Force For Grain Boundary Migration Research Articles

Using 3D X-ray Microscopy to Understand the Driving Force for Grain Boundary Migration in Polycrystals

Using 3D X-ray Microscopy to Understand the Driving Force for Grain Boundary Migration in Polycrystals

Effect of boundary grooving on grain growth by Potts model simulations

Grain growth in thin films is a technologically important and scientifically fascinating topic: As the grain size influences many mechanical and optical properties of a material, any change in the grain structure and therewith in the grain size changes also the materials properties. There are many factors influencing coarsening of the microstructure such as grain boundary properties or the presence of particles; additionally the film thickness becomes rather important. It has been observed that when the grain size reaches the magnitude of the layer thickness, coarsening slows down and may even stagnate. For thin films, surface effects such as grain boundary grooving become important. In general, grooves are totally left out of implementations in the standard Potts model. In the current investigation, we introduce grain boundary grooves in the Potts model as physical entities. In the analysis, we show how the mere presence of such grooves reduces the driving force of grain boundary migration at the surface tremendously at any stage of coarsening.

Grain Boundary Migration in Polycrystals

Grain boundaries in polycrystalline materials migrate to reduce the total excess energy. It has recently been found that the factors governing migration rates of boundaries in bicrystals are insufficient to explain boundary migration in polycrystals. We first review our current understanding of the atomistic mechanisms of grain boundary migration based on simulations and high-resolution transmission electron microscopy observations. We then review our current understanding at the continuum scale based on simulations and observations using high-energy diffraction microscopy. We conclude that detailed comparisons of experimental observations with atomistic simulations of migration in polycrystals (rather than bicrystals) are required to better understand the mechanisms of grain boundary migration, that the driving force for grain boundary migration in polycrystals must include factors other than curvature, and that current simulations of grain growth are insufficient for reproducing experimental observations, possibly because of an inadequate representation of the driving force.

Interface welding mechanism and strengthening principle during friction stir spot welding of ultra-high strength C–Mn–Si martensitic steel

Solid-state welding mechanism of ultra-high strength C–Mn–Si martensitic steel during friction stir spot welding (FSSW) was clarified and interface strengthening principle was revealed. We found that the generated oxides in the interface became spherical and dispersed, which was caused by selective oxidation due to the reduced oxygen partial pressure during high welding temperature. Then, these oxides were further refined and dispersed by severe material flow around the welding interface. Consequently, the refined and spherical (Mn, Si, Al)O amorphous oxides were formed. In addition, strong material flow introduced large drive force for grain boundary migration around the welding interface, which further facilitated the migration and dispersion of the generated (Mn, Si, Al)O oxides, giving rise to a high-strength welding interface.

Influencing Mechanisms of Prior Cold Deformation on Mixed Grain Boundary Network in the Thermal Deformation of Ni80A Superalloy.

Within the grain boundary engineering (GBE) of alloys, a mixed grain boundary network with random grain boundaries interrupted by twin boundaries, contributes to enhancing the overall grain boundary-related properties. The higher density of twin boundaries is pursued herein. Furthermore, a two-stage deformation method, i.e., prior cold deformation followed by thermal deformation, was proposed for improving the mixed grain boundary network in the thermal deformation of Ni80A superalloy. The influence of prior cold deformation on the mixed grain boundary network was investigated through a series of two-stage deformation experiments. The analysis of the stress–strain curves shows that the critical strain for dynamic recrystallization (DRX) and peak strains decrease significantly under the effect of prior cold deformation. In comparison to the necklace-like microstructures that occur after a single thermal deformation, the microstructures apparent after a two-stage deformation are characterized by finer DRX grains with abundant Σ3n twin boundaries, with a significantly improved density of the Σ3n twin boundaries (BLDΣ3n) by a factor of around nine. With increasing prior cold strain, the grain size, after a two-stage deformation, decreases continuously, while the BLDΣ3n increases firstly and then decreases. The mechanisms for improving the mixed grain boundary network via two-stage deformation were uncovered. The sub-grain boundaries formed in prior cold deformation stimulate the nucleation of DRX grains and twins; meanwhile, the driving force for grain boundary migration is enhanced due to prior stored energy. Then, DRX is activated in advance and occurs more completely, thereby promoting the formation of Σ3n twin boundaries.

