Geometrically Necessary Dislocation Density Research Articles

An integrated exploration from microstructure to mechanics in austenite to pearlite transformation of high carbon steel under high magnetic fields

The effects of a high magnetic field (12 T) on the microstructural evolution and mechanical properties of high carbon steel during isothermal pearlitic transformation at 720 °C were investigated. The application of a high magnetic field effectively promotes pearlitic transformation and leads to a reduction in the lamellar spacing and the geometrically necessary dislocation density (GND) as well as to a slight increase in the grain size of the pearlite, which leads to a decrease in hardness. This is because the magnetic field reduces the magnetic Gibbs energy of ferrite and cementite, resulting in an increase in the driving force of phase transformation, which shortens the pearlite maturation time and reduces the nucleation barriers of pearlite, thereby accelerating the growth rate of pearlite. In addition, the interfacial energy of ferrite/cementite was found to be increased by the magnetic field from the thermodynamic point of view, and the mechanism of action of the magnetic field -induced precipitation of cementite in the form of particles and short rods was elucidated. The present work will enhance the understanding of the mechanism of magnetic field-induced phase transformation in iron-based materials.

A study of dynamic recovery and recrystallisation mechanisms in aluminium alloy AA7050 at different thermomechanical processing conditions

The effects of hot deformation strain rates and temperatures on aluminium alloys' dynamic recovery and recrystallisation mechanisms have been widely discussed in the literature. However, their influence remains controversial due to a need for comprehensive and detailed thermomechanical testing and characterisation data across a wide range of hot deformation conditions. In this study, hot compression tests of AA7050 were conducted at strain rates of 0.0005–5 s−1 and temperatures of 380–460 °C. The geometrically necessary dislocation (GND), low-angle grain boundary (LAGB) and high-angle grain boundary (HAGB) were acquired by the latest high angular resolution, high-speed EBSD detector (OI Symmetry 2), and their underlying mechanisms were analysed in relation to Zener-Hollomon parameter (Z). It was found that within the tested range of the hot compression condition (ln (Z) between 20.23 and 29.45), continuous dynamic recrystallisation (CDRX) predominates at lower ln (Z) values with its activity being initially increased and then decreased as ln (Z) rises, while discontinuous dynamic recrystallisation (DDRX) becomes dominant at higher ln (Z) levels. This transition of the dominant mechanism is intriguingly reflected in the evolution of HAGB length, which increases, then decreases and finally increases again. The LAGB length shows a relatively linear relationship with ln (Z), and the average GND density exhibits a near-linear correlation until reaching a plateau. Based on the obtained results, the transformation of the dominant microstructural evolution mechanisms with increasing ln (Z) was clarified: from grain growth, to recovery, to CDRX, and then to DDRX, along with the quantitative trend of HAGB length per unit area. This transformation mechanism is believed to encompass the full range of material processing window, providing a basis for justifying the previous controversial proposition in literature and a guide for defining and fabricating microstructures in manufacturing applications.

Resolving localized geometrically necessary dislocation densities in Al-Mg polycrystal via in situ EBSD

The distribution of geometrically necessary dislocation (GND) densities is critical to understanding the heterogeneous plastic deformation at intragranular scales in polycrystals. In this work, we performed an in situ electron backscatter diffraction (EBSD) measurement during the tensile test on a polycrystalline Al-Mg alloy. The EBSD patterns were processed through the integrated digital image correlation algorithm to enhance angular resolution. Based on the Nye dislocation density tensor, GND densities of 18 dislocation types in fcc crystals were resolved and mapped at macroscopic strains ranging from 5% to 16%. The evolution of GND distribution showed that GNDs were generated near grain boundaries at small strains and later localized at grain interiors along subgrain boundaries and slip bands at large strains. The inhomogeneous increase in GND densities of different dislocation types, representing dislocation substructures, along the subgrain boundaries was disclosed. Meanwhile, high GND densities were observed along the slip bands when a double noncoplanar slip system was activated inside the grains. The obstructed movement of dislocations by Lomer junctions explained the GND storage in different {111} slip planes. The existence of Lomer junctions was proven by Burgers circuit analysis with high-resolution transmission electron microscopy, which explained the increase in [101] screw dislocation density according to the dislocation reaction.

