Intragranular Misorientation Research Articles

Diffraction-based misorientation mapping: A continuum mechanics description

As the typical intragranular misorientation parameters, Kernel Averaged Misorientation (KAM) and Grain Reference Orientation Deviation (GROD) are widely used in diffraction-based misorientation mapping, while their evolution laws under various conditions and physical meanings in continuum mechanics description are rarely investigated systematically. Therefore, we designed several comparative experiments considering the influences of grain boundaries (single-crystalline vs. poly-crystalline), sample geometries (smooth vs. notched) and plastic strain modes (tension vs. buckling) on KAM & GROD evolution, and captured the intragranular misorientation, dislocation density, and material distortion synchronously based on coupled EBSD-ECCI-DIC mapping in this research. Meanwhile, we also discussed the physical meanings of KAM & GROD based on continuum mechanics description and provided the theoretical explanations to phenomena observed in the above experiments. KAM results from three in-surface invariants (ρGNDI, ρGNDII & ρGNDIII) of GND density tensor ρGND induced by plastic strain distribution incompatible with the activated slip systems in unloaded elastic-plastic condition, which cause the same lattice curvature effects as three elastic strain modes with non-zero curl (buckling, in-surface bending & torsion) in purely elastic condition. GROD reflects neither local plastic strain nor local material rotation alone, but its “V-type” distribution near the neutral surface reflects the buckling curvature of single-crystal. Besides, KAM¯ & GROD¯ averaged over multiple grains can be used to estimate the nominal plastic strain applied in poly-crystal.

Micro-mechanisms of microstructural damage due to low cycle fatigue in CoCuFeMnNi high entropy alloy

Low cycle fatigue behavior of equiatomic CoCuFeMnNi high entropy alloy was investigated under fully reversible strain control mode followed with detailed microstructural characterization using electron back scatter diffraction. There is an increase in the intragranular misorientation and geometrically necessary dislocation density with increase in the strain amplitude that leads to accumulation of damage and intergranular cracking. The interaction of dislocations with copper rich nano-clusters, solute environment and grain boundaries affect slip reversibility, thereby deciding cyclic deformation behaviour. Annealing twin boundaries are resistant to damage and increasing their population density by grain boundary engineering can improve performance of CoCuFeMnNi alloy.

Study of potential recrystallization nuclei in the cold-rolled microstructure of an electrical steel by electron backscatter diffraction

Strain induced boundary migration (SIBM) is widely recognized to be the main mechanism corresponding to recrystallization in metals of low or medium amount of deformation. The nucleation process in recrystallization of heavily deformed metals is, however, less understood for key issues such as how the nuclei are formed and where they are located. The evolution of texture from deformation to recrystallization cannot thus be explained well. In this study, an attempt was conducted to identify the potential recrystallization nuclei (PRN) in the cold-rolled microstructure of an electrical steel by electron backscatter diffraction (EBSD). This work demonstrates that the SIBM mechanism can be the main mechanism corresponding to recrystallization nucleation in a heavily deformed steel. The same area in both the cold-rolled and partially recrystallized states was analysed using EBSD to obtain the correlation between the recrystallized grains and the cold-rolled substructures. The deformed grains having high stored energy were first selected, followed by identifying substructures surrounded entirely or partly by high angle boundaries in these heavily deformed grains. The deformation induced grains having low intra-granular misorientation of 2° or less exhibit a very similar orientation distribution to that of the recrystallized grains and are proposed to be the PRN in subsequent recrystallization.

Investigation of the Relationship Between Microstructural Features and Strain Localization in Polycrystalline 316 L

In this paper, strains are monitored in-situ at the surface of a polycrystalline 316 L sample loaded quasi-statically in uniaxial tension. Initial orientation data collected over thousands of grains is compared with the strain data evolution in order to investigate, with statistical significance, the relationship between the microstructural features and the strain localization patterns emerging at the grain scale. It is shown quantitatively that high values of strain appear early and primarily around grain boundaries, before growing into a network spanning several grains and grain boundaries. Strains are also heterogeneous within a grain, with the heterogeneity tending to be more pronounced in larger grains. Statistical analyses demonstrate that the usual microstructural descriptors—such as Taylor factors, average intragranular misorientation angles or intergranular misorientation angles—do not display any correlation with the localization network. Furthermore, higher Schmid factors, albeit exhibiting some weak correlation with higher strains, fail to systematically identify the grains that experience the largest strains. It is thus proposed to analyze three-dimensional descriptors of orientation expressed in the Rodrigues space and they are shown to help readily identify orientations that exhibit high strains early in the loading. Additionally, the study of the full three-dimensional misorientation information, expressed in the reduced Rodrigues space, clearly highlights the fact that some misorientations oppose localization at certain boundaries in the microstructure at hand. Hence, considering the full three-dimensional orientation (and misorientation) data instead of just scalar descriptors is demonstrated to be of great interest when investigating the relationship between microstructural features and strain localization.

