Revealing geometrically necessary dislocation density from electron backscatter patterns via multi-modal deep learning

Investigations of dislocation-type evolution and strain hardening during mechanical twinning in Fe-22Mn-0.6C twinning-induced plasticity steel

Influence of prestraining and ageing on the fatigue properties of a dual phase sheet steel with tensile strength of 410 MPa: Fredriksson, K., Melander, A. and Hedman, M. Scand. J. Metall. 1989 18, (4), 155–165

The Equal Channel Angular Extrusion process is used to modify the microstructure of an AA1050 aluminum alloy in order to produce an ultra fine grained material. Due to the severe plastic deformation undergone by the material during the ECAE process, the subsequent behavior of the material is non-conventional and difficult to model with classical constitutive laws (e.g. ECAE aluminum presents a large initial back-stress which must be adequately incorporated in the model). In this study, the evolution of the back-stress during the ECAE process is analyzed. Two different numerical models were investigated in this respect. The first one is a single crystal strain gradient plasticity model based on dislocation densities. The second model is the Teodosiu and Hu’s hardening model, which is a microstructuraly based phenomenological model at the macroscale. The results provided by the two models are obviously distinct. Nevertheless, some common trends can be pointed out, among which the amplitude of the back-stress that is similar. In agreement with the cyclic deformation mode of the studied route C ECAE process, the evolution of the predicted back-stress is also cyclic in both models. INTRODUCTION The Equal Channel Angular Extrusion (ECAE) process is used in the present study to produce ultra fine grained aluminum. It is well-known that a decrease in the grain size of a material is accompanied by an increase of the yield strength as can be represented by the HallPetch relation [1]. Due to their particular mechanical properties, an increasing interest is currently dedicated to the study of ultra fine grained materials. However, the modeling of these materials is not straightforward. The material deformed by the ECAE process is far from its virgin state. Very large plastic strains (in the studied case, the plastic equivalent strain is 1.15 per pass) are imposed to the material. In the framework of this study, several mechanical tests were performed on the aluminum produced by ECAE in order to assess its mechanical behavior [2]. It appeared that a significant kinematic hardening was observed. Furthermore, the ECAE aluminum presented an initial backstress resulting from the deformation that occurred during the ECAE process. This contribution assesses the performance of two different numerical models for an accurate modeling of ECAE processed aluminum. A single crystal strain gradient plasticity model was scrutinized in this respect. This model uses as internal variables the densities of statistically stored dislocations (SSD) and geometrically necessary dislocations (GND). The evolution of the SSD densities is based on a balance between dislocation accumulation and annihilation rates depending on the slip rates. The GND densities on the other hand result from the incompatibilities in the crystal lattice due to gradient of the dislocation slip. Both GND and SSD densities are taken into account for the isotropic hardening of the material. The GND densities naturally induce a physically based kinematic hardening through their internal stresses (i.e. the back-stress, computed as a function of the GND densities gradient). In addition, a macroscopic phenomenological hardening model was investigated. The Teodosiu and Hu's hardening model [3;4] is a physically-based microstructural model. Basically, it is able to describe both kinematic and isotropic hardening, reflecting the influence of the dislocation structures and their evolutions, at a macroscopic scale. It permits to describe complex hardening behaviors induced by strain-path changes. The goals of this research are multiple. First, different numerical models were used to predict the evolution of the back-stress during an ECAE process. This yields new insights and more accurate material parameters as used in phenomenological models adapted to ECAE materials (mainly a reasonable initial back-stress). The modeling of the ECAE process also results in an improved knowledge of the mechanisms involved during this forming process. Finally, this research permits the comparison of two promising yet different models with very different approaches on a relevant application.

Influence of plastic deformation heterogeneity on development of geometrically necessary dislocation density in dual phase steel

Characterization of geometrically necessary dislocation evolution during creep of P91 steel using electron backscatter diffraction

Effects of temperature and load on fretting fatigue induced geometrically necessary dislocation distribution in titanium alloy

Relationships between microstructures and hardening nature of laser powder bed fused (L-PBF) 316 L stainless steel have been studied. Using integrated experimental efforts and calculations, the evolution of microstructure entities such as dislocation density, organization, cellular structure and recrystallization behaviors were characterized as a function of heat treatments. Furthermore, the evolution of dislocation-type, namely the geometrically necessary dislocations (GNDs) and statistically stored dislocations (SSDs), and their impacts on the hardness variation during annealing treatments for L-PBF alloy were experimentally investigated. The GND and SSD densities were statistically measured utilizing the Hough-based EBSD method and Taylor's hardening model. With the progress of recovery, the GNDs migrate from cellular walls to more energetically-favourable regions, resulting in the higher concentration of GNDs along subgrain boundaries. The SSD density decreases faster than the GND density during heat treatments, because the SSD density is more sensitive to the release of thermal distortions formed in printing. In all annealing conditions, the dislocations contribute to more than 50% of the hardness, and over 85.8% of the total dislocations are GNDs, while changes of other strengthening mechanism contributions are negligible, which draws a conclusion that the hardness of the present L-PBF alloy is governed predominantly by GNDs.

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.

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.

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.

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.

Subgrain geometrically necessary dislocation density mapping in spalled Ta in three dimensions

Geometrically necessary dislocations distribution in face-centred cubic alloy with varied grain size

There are two widely used examination methods to study microstructure of polycrystalline materials, namely the automated electron backscatter diffraction (EBSD) and the X-ray diffraction line profile analysis (XLPA). Both methods are suitable to determine quality and quantity of crystallographic defects or irregularities within crystalline structures. However, the EBSD method can be used to estimate the density of only geometrically necessary dislocations (GND), while the XLPA method can give the total dislocation density. A novel software was developed for the determination of GND density from misorientations measured between the neighbouring pixels in EBSD images. Therefore EBSD method is a local, while XLPA method is a non-local procedure to determine dislocation densities. In fact, the calculated GND density depends on the applied step size of EBSD measurements, namely GND densities increase with decreasing the step size. So this leads to a question of how large applied step size of EBSD measurements gives a good approximation for the real GND density in a given polycrystalline material.

Effect of deformation heterogeneity on development of geometrically necessary dislocation density in heterogeneous-structured CrMnFeCoNi high-entropy alloy