Deformation behavior, microstructure evolution and phase transformation of dual-phase Mg-Li-Zn-Sr-Ca alloy under isothermal compression

The deformation behavior, phase transformation and microstructure evolution of dual-phase Mg-Li-Zn-Sr-Ca alloy under different deformation parameters were investigated through isothermal compression experiments. Serrated flow behavior was observed in the flow curves, indicating a strain aging behavior. R=0.9971 and AARE=3.88 % demonstrate the reliable predictive capability of established constitutive model. Hot processing maps indicate that instability region is only at T=423–490 K, ε̇ =0.007 s–1-1 s–1. As the temperature exceeds 523 K, needle-shaped phases precipitated from the β-Li phase, which was confirmed to be α-Mg phase. With increasing temperature and reducing strain rate, the quantity and size of them increased. Furthermore, its precipitation may be due to the high lattice diffusion coefficient of the β-Li phase. The degree of dynamic recrystallization (DRX) increased, the proportion of low-angle grain boundaries (LAGBs) and kernel average misorientation (KAM) decreased, these phenomena primarily associated with the dynamic recovery (DRV) and DRX processes. In addition, under the same processing parameters, the degree of DRX in the α-Mg phase is higher than that of the β-Li phase, the density of geometrically necessary dislocations (GND) of the α-Mg phase is higher than that of the β-Li phase. The β-Li phase can be activated more slip system and it can reduce the accumulation of dislocations. Meanwhile, the high density of GND of the α-Mg phase also predicts a higher strain energy and a greater drive force for recrystallisation. As the temperature rises, the intensity of the (0002) basal texture of the α-Mg phase increased, which is attributed to the selective growth of DRXed grains.

Effect of microstructure evolution on impact toughness in advanced ultra-high strength steel

The microstructure evolution and strength-toughness matching relationship of advanced ultra-high strength steel were studied under the tempering temperature range of 200–400 °C. The Charpy impact absorption energy of U-notch and V-notch focused on the crack initiation and crack propagation processes, respectively. The peak impact absorption energy of the U-notch appeared at 300 °C due to reduced stress concentration from low GND (Geometrically Necessary Dislocations) density. The optimal mechanical properties were found after tempering at 250 °C, where martensitic blocks hindered crack propagation, resulting in the peak impact energy of V-notch.

Effects of local strain on the plastic deformation and fracture mechanism of heterogeneous multilayered aluminum

Elucidating the effect of local strain on the mechanical properties is of great significance for the design of high-performance layered metals. For this purpose, we conceived the present study, featured by tailoring the local strain by layer thickness design, and simultaneous monitoring of local strain and geometrically necessary dislocations (GNDs) via coupling in-situ electron backscatter diffraction (EBSD) and high-resolution digital image correlation (DIC). In addition, synchrotron X-ray micro-computed tomography (μCT) was employed to analyze the microcracks that serve as another form of strain localization. Such detailed experimental studies revealed that the interfacial strain gradient was rapidly elevated, and the strain localization band was effectively dispersed as the layer thickness decreased. This leads to two typical transitions, from grain-boundary-related to layer-interface-related plastic deformation mode, and from macroscopic shear to zig-zag fracture mode. Their influences on the mechanical properties, as well as underlying mechanisms, were discussed based on the relationship among the layer thickness, strain gradient, strain localization, GND density, and microcracks. Our work not only contributes to the fundamental understanding of the mechanical behavior of multilayered metals but also offers guidance for the structural design of high-performance metals aimed at achieving superior strength-ductility combinations.

