Journal articles: 'Geometrically necessary dislocation densities (GND)'

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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.

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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.

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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.

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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.

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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.

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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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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.

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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.

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Ma, Yidan, Guisen Liu, Shuqing Yang, Ran Chen, Shuopeng Xu, and Yao Shen. "Effects of Strain Rate on the GND Characteristics of Deformed Polycrystalline Pure Copper." Metals 14, no. 5 (2024): 582. http://dx.doi.org/10.3390/met14050582.

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Geometrically necessary dislocations (GNDs) play a pivotal role in polycrystalline plastic deformation, with their characteristics notably affected by strain rate and other factors, but the underlying mechanisms are not well understood yet. We investigate GND characteristics in pure copper polycrystals subjected to tensile deformation at varying strain rates (0.001 s−1, 800 s−1, 1500 s−1, 2500 s−1). EBSD analysis reveals a non-linear increase in global GND density with the strain rate rising, and a similar trend is also observed for local GND densities near the grain boundaries and that in the grain interiors. Furthermore, GND density decreases from the grain boundaries towards the grain interiors and this decline slows down at high strain rates. The origin of these trends is revealed by the connections between the GND characteristics and the behaviors of relevant microstructural components. The increase in grain boundary misorientations at higher strain rates promotes the increase of GND density near the grain boundaries. The denser distribution of dislocation cells, observed previously at high strain rates, is presumed to increase the GND density in the grain interiors and may also contribute to the slower decline in GND density near the grain boundaries. Additionally, grain refinement by higher strain rates also promotes the increase in total GND density. Further, the non-linear variation with respect to the strain rate, as well as the saturation at high strain rates, for grain boundary misorientations and grain sizes align well with the non-linear trend of GND density, consolidating the intimate connections between the characteristics of GNDs and the behaviors of these microstructure components.

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Wagner, Francis, Nathalie Allain-Bonasso, Stephane Berbenni, and David P. Field. "On the Use of EBSD to Study the Heterogeneity of Plastic Deformation." Materials Science Forum 702-703 (December 2011): 245–52. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.245.

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This paper deals with the study of plastic heterogeneity. It aims to study the role of both grain size and orientation distributions in the development of such heterogeneity. The considered material is an IF steel. EBSD maps have been made on the same areas before and after several degrees of extension. Parameters such as GOS (Grain Orientation Spread) or GOS/D (D the diameter of the grain) or GND (Geometrically Necessary Dislocation) densities have been determined for the whole set of grains as well as for subpopulations (smallest grains, largest grains for example). It appears that the character of neighboring grains plays a more important role than any of these parameters alone.

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Wang, Shuo, Xiao Yang, Jieming Chen, et al. "Effects of Building Directions on Microstructure, Impurity Elements and Mechanical Properties of NiTi Alloys Fabricated by Laser Powder Bed Fusion." Micromachines 14, no. 9 (2023): 1711. http://dx.doi.org/10.3390/mi14091711.

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For NiTi alloys prepared by the Laser Powder Bed Fusion (LPBF), changes in the building directions will directly change the preferred orientation and thus directly affect the smart properties, such as superelasticity, as well as change the distribution state of defects and impurity elements to affect the phase transformation behaviour, which in turn affects the smart properties at different temperatures. In this study, the relationship between impurity elements, the building directions, and functional properties; the effects of building directions on the crystallographic anisotropy; phase composition; superelastic properties; microhardness; geometrically necessary dislocation (GND) density; and impurity element content of NiTi SMAs fabricated by LPBF were systematically studied. Three building directions measured from the substrate, namely, 0°, 45° and 90°, were selected, and three sets of cylindrical samples were fabricated with the same process parameters. Along the building direction, a strong <100>//vertical direction (VD) texture was formed for all the samples. Because of the difference in transformation temperature, when tested at 15 °C, the sample with the 45° orientation possessed the highest strain recovery of 3.2%. When tested at the austenite phase transformation finish temperature (Af)+10 °C, the 90° sample had the highest strain recovery of 5.83% and a strain recovery rate of 83.3%. The sample with the 90° orientation presented the highest microhardness, which was attributed to its high dislocation density. Meanwhile, different building directions had an effect on the contents of O, C, and N impurity elements, which affected the transformation temperature by changing the Ni/Ti ratio. This study innovatively studied the impurity element content and GND densities of compressive samples with three building directions, providing theoretical guidance for LPBFed NiTi SMA structural parts.

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Koneva, Nina, Natal'ya Popova, Marina Fedorischeva, and Eduard Kozlov. "Geometrically Necessary Dislocations in Deformed Martensitic Steel." Advanced Materials Research 1013 (October 2014): 23–30. http://dx.doi.org/10.4028/www.scientific.net/amr.1013.23.

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Effect of a size of closed structural formation on accumulation of dislocation density and its components at plastic deformation is studied. Main attention is given to a role of a division of boundaries of a different type. Structural formation sizes are determined and different parameters of structure defining micro-and mezolevel at development of plastic deformation mechanisms are distinguished. A role of statistically stored dislocations (SSD) and geometrically necessary dislocations (GND) for defect structure formation of a material is examined. It is determined that than a size of closed structural formation is less than that a component of GND is larger and component of SSD is less. The work is based on results of TEM reserches of a structure of deformed materials.

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Weng Mei Kok, Heoy Geok How, Hun Guan Chuah, and Yew Heng Teoh. "Investigating Roughness Effect to Geometrically Necessary Dislocation in Micro-Indentation using Finite Element Analysis." Journal of Advanced Research in Applied Mechanics 104, no. 1 (2023): 25–32. http://dx.doi.org/10.37934/aram.104.1.2532.