A method for including diffusive effects in texture evolution

This work describes a model for representing grain misorientation in continuum models for texture evolution. The model relies on a connection, derived here, between the fluctuation of the reorientation velocity in discrete models of texture evolution and an isotropic diffusion operator that can be used to represent misorientation effects in continuum models for texture evolution. Previous work has developed a method for computing the fluctuation of the reorientation velocity in discrete models. These values, along with the average reorientation velocity, are used to set up inhomogeneous continuum advection and diffusion operators. The complete homogenized continuum model uses the discrete harmonics to represent and evolve the orientation distribution function, now including a diffusion operator representing the effects of intragranular misorientation. Results from the new model are compared to fully-resolved crystal plasticity finite element simulations and experimental data to demonstrate the accuracy of the proposed diffusion operator and the overall method for simulating texture evolution.

Relationship between Stress Relaxation and Intragranular Misorientation in Cu-Ni-Si alloy Subjected to Continuous Cyclic Bending

Relationship between Stress Relaxation and Intragranular Misorientation in Cu-Ni-Si alloy Subjected to Continuous Cyclic Bending

Influence of hot-working conditions on grain growth of superalloy 718

The grain growth behavior of superalloy 718 was investigated using high-temperature compression tests and subsequent heat treatment. Abnormal grain growth (AGG) induced by low plastic strains was observed during thermal processing, which included solution heat treatment, and annealing, causing the matrix grains to coarsen from ∼12 μm to 80 μm in diameter. Both the plastic strain and displacement rate during deformation had large influences on the occurrence of AGG, which was mainly observed in regions of low plastic strain; the plastic strain range where AGG occurred increased with decreasing displacement rate. In particular, deformation at low displacement rates (within the same range as dynamic recrystallization) easily produced grain growth during solution heat treatment. Such grain growth was referred to as irregular grain growth (IGG) to distinguish it from AGG. Both the AGG and IGG processes were initiated when the intragranular misorientation exceeded a critical level, causing an increase in the twin boundary ratio and a decrease in intragranular misorientation. The nuclei of AGG grains were the nucleation of newly recrystallized grains without dislocation.

Superior energy absorption in porous magnesium: Contribution of texture development triggered by intra-granular misorientations

The effect of the initial crystallographic texture and its development on the energy absorption capability of porous magnesium (Mg) with parallel cylindrical pores and a fiber texture was studied. The fiber texture, whose symmetrical axis is oriented along the longitudinal axis of pores, was modeled using crystal plasticity finite element method (FEM). Subsequently, the effect of the preferred orientation angle of the basal planes in Mg grains, denoted as the angle α, on the compressive deformation along the longitudinal axis of pores was analyzed. The analyses revealed that the orientation angle α of the basal planes strongly affects the development of the intra-granular crystallographic misorientations, which dominates the compressive deformation and energy absorption capability. When the angle α is low, a strong deformation constraint, originating from inter-granular interaction, occurs at the grain boundaries. Owing to the constraint, large intra-granular crystallographic misorientations occur during deformation. Consequently, the axial symmetry of the fiber texture becomes asymmetric, which causes the appearance of a plateau stress region, where compressive deformation proceeds with a small increase in stress. As a result, superior energy absorption is achieved for a low angle α. The crystal plasticity analyses also indicate that an ideal plateau stress region, where deformation proceeds with almost no increase in stress, appears by controlling the initial fiber texture using a compressive preloading on a porous Mg sample prepared via the present directional solidification process. Owing to the superior plateau stress region, the porous Mg achieves high energy absorption efficiency and capability simultaneously.

