Academic literature on the topic 'Geometrically necessary dislocation densities (GND)'

A unified physically based microstructural representation of f.c.c. crystalline materials has been developed and implemented to investigate the microstructural behaviour of f.c.c. crystalline aggregates under inelastic deformations. The proposed framework is based on coupling a multiple-slip crystal plasticity formulation to three distinct dislocation densities, which pertain to statistically stored dislocations (SSDs), geometrically necessary dislocations (GNDs) and grain boundary dislocations. This interrelated dislocation density formulation is then coupled to a specialized finite element framework to study the evolving heterogeneous microstructure and the localized phenomena that can contribute to failure initiation as a function of inelastic crystalline deformation. The GND densities are used to understand where crystallographic, non-crystallographic and cellular microstructures form and the nature of their dislocation composition. The SSD densities are formulated to represent dislocation cell microstructures to obtain predictions related to the inhomogeneous distribution of SSDs. The effects of the lattice misorientations at the grain boundaries (GBs) have been included by accounting for the densities of the misfit dislocations at the GBs that accommodate these misorientations. By directly accounting for the misfit dislocations, the strength of the boundary regions can be more accurately represented to account for phenomena associated with the effects of the GB strength on intergranular deformation heterogeneities, stress localization and the nucleation of failure surfaces at critical regions, such as triple junctions.

A gradient-enhanced crystal plasticity model is presented that explicitly accounts for the evolution of the densities of geometrically necessary dislocations (GNDs) on individual slip systems of deforming crystals. The GND densities are fully coupled with the crystal slip rule. Application of the model to two distinct and technologically important crystal types, namely hcp Ti and ccp Ni, is given. For the hcp crystals, slip is permitted with a -type slip directions on basal, prismatic and pyramidal planes and c + a -type slip directions on pyramidal planes. First, a single crystal under four-point bending is simulated as the uniform strain gradient expected in the central span provides a good validation of the code. Then, uniaxial deformation of a model near- α Ti polycrystal has been analysed. The resulting distributions of GND densities that develop on the various slip system types have been compared with independent experimental observations. The model predicts that GND density on the c + a systems is approximately an order of magnitude lower than that for a -type systems in agreement with experiment. For the ccp case, slip is considered to take place on the <110>{111} slip systems. Thermal loading of a single-crystal nickel alloy sample containing carbide particles of size approximately 30 μm has been analysed. Detailed comparisons are presented between model predictions and results of high-resolution electron backscatter diffraction (EBSD) measurements of the micro-deformations, lattice rotations, curvatures and GND densities local to the nickel–carbide interface. Qualitatively, good agreement is achieved between the coupled and decoupled model elastic strains with the EBSD measurements, but lattice rotations and GND densities are quantitatively well predicted by the coupled crystal model but are less well captured by the decoupled model. The GND coupling is found to lead to reduced lattice rotations and plastic strains in the region of highest heterogeneity close to the Ni matrix/particle interface, which is in agreement with the experimental measurements. The results presented provide objective evidence of the effectiveness of gradient-enhanced crystal plasticity finite element analysis and demonstrate that GND coupling is required in order to capture strains and lattice rotations in regions of high heterogeneity.

This study focused on the analysis of geometrically necessary dislocation (GND) densities for five selected fine-grained magnesium samples. Among the samples, three were tested under different fatigue-loading conditions at 0 °C, one experienced quasi-static tensile loading at 0 °C, and one represented the as-rolled state. The fatigue-tested samples were chosen according to the relationship between the maximum loading stress of a test and the material’s yield strength. This study provides new insights on the deformation mechanism of fine-grained magnesium at 0 °C. It is observed that the average GND densities were increased by 95~111% for the tested samples when compared with the as-rolled sample. It is especially interesting that there is a significant increase in the average GND density for the sample that experienced the fatigue loading with a low-maximum applied stress, and the maximum applied stress was lower than the material’s yield strength. This observation implies that the grain boundary mediated the dislocation-emission mechanism.