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Surface roughness is a well-known factor in effecting to the hardness value in low indentation depth. The rougher surface induces a greater hardness value. However, the hardening mechanisms, such as the effect of geometrically necessary dislocations (GNDs), with surface roughness is rarely discussed. Therefore, the current study revealed the relationship between the surface roughness effect and the material dislocation through GNDs by using finite element analysis. 3D Crystal plasticity finite element indentation model was developed with various surface roughness between 24 to 140 nm and a range of indentation depth 3.55 to 12.27 µm to indent on the copper (111) material. The experimental indentation work was performed to validate the finite element model. The surface roughness was discovered to contribute to GND density. The GNDs distribution is highly dependent on the geometry of surface asperities, as the surface get rougher the GNDs distribution tends to be inhomogeneous. The GND density is exponentially proportional to the roughness effect. The GND density increases from 3.58 × 1014 m-2 for surface roughness 24 nm to 1.01 × 1015 m-2 for surface roughness 140 nm at indentation depth 3.55 µm. Therefore, GND density which contributes to hardening effect causes rougher surface to induce greater hardness value.

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Liu, Yao, and Songlin Cai. "Gradients of Strain to Increase Strength and Ductility of Magnesium Alloys." Metals 9, no. 10 (2019): 1028. http://dx.doi.org/10.3390/met9101028.

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A strain gradient was produced in an AZ31B magnesium alloy through a plastic deformation of pure torsion at a torsional speed of π/2 per second. Compared with the base material and with the alloy processed by conventional severe plastic deformation, the magnesium alloy provided with a strain gradient possesses high strength preserving its ductility. Microstructural observations show that strain gradient induces the formation of an inhomogeneous microstructure characterized by statistically stored dislocation (SSD) density gradient and geometrically necessary dislocation (GND). GNDs and dislocation density gradient provide extra strain hardening property, which contributes to the improvement of ductility. The combination of SSD density gradient and GND can simultaneously improve the strength and ductility of magnesium alloy.

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Seyed Salehi, Majid, Nozar Anjabin, and Hyoung S. Kim. "Study of Geometrically Necessary Dislocations of a Partially Recrystallized Aluminum Alloy Using 2D EBSD." Microscopy and Microanalysis 25, no. 3 (2019): 656–63. http://dx.doi.org/10.1017/s1431927619000382.

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AbstractDuring recrystallization, the growth of fresh grains initiated within a deformed microstructure causes dramatic changes in the dislocation structure and density of a heavily deformed matrix. In this paper, the microstructure of a cold rolled and partially recrystallized Al-Mg alloy (AA5052) was studied via electron backscattered diffraction (EBSD) analysis. The structure and density of the geometrically necessary dislocations (GNDs) were predicted using a combination of continuum mechanics and dislocation theory. Accordingly, the Nye dislocation tensor, which determines the GND structure, was estimated by calculation of the lattice curvature. To do so, five components of the Nye dislocation tensor were directly calculated from the local orientation of surface points of the specimen, which was determined by two-dimensional EBSD. The remaining components of GNDs were determined by minimizing a normalized Hamiltonian equation based on dislocation energy. The results show the elimination of low angle boundaries, lattice curvature, and GNDs in recrystallized regions and the formation of low angle boundaries with orientation discontinuities in deformed grains, which may be due to static recovery.

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Shlyannikov, Valery, Andrey Tumanov, and Ruslan Khamidullin. "Strain-gradient effect on the crack tip dislocations density." Frattura ed Integrità Strutturale 14, no. 54 (2020): 192–201. http://dx.doi.org/10.3221/igf-esis.54.14.

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In this study, the influence of a material’s plastic properties on the crack tip fields and dislocation density behavior is analytically and numerically analyzed using the conventional mechanism-based strain-gradient plasticity (CMSGP) theory established using the Taylor model. The material constitutive equation is implemented in a commercial finite element code by a user subroutine, and the crack tip fields are evaluated with novel parameters in the form of the intrinsic material length, characterizing the scale over which gradient effects become significant. As a consequence of the strain-gradient contribution, FE results show a significant increase in the magnitude of the stress fields of CMSGP when the material length parameter is considered. It is found that the density of geometrically necessary dislocations (GND) is large around the crack tip, but it rapidly decreases away from the crack tip. On the contrary, the density of statistically stored dislocations (SSD) is not as large as geometrically necessary dislocations around the crack tip, but it decreases much slower than GND away from the crack tip. A couple effect of material work hardening and the crack tip distance is identified.

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Gupta, Vipul K., and Sean R. Agnew. "A Simple Algorithm to Eliminate Ambiguities in EBSD Orientation Map Visualization and Analyses: Application to Fatigue Crack-Tips/Wakes in Aluminum Alloys." Microscopy and Microanalysis 16, no. 6 (2010): 831–41. http://dx.doi.org/10.1017/s1431927610093992.

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AbstractA simple algorithm is developed and implemented to eliminate ambiguities, in both statistical analyses of orientation data (e.g., orientation averaging) and electron backscattered diffraction (EBSD) orientation map visualization, caused by symmetrically equivalent orientations and the wrap-around or umklapp effect. Using crystal symmetry operators and the lowest Euclidian-distance criterion, the orientation of each pixel within a grain is redefined. An advantage of this approach is demonstrated for direct determination of the representative orientation of a grain within an EBSD map by mean, median, or quaternion-based averaging methods that can be further used within analyses or visualization of misorientation or geometrically necessary dislocation (GND) density. If one also considers the lattice curvature tensor, five components of the dislocation density tensor—corresponding to a part of the GND content—may be inferred. The methodology developed is illustrated using EBSD orientation data obtained from the fatigue crack-tips/wakes in aerospace aluminum alloys 2024-T351 and 7050-T7451.