Understanding the effects of recrystallization and strain induced boundary migration on ∑3 twin boundary formation in Ni-base superalloys during iterative sub-solvus annealing

The formation of ∑3 twin boundaries in an experimental low stacking fault Ni-based superalloy containing 24 wt% Co was investigated. Normalized microstructures were hot deformed to strain limits of 0.10 and 0.50 at a strain rate of 0.1/s and a temperature of 1020 °C. The hot-deformed microstructures were characterized using electron backscatter diffraction, and were subsequently subjected to a series of iterative sub-solvus anneal heat treatments at 1100 °C for one to two minutes. By characterizing the changes in the microstructure and grain boundary character distribution as a function of annealing time, this investigation sought to quantify and detail how twin boundary generation and growth occurs during annealing. This behavior was investigated in the same alloy, but with two distinct as-deformed starting microstructures associated with the different strain limits. The starting microstructures possessed varying levels of intragranular misorientation networks, which were found to have greatly affected the resultant formation of ∑3 annealing twin boundaries. Strain induced boundary migration (SIBM) was observed to have been restricted in the iteratively annealed sample deformed to a strain of 0.10. Due to the sub-solvus heat treat temperature, grain boundary precipitates were present in the microstructure which limited the mobility of the grain boundaries and suppressed grain growth. As a result, the expansion in the length fraction of ∑3 twin boundaries was limited as a function of annealing time. The sample deformed to 0.50 strain, however, was shown to have recrystallized both upon deformation and subsequent annealing. Although recrystallization was found to largely remove much of the pre-existing twin boundaries, the mobility of the newly formed boundaries during growth of the recrystallized grains resulted in a dramatic increase in both the density and length fraction of twin boundaries.

Effect of alloying elements on room temperature stretch formability in Mg alloys

The effect of alloying elements on room temperature stretch formability and its deformation mechanism was investigated using pure magnesium and its binary alloys containing an element of Ag, Al, Ca, Li, Mn, Pb, Sn, Y and Zn, respectively. All of the alloys as well as pure magnesium were produced by extrusion and had a similar average grain size. The alloying elements clearly affected stretch formability as measured by Erichsen testing. The addition of manganese or yttrium element played a role in improving formability; on the other hand, most of the alloying elements did not improve formability, as exhibited by their limited dome height values, which were similar to or lower than that of pure magnesium. This resulted from their differences in deformation mode. An intragranular misorientation axis analysis using electron back-scatter diffraction results revealed that the Mg-Y alloy had a high fraction of grains amenable to non-basal dislocation slips, which is a helpful deformation mode for improving formability. In contrast, pure magnesium and the Mg-Mn alloy, which had a high limited dome height, did not have a high fraction of such grains. Grain boundary sliding compensated for the lack of <c>-component, such as activating non-basal dislocation slips.

Modeling of intragranular misorientation and grain fragmentation in polycrystalline materials using the viscoplastic self-consistent formulation

The recently established methodology to use known algorithmic expressions of the second moments of the stress field in the grains of a polycrystalline aggregate for calculating average fluctuations of lattice rotation rates and the associated average intragranular misorientation distributions using the mean-field viscoplastic self-consistent (VPSC) formulation is extended to solve the coupled problem of considering the effect of intragranular misorientations on stress and rotation rate fluctuations. In turn, these coupled expressions are used to formulate and implement a grain fragmentation (GF) model in VPSC. Case studies, including tension and plane-strain compression of face-centered cubic polycrystals are used to illustrate the capabilities of the new model. GF-VPSC predictions of intragranular misorientation distributions and texture evolution are compared with experiments and full-field numerical simulations, showing good agreement. In particular, the inclusion of misorientation spreads reduced the intensity of the deformed texture and thus improved the texture predictions. Moreover, considering that intragranular misorientations act as driving forces for recrystallization, the new GF-VPSC formulation is shown to enable modeling of microstructure evolution during deformation and recrystallization, in a computationally efficient manner.

Microstructural characterization of as-fabricated and irradiated U-Mo fuel using SEM/EBSD

Electron Backscattered Diffraction (EBSD) is an effective technique for revealing many details about the microstructure of materials, e.g. crystallographic orientation, grain size, grain boundary properties, texture, intragranular misorientation, and subgrain formation. Since these details are of interest for improving the irradiation performance understanding of any irradiated nuclear fuel (e.g. swelling behavior), this technique has been applied successfully on U-7 wt% Mo before and after irradiation. This fuel is a high-density, low-enriched uranium fuel currently being developed for application in research and test reactors. Based on the results of this characterization, it was found that when as-fabricated U-7 wt% Mo is irradiated to around 5.3 × 1021 fissions/cm3 the original large grains (diameter ∼4 μm) are subdivided into much smaller grains (diameter ∼0.3 μm) and most of these subdivided grain boundaries are low angle boundaries. The EBSD analysis suggests that the grain subdivision in the irradiated U-7 wt% Mo was driven by polygonization, not recrystallization as defined by classic metallurgy as a result of heavy cold work followed by heat treatment.