Effects of thermal exposure on microstructure deformation and evolution of shot peened nickel-based single crystal superalloy

Microstructure deformation and thermally activated microstructural evolution of nickel-based single crystal (NBSC) superalloy subjected to shot peening (SP) were investigated. SP induced high-density dislocations and activated the octahedral slip system {111} 〈110〉 of NBSC superalloy. Under 0.25 mmA SP intensity, there appeared a severely deformed layer with a depth of 2.5–3.0 μm beneath the surface. High SP intensity resulted in rougher surface morphology, more dense slip bands, deeper cold work layer and larger mean geometrically necessary dislocation (GND) density. However, the deformed microstructure was thermodynamically unstable. Dislocation annihilation and rearrangement were the main thermally activated mechanism of microstructural evolution, and high temperature promoted dislocation movement and consumption. Under 0.25 mmA SP intensity after 24 h thermal exposure, GND density decreased from 4.86 × 1014 m−2 to 2.72 × 1014 m−2, and the depth of cold work layer decreased from 67 μm to 62 μm. In addition, SP treatment provided rapid diffusion channels for alloy elements, while thermal exposure further aggravated element diffusion.

On the role of geometrically necessary dislocations in void formation and growth in response to shock loading conditions in wrought and additively manufactured Ta

This study investigates the role of geometrically necessary dislocations (GNDs) and microstructure on void nucleation and growth in wrought and additively manufactured (AM) tantalum subjected to high-strain rate loading. Multi-modal 3D data was collected using TriBeam tomography to calculate GND densities and their spatial relationship to voids. A microstructural comparison between the wrought and AM samples identified distinct void shapes and locations, with intragranular voids and more spherical voids frequently observed in the AM dataset. Results indicate that voids preferentially form at both high-angle grain boundaries and low-angle subgrain boundaries, the latter of which are frequently observed in the AM material. Through a radial distribution analysis of all voids in the datasets, significant GND localization to near-void-surface regions was observed in both samples. 3D crystal plasticity simulations were employed to extend the experimental observations, revealing higher void growth rates in [111] oriented grains when compared to [001] grains. The simulations also suggest that GNDs can be generated as part of the void growth process, with more GND accumulation for growth in a [111] grain than a [001] grain. These findings provide valuable insights into the links between nanoscale void nucleation, mesoscale void growth, and microstructural effects in dynamically loaded tantalum.

Parameter optimization and anisotropy mechanism in different build directions of the microstructures and mechanical properties for laser directed energy deposited Ti6Al4V alloy

The effects of laser power, scanning speed, and build directions (BDs) on the microstructural evolution and mechanical properties of laser directed energy deposited (LDEDed) Ti6Al4V alloy were systematically investigated in this study. All the finished LDED specimens were not heat treated and the tensile properties were not influenced by surface roughness. Particularly, the differences in grain size, grain boundary distribution, geometrically necessary dislocation (GND) density, grain orientation spread (GOS), and Schmid factor (SF) of the specimens in different BDs were investigated by scanning electron microscopy, electron backscattering diffraction, transmission electron microscopy, and tensile test. The results showed that the aspect ratio, dilution rate, and deposition angle all tended to increase with increasing laser power and scanning speed. The yield strength and the ultimate tensile strength decreased with the increase of laser power, while the elongation was the opposite. The parent grain reconstruction results indicated that the high-temperature transition phase (β phase) of the 0° LDEDed specimen was equiaxial, whereas that of the 90° LDEDed specimen was columnar. The differences in the β phase of the specimens in different BDs were directly inherited to the corresponding low-temperature sub-phase (α phase), resulting in finer grain sizes, greater GND density, larger GOS, and smaller SF in the 0° LDEDed specimen, thereby contributing to higher strength and hardness. In contrast, these values were reversed for the 90° LDEDed specimen, resulting in better plasticity and toughness. Finally, the anisotropy mechanism of the microstructures and mechanical properties of the LDEDed Ti6Al4V alloy in different BDs were revealed. This work could provide more systematic and comprehensive guidance in parameter optimization and offer valuable insights into the anisotropy mechanism of the microstructures and mechanical properties of LDEDed Ti6Al4V alloy.

