Non-equilibrium Grain Boundaries Research Articles

A multiscale FEM-MD coupling method for investigation into atomistic-scale deformation mechanisms of nanocrystalline metals under continuum-scale deformation

This study aims to develop a multiscale bridging method for investigating nanocrystalline metals based on macro-scale deformation. For this purpose, we propose a hierarchical multiscale computational method that can focus on some of the elements in a finite element model for scale bridging to atomistic-scale models. This method assumes that atomistic-scale nanocrystalline models are related to the integration points in a finite element and deform based on the macro-scale deformation. Nanocrystalline aluminum was chosen for the validation of the multiscale method. The finite element method (FEM) and the molecular dynamics (MD) method were used for continuum-scale and atomistic-scale simulations, respectively. We utilized the notion of the CauchyBorn rule (CBR) for communicating deformation information from the continuum scale to the atomistic scale. We studied three different cases with two nanocrystalline models and two loading cases to compare differences resulting from crystal structures and loading. Based on the crystal structure change during relaxation, nonequilibrium grain boundaries (NEGBs) were shown to play a role as deformation mechanisms in the plastic regime and induce the onset and migration of crystal defects, including deformation twins, as reported in the experiment. Furthermore, the crystal orientation dependence of the onset of crystal defects was confirmed by the comparison of the results from the two different nanocrystalline models. The qualitative agreement of the results with experimental observations is also confirmed. The proposed ‘FEM-MD’ method can bridge a large-scale gap, for example, from a nano-scale to a continuum-scale such that an MD model can be coupled to a millimeter or centimeter scale compared to other embedding methods. The present method is ideal for investigating the dislocation behavior of nanocrystalline materials, which contain multi-grained nanostructure at finite temperature, undergoing various loading scenarios at the macro-scale.

Interaction between disclinated non-equilibrium grain boundaries and radiation-induced interstitial/vacancy in tungsten

Experimental works show that there are plenty of disclinated non-equilibrium grain boundaries (GBs) in polycrystalline materials obtained by the severe plastic deformation method. How these GBs affect the irradiation-induced defects is still an open question. In the present work, molecular dynamics simulation was used to investigate the interaction between disclinated non-equilibrium GBs and irradiation-induced interstitial/vacancy in tungsten. There exists a long-range stress field around the disclinated non-equilibrium GBs. Such a long-range stress field leads to strong interaction between interstitial/vacancy and the GB. The interaction energy calculations suggest that interstitial and vacancy can be attracted strongly by non-equilibrium GBs containing negative and positive disclinations, respectively. This unique interaction behavior is further confirmed by diffusion of interstitials/vacancies near these GBs. The present work clearly demonstrates that disclinated non-equilibrium GBs are stronger irradiation-induced defect sinks than their equilibrium counterparts. So increasing the proportion of disclinated non-equilibrium GBs may be an effective way to develop new-generation irradiation-resistant materials.

Disclination-dislocation based model for grain boundary stress field evolution due to slip transmission history and influence on subsequent dislocation transmission

This work demonstrates how the structure of a grain boundary (GB) and its evolution due to slip transmission history influences subsequent dislocation transmission. First, a model for the evolution of stress fields within grain boundaries that accounts for the effects of coherent dislocation transmission is introduced. Starting with a disclination-based construct of GBs at minimum energy (equilibrium), the model describes the evolution of the GB stress field to a state characteristic of excess energy (non-equilibrium) due to the incorporation of residual Burgers vector content following sequential slip transmission events. Several essential features of this model are verified via molecular dynamics simulations of lattice dislocation absorption. Second, this model is implemented into a discrete dislocation dynamics (DDD) code and simulations are performed to understand the influence of Non-equilibrium GB stress fields, conditioned by the slip transmission history, on subsequent dislocation transmission. DDD simulations reveal that the critical resolved stress necessary for slip propagation can be reduced by ∼80% with continued absorption of residual dislocation content. Moreover, DDD simulations prove that a comprehensive consideration of both the binding and driving stresses, and the evolution of the transmission configuration is necessary to quantify the influence of the mechanical state of the GB on slip propagation. Overall, this work provides important insights into the role of GB structure evolution, conditioned by prior deformation history, on intergranular plasticity.