Proton irradiation damage in cold worked Nb-stabilized 20Cr-25Ni stainless steel

Micro-scale damage with a topographical contrast has been observed in cold-worked Nb-stabilised 20%Cr-25%Ni stainless steel, following irradiation with 2.2 MeV protons at 400 °C and a dose rate of ∼10−5 dpa/s. After an irradiation dose of 3 and 5 dpa, microstructural changes were found to a depth of 22 μm below the irradiated surface, coincident with the estimated mean range of protons in the material as predicted by the TRIM code. Large variations of intragranular mis-orientations, in combination with a depletion of chromium at grain boundaries, were observed in the proton-irradiated layer. This was accompanied by an increase in nano-hardness, which was linked to a partial transformation of tangled dislocation networks into dislocation loops. Such visible microstructural changes have not been reported before in the absence of post-irradiation annealing treatments.

A digital image correlation study of a NiTi alloy subjected to monotonic uniaxial and cyclic loading-unloading in tension

This digital image correlation study details the mechanical behaviour and pattern evolution of the transformation band of a 56Ni-44Ti wt% shape memory alloy subjected to monotonic uniaxial and loading-unloading cycles in tension. The broadened single inclined band front and multiple criss-crossing patterns are found to relieve the in-plane moment caused by local shear strains and straighten the sample edges during testing. The magnitude of the maximum local strain rate suggests its feasibility to understand the direction and extent of the localised transformation. Specifically, the changes to the maximum local strain rate during monotonic uniaxial tension are generally analogous to the stages in the macroscopic stress-strain curve. The microstructure before and after mechanical testing was characterised via electron back-scattering diffraction. Estimates of the kernel average misorientation show that residual strains upon unloading are linked to high intragranular misorientation within the original B2 grains and the remnant B19′ variants.

Evolution of microstructure, texture and mechanical properties of ZK60 magnesium alloy in a single rolling pass

The evolution of microstructure and texture in a single rolling pass was investigated at rolling temperature of 250 ℃. Based on the analysis of microstructure evolution, thickness reduction of 31% was identified as a critical deformation strain for the occurrence of continuous dynamic recrystallization (CDRX) in this work. CDRX strikingly refined the grain size and improved the microstructure homogeneity. The results based on intragranular misorientation axis analysis showed that the activation of abundant stochastic stored dislocations with a broad range of orientations developed in CDRX was the main reason of the transformation from <10−10>//RD texture to randomized texture along <10−10>-<11−20> arc in inverse pole figure. Microhardness distribution was mainly influenced by the fraction of deformed grains. Grain refinement increased yield stress and uniform elongation, while weaker texture only increased uniform elongation.

Configuration of dislocations in low-angle kink boundaries formed in a single crystalline long-period stacking ordered Mg-Zn-Y alloy

The dislocation configuration around low-angle kink boundaries formed in bent single crystalline long-period stacking ordered (LPSO) Mg85Zn6Y9 alloys was investigated. Intragranular misorientation axis (IGMA) analysis through SEM/EBSD observation and g•b analysis through TEM observation were conducted. Various kink bands possessing different lattice rotation axes ranging from <11¯00> to <12¯10>, i.e. along <11¯00>, <uvt0>, and <12¯10> were revealed using IGMA analysis. TEM observation with g•b analysis unveiled that the <11¯00>-rotation kink boundary observed using IGMA analysis consisted of basal <a> edge dislocations with one Burgers vector, while the <12¯10>/<uvt0>-rotation kink boundaries were comprised of basal <a> edge dislocations with more than one Burgers vector. Low-angle kink boundaries were regarded as low-angle tilt boundaries consisting of perfect basal <a> dislocations, regardless of their rotation axes. The formation of various kink bands with <uvt0>-combination-rotation axes ranging from <11¯00> to <12¯10> suggests that the statistically stored basal <a> dislocations may turn into geometrically necessary basal <a> edge dislocations during the initial stage of low-angle kink boundary formation. When a kink boundary is considered as a disclination, IGMA analysis capable of determining the lattice rotation axis and the angle is effective in evaluating the Frank vector of the kink boundary.

