μm to investigate the physical mechanisms at the origin of the Hall- Petch law. In particular, the long-range stress (back stress) induced by the density of polarized dislocations ( GNDs ) accumulated at GBs is quantified separately from the short-range stress associated with the forest dislocation ( SSDs ) density. We show that the back stress and the associated strain hardening is independent of grain size at low strain. Hence, the grain size effect reproduced by 3D-DD simulations is controlled by an increase of the CRSS when decreasing grain size. Such evolution of the CRSS amplitude is controlled by two competing strengthening mechanisms justifying the generic 1/√d dependent form of the Hall- Petch law observed in simulations and experiments.

We present here a quantitative study of dislocation cross-slip, an essential thermally activated process in deformation of metals, in discrete dislocation dynamics (DDD) simulations. We implemented a stress-dependent line-tension model in DDD simulations, with minimal information from molecular dynamics (MD) simulations. This model allows reproducing in DDD simulations the probabilistic cross-slip rate calculated in MD simulations for Cu in a large range of stresses and temperatures. The implementation of an atomically-scale accurate cross-slip model allows simulating more accurately phenomena such as deformation softening, dislocation-precipitate interaction and dislocation patterning in DDD simulations.

The influence of grain orientation on the resolved stress of long-range internal stress associated with geometrically necessary dislocations ( GNDs ) is numerically investigated. The GNDs accumulated at grain boundaries ( GBs ) do not systematically generate back stress to inhibit the dislocation motion. Surprisingly, relatively low anti-back stress promoting the plastic slip is derived from GNDs at certain GBs , which originates from a dependence of the expansion direction of dislocations on the grain orientation. This discovery on the deformation behavior of polycrystals provides guidelines to improve the physical content of current crystal plasticity models.

Most of crystalline materials exhibit a hysteresis on their deformation curve when mechanically loaded in alternating directions. This Bauschinger effect is the signature of mechanisms existing at the atomic scale and controlling the materials damage and ultimately their failure. Here, three-dimensional simulations of dislocation dynamics and statistical analyses of the microstructure evolution reveal two original elementary mechanisms. An asymmetry in the dislocation network junctions arising from the stress driven curvatures and the partial reversibility of plastic avalanches give an explanation to the traction-compression asymmetry observed in FCC single-crystals. These mechanisms are then connected in a physically justified way to larger-scale representations using a dislocation density based theory. Parameter-free predictions of the Bauschinger effect and strain hardening during cyclic deformation in different materials and over a range of loading directions and different plastic strain amplitudes are found to be in excellent agreement with experiments. This work brings invaluable mechanistic insights for the interpretation of experiments and for the design of structural components to consolidate their service life under cyclic load.

The motion of dislocations, as computed by dislocation dynamics simulations, depends on theunderlying energetic model casted within a continuum approach. This model is nevertheless stilldebated due to the diculty in capturing the behavior of the atoms in the core of dislocations.Here, we investigate the influence of the corresponding material core parameters on the outcomeof dislocation dynamics simulations of the Orowan bypassing mechanism. A parametric studyfirst reveals a large dispersion of the critical Orowan stress. Within a semi empirical approach,a new predictive equation is then motivated to encompass the core parameters, and extend theoriginal formula proposed by Bacon, Kocks and Scattergood. Emphasizing the need to carefullyselecting these parameters, we finally advocate the use of the Orowan mechanism to calibratedislocation dynamics simulations.

At low strain, geometrically necessary dislocations (GND) confined in the close vicinity of grain boundaries can be approximated as a dislocation wall structure called a GND facet. Analytical solutions derived from Field Dislocations Mechanics (FDM) theory allow calculating the stress components associated with the GND facets but are unable to account for the stress field variation induced by finite size effect. Dislocation dynamics simulation is used to investigate the true stress field of GND facets. The geometry, dimension and dislocation density of three generic types of GND facets (twist, tilt and epitaxial facets) are systematically studied. In all cases, the stress field generated by GND facets is proportional to the surface GND density and its spatial distribution can be recovered using FDM solution combined with two scaling parameters identified from DD simulation results. This calculation procedure can be generalized to any crystal structure by relating the components of the surface Nye’s tensor to the solutions of simple cubic slip systems. Finally, static and dynamic tests are made to validate the calculation of back stress within regular grains bounded by GND facets.

Dislocation dynamics simulation is used to investigate the effect of grain size and grain shape on the flow stress in model copper grains. We consider grains of 1.25–10 μm size, three orientations (<135>, <100> and <111>) and three shapes (cube, plate and needles). Two types of periodic aggregates with one or four grains are simulated to investigate different dislocation flux at grain boundaries. It is shown that in all cases the flow stress varies linearly with the inverse of the square root of the grain size, with a proportionality factor varying strongly with the grain orientation and shape. Simulation results are discussed in the light of other simulation results and experimental observations. Finally, a simple model is proposed to account for the grain shape influence on the grain size effect.