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Guo, Yilin, Qinghao Yang, Mingjia Li, et al. "Improving Structural Stability and Thermal Stability of Copper Alloy by Introducing Completely Coherent Ceramic Dispersoids." Metals 13, no. 2 (2023): 338. http://dx.doi.org/10.3390/met13020338.

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When ceramic particles are incoherent with copper matrices, or when large coherent strains exist due to the differences between their crystal structure and lattice parameters in traditional dispersion-strengthened copper alloys, the strengthening effect of dispersoids at high temperatures is reduced. In the present work, a Cu-0.48Al-3.5Yb2O3 alloy was fabricated by mechanical alloying and spark plasma sintering. The investigation results prove that completely coherent inert ceramic particle YbAlO3 without coherent strains is introduced into the copper matrix. The microstructural evolution and thermal stability of the alloy after annealing at high temperatures are investigated and discussed, and it is found that the alloys exposed at 600~800 °C for 3 h exhibit excellent thermal stability and exceptional structural stability. The exceptional resistance to grain growth in the alloy can be attributed to the Zener pinning effect provided by the fine dispersion of YbAlO3 particles. High-density geometrically necessary dislocation (GND) is retained in the alloy even after annealing at 800 °C for 3 h, as is the presence of parallel GND rows because they do not easily react with opposite rows to annihilate the dislocation. At the same time, dispersed YbAlO3 acts as a strong obstacle to moving the GND. The present work proves that the structural stability of copper can be significantly improved by introducing completely coherent dispersed particles.

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Kashiwar, Ankush, Horst Hahn, and Christian Kübel. "In Situ TEM Observation of Cooperative Grain Rotations and the Bauschinger Effect in Nanocrystalline Palladium." Nanomaterials 11, no. 2 (2021): 432. http://dx.doi.org/10.3390/nano11020432.

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We report on cooperative grain rotation accompanied by a strong Bauschinger effect in nanocrystalline (nc) palladium thin film. A thin film of nc Pd was subjected to cyclic loading–unloading using in situ TEM nanomechanics, and the evolving microstructural characteristics were investigated with ADF-STEM imaging and quantitative ACOM-STEM analysis. ADF-STEM imaging revealed a partially reversible rotation of nanosized grains with a strong out-of-plane component during cyclic loading–unloading experiments. Sets of neighboring grains were shown to rotate cooperatively, one after the other, with increasing/decreasing strain. ACOM-STEM in conjunction with these experiments provided information on the crystallographic orientation of the rotating grains at different strain levels. Local Nye tensor analysis showed significantly different geometrically necessary dislocation (GND) density evolution within grains in close proximity, confirming a locally heterogeneous deformation response. The GND density analysis revealed the formation of dislocation pile-ups at grain boundaries (GBs), indicating the generation of back stresses during unloading. A statistical analysis of the orientation changes of individual grains showed the rotation of most grains without global texture development, which fits to both dislocation- and GB sliding-based mechanisms. Overall, our quantitative in situ experimental approach explores the roles of these different deformation mechanisms operating in nanocrystalline metals during cyclic loading.

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Wang, Xiao, Zechen Du, Fubao Zhang, Yu Zhu, Yu Liu, and Hui Wang. "Plastic Damage Assessment in 316 Austenitic Steel Using the Misorientation Parameters from an In Situ EBSD Technique." Crystals 12, no. 8 (2022): 1126. http://dx.doi.org/10.3390/cryst12081126.

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Plastic damage assessment in 316 austenitic steel was performed in this research by using the misorientation parameters derived from an in situ EBSD technique. With the increase in plastic strain, the misorientation parameters, such as the Grain Reference Orientation Deviation (GROD), Grain Orientation Spread (GOS), the Grain Orientation Spread over the grain Diameter (GOS/D), and Geometrically Necessary Dislocation (GND) density presented a growing trend. Nevertheless, the variation in GROD did not show a monotony trend, and the relative increase in the amplitude of GOS and GND density was less in the late plastic stage. Compared with the above parameters, the (GOS)/D exhibited a near-linear increase during the plastic tensile stage. As the specimen was stretched to a strain of 56.99%, the (GOS)/D increased 8.9 times compared with the original specimen. The results showed that the (GOS)/D parameter has the potential of becoming an indicator for the assessment of plastic damage in 316 steel.

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Mughrabi, Haël, and Bernhard Obst. "Misorientations and geometrically necessary dislocations in deformed copper crystals: A microstructural analysis of X-ray rocking curves." International Journal of Materials Research 96, no. 7 (2005): 688–97. http://dx.doi.org/10.1515/ijmr-2005-0122.

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Abstract In this study, the deformation-induced misorientations that are typically found in face-centred cubic single crystals deformed in single slip into stage II (and early stage III) of the work-hardening curve are discussed with respect to the experimentally observed broadening of X-ray rocking curves. By making use of well-established empirical relationships between characteristic features of the microstructure and the flow stress, some of the ambiguities of earlier interpretations of rocking curves could be avoided, and relationships between the half-widths of the rocking curves, the density of geometrically necessary dislocations, and the flow stress could be derived for both the tilt misorientations due to the kink bands lying perpendicular to the primary Burgers vector and the twist misorientations originating from the dislocation networks (grids, sheets) lying parallel to the primary glide plane. An evaluation of largely unpublished experimental rocking-curve data obtained on different crystallographic sections of deformed copper single crystals yielded a linear relationship between the broadening of the rocking curves and the flow stress. In terms of the predictions of the model developed, this implies that the ratio of the density of the geometrically necessary dislocations (that are responsible for the misorientations) to the total dislocation density remains constant during deformation, at least up to flow stresses of about 50 MPa. The absolute densities of the geometrically necessary dislocations are found to be a small fraction (at most ca. 5%) of the total dislocation densities. In terms of the evolution laws of deformation-induced dislocation boundaries proposed in the literature, it is concluded that both kink bands and grids/ sheets follow the characteristics of so-called geometrically necessary boundaries.