Quantifying geometrically necessary dislocations in quartz using HR-EBSD: Application to chessboard subgrain boundaries

This study presents the first use of high-angular resolution electron backscatter diffraction (HR-EBSD) to quantitatively characterise geometrically necessary dislocations in quartz subgrain structures. HR-EBSD exploits cross-correlation of diffraction patterns to measure intragranular misorientations with precision on the order of 0.01° with well-constrained misorientation axes. We investigate the dislocation structures of chessboard subgrains in quartz within samples from the Greater Himalayan Sequence, Nepal. Our results demonstrate that chessboard subgrains are formed primarily from two sets of subgrain boundaries. One set consists primarily of {m}[c] edge dislocations, the other consists primarily of dislocations with <a> Burgers vectors. Apparent densities of geometrically necessary dislocations vary from > 1013 m−2 within some subgrain boundaries to < 1012 m−2 within subgrain interiors. The results suggest that at pressures above approximately 10 kbar, chessboard subgrains may form within the α-quartz stability field. Most importantly, this study demonstrates the potential of HR-EBSD as an improved method for analysis of intragranular microstructures in quartz that are used as indicators of deformation conditions.

Predicting intragranular misorientation distributions in polycrystalline metals using the viscoplastic self-consistent formulation

In a recent paper, we reported the methodology to calculate intragranular fluctuations in the instantaneous lattice rotation rates in polycrystalline materials within the mean-field viscoplastic self-consistent (VPSC) model. This paper is concerned with the time integration and subsequent use of these fluctuations to predict orientation-dependent misorientation distributions developing inside each grain representing the polycrystalline aggregate. To this end, we propose and assess two approaches to update the intragranular misorientation distribution within the VPSC framework. To illustrate both approaches, we calculate intragranular misorientations in face-centered cubic polycrystals deformed in tension and plane-strain compression. These predictions are tested by comparison with corresponding experiments for polycrystalline copper and aluminum, respectively, and with full-field calculations. It is observed that at sufficiently high strains some grains develop large misorientations that may lead to grain fragmentation and/or act as driving forces for recrystallization. The proposed VPSC-based prediction of intragranular misorientations enables modeling of grain fragmentation, as well as a more accurate modeling of texture using a computationally efficient mean-field approach, as opposed to computationally more expensive full-field approaches.

Kink deformation in a beta titanium alloy at high strain rate

Kink deformation is uncommonly observed in Ti-35V-15Cr-0.3Si-0.1C beta titanium alloy deformed at 5 × 103s−1. Band structures have formed on the deformed samples. Electron back scattered diffraction analyses prove those band structures are kink bands rather than commonly reported twins in beta alloys with high niobium. The kink bands are classified into three categories since the intragranular misorientation axis analyses reveal that three lattice rotation axes (Taylor axes) exist among the kink bands. The three Taylor axes are [11̅0], [54̅1], [121̅] and the corresponding three slip mode of the dislocation kink model are (112)[111̅], (123)[111̅], (101)[11̅1̅] respectively. It is demonstrated that the selection of the slip mode in a kink bands is dominated by the loading axis. A slip system would have the priority to be selected as the slip mode of the kink deformation if the loading axis is close to the normal direction of the slip plane and the perpendicular direction of the slip direction.

Microstructural evolution during thermal annealing of ice-Ih

We studied the evolution of the microstructure of ice-Ih during static recrystallization by stepwise annealing experiments. We alternated thermal annealing and electron backscatter diffraction (EBSD) analyses on polycrystalline columnar ice pre-deformed in uniaxial compression at temperature of −7 °C to macroscopic strains of 3.0–5.2. Annealing experiments were carried out at −5 °C and −2 °C up to a maximum of 3.25 days, typically in 5–6 steps. EBSD crystal orientation maps obtained after each annealing step permit the description of microstructural changes. Decrease in average intragranular misorientation at the sample scale and modification of the misorientation across subgrain boundaries provide evidence for recovery from the earliest stages of annealing. This initial evolution is similar for all studied samples irrespective of their initial strain or annealing temperature. After an incubation period ≥1.5 h, recovery is accompanied by recrystallization (nucleation and grain boundary migration). Grain growth proceeds at the expense of domains with high intragranular misorientations, consuming first the most misorientated parts of primary grains. Grain growth kinetics fits the parabolic growth law with grain growth exponents in the range of 2.4–4.0. Deformation-induced tilt boundaries and kink bands may slow down grain boundary migration. They are stable features during early stages of static recrystallization, only erased by normal growth, which starts after >24 h of annealing.