Nanoindentation study on early-stage radiation damage in single-phase concentrated solid solution alloys

Concentrated solid solution alloys (CSAs) comprising multiple components have unlocked novel pathways for materials design, particularly in enhancing radiation tolerance. It is imperative to detect early-stage radiation damage in CSAs to gain insights into damage initiation and accumulation mechanisms. In this study, nanoindentation is employed to assess the impact of irradiation on deformation mechanisms in single crystal CSAs, specifically NiCo, NiFe, and NiCoFeCr. It is discovered that pile-up behavior in CSAs significantly affected by irradiation: pile-up induces 10–20 % increase in the contact area before irradiation that is independent of the penetration depth but 20–30 % after irradiation, which substantially affects hardness analyses. Within the context of strain gradient plasticity theory, distinct radiation-induced hardening in three CSAs is interpreted by two components: one is from the radiation-induced defects, and the other is the increase in density of geometrically necessary dislocations (GNDs) associated with indentation size effect (ISE). Quantitative analysis shows that the radiation-induced defects produce obvious hardening in NiFe and NiCoFeCr sample, but not in the NiCo sample. Meanwhile, the irradiation induces a higher GND density in NiCo and NiFe, but not in NiCoFeCr, which is interpreted by the volume change of the plastic zone.

Microstructural and mechanistic insights into the Tension–Compression asymmetry of rapidly solidified Fe–Cr alloys: A phase field and strain gradient plasticity study

Rapid solidification in Additively Manufactured (AM) metallic materials results in the development of significant microscale internal stresses, which are attributed to the printing induced dislocation substructures. The resulting backstress due to the Geometrically Necessary Dislocations (GNDs) is responsible for the observed Tension–Compression (TC) asymmetry. We propose a combined Phase Field (PF)-Strain Gradient J2 Plasticity (SGP) framework to investigate the TC asymmetry in such microstructures. The proposed PF model is an extension of Kobayashi’s dendritic growth framework, modified to account for the orientation-based anisotropy and multi-grain interaction effects. The SGP model has consideration for anisotropic temperature-dependent elasticity, dislocation strengthening, solid solution strengthening, along with GND-induced directional backstress. This model is employed to predict the solute segregation, dislocation substructure and backstress development during solidification and the post-solidification anisotropic mechanical properties in terms of the TC asymmetry of rapidly solidified Fe–Cr alloys. It is observed that higher thermal gradients (and hence, cooling rates) lead to higher magnitudes of solute segregation, GND density, and backstress. This also correlates with a corresponding increase in the predicted TC asymmetry. The results presented in this study point to the microstructural factors, such as dislocation substructure and solute segregation, and mechanistic factors, such as backstress, which may contribute to the development of TC asymmetry in rapidly solidified microstructures.

Restraining geometrically-necessary dislocations to the active slip systems in a crystal plasticity-based finite element framework

Strain gradients have been cast in the form of geometrically-necessary dislocations (GND) to relate the length-scale dependence of strength and to determine potential sites for failure initiation. The literature contains various different incompatibility measures, the main ones being: the total form (∇×Fp), the rate form for large displacements (∇×γ̇anaFp), and the slip gradient form (∇γ̇a). Here, these different approaches are compared rigorously for the first time. Obtaining GND densities when using the total form is a rank-deficit linear problem, solved by singular value decomposition (SVD) known as the Least Squares Minimization (L2 method). Alternative methods for finding GND densities such as Karush–Kuhn–Tucker (KKT) optimization are also investigated. Both L2 and KKT methods predict unrealistic GND densities on inactive slip systems leading to excessive strain hardening; even for a single crystal single slip case. Therefore, the restriction of GNDs to the active slip systems by using a threshold based on the total slip is proposed. This restriction reveals relatively consistent results for various single crystal single slip cases including: simple shear, uniaxial tension, and four-point bending. In addition, the small numerical differences in the slip leads to large discrepancies in the flow stress due to error accumulation, even for strain-gradient-free uniaxial tension, hence a threshold for the GND density increment (2×102 m−2) is used in all models to avoid formation of erroneous GND densities. Finally, the proposed method is applied to the evolution of the GND density for a grain inside a polycrystal aggregate that posses a complex stress state. The lowest incompatibility error is obtained by both of the total forms that use the curl of the plastic deformation gradient with the active slip system restriction suggesting them to be the most reliable GND measures.