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Wan, Chang Feng, Dong Feng Li, Hai Long Qin, Ji Zhang, and Zhong Nan Bi. "Length-Scale-Dependent Micromechanical Modeling for Precipitate Hardening in Inconel 718 Superalloy." Solid State Phenomena 315 (March 2021): 84–89. http://dx.doi.org/10.4028/www.scientific.net/ssp.315.84.

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In this paper, a micromechanical finite element (FE) model has been proposed to investigate the effect of the nanoscale precipitates on the development of microplasticity for Inconel 718 (IN718) superalloy. A strain gradient crystal plasticity formulation has been developed with the considerations of the evolution of statistically stored dislocation density and geometrically necessary dislocation density. The mesh convergence has been examined, showing that sufficiently fine mesh is required in the FE model. The results show that the model with strain gradient effect incorporated shows less peak plastic strain and higher value of dislocation density than the model with no strain gradient effect. The present study indicates that the strain hardening process at the scale of strengthening precipitate is mainly governed by the evolution of geometrically necessary dislocation densities.

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Hua, Jun, and Alexander Hartmaier. "Determining Burgers vectors and geometrically necessary dislocation densities from atomistic data." Modelling and Simulation in Materials Science and Engineering 18, no. 4 (2010): 045007. http://dx.doi.org/10.1088/0965-0393/18/4/045007.

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Xiong, Yunfeng, Zongmin Li, and Tao Liu. "Toughening and Hardening Limited Zone of High-Strength Steel through Geometrically Necessary Dislocation When Exposed to Electropulsing." Materials 15, no. 17 (2022): 5847. http://dx.doi.org/10.3390/ma15175847.

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The enhancement of both low-temperature impact toughness and the hardness of a high strength steel heat-affected zone (HAZ) is investigated by using high-density electropulsing (EP). The athermal and thermal effects of EP on HAZ microstructure and resultant mechanical properties were examined based on physical metallurgy by electron backscattered diffraction and on tests of hardness and impact toughness at −60 °C, respectively. EP parameters were carefully determined to avoid electro-contraction and excessive pollution of the base metal by using numerical simulation. The EP results show that the mean impact toughness and hardness of HAZ are 2.1 times and 1.4 times improved, respectively. In addition to the contribution of microstructure evolution, geometrically necessary dislocation (GND) is also a contributor with an increase of 1.5 times, against the slight decrease in dislocation line density and dislocation density. The mechanisms behind this selective evolution of dislocation components were correlated with the localized thermal cycle EP, i.e., the competition among thermo- and electro-plasticity, and work-hardening due to local thermal expansion. The selective evolution enables the local thermal cycle EP tailor the martensitic substructure that is most favorable for toughness and less for hardness. This selective span was limited within 4 mm for a 5 mm thick sample. The local thermal cycle EP is confirmed to be capable of enhancing in both toughness and hardness within a millimeter-scale region.

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Merriman, C. C., and David P. Field. "Observations of Dislocation Structure in AA 7050 by EBSD." Materials Science Forum 702-703 (December 2011): 493–98. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.493.

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During and after plastic deformation of metals, dislocations tend to evolve into generally well-defined structures that may include tangles, bands, cell walls, and various additional features. Observation of these structures by electron backscatter diffraction is only accomplished by analysis of changes in orientation from one position to the next. Excess (or geometrically necessary) dislocation densities can be inferred from 2D measurements or obtained directly from 3D measurements as indicated by Nye’s dislocation density tensor. Evolution of excess dislocation densities was measured for a split channel die specimen of aluminum alloy 7050 in the T7451 temper. Densities evolved by a factor or 1.6 for compressive deformations of 15%.

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Huang, Hualong, Taomei Zhang, Chao Chen, Seyed Reza Elmi Hosseini, Jiaqi Zhang, and Kechao Zhou. "Anisotropy in the Tensile Properties of a Selective Laser Melted Ti-5Al-5Mo-5V-1Cr-1Fe Alloy during Aging Treatment." Materials 15, no. 16 (2022): 5493. http://dx.doi.org/10.3390/ma15165493.

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In this work, the anisotropic microstructure and mechanical properties of selective laser melted (SLMed) Ti-5Al-5Mo-5V-1Cr-1Fe (Ti-55511) alloy before and after aging treatment are investigated. Owing to the unique thermal gradient, the prior columnar β grains with {001} texture component grow in the building direction, and the mechanical properties of the as-fabricated Ti-55511 alloy exhibit slight anisotropy. Aging treatment creates uniform precipitation of the α phase at the boundaries as well as the interior of β grains. Due to the microstructure of the aged samples with a weak texture, the mechanical properties exhibit almost isotropic characteristics with an ultimate tensile strength of 1133 to 1166 MPa, yield strength of 1093 to 1123 MPa, and elongation from 13 to 16%, which meet the aerospace allowable specification very well. By XRD and EBSD analyses, the total dislocation density of the aged samples (~134.8 × 1013 m−2) is significantly lower than that of the as-fabricated samples (~259.4 × 1013 m−2); however, the aged samples exhibit a higher geometrically necessary dislocation (GND) density (~28.5 × 1013 m−2) compared with the as-fabricated samples GND density (~2.9 × 1013 m−2). Thus, a new approach to strengthening theory for estimating the anisotropic mechanical properties of AM alloys is proposed.