Microstructural internal lengths play an important role on the local and macroscopic mechanical behaviors of steels. In this study, the dislocation density gradients near grain boundaries in a ferritic steel are investigated using SEM/EBSD together with instrumented nanoindentation for undeformed and pre-deformed aluminum-killed steels (Al-k) at 3% and 18% tensile plastic strains. The effect of the distance to grain boundaries on Geometrically Necessary Dislocations (GND) densities is first determined by analyzing orientation gradients from 2D-EBSD maps. Then, nanohardness measurements are performed in the vicinity of grain boundaries. Data analyses show a clear correlation between the spatial gradients of GND density and the ones of nanohardness. Using a mechanistic model, the total dislocation densities are estimated from the measured nanohardness values. From both GND and total dislocation density profiles, the value of an internal length, denoted λ, is estimated from the analysis of dislocation density gradients near grain boundaries. At the end, the capabilities of 2D-EBSD and nanoindentation methods to assess this value are discussed.

Microstructural internal lengths play an important role on the local and macroscopic mechanical behaviors of steels. In this study, the dislocation density gradients near grain boundaries in a ferritic steel are investigated using SEM/EBSD together with instrumented nanoindentation for undeformed and pre-deformed aluminum-killed steels (Al-k) at 3% and 18% tensile plastic strains. The effect of the distance to grain boundaries on Geometrically Necessary Dislocations (GND) densities is first determined by analyzing orientation gradients from 2D-EBSD maps. Then, nanohardness measurements are performed in the vicinity of grain boundaries. Data analyses show a clear correlation between the spatial gradients of GND density and the ones of nanohardness. Using a mechanistic model, the total dislocation densities are estimated from the measured nanohardness values. From both GND and total dislocation density profiles, the value of an internal length, denoted λ, is estimated from the analysis of dislocation density gradients near grain boundaries. At the end, the capabilities of 2D-EBSD and nanoindentation methods to assess this value are discussed.

Microstructural internal lengths play an important role on the local and macroscopic mechanical behaviors of steels. In this study, the dislocation density gradients near grain boundaries in a ferritic steel are investigated using SEM/EBSD together with instrumented nanoindentation for undeformed and pre-deformed aluminum-killed steels (Al-k) at 3% and 18% tensile plastic strains. The effect of the distance to grain boundaries on Geometrically Necessary Dislocations (GND) densities is first determined by analyzing orientation gradients from 2D-EBSD maps. Then, nanohardness measurements are performed in the vicinity of grain boundaries. Data analyses show a clear correlation between the spatial gradients of GND density and the ones of nanohardness. Using a mechanistic model, the total dislocation densities are estimated from the measured nanohardness values. From both GND and total dislocation density profiles, the value of an internal length, denoted λ, is estimated from the analysis of dislocation density gradients near grain boundaries. At the end, the capabilities of 2D-EBSD and nanoindentation methods to assess this value are discussed.

AbstractStudies of dislocation density evolution are fundamental to improved understanding in various areas of deformation mechanics. Recent advances in cross-correlation techniques, applied to electron backscatter diffraction (EBSD) data have particularly shed light on geometrically necessary dislocation (GND) behavior. However, the framework is relatively computationally expensive—patterns are typically saved from the EBSD scan and analyzed offline. A better understanding of the impact of EBSD pattern degradation, such as binning, compression, and various forms of noise, is vital to enable optimization of rapid and low-cost GND analysis. This paper tackles the problem by setting up a set of simulated patterns that mimic real patterns corresponding to a known GND field. The patterns are subsequently degraded in terms of resolution and noise, and the GND densities calculated from the degraded patterns using cross-correlation ESBD are compared with the known values. Some confirmation of validity of the computational degradation of patterns by considering real pattern degradation is also undertaken. The results demonstrate that the EBSD technique is not particularly sensitive to lower levels of binning and image compression, but the precision is sensitive to Poisson-type noise. Some insight is also gained concerning effects of mixed patterns at a grain boundary on measured GND content.

