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Academic literature on the topic 'Geometrically necessary dislocation densities (GND)'
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Journal articles on the topic "Geometrically necessary dislocation densities (GND)"
1
Rezvanian, O., M. A. Zikry, and A. M. Rajendran. "Statistically stored, geometrically necessary and grain boundary dislocation densities: microstructural representation and modelling." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2087 (2007): 2833–53. http://dx.doi.org/10.1098/rspa.2007.0020.
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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.
2
Dunne, F. P. E., R. Kiwanuka, and A. J. Wilkinson. "Crystal plasticity analysis of micro-deformation, lattice rotation and geometrically necessary dislocation density." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 468, no. 2145 (2012): 2509–31. http://dx.doi.org/10.1098/rspa.2012.0050.
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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.
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Li, Qizhen. "Geometrically Necessary Dislocation Analysis of Deformation Mechanism for Magnesium under Fatigue Loading at 0 °C." Crystals 13, no. 3 (2023): 490. http://dx.doi.org/10.3390/cryst13030490.
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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.
4
Chamma, Layal, Jean-Marc Pipard, Artem Arlazarov, Thiebaud Richeton, Jean-Sébastien Lecomte, and Stéphane Berbenni. "A combined EBSD/nanoindentation study of dislocation density gradients near grain boundaries in a ferritic steel." Matériaux & Techniques 110, no. 2 (2022): 203. http://dx.doi.org/10.1051/mattech/2022005.
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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.
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Chamma, Layal, Jean-Marc Pipard, Artem Arlazarov, Thiebaud Richeton, Jean-Sébastien Lecomte, and Stéphane Berbenni. "A combined EBSD/nanoindentation study of dislocation density gradients near grain boundaries in a ferritic steel." Matériaux & Techniques 110, no. 2 (2022): 203. http://dx.doi.org/10.1051/mattech/2022005.
Full textAbstract:
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.
6
Chamma, Layal, Jean-Marc Pipard, Artem Arlazarov, Thiebaud Richeton, Jean-Sébastien Lecomte, and Stéphane Berbenni. "A combined EBSD/nanoindentation study of dislocation density gradients near grain boundaries in a ferritic steel." Matériaux & Techniques 110, no. 2 (2022): 203. http://dx.doi.org/10.1051/mattech/2022005.
Full textAbstract:
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.
7
Hansen, Landon T., Brian E. Jackson, David T. Fullwood, et al. "Influence of Noise-Generating Factors on Cross-Correlation Electron Backscatter Diffraction (EBSD) Measurement of Geometrically Necessary Dislocations (GNDs)." Microscopy and Microanalysis 23, no. 3 (2017): 460–71. http://dx.doi.org/10.1017/s1431927617000204.
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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.
8
Demouchy, Sylvie, Manuel Thieme, Fabrice Barou, Benoit Beausir, Vincent Taupin, and Patrick Cordier. "Dislocation and disclination densities in experimentally deformed polycrystalline olivine." European Journal of Mineralogy 35, no. 2 (2023): 219–42. http://dx.doi.org/10.5194/ejm-35-219-2023.
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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.
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Seret, Anthony, Charbel Moussa, Marc Bernacki, Javier Signorelli, and Nathalie Bozzolo. "Estimation of geometrically necessary dislocation density from filtered EBSD data by a local linear adaptation of smoothing splines." Journal of Applied Crystallography 52, no. 3 (2019): 548–63. http://dx.doi.org/10.1107/s1600576719004035.
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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.
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Sedaghat, Omid, та Hamidreza Abdolvand. "Strain-Gradient Crystal Plasticity Finite Element Modeling of Slip Band Formation in α-Zirconium". Crystals 11, № 11 (2021): 1382. http://dx.doi.org/10.3390/cryst11111382.
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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.