CALPHAD-informed phase-field modeling of grain boundary microchemistry and precipitation in Al-Zn-Mg-Cu alloys

The grain boundary (GB) microchemistry and precipitation behaviour in high-strength Al-Zn-Mg-Cu alloys has an important influence on their mechanical and electrochemical properties. Simulation of the GB segregation, precipitation, and solute distribution in these alloys requires an accurate description of the thermodynamics and kinetics of this multi-component system. CALPHAD databases have been successfully developed for equilibrium thermodynamic calculations in complex multi-component systems, and in recent years have been combined with diffusion simulations. In this work, we have directly incorporated a CALPHAD database into a phase-field framework, to simulate, with high fidelity, the complex kinetics of the non-equilibrium GB microstructures that develop in these important commercial alloys during heat treatment. In particular, the influence of GB solute segregation, GB diffusion, precipitate number density, and far-field matrix composition, on the growth of a population of GB η-precipitates, was systematically investigated in a model Al-Zn-Mg-Cu alloy of near AA7050 composition. It is shown that the GB solute distribution in the early stages of ageing was highly heterogeneous and strongly affected by the distribution of GB η-precipitates. Significant Mg and Cu GB segregation was predicted to remain during overageing, while Zn was rapidly depleted. This non-trivial GB segregation behaviour markedly influenced the resulting precipitate morphologies, but the overall precipitate transformation kinetics on a GB were relatively unaffected. Furthermore, solute depletion adjacent to the GB was largely determined by Zn and Mg diffusion, which will affect the development of precipitate free zones during the early stages of ageing. The simulation results were compared with scanning transmission electron microscopy and atom probe tomography characterisation of alloys of the similar composition, with good agreement.

Role of equilibrium and non-equilibrium grain boundary stress fields on dislocation transmission

This study presents an approach to investigate the influence of intergranular stresses induced by equilibrium and non-equilibrium grain boundaries (GBs) on dislocation transmission via the discrete dislocation dynamics simulation method. First, a disclination-based construct is used to describe the equilibrium intergranular stress fields of two symmetric tilt GBs. Then, slip transfer through these GBs is simulated via an algorithm that predicts dislocation transmission considering geometric and plastic dissipation criteria. Results show that the locations for transmission and the glide of residual dislocations are strongly correlated with GB stresses. Next, ordered structural defects in the equilibrium GBs are modified using a new approach to simulate disruptions in GB structure caused by dislocation transmission, creating non-equilibrium GBs. Slip transmission preferentially occurs near the non-equilibrium defects, illustrating the effect of modified GB screening characteristics due to prior dislocation transmission. The present work provides a basis for physically representative modeling of GBs and dislocation-GB phenomena in mesoscale simulations of polycrystalline plasticity.

Vacancy release upon heating of an ultrafine grain Al-Zr alloy: In-situ observations and theoretical modeling

The present study demonstrates the direct observation of pore formation by rapid release of vacancies in ultrafine grain (UFG) Al-0.4at%Zr alloy during in-situ annealing in a scanning transmission electron microscope. The ultrafine grain structure was preliminary obtained by high pressure torsion processing at a hydrostatic pressure of 6 GPa up to 10 revolutions. In-situ annealing reveals the rapid formation of pores in triple junctions (TJs) of grain boundaries (GBs) during the first few minutes followed by their subsequent slow resorption with the complete disappearance of some of them. During annealing, no noticeable displacement of GBs is observed. By considering the evolution of non-equilibrium GBs inherited by the severe plastic deformation, a theoretical description is suggested which describes: (i) the pore formation at disclinated TJs as a thermodynamically driven process of free volume dissolution through generation of vacancies, which then migrate to the TJs and coagulate at them with growth of the pores diminishing the strain energy of the TJ disclinations, and (ii) further decrease of the TJ disclination strain energy through the climb of extrinsic GB dislocations towards the disclinated TJs, accompanied with dissolution of the TJ pores by emission of vacancies which provide the dislocation climb. The rapid release of excess vacancies during the early stage of heat treatment is consequently identified as a phenomenon responsible for accelerated atomic mobility. This work hence provides a new perspective for understanding the accelerated precipitation kinetics observed in severely deformed alloys.

The role of non-equilibrium grain boundary in micro-deformation and failure mechanisms of Bicrystal structural tungsten

The molecular dynamics (MD) simulation is performed to obtain the mechanical properties and plastic deformation mechanism of bicrystal structural tungsten (BS W) with equilibrium grain boundaries (EGBs) and non-equilibrium grain boundaries (NEGBs) under tension at different strain rates. The BS W with NEGBs has shown excellent comprehensive mechanical properties, and its yield strength is only about 1.5 Gpa (~10%) lower than that of the BS W with EGBs. The yield strain of BS W with NEGBS is about double than that with EGBs. The micro-deformation mechanisms for BS W with NEGBs under tension are dislocation emission and movement, GBs interaction, and phase transition. However, the failure modes of BS W with EGBs are intergranular brittle fracture of crack near the GBs, and the strain rate has little effect on the fracture. The phase transition mechanism for BS W with NEGBs under the tension loading strain rate of 0.0001 ps−1 is atomic slippage, but that of 0.001 ps−1 is stress concentration induced quasi-reconstructive phase transition. At the loading strain rate of 0.0001 ps−1, dislocation emission and movement to the GBs would form the non-slippable crack dislocations for crack initiation. However, at the loading strain rate of 0.001 ps−1, the crack propagation is considered as a zigzag-shaped form on account that the phase transition induced stress relaxation. The NEGBs could improve plasticity without sacrificing strength, providing a theoretical method for nano-structure design, material modification, and sustainable material plain.