Abstract. We report a comprehensive data set characterizing and quantifying the geometrically necessary dislocation (GND) density in the crystallographic frame (ραc) and disclination density (ρθ) in fine-grained polycrystalline olivine deformed in uniaxial compression or torsion, at 1000 and 1200 ∘C, under a confining pressure of 300 MPa. Finite strains range from 0.11 up to 8.6 %, and stresses reach up to 1073 MPa. The data set is a selection of 19 electron backscatter diffraction maps acquired with conventional angular resolution (0.5∘) but at high spatial resolution (step size ranging between 0.05 and 0.1 µm). Thanks to analytical improvement for data acquisition and treatment, notably with the use of ATEX (Analysis Tools for Electron and X-ray diffraction) software, we report the spatial distribution of both GND and disclination densities. Areas with the highest GND densities define sub-grain boundaries. The type of GND densities involved also indicates that most olivine sub-grain boundaries have a mixed character. Moreover, the strategy for visualization also permits identifying minor GND that is not well organized as sub-grain boundaries yet. A low-temperature and high-stress sample displays a higher but less organized GND density than in a sample deformed at high temperature for a similar finite strain, grain size, and identical strain rate, confirming the action of dislocation creep in these samples, even for micrometric grains (2 µm). Furthermore, disclination dipoles along grain boundaries are identified in every undeformed and deformed electron backscatter diffraction (EBSD) map, mostly at the junction of a grain boundary with a sub-grain but also along sub-grain boundaries and at sub-grain boundary tips. Nevertheless, for the range of experimental parameters investigated, there is no notable correlation of the disclination density with stress, strain, or temperature. However, a broad positive correlation between average disclination density and average GND density per grain is found, confirming their similar role as defects producing intragranular misorientation. Furthermore, a broad negative correlation between the disclination density and the grain size or perimeter is found, providing a first rule of thumb on the distribution of disclinations. Field dislocation and disclination mechanics (FDDM) of the elastic fields due to experimentally measured dislocations and disclinations (e.g., strains/rotations and stresses) provides further evidence of the interplay between both types of defects. At last, our results also support that disclinations act as a plastic deformation mechanism, by allowing rotation of a very small crystal volume.

An implementation of smoothing splines is proposed to reduce orientation noise in electron backscatter diffraction (EBSD) data, and subsequently estimate more accurate geometrically necessary dislocation (GND) densities. The local linear adaptation of smoothing splines (LLASS) filter has two advantages over classical implementations of smoothing splines: (1) it allows for an intuitive calibration of the fitting versus smoothing trade-off and (2) it can be applied directly and in the same manner to both square and hexagonal grids, and to 2D as well as to 3D EBSD data sets. Furthermore, the LLASS filter calculates the filtered orientation gradient, which is actually at the core of the method and which is subsequently used to calculate the GND density. The LLASS filter is applied on a simulated low-misorientation-angle boundary corrupted by artificial orientation noise (on a square grid), and on experimental EBSD data of a compressed Ni-base superalloy (acquired on a square grid) and of a dual austenitic/martensitic steel (acquired on an hexagonal grid). The LLASS filter leads to lower GND density values as compared to raw EBSD data sets, as a result of orientation noise being reduced, while preserving true GND structures. In addition, the results are compared with those of filters available in theMTEXtoolbox.

Two methods for the determination of geometrically necessary dislocation (GND) densities are implemented in a lower-order strain-gradient crystal plasticity finite element model. The equations are implemented in user material (UMAT) subroutines. Method I has a direct and unique solution for the density of GNDs, while Method II has unlimited solutions, where an optimization technique is used to determine GND densities. The performance of each method for capturing the formation of slip bands based on the calculated GND maps is critically analyzed. First, the model parameters are identified using single crystal simulations. This is followed by importing the as-measured microstructure for a deformed α-zirconium specimen into the finite element solver to compare the numerical results obtained from the models to those measured experimentally using the high angular resolution electron backscatter diffraction technique. It is shown that both methods are capable of modeling the formation of slip bands that are parallel to those observed experimentally. Formation of such bands is observed in both GND maps and plastic shear strain maps without pre-determining the slip band domain. Further, there is a negligible difference between the calculated grain-scale stresses and elastic lattice rotations from the two methods, where the modeling results are close to the measured ones. However, the magnitudes and distributions of calculated GND densities from the two methods are very different.