Dislocation Distribution, Crystallographic Texture Evolution, and Plastic Inhomogeneity of Inconel 718 Fabricated by Laser Powder Bed Fusion

Plastic inhomogeneity, particularly localized strain, is one of the main mechanisms responsible for failures in engineering alloys. This work studies the spatial arrangement and distribution of microstructure (including dislocations and grains) and their influence in the plastic inhomogeneity of Inconel 718 fabricated by additive manufacturing (AM). The bidirectional scanning strategy with no interlayer rotation results in highly ordered alternating arrangements of coarse Goss‐like {110}<001> textured grains separated by fine Cube‐like {100}<001> textured grains. The bidirectional strategy also results in an overall high density of geometrically necessary dislocations (GNDs) that are particularly dense in the fine grains. Although the Cube‐like texture desirable for isotropy is dominant, it gradually weakens during plastic deformation and the undesirable Goss‐like component (second most dominant in the as‐built microstructure) increases. The highly clustered and bimodal distribution of fine and coarse grains, textures, and GND densities causes fast localized roughening during deformation, particularly along the line row of fine Cube‐like grains. However, the chessboard strategy results in a lower GND density and a comparatively more random distribution of crystallographic texture and GNDs, with a dominant Cube‐like component (and much lower Goss‐like texture) that remains stable throughout plastic deformation. This results in more uniform deformation, reducing plastic inhomogeneity.

Effects of Strain Rate on the GND Characteristics of Deformed Polycrystalline Pure Copper

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.

A model of strain hardening for stage IV based on lattice curvature induced dislocations and grain fragmentation

A new model is presented for the interpretation of the nearly linear Stage IV large strain hardening behavior observed in polycrystalline metals. The approach is based on the orientation change of the grains that induces a curvature of the crystallographic lattice and produces geometrically necessary dislocations (GNDs). The GND density is dependent on grain size, the latter is decreasing in a reciprocal manner with plastic strain in Stage IV. The GNDs are added to the dislocation density present at the end of Stage III in the Taylor relation to obtain an analytical formula for the strain hardening behavior of the material. The model is applied to polycrystalline nickel, copper, and commercially pure aluminum and produced good agreement with experiments. As grain fragmentation is a common phenomenon of all metals during large strain at low temperature, this model explains the universal nature of Stage IV.

In-situ EBSD tensile revealing the evolution mechanism of high angle grain boundaries in Al–Zn–Mg alloy profile with heterogeneous structures

The evolution of grain boundary (GB) of an Al–Zn–Mg alloy profile with heterogeneous structures is studied based on in-situ EBSD tensile. This evolution is not only related to its grain boundary misorientation angle (GBMA) and slip transfer parameter (m'/(Δb/b)) but also to the behavior of the geometrically necessary dislocation (GND) tensor in the deformation. The effect of GBMA and m'/(Δb/b) for three types of high angle grain boundary (HAGB) on GND density and back stress has been revealed. The increase of GND density is not obvious near the HAGBs with 45°–55° GBMA of neighboring coarse grains or neighboring fibrous grains. The optimal grain boundary for forming back stress is the HAGBs between coarse grain and fibrous grain, which has 35°–45° GBMA and a low m'/(Δb/b). The back stress is hard to form near these HAGBs with 25°–35° GBMA and a low m'/(Δb/b). Combined with the neighboring grain type, slip transfer and GBMA, the new criterion is proposed to predict GND behavior near HAGBs.

New insights on dislocation forming mechanism of nickel-based superalloy fabricated by laser powder bed fusion

In this work, the forming mechanism of dislocation in laser powder bed fusion (LPBF) built IN738LC alloy was elucidated by studying the intrinsic relationships between the density and distribution of dislocation and the orientation and size of dendrite. The substructures with different dislocation densities and cell spacings were customized by controlling solidification conditions, and analyzed by multi-scale characterizing methods. The results show that an increase in geometrically necessary dislocation (GND) density from 1.48 × 1014 to 1.82 × 1014m−2 is accompanied by a decrease in cell spacing from 1046 nm to 640 nm as the solidification rate increases. However, the relationship between GND density and cell spacing doesn't follow Ashby's model. This indicates that GNDs are not entirely generated by thermal strain itself. On the other hand, the characterization results of cell structures show that a number of misfit dislocations are formed by the thermal strain induced deflection growth of the dendrites. These prove that the dislocations are comprehensively generated by thermal strain itself and dendritic deflection growth.