Regionalization of microstructure characteristics and mechanisms of slip transmission in oriented grains deposited by wire arc additive manufacturing

Regionalization of microstructure regulation and mechanical property adjustment during the thermal cycle of the deposition process plays a vital role in the grain morphology and orientation of aluminum alloy components manufactured using wire arc additive manufacturing (WAAM) technology. However, the microscopic mechanism of the mechanical property difference caused by uneven microstructure in different regions remains unclear for the WAAM 2319 alloy. The geometric properties of grains are described quantitatively in different regions for the WAAM 2319 alloy through EBSD data processing and analysis. The effect of grain orientation on grain boundary, including subgrain boundaries and the boundary of coincidence site lattice (CSL boundary), are explored with EBSD data. The grain boundary and dislocations are characterized by transmission electron microscopy (TEM). The distribution of geometrically necessary dislocation (GND) in the WAAM block at different regions is studied through EBSD analysis. The high Schmidt factor or Taylor factor (M) percentage was quantitatively calculated in different regions. Then the relationship between grain morphology and plastic deformation ability is established through these factors. The results indicate that the average grain size is small and located in the top and middle of the WAAM sample with a low critical Taylor factor (Mc). The Taylor factor in most grains easily exceeds Mc (Mc < M), which causes most dislocations to pass through grain boundaries quickly, and plastic deformation easily occurs in these regions. There are various CSL boundaries except Σ3 boundaries existing in the middle of the sample, which can maintain the high mobility of the grain boundaries. Therefore, more slip transmission in the middle of the WAAM sample can provide the driving force for grain boundary migration. Most grains with a high subgrain boundary density (above 2.5) and the geometrically necessary dislocation (GND) density (5 × 1014 m−2) can hinder the movement of dislocations and improve the strength of materials at the sidewall of the sample. The Schmidt factor of columnar crystals is generally low (below 0.25), and the sliding system does not start rapidly in columnar crystals, especially at the bottom of the WAAM sample.

Effect of extrusion ratios on microstructure evolution and strengthening mechanisms of a novel P/M nickel-based superalloy

A novel P/M nickel-based superalloy is developed with an excellent combination of strength and ductility for use in turbine disks. This superalloy is prepared through hot isostatic pressing (HIP) and subsequent hot extrusion (HEX) with different extrusion ratios (λ). The effects of λ on the evolution and mechanism of γ′ precipitation behavior, grain refinement, microtexture, and mechanical properties are systematically studied. As λ increases, the primary γ′ phase fraction decreases from 17.22% to 8.47%, and the precipitation morphology changes from an irregular to a spherical shape. Increasing λ is beneficial to dynamic recrystallization. Fully recrystallized fine grains with a diameter of 4.47 μm are obtained at an optimal λ = 5.0, a decrease of 76% compared with the HIPed alloy. Abnormal grain coarsening was observed at a higher λ with 8.5 owing to the lack of γ′ pinning and a stronger driving force for grain boundary migration induced by deformation heat. The yield strength (YS) and ductility of the HEXed alloy are over 30% higher than those of the HIPed alloy, thanks to refined grains and the γ′ phase. The alloy extruded with λ of 5.0 exhibits a high YS of 1376 MPa with a ductility of 22.6% at room temperature and a YS of 1208 MPa with a ductility of 18.3% at 700 °C, which are better than those of other superalloys. A multi-mechanistic strengthening model is constructed by correlating the chemical composition, size and fraction of γ′, grain size, and YS. The calculations suggest that precipitation strengthening contributes more than 60% of the YS. Extrusion can dramatically enhance the YS of the superalloy owing to the increment of grain boundary strengthening and precipitation strengthening. This work provides a practical route and theoretical support for optimizing microstructure and enhancing the mechanical properties of a HIPed P/M nickel-based superalloy.

Double-sided friction stir spot welding of ultra-high strength C-Mn-Si martensitic steel by adjustable probes

High-quality joints of ultra-high strength C-Si-Mn quenched and tempered martensitic steel were successfully fabricated by double-sided friction stir spot welding (FSSW) with adjustable probes. We found that the mechanical properties of the welded joints increased with the rotation speed, due to the increase of hard phase and strengthened welding interface. In the surroundings of the shoulder/probe interface, a large amount of martensite was formed resulting from the higher austenitizing temperature and the higher cooling rate. In addition, severe material flow vertical to the welding interface and strong relative slip along the interface conspicuously favored the fragmentation and dispersion of the oxides, and the drive force for grain boundary migration introduced by severe material flow further promoted the dispersion of the oxides. Consequently, a high-quality welding interface was fabricated, and a high-strength welded joint with a stable plug failure was obtained. Furthermore, we pointed out that soundly welded high strength interface of ultra-high strength steel can be obtained by higher welding temperature and introducing strong material flow vertical to the interface.