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Cleja-Ţigoiu, Sanda. "Disclinations and GND tensor effects on the multislip flow rule in crystal plasticity." Mathematics and Mechanics of Solids 25, no. 8 (2020): 1643–76. http://dx.doi.org/10.1177/1081286519896394.

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This paper deals with new elastoplastic models for crystalline materials with microstructural defects, such as dislocations and disclinations, which are consistent with the multislip plastic flow rule, and compatible with the free energy imbalance principle. The defect free energy function is a function of the disclination tensor and its gradient, and of the geometrically necessary dislocation (GND) tensor, via the Cartan torsion. By applying the free energy imbalance, the appropriate viscoplastic (diffusion-like) evolution equations are derived for shear plastic rates (in slip systems) and for the disclination tensor. The two sets of differential (or partial differential, i.e., non-local) equations describe the rate form of the adopted disclination–dislocation model. The first set is typical for finite deformation formalism, while the second set refers to the evolution equations with respect to the reference configuration. The dislocation appears to be a source for producing disclination defects. A pure dislocation elastoplastic model is also proposed. Multislip models with disclination within the small deformation approach are derived from the finite deformation models. The initial and boundary value problems are formulated and the incremental (rate) equilibrium equation leads to a variational equality for the velocity field, at any time, which is coupled with the rate type models for the set of variables. First, the elastic problem is solved for a certain time interval by assuming that the existing defects inside the body remain inactive. Subsequently, the variational equality is solved for the velocity field, at any time, if the slip systems are activated. Consequently, the state of the body with defects is defined by the solution of the differential-type equations, when the velocity field is known for a certain time interval. Appropriate initial conditions are necessary, including those associated with defects which became active. Finally, an update algorithm must be provided in order to compute the fields at the current moment.

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30

Trishkina, L. I., T. V. Cherkasova, A. A. Klopotov, and A. I. Potekaev. "Mechanisms of Solid-Solution Hardening of Single-Phase Cu-Al and Cu-Mn Alloys with a Mesh Dislocation Substructure." Izvestiya of Altai State University, no. 4(120) (September 10, 2021): 59–65. http://dx.doi.org/10.14258/izvasu(2021)4-09.

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The dislocation structure and dislocation accumulation during deformation of polycrystalline FCC solid solutions of Cu-Al and Cu-Mn systems are studied by transmission diffraction electron microscopy. The Al content in Cu-Al alloys varies from 0.5 to 14 at.%. The Mn content in Cu-Mn alloys varies in the range of 0.4 ÷ 25 at.%. Alloys with a grain size in the range of 20 ÷ 240 µm are studied. The alloy samples are deformed by stretching at a rate of 2×10-2c-1 to failure at 293 K. The structure of samples deformed to various degrees of deformation is studied on foils using electron microscopes at an accelerating voltage of 125 kV. For each degree of deformation, the scalar dislocation density and its components are measured: statistically stored dislocations ρS and geometrically necessary dislocations ρG and some other parameters of the defective structure. The mechanisms and their contributions due to mesh and mesh-mesh dislocation substructures (DSS) are determined using the example of substructural and solid-solution hardening in polycrystalline Cu-Al and Cu-Mn alloys. The relative role of various mechanisms in the formation of the resistance to deformation of alloys at different grain sizes is determined. The role of the packaging defect energy on the value of solid-solution hardening for different grain sizes is revealed. The average scalar dislocation density is considered and determined along with its components: statistically stored dislocations ρS and geometrically necessary dislocations ρG. The dependences of the flow stress on the square root of the densities of geometrically necessary dislocations and the densities of statistically stored dislocations are found.

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Öztop, Muin S., Christian F. Niordson, and Jeffrey W. Kysar. "Length-scale effect due to periodic variation of geometrically necessary dislocation densities." International Journal of Plasticity 41 (February 2013): 189–201. http://dx.doi.org/10.1016/j.ijplas.2012.09.001.

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32

Ma, A., Franz Roters, and Dierk Raabe. "A Dislocation Density Based Constitutive Model for Crystal Plasticity FEM." Materials Science Forum 495-497 (September 2005): 1007–12. http://dx.doi.org/10.4028/www.scientific.net/msf.495-497.1007.

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Crystallographic slip, i.e. movement of dislocations on distinct slip planes, is the main source of plastic deformation of most metals. Therefore, it was an obvious idea to build a constitutive model based on dislocation densities as internal state variables in the crystal plasticity. In this paper the dislocation model recently proposed by Ma and Roters (Ma A. and Roters F., Acta Materialia, 52, 3603-3612, 2004) has been extended to a nonlocal model through separating the statistically stored dislocation and geometrically necessary dislocation densities. A nonlocal integration algorithm is proposed, which can be more easily used in conjunction with commercial software such as MARC and ABAQUS than the model proposed in the work of Evers(Evers L.P., Brekelmans W.A.M., Geers M.G.D., Journal of the Mechanics and Physics of Solids, 52, 2379-2401, 2004).

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Xu, Hong, You Zhou, Yu-Jie Zou, et al. "Effect of Pulsed Current on the Tensile Deformation Behavior and Microstructure Evolution of AZ80 Magnesium Alloy." Materials 13, no. 21 (2020): 4840. http://dx.doi.org/10.3390/ma13214840.