La compréhension des mécanismes de déformation dans les matériaux cristallins passe par la caractérisation fine des microstructures. Dans le cadre de la microscopie électronique à balayage, la mesure précise des gradients d’orientation et des déformations élastiques du cristal est l’objectif des méthodes dites à haute résolution angulaire. Pour cela, elles emploient des techniques de corrélation d’images numériques afin de recaler les clichés de diffraction électronique. Cette thèse propose une méthode de recalage originale. Le champ de déplacement à l’échelle du scintillateur est décrit par une homographie linéaire. Il s’agit d’une transformation géométrique largement utilisée en vision par ordinateur pour modéliser les projections. L’homographie entre deux clichés est mesurée à partir d’une grande et unique région d’intérêt en utilisant un algorithme de Gauss-Newton par composition inverse numériquement efficace. Une correction des distorsions optiques causées par les lentilles de la caméra lui est intégrée et sa convergence est assurée par un pré-recalage des clichés. Ce dernier repose sur des algorithmes de corrélation croisée globale basés sur les transformées de Fourier-Mellin et de Fourier. Il permet de rendre compte des rotations allant jusqu’à une dizaine de degrés avec une précision comprise typiquement entre 0,1 et 0,5°. La détermination de l’homographie est indépendante de la géométrie de projection. Cette dernière n’est considérée qu’à l’issue du recalage pour déduire analytiquement les rotations et les déformations élastiques. La méthode est validée numériquement sur des clichés simulés distordus optiquement, désorientés jusqu’à 14° et présentant des déformations élastiques équivalentes jusqu’à 5×10⁻². Cette étude montre que la mesure précise de déformations élastiques comprises entre 1×10⁻⁴ et 2×10⁻³ nécessite de corriger la distorsion optique radiale, même lorsque la désorientation est faible. Finalement, la méthode est appliquée à des clichés acquis par diffraction des électrons rétrodiffusés (EBSD) et en transmission en utilisant la nouvelle configuration TKD on-axis (transmission Kikuchi diffraction). Des métaux polycristallins déformés plastiquement ainsi que des semi-conducteurs sont caractérisés. La méthode retranscrit des détails fins de la microstructure d’un acier martensitique trempé et revenu et d’un acier sans interstitiels déformé de 15% en traction, malgré la détérioration du contraste de diffraction induit par la déformation plastique. Les structures de déformation sont également analysées dans de l’aluminium nanostructuré obtenu par déformation plastique sévère grâce au couplage de la méthode de recalage et de la configuration TKD on-axis. Ce couplage permet d’atteindre simultanément une haute résolution spatiale (3 à 10 nm) et une haute résolution angulaire (0,01 à 0,05°). Des cartes de déformation élastiques sont obtenues à l’échelle de quelques nanomètres dans une lame mince de SiGe et les densités de dislocations dans un monocristal de GaN sont déterminées avec une résolution voisine de 2,5×10⁻³ µm⁻¹ (soit 8×10¹² m⁻²)
Understanding the deformation mechanisms in crystalline materials requires a fine characterization of microstructures. The precise measurement of lattice rotations and elastic strains in the scanning electron microscope is the aim of the so-called high-angular resolution methods. For this purpose, digital image correlation techniques are used in order to register electron diffraction patterns. In this thesis, an original registration approach is proposed. The displacement field across the whole scintillator is modelled by a linear homography. Such a shape function is often met is the field of computer vision to describe projective transformations. The homography between two patterns is measured from a single and large region of interest using a numerically efficient inverse-compositional Gauss-Newton algorithm. It integrates a correction of optical distortions caused by camera lenses and its convergence is ensured by a pre-alignment step of the patterns. The latter relies on global cross-correlation algorithms based on Fourier-Mellin and Fourier transforms. It fairly accounts for rotations up to approximately ten degrees with an accuracy typically between 0.1 and 0.5°. The homography is measured independently from the projection geometry, which is only considered afterwards to analytically deduce the rotations and elastic strains. The proposed method is validated numerically from simulated and optically distorted patterns showing disorientations up to 14° in the presence of elastic strains up to 5×10⁻². The accurate measurement of elastic strains between 1×10⁻⁴ and 2×10⁻³ requires a correction of radial distortion effects, even when the disorientation angle is small. Finally, the method is applied to patterns acquired by means of electron backscatter diffraction (EBSD) and in transmission using the new on-axis transmission Kikuchi diffraction (TKD) configuration. Plastically deformed polycrystalline metals as well as semiconductors are characterized. The method highlights fine details of the microstructure of a quenched and tempered martensitic steel and of an interstitial free steel deformed by 15% in tension, although plastic deformation deteriorates the diffraction contrast. The deformation structures in a nanostructured aluminium obtained by severe plastic deformation are also analysed by coupling the image registration method to the on-axis TKD configuration. This coupling allows a high spatial resolution (3 to 10 nm) and a high angular resolution (0.01 to 0.05°) to be reached simultaneously. Elastic strain maps are obtained at the nanoscale in a SiGe thin foil. The geometrically necessary dislocation densities in a GaN single crystal are mapped with a resolution of about 2.5×10⁻³ µm⁻¹ (i.e. 8×10¹² m⁻²)