Phase field modelling of diffusion induced grain boundary migration in binary alloys.

The Phase field method has been used to study Diffusion Induced Grain boundary Migration (DIGM) in binary alloys. Simulations are performed for a simple hypothetical binary substitutional solid solution. The model is developed by taking into account the elastic interactions arising due to changes in concentration across a grain boundary when solutes are diffusing along the grain boundary. This gives a coupling term in the Gibbs energy functional that acts as a driving force for grain boundary migration. Two different kinds of coupling terms are studied: one acting on both the abutting grains and the other acting on only one grain. The former gives a freedom of choice as to in which direction the grain boundary will move, and is considered more general, whereas the latter only moves in one direction, regardless of the shape of the grain boundary. The results from the model are in qualitative agreement with previous experimental studies.

Ultra-strong, ductile and thermally stable ultrafine grained 5083 Al alloy fabricated by high pressure torsion using pre-sintered powders

This work developed a novel strategy that employed powder metallurgy, high pressure torsion and subsequent annealing treatment to prepare fully recrystallized ultrafine-grained (UFG) 5083 Al alloy. The fabricated specimens showed excellent thermal stability even at 773 K, which was mainly attributed to the fine Al6(Mn, Fe) precipitates and oxide dispersoids that reduced the driving force for grain boundary migration by pinning. The mechanical properties primarily depended on the grain size. The specimens with the average grain sizes ranging from 0.39 to 0.81 µm exhibited good balance of strength and ductility, and the highest yield strength (454 MPa) together with decent elongation (0.11) were achieved when the grain size is 0.39 µm. In addition to grain boundary strengthening, the dislocation source-limited hardening greatly contributed to the yield strength of the fully recrystallized UFG alloy. The extra-hardening mechanism as well as the unique features of deformation including distinct yield point and large Lüders band was investigated in detail.

Two-Level Elastoviscoplastic Model: An Application to the Analysis of Grain Structure Evolution under Static Recrystallization

Multilevel modeling of structural evolution in polycrystals, which determines the macroscopic material properties, is currently one of the central research problems. The defect and grain/subgrain structure of polycrystalline materials changes greatly during thermomechanical processing. The grain structure is significantly affected by recrystallization, which leads to the formation of slightly defective recrystallization nuclei and their subsequent growth due to the absorption of more defective neighboring grains. This paper is aimed to develop a mathematical model for describing the behavior of polycrystalline materials during plastic deformation and subsequent heating to recrystallization temperatures. The main task is to describe grain structure evolution in polycrystals during this process. The considered recrystallization mechanism is based on the displacement of original grain boundary segments. As a result of preliminary cold plastic deformation, energy accumulates at defects (primarily dislocations) in neighboring grains. The energy difference between neighboring grains is the main driving force of grain boundary migration. When the recrystallized grain grows, the extent of the new high-angle boundary increases; the amount of energy expended for the boundary formation must be smaller than the decrease in the stored energy due to defect elimination. The subgrains adjacent to the grain boundary are the recrystallization nuclei in the considered deformation mechanism. They start to grow into the more defective grain when the Bailey-Hirsch criterion is satisfied. This study deals with polycrystalline materials with low stacking fault energy for which the effect of heating on the subgrain structure is insignificant. The energy stored in grains and subgrains is calculated using a two-level statistical model that considers individual grains and subgrains. Plastic deformation is assumed to occur through edge dislocation glide. A method is proposed for isolating flat boundary regions (facets) of new (recrystallized) grains, based on minimizing the grain boundary energy in the vicinity of the new boundary. This approach describes some experimentally observed recrystallization effects, such as the elongation of recrystallized grains in the initial recrystallization direction and the appearance of grain boundary facets that allow for boundary mobility.