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In this work, the tensile deformation behavior of an as-extruded AZ80 magnesium alloy under pulsed current (PC) was investigated based on microstructure observations. We found that compared with the tensile tests at room temperature (RT) and given temperature (GT), the flow stress is reduced due to both thermal and athermal effects of pulsed current. A quasi-in-situ electron backscatter diffraction (EBSD) analysis reveals that at the same strain, the geometrically necessary dislocation (GND) density of the RT sample is the highest, followed by the GT sample and the PC sample. This proves that the athermal effect can promote the annihilation of dislocations and slow down dislocation pileup, which reduces the flow stress. In addition, the twinning behavior under different deformation conditions was studied; the twins are {10−12} tension twins, which are activated with the assistance of local stress. We found that the twin fraction in the PC sample is lower than that in the RT and GT samples, due to the least accumulation of GNDs at grain boundaries, which decreases the nucleation of {10−12} tension twins.

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34

Li, Xiuqing, Qian Zhang, Wenpeng Lou, Fengjun Li, Jianjun Liang, and Shimin Gu. "Microstructure and Texture of Pure Copper under Large Compression Deformation and Different Annealing Times." Coatings 13, no. 12 (2023): 2093. http://dx.doi.org/10.3390/coatings13122093.

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In this study, the plastic deformation of pure copper under room-temperature compression and different annealing times was examined, and the microstructure and texture evolution were studied via scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and microhardness tests. The results showed that when the deformation degree was 93.75%, the microhardness increased from 76 HV (Vickers hardness) before deformation to 110 HV. After annealing, the hardness decreased with increasing annealing time, and the pure copper grain size could be refined from 150 μm to 6.15 μm. An increase in annealing time did not continue to promote recrystallization, while the effect on grain refinement was weakened. The geometrically necessary dislocation (GND) density decreased from 6.0 × 1014/m2 to 4.83 × 1014/m2 after annealing, which implies that static recrystallization occurs at the cost of dislocation consumption during the annealing process. The compression deformation of pure copper produced a strong deformation weave (<001> orientation), and a portion of the deformation weave within the material was transformed into a recrystallization weave (<111> orientation) after the annealing process.

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Tao, Ping, Fei Ye, Jianming Gong, Richard A. Barrett, and Seán B. Leen. "A dislocation-based yield strength model for nano-indentation size effect." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 235, no. 6 (2021): 1238–47. http://dx.doi.org/10.1177/1464420721992796.

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This paper presents a dislocation-based yield strength model for the nano-indentation size effect. The model is based on functional expressions involving the densities of statistically stored dislocations and geometrically necessary dislocations. A single-phase austenitic stainless steel (316L) and a ferrite-austenite dual-phase steel (2205) are used here as the case-study materials to validate the proposed model. Experimental testing and finite element modelling of nano-indentation of the two materials are presented. Experimental tests are performed in the indentation load range from 1000[Formula: see text] to 10000[Formula: see text]. For 2205 steel, finite element modelling is performed using a dual-phase microstructure-based model. It is shown that, with consideration of statistically stored dislocations and geometrically necessary dislocations, finite element modelling results can reproduce measured load–displacement curves and hence, the size effect, within an error range of about 5%.

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Wallis, David, Lars N. Hansen, T. Ben Britton, and Angus J. Wilkinson. "Geometrically necessary dislocation densities in olivine obtained using high-angular resolution electron backscatter diffraction." Ultramicroscopy 168 (September 2016): 34–45. http://dx.doi.org/10.1016/j.ultramic.2016.06.002.

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Li, Zhaosen, Jinyang Ge, Bin Kong, Deng Luo, Zhen Wang, and Xiaoyong Zhang. "Strain Rate Dependence and Recrystallization Modeling for TC18 Alloy during Post-Deformation Annealing." Materials 16, no. 3 (2023): 1140. http://dx.doi.org/10.3390/ma16031140.

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In this paper, the dependence of dynamic recrystallization (DRX) and post-dynamic recrystallization (PDRX) of TC18 alloy on strain rate within the range of 0.001 s−1~1 s−1 was investigated through isothermal compression and subsequent annealing in the single-phase region. Electron backscatter diffraction (EBSD) characterization was employed to quantify microstructure evolution and to reveal the recrystallization mechanism. At the thermo-deformation stage, the DRX fraction does not exceed 10% at different strain rates, due to the high stacking fault energy of the β phase. During the subsequent annealing process, the total recrystallization fraction increases from 10.5% to 79.6% with the strain rate increasing from 0.001 s−1 to 1 s−1. The variations in the geometrically necessary dislocation (GND) density before and after annealing exhibit a significant discrepancy with the increasing strain rate, indicating that the GND density is a key factor affecting the PDRX rate. The PDRX mechanisms, namely meta-dynamic recrystallization (MDRX), continuous static recrystallization (CSRX) and discontinuous static recrystallization (DSRX), were also revealed during the annealing process. A new kinetic model coupling DRX and PDRX was proposed to further describe the correlation between recrystallization and the strain rate during continuous deformation and annealing. This new model facilitates the prediction of recrystallization fraction during isothermal deformation and annealing of titanium alloys.

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38

Salliot, Freddy, András Borbély, Denis Sornin, et al. "Dislocation Hardening in a New Manufacturing Route of Ferritic Oxide Dispersion-Strengthened Fe-14Cr Cladding Tube." Materials 17, no. 5 (2024): 1146. http://dx.doi.org/10.3390/ma17051146.

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The microstructure evolution associated with the cold forming sequence of an Fe-14Cr-1W-0.3Ti-0.3Y2O3 grade ferritic stainless steel strengthened by dispersion of nano oxides (ODS) was investigated. The material, initially hot extruded at 1100 °C and then shaped into cladding tube geometry via HPTR cold pilgering, shows a high microstructure stability that affects stress release heat treatment efficiency. Each step of the process was analyzed to better understand the microstructure stability of the material. Despite high levels of stored energy, heat treatments, up to 1350 °C, do not allow for recrystallization of the material. The Vickers hardness shows significant variations along the manufacturing steps. Thanks to a combination of EBSD and X-ray diffraction measurements, this study gives a new insight into the contribution of statistically stored dislocation (SSD) recovery on the hardness evolution during an ODS steel cold forming sequence. SSD density, close to 4.1015 m−2 after cold rolling, drops by only an order of magnitude during heat treatment, while geometrically necessary dislocation (GND) density, close to 1.1015 m−2, remains stable. Hardness decrease during heat treatments appears to be controlled only by the evolution of SSD.