Structural insights into T1 precipitation and age hardening by Zn alloying for T6 treated Al–Cu–Li based alloys with a high Cu/Li ratio

T1 (Al2CuLi) nano-phase precipitation has been a major focus in developing new multi-microalloyed Al–Cu–Li alloys. Nevertheless, more understanding is required. This work investigated the effect of Zn alloying on the microstructure and mechanical properties of multi-element Al–Cu–Li alloys with a high Cu/Li ratio using a combination of advanced electron microscopy and first-principles calculations. Zn alloying (i) induced a higher density of geometrically-necessary dislocations after solid-solution treatment, which increased the T1 nucleation rate during the early aging stage; (ii) promoted T1 growth by substituting Al or Cu atoms in the T1 structure; and (iii) profoundly increased the aging kinetics, the age hardening response, and the strength. In addition, the co-segregation of Zn, Mg and Cu at the T1/Al interface helped to stabilize the fine T1 nano-platelets. These structural insights into T1 precipitation and age hardening by Zn alloying can help to guide the optimal design of high-performance Zn micro-alloyed multi-element Al–Cu–Li alloys.

Origins of HDI stress in copper–brass laminates with dual-heterostructured interfaces

In this work, a copper–brass hetero-laminate with dual-heterostructured interfaces was fabricated by diffusion welding in combination with cold deformation and annealing. These dual-heterostructured interfaces possess the characteristics of both gradient interface and sharp interface. The evolutions of geometrically necessary dislocations (GNDs) and local strains near these dual-heterostructured interfaces were investigated by in-situ and quasi in-situ tests. By employing a constitutive model, the evolutions of GND density and the HDI synergistic strengthening mechanism were systematically explored. The results demonstrated that the distribution of GNDs and local strains near the coarse/fine-grained interface exhibited a gradient feature, without any obvious concentrations of GNDs and strains, which can be attributed to the transition effect of the gradient interface. Furthermore, the density of sample-scale GNDs accumulated near the coarse/fine-grained interface was found to be at least one order of magnitude lower than that of grain-scale GNDs accumulated near grain boundaries. Both the constitutive model and experimental results confirmed that grain-scale GNDs serve as the primary origins of significant HDI stress, rather than the sample-scale GNDs.

Estimating dislocation density from electron backscatter diffraction data for an AZ31/Mg-0.6Gd hybrid alloy fabricated by high-pressure torsion

ABSTRACT The Geometrically Necessary Dislocation (GND) density was estimated from Electron Backscatter Diffraction (EBSD) data for an AZ31/Mg-0.6Gd (wt.%) hybrid material fabricated by high-pressure torsion (HPT) at room temperature through an equivalent strain range of ϵeq = 0.3–144 using Kernel Average Misorientation (KAM) and the Nye tensor approaches. The results show that generally the GND densities are significant at the beginning of the deformation (ϵeq = 0.3) and decrease in both alloys when ϵeq increases. The Mg-0.6Gd alloy exhibits a lower GND density due to rapid dynamic recrystallization. These results were compared to the GND densities measured in AZ31 and Mg-0.6Gd mono-materials processed separately by HPT under the same experimental conditions. In these mono-materials the GND densities increase with increasing equivalent strain up to 7 and then decrease with further straining. The Mg-0.6Gd and AZ31 regions of the hybrid material exhibit higher GND densities than the mono-materials particularly at low strain where the disc thickness and the bonding of the AZ31/Mg-0.6Gd interfaces cause more deformation heterogeneity in the hybrid material. It is shown that the GND density evolution as a function of ϵeq has the same tendency for the KAM and the Nye approaches but the average values are significantly higher with the Nye approach. An analysis suggests that the Nye approach overestimates the GND density of the Mg-based alloys.