A finite-deformation dislocation density-based crystal viscoplasticity constitutive model for calculating the stored deformation energy

A previously-developed infinitesimal strain and dislocation density based crystal viscoplasticity constitutive theory is reformulated in the finite deformation regime in a thermodynamically consistent manner. The constitutive equations are then numerically implemented into the Abaqus/Standard finite element package. The constitutive model is primarily verified and calibrated with respect to single crystal aluminum experiments and then the distribution of stored deformation energy in aluminum bicrystals and polycrystals is investigated to estimate the driving forces for grain boundary migration due to the stored energy difference across grain boundary. Our statistical analysis shows that the onset of strain induced grain boundary migration in a polycrystalline microstructure is basically dependent on the spatial distribution of the stored deformation energy rather than the overall stored deformation energy value; and it preferably occurs in a few predictable specific regions where certain grain orientations meet at a grain boundary across which high values of stored energy difference happens.

On the plastic driving force of grain boundary migration: A fully coupled phase field and crystal plasticity model

Dislocations stored in heavily deformed materials play an important role in driving microstructure evolution. Here, we developed a full coupling model that concurrently couples the phase field method with crystal plasticity finite element analysis to study grain boundary (GB) migration under a plastic driving force. In our model, we describe multiple active grains in GB regions with crystal plasticity theory and use a weighted sum of their properties (i.e., stress and elastic/plastic potentials, etc.) to evaluate the plastic driving force for GB migration. The model can qualitatively capture the absorption of dislocations by mobile GBs through re-initialization of slip system resistances of newly active grains. A finite element based preconditioned Jacobian-free Newton-Krylov approach is used to simultaneously solve all the nonlinear partial differential equations for the coupled physics models. Determining model parameters and validation of the model are accomplished by simulating copper bicrystals and comparing the results to available experiments. This model provides a useful tool for effectively simulating GB migration in metals undergoing large plastic deformation. All the developments have been implemented in the MOOSE/MARMOT simulation package.

Twin boundary characters established during dynamic recrystallization in a nickel alloy

For the purpose of providing fundamentals for grain boundary engineering design for high-temperature alloys, twin boundary characters are studied quantitatively in a nickel alloy during DRX to improve the understanding of twin boundary evolution during hot deformation. The nickel alloy samples were hot compressed at temperatures of 1120–1180°C and strain rates of 0.1s−1 and 1s−1 to a fixed true strain of 1.1. Refined equiaxed grain structure is obtained with abundant twin boundaries. Most of the twin boundaries form inside the grains, being highly coherent and showing rather limited mutual interaction. An inversely proportional relationship is found between Σ3 twin boundary length density (BLDΣ3) and DRX grain size (DDRX). An analytical model is derived here, in good agreement with current experimental results, indicating that the stored strain energy difference across grain boundary is the main driving force for grain boundary migration and determines the annealing twin formation during DRX. Σ3 twin boundary length density (BLFΣ3) developed in DRX was found varying within a small range of 44%–48%, which is shown to result from the inverse proportionality between grain boundary length density (BLDGB) and DDRX as well as the inverse proportionality between BLDΣ3 and DDRX.

Influence of stored energy on twin formation during primary recrystallization

The formation of annealing twins can always be observed in materials with low to medium stacking fault energy. During annealing, a deformed material can undergo recovery, primary recrystallization and/or grain growth. The ∑3n formation during recovery-like stage has been studied with grain boundary engineering (GBE). For the grain growth, the growth accident and the nucleation of twins have been proposed as two main mechanisms of twinning. And some studies reveal that the driving force of grain boundary migration has an influence on the formation of annealing twins. In this paper, a nickel-based alloy with low stacking fault energy is cold rolled with different strain amounts followed by an annealing at high temperature. Then the twin formation during primary recrystallization stage has been studied considering the influence of stored energy by deformation. The kinetic of twin formation is also determined during this stage as a function of deformation. It was found that this kinetic depends on the grain size and the driving force which is related to the stored energy during the cold rolling.

Strain Induced Abnormal Grain Growth in Nickel Base Superalloys

Under certain circumstances abnormal grain growth occurs in Nickel base superalloys during thermomechanical forming. Second phase particles are involved in the phenomenon, since they obviously do not hinder the motion of some boundaries, but the key parameter is here the stored energy difference between adjacent grains. It induces an additional driving force for grain boundary migration that may be large enough to overcome the Zener pinning pressure. In addition, the abnormal grains have a high density of twins, which is likely due to the increased growth rate.