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Moerman, Jaap, Patricia Romano Triguero, Cem Tasan, and Peter van Liempt. "Evaluation of Geometrically Necessary Dislocations Density (GNDD) near Phase Boundaries in Dual Phase Steels by Means of EBSD." Materials Science Forum 702-703 (December 2011): 485–88. http://dx.doi.org/10.4028/www.scientific.net/msf.702-703.485.

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The accumulation of dislocations around hard particles such as martensite in Dual Phase steel has a prominent influence on the mechanical properties of multiphase steels. The origin of these so-called Geometrically Necessary Dislocations (GNDs) is either due to the transformation strain, or to strain gradients that arise during deformation. The generation of deformation-GNDs is explained by Ashby’s theory [1] regarding deformation of a plastic mass that contains dispersed undeformable particles. It is argued that the GNDs pile up locally against the ferrite-martensite interface. This work reports the calculated density of GNDs from high resolution Electron BackScatter Diffraction (EBSD) measurements. By measuring the lattice orientation within the grains, the lattice curvature can be quan-tified, which can be directly related to the presence of GNDs. The density of the GNDs can then be estimated either directly through kernel average misorientations, or through the calculation of the dislo-cation tensor. From this first approximation of the GND density a GNDD map has been obtained by two recently developed approaches. This map shows an enhanced dislocation density around the mart-ensite particles due to volume change during transformation. The kernel choice and step size depend-ency of the results are also investigated.

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Witzen, Wyatt A., Andrew T. Polonsky, Tresa M. Pollock, and Irene J. Beyerlein. "Three-dimensional maps of geometrically necessary dislocation densities in additively manufactured Ni-based superalloy IN718." International Journal of Plasticity 131 (August 2020): 102709. http://dx.doi.org/10.1016/j.ijplas.2020.102709.

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Xie, Qingge, Zhi Li, Hongchuan Ma, et al. "Correlation between dislocation hardening and the geometrically-necessary-dislocation densities in a hexagonal-close-packed Zr-2wt%Ti alloy." Materials Science and Engineering: A 868 (March 2023): 144768. http://dx.doi.org/10.1016/j.msea.2023.144768.

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42

Wang, Xiao, Zhengqing Zhou, Sheng Liu, and Mingyu Huang. "Investigation of the evolution of Geometrically Necessary Dislocation (GND) tensor in a type 316 steel by using in-situ EBSD technique." Materials Letters 286 (March 2021): 129254. http://dx.doi.org/10.1016/j.matlet.2020.129254.

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Li, Yujiao, Shoji Goto, Aleksander Kostka, and Michael Herbig. "Local measurement of geometrically necessary dislocation densities and their strengthening effect in ultra-high deformed pearlite." Materials Characterization 203 (September 2023): 113132. http://dx.doi.org/10.1016/j.matchar.2023.113132.

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44

Hu, Li, Zeyi Shen, Xiaojuan Chen, Keyu Hu, Ming Tang, and Li Wang. "Microstructure Characteristics of Porous NiTi Shape Memory Alloy Synthesized by Powder Metallurgy during Compressive Deformation at Room Temperature." Metals 13, no. 11 (2023): 1806. http://dx.doi.org/10.3390/met13111806.

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Porous NiTi shape memory alloys (SMAs) possess compatible mechanical properties with human bones and can effectively reduce the risk of stress shielding and stress concentration; therefore, they have been termed promising candidates for orthopedic implants. However, microstructure characteristics of porous NiTi SMAs during plastic deformation have rarely been investigated. The present study aims to specifically investigate microstructure characteristics and the corresponding underlying mechanisms of fabricated porous NiTi SMAs via a conventional sintering (CS) process with NaCl space holder during compressive deformation at room temperature. To realize the aforementioned target, X-ray diffraction (XRD), scanning electron microscope (SEM), electron backscattered diffraction (EBSD), transmission electron microscopy (TEM), and high-resolution transmission electron microscopy (HRTEM) are applied in the present study. The results show that the fabricated porous NiTi SMA is 51.8% for porosity, 181.65 μm for the average pore size, and 0.78 μm for the average grain size. Many Ni4Ti3 and NiTi2 phases are formed in the mixed matrix with dominant B2 (NiTi) and some B19′ (NiTi). Severe inhomogeneous deformation happens within compressed specimens, leading to the occurrence of tangled dislocation and shear bands. Microcracks occur within fabricated porous NiTi SMAs at a deformation degree of 9.2%; then, they extend quickly to form macrocracks, which finally results in the failure of regions between pores. The observed nanocrystallization and amorphization around microcrack tips within the 12.5%-deformed sample can be attributed to the relatively small grain size and the grain segmentation effect via statistically stored dislocation (SSD) and geometrically necessary dislocation (GND).

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Zhu, Chaoyi, Veronica Livescu, Tyler Harrington, Olivia Dippo, George T. Gray, and Kenneth S. Vecchio. "Investigation of the shear response and geometrically necessary dislocation densities in shear localization in high-purity titanium." International Journal of Plasticity 92 (May 2017): 148–63. http://dx.doi.org/10.1016/j.ijplas.2017.03.009.