Ultra-fine grained materials with sub-micrometer grain size exhibit superior mechanical properties when compared with conventional fine-grained material as well as coarse-grained materials. Severe plastic deformation (SPD) techniques have been shown to be an effective way to modify the microstructure in order to improve the mechanical properties of the material. Crystalline materials require dislocations to accommodate plastic strain gradients and maintain lattice continuity. The lattice curvature exists due to the net dislocation that left behind in material during deformation. The characterization of such defects is important to understand deformation accumulation and the resulting mechanical properties of such materials. However, traditional techniques are limited. For example, the spatial resolution of EBSD is insufficient to study materials processed via SPD, while high dislocation densities make interpretations difficult using conventional diffraction contrast techniques in the TEM. A new technique, precession electron diffraction (PED) has gained recognition in the TEM community to solve the local crystallography, including both phase and orientation, of nanocrystalline structures under quasi-kinematical conditions. With the assistant of precession electron diffraction coupled ASTARÔ, the structure evolution of equal channel angular pressing processed commercial pure titanium is studied; this technique is also extended to two-phase titanium alloy (Ti-5553) to investigate the existence of anisotropic deformation behavior of the constituent alpha and beta phases.

As the laser spot size in micro-scale laser shock peening is in the order of magnitude of several microns, the anisotropic response of grains will have a dominant influence on its mechanical behavior of the target material. Furthermore, conventional plasticity theory employed in previous studies needs to be reexamined due to the length scale effect. In the present work, the length scale effects in microscale laser shock peening have been investigated. The crystal lattice rotation underneath the shocked surface was determined via Electron Backscatter Diffraction (EBSD). From these measurements, the geometrically necessary dislocations (GND) density that the material contains has been estimated. The yield strength increment was then calculated from the GND distribution by using Taylor model and integrated into each material point of the FEM simulation. Finite element simulations, based on single crystal plasticity, were performed of the process for both with and without considering the GND hardening and the comparison has been conducted.

The intent of this work is to derive a physically motivated mathematical form for the gradient plasticity that can be used to interpret the size effects observed experimentally. This paper addresses a possible, yet simple, link between the Taylor’s model of dislocation hardening and the strain gradient plasticity. Evolution equations for the densities of statistically stored dislocations and geometrically necessary dislocations are used to establish this linkage. The dislocation processes of generation, motion, immobilization, recovery, and annihilation are considered in which the geometric obstacles contribute to the storage of statistical dislocations. As a result a physically sound relation for the material length scale parameter is obtained as a function of the course of plastic deformation, grain size, and a set of macroscopic and microscopic physical parameters. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

RPV steels are industrial alloys with very complicated microstructures. The characterization of the evolution of microstructural features that can affect the hardness of this type of steel can provide information on parameters that may be considered for modeling the mechanical behavior of these materials. Thermal aging at temperatures higher than the operating temperatures of nuclear reactors may provide some information that could be related to enhanced diffusion irradiation effects. Thermal aging may also provide data about the evolution of RPV steels submitted to heat treatment within the temperature domain proposed for RPV thermal annealing. We present the results of heat treatments (450°C, 500°C, and 550°C) carried out on samples of an A533B Cl.1 (JRQ) steel up to 1000 h. JRQ steel has a heterogeneous microstructure, with well-separated ferrite and bainite islands observed at high magnification. The thermal aging of JRQ steel at 450°C, 500°C, and 550°C promoted an increase in hardness in both bainite and ferrite, with the increase more significant in bainite than in ferrite. For the thermal treatment at 550°C, a maximum of the density of precipitates (per μm2) in the treatments was observed over a period of 500 h. This coincides with the depletion of the alloying elements in the bainite matrix and a decrease of HV in bainite. Copper-rich nanoprecipitates (< 6 nm in size) were observed in the samples treated at 550°C for 500 and 1000 h. The Cu content in the nanoprecipitates increases with aging time. Finally, the HV of the samples treated at 550°C for up to 500 h is a function of the Geometrically Necessary Dislocation (GND) density, which was obtained from EBSD cartographies. GND density is at the same time a function of the density of the precipitates (40–300 nm in size).