Microstructure through an Ice Sheet

Ice cores through an ice sheet can be regarded as a sample of a unique natural deformation experiment lasting up to a million years. Compared to other geological materials forming the earth‘s crust, the microstructure is directly accessible over the full depth. Controlled sublimation etching of polished ice sections reveals pores, air bubbles, grain boundaries and sub-grain boundaries at the surface. The microstructural features emanating at the surface are scanned. A dedicated method of digital image processing has been developed to extract and characterize the grain boundary networks. First preliminary results obtained from an ice core drilled through the Greenland ice sheet are presented. We discuss the role of small grains in grain size analysis and derive from the shape of grain boundaries the acting driving forces for grain boundary migration.

Strain incompatibility and its influence on grain coarsening during cyclic deformation of ARB copper

It is well known that the characteristic length scale in ultra-fine grained and nanocrystalline metals has a significant effect on the mechanical behaviour. The inhibited ability to accommodate imposed strain with conventional dislocation mechanism has led to the activation of unconventional deformation mechanisms. For one, grain coarsening at shear bands has been observed to occur within metals with sub-micron grain size upon cyclic deformation. Such grain coarsening is often linked to the observed cyclic softening behaviour. The purpose of this study was to investigate the relationship between strain localisation associated with shear banding and the observed deformation-induced grain coarsening in ultra-fine grained metals. The investigation was carried out using ultra-fine grained, oxygen-free high conductivity copper processed by accumulative roll-bonding. A close relationship between strain localisation and deformation-induced grain coarsening was revealed. As strain localisation is not only found at shear bands, but also at other places whereby heterogeneous microstructure or geometric discontinuity is present, hence the present study bears a general significance. Such strain localisation sites may also include a hard constituent embedded in a relatively ductile matrix, micro-crack tips and artificial notches. The stress concentration at these sites provides a high input of strain energy for grain boundary motion leading to grain coarsening. Furthermore, when the grain size is very small, the stress gradient leading away from the stress concentration sites is also believed to increase the driving force for grain boundary migration within the affected regions.

A phase-field model of stress effect on grain boundary migration

We developed a phase-field model to study the stress-driven grain boundary migration in elastically inhomogeneous polycrystalline materials with arbitrary elastic inhomogeneity and anisotropy. The dependence of elastic stiffness tensor on grain orientation is taken into account, and the elastic equilibrium equation is solved using the Fourier spectral iterative-perturbation method. We studied the migration of planar and curved grain boundaries under an applied stress. The relation between grain boundary migration velocity and driving force is found to be linear in the steady-state regime. Our study shows that the stress distribution depends on the relative misorientation between the grains and the nature of the applied load. As a consequence, the mechanism of grain boundary migration is different when the load is applied parallel or perpendicular to a grain boundary. The bulk mechanical driving force for grain boundary migration is provided by the difference in the level of stress in the adjoining grains which arise due to difference in elastic moduli. We further show that under certain conditions an applied stress may act as a precursor to abnormal grain growth.

One-step and iterative thermo-mechanical treatments to enhance Σ3 n boundaries in a Ti-modified austenitic stainless steel

The article discusses the results of a study on low-strain thermo-mechanical (one-step and iterative) processing to enhance Σ3 n boundaries in a Ti-modified austenitic stainless steel (alloy D9). Solution annealed (SA) specimens were subjected to 10% thickness reduction by rolling followed by annealing at 1173, 1223, and 1273 K for 0.5, 1, and 2 h. Anomalous grain growth with moderate increase in Σ3 n boundaries was observed after annealing at 1,173 K for 0.5 to 2 h. Prolific multiple twinning with minimum deviation of Σ3 and Σ9 boundaries from ideal orientation was achieved after annealing at 1,273 K for 0.5 to 2 h. A significant disruption in random boundary connectivity was obtained in these conditions due to the presence of large number of Σ3-Σ3-Σ9/Σ3-Σ9-Σ27 triple junctions. Iterative processing (up to 4 cycles) employing 10% thickness reduction followed by annealing at 1,273 K for 0.5 h revealed fluctuations in the evolution of Σ3 boundaries. The Σ3 fraction increased after 2nd and 4th iteration and there is a drop after 3rd iteration. This was attributed to the increased driving force for grain boundary migration due to dislocation pile-up at twin boundaries during earlier iterations. A two step iterative processing comprising of 10% deformation followed by annealing at 1,273 K for 0.5 h is the recommended thermo-mechanical processing to achieve enhanced fraction of Σ3 n boundaries (~73%) in alloy D9.