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46

Barabash, Rozaliya I., Hongbin Bei, Yanfei Gao, Gene E. Ice, and Easo P. George. "3D x-ray microprobe investigation of local dislocation densities and elastic strain gradients in a NiAl-Mo composite and exposed Mo micropillars as a function of prestrain." Journal of Materials Research 25, no. 2 (2010): 199–206. http://dx.doi.org/10.1557/jmr.2010.0043.

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3D spatially-resolved polychromatic microdiffraction was used to nondestructively obtain depth-dependent elastic strain gradients and dislocation densities in the constituent phases of a directionally solidified NiAl–Mo eutectic composite consisting of ∼500–800 nm Mo fibers in a NiAl matrix. Measurements were made before and after the composite was compressed by 5% and 11%. The Mo fibers were analyzed both in their embedded state and after the matrix was etched to expose them as pillars. In the as-grown composite, due to differential thermal contraction during cooldown, the Mo phase is under compression and the NiAl phase is in tension. After the prestrains, the situation is reversed with the Mo phase in tension and NiAl matrix in compression. This result can be explained by taking into account the mismatch in yield strains of the constituent phases and the elastic constraints during unloading. The dislocation density in both the Mo and NiAl phases is found to increase after prestraining. Within experimental uncertainty there is little discernible difference in the total dislocation densities in the Mo phase of the 5% and 11% prestrained specimens. However, the density of the geometrically necessary dislocations and the deviatoric strain gradients increase with increasing prestrain in both the Mo and NiAl phases.

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Liu, Dekun, Jian Yang, Yinhui Zhang, and Rongbin Li. "Effect of C and Si contents on microstructure and impact toughness in CGHAZ of offshore engineering steel." Metallurgical Research & Technology 119, no. 6 (2022): 615. http://dx.doi.org/10.1051/metal/2022087.

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The combined effect of the C and Si contents on the microstructure and low-temperature impact toughness of heat-affected zone (HAZ) of the offshore engineering steel. As the C and Si content is decreased from 0.09 to 0.07 wt.% and 0.12 to 0.03 wt.%, the HAZ toughness at −40 °C is increased from 36 to 180 J, and the hardness in the coarse-grained heat-affected zone (CGHAZ) is decreased from 325 to 297 HV0.05. The higher C and Si content promote the precipitation of M23C6 and cementite, but restrain the formation of MC and M2C carbide in the present developed steels. The microstructures in the CGHAZ are comprised of a mixture of martensite and bainite after the welding with the heat input of 50 kJ/cm and are similar with the different C and Si contents. As the C and Si contents are decreased, the density of the geometrically necessary dislocation (GND) is increased. The fracture is changed from brittle to ductile manner, and the cleavage facet size is decreased from 23 to 11 µm. Reducing the C and Si contents significantly decreases the packet size from 25 to 17 µm, thereby leading to the improvement of HAZ toughness.

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KYSAR, J., Y. GAN, T. MORSE, X. CHEN, and M. JONES. "High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities." Journal of the Mechanics and Physics of Solids 55, no. 7 (2007): 1554–73. http://dx.doi.org/10.1016/j.jmps.2006.09.009.

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Brown, Judith A., and M. A. Zikry. "Behaviour of crystalline–amorphous interfaces in energetic aggregates subjected to coupled thermomechanical and laser loading." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (2015): 20150548. http://dx.doi.org/10.1098/rspa.2015.0548.

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The behaviour of energetic aggregates was investigated for quasi-static compression and high strain rate thermomechanical compression behaviour that is coupled to laser irradiation. A dislocation-density-based crystal plasticity formulation was used to represent energetic crystalline behaviour, a finite viscoelastic formulation was used for the polymer binder and a coupled electromagnetic (EM)–thermomechanical computational scheme was used to predict aggregate response. Aggregates with different crystal sizes were considered to account for physically representative energetic microstructures and to understand the effects of crystal–crystal and crystal–binder interactions. The presence of smaller embedded crystals in the binder ligaments inhibited viscous sliding, and resulted in global hardening of the aggregate, which led to large stress gradients, localized plasticity and dislocation-density accumulation. The embedded crystals also increased scattering of the EM wave within the binder ligaments and increased the localization of EM energy and laser heat generation. Geometrically, necessary dislocation densities and stress gradients were calculated to characterize how hardening at the binder interfaces can lead to strengthening or defect nucleation.

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Cao, Yupeng, Pengfei Zhu, Yongfei Yang, et al. "Dislocation Mechanism and Grain Refinement of Surface Modification of NV E690 Cladding Layer Induced by Laser Shock Peening." Materials 15, no. 20 (2022): 7254. http://dx.doi.org/10.3390/ma15207254.

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Abstract:

To investigate the relationship between the dislocation configuration and the grain refinement in the NV E690 cladding layer caused by laser shock peening, NV E690 high-strength steel powder was used to repair prefabricated pits in samples of 690 high-strength steel by laser cladding, where the laser shock peening of the cladding layer was performed by laser shock at different power densities. X-ray diffraction, scanning electron microscopy, and transmission electron microscopy were used to observe the microstructures of these samples before and after the laser shock process. The results showed that the metallurgical bonding between the cladding layer and the substrate after laser cladding repair was good. When the laser power density was 4.77 GW/cm2, multiple edge dislocations, dislocation dipoles, and extended dislocations were distributed over the cladding layer. When the laser power density was 7.96 GW/cm2, a geometrically necessary dislocation divided the large original grain into two subgrains with different orientations. When the laser power density was 11.15 GW/cm2, geometric dislocations divided the entire large grain into fine grains. The grain refinement model of the NV E690 cladding layer, when treated by laser shock peening, can describe the grain refinement process induced by the dislocation movement of this cladding layer.

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Journal articles on the topic 'Geometrically necessary dislocation densities (GND)'

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