Molecular dynamics simulation of the effect of cyclic stresses on nanocrystals with nonequilibrium grain boundaries: the role of the grain size

Grain boundaries (GBs) in bulk nanostructured materials processed by severe plastic deformation (SPD) have a nonequilibrium structure caused by extrinsic grain boundary dislocations (EGBDs) absorbed during deformation. Under external influences (annealing or cyclic straining) these GBs relax towards equilibrium resulting in a release of the excess energy of nanomaterials. Using our earlier developed method, atomic models of nanocrystals with nonequilibrium GBs having grain sizes of 10, 15, and 20 nm are constructed and relaxed by molecular dynamics. Then, the effect of oscillating tension-compression stresses with amplitudes of 2, 3 and 4 GPa on the systems thus obtained is simulated. Relaxation of nonequilibrium GBs by dislocation emission is found and the effect is shown to be independent of the grain size.

Microstructure and strengthening model of Al-3%Mg alloy in a heat treated state subjected to ECAP process

Purpose: The aim of this paper is to investigate the microstructure evolution of a heat treated Al-3%Mg aluminium alloy subjected to the ECAP (equal channel angular pressing process). Design/methodology/approach: Commercial Al-3%Mg alloy subjected to the solution treatment followed by an artificial aging was subjected to the 6 ECAP passes using a processing route Bc. Then the microstructure investigations using a light microscopy, scanning electron microscopy and transmission electron microscopy were carried out. Additionally the XRD technique was used to calculate lattice micro strain and dislocation density. Findings: The experimental results showed that the obtained microstructure is refined by mutual interactions of shear and microshear bands. The TEM investigation revealed typical for deformed aluminium alloys structure constituents such as dislocation-free grains, nonequilibrium grain boundaries, dislocation cell and (sub)grain structures. Research limitations/implications: The presented investigation results were carried out on samples, not on final products. Practical implications: Current research is moving towards to develop high strength material having a ultra-fine grained microstructure and increased mechanical strength. Originality/value: The paper focuses on the microstructure characterization of ECAP processed Al-3%Mg aluminium alloy. The relationship between the obtained microstructure and its contribution to the Yield strength is investigated.

Molecular Dynamics Simulation of Nonequilibrium Grain Boundaries in Ultrafine-Grained Nickel and their Relaxation under Cyclic Loading

Atomistic simulations of the structure, energy and relaxation under the action of high frequency cyclic straining are carried out for columnar nickel nanocrystals with [112] column axis, the grain boundaries (GBs) of which are in a nonequilibrium state caused by the presence of extrinsic grain boundary dislocations (EGBDs). A special method of introducing EGBDs is used to create initial structures with nonequilibrium GBs. Energy of GBs as a function of the degree of nonequilibrium is evaluated and qualitatively compared to the results of dislocation and disclination modeling. It is shown that under loading by symmetrically oscillating stresses the nonequilibrium GBs generate lattice dislocations, which travel across the grains and are absorbed by opposite GBs thus resulting in a relaxation of the structure, long-range stress fields and the energy of GBs.

Nonequilibrium grain boundaries and their relaxation under oscillating stresses in columnar nickel nanocrystals studied by molecular dynamics

Atomic structure of columnar nickel nanocrystals with [1 1 2] column axis having nonequilibrium grain boundaries (GBs) containing extrinsic grain boundary dislocations (EGBDs) and its evolution under oscillating stresses are studied by molecular dynamics method. Energy of GBs as a function of the degree of nonequilibrium is evaluated. It is found that under loading by symmetrically oscillating stresses the nonequilibrium GBs generate lattice dislocations, which travel across the grains and are absorbed by opposite GBs thus resulting in a relaxation of the structure, long-range stress fields and the energy of GBs.

A method for the construction of initial structures for molecular dynamics simulations of nanocrystals with nonequilibrium grain boundaries containing extrinsic dislocations

A method for the construction of initial atomic models of nanocrystals with extrinsic grain boundary dislocations (EGBDs) in grain boundaries (GBs) for molecular dynamics (MD) simulations is developed. The method is realized for f.c.c. nanocrystals with columnar grains having common crystallographic axis [112] parallel to the column axis and thus divided only by [112] tilt GBs. This system is convenient for studies of interactions between GBs and lattice dislocations, since each grain can be deformed by edge dislocations of only one slip system, which have lines parallel to the [112] axis. In order to introduce extrinsic dislocations to the boundaries of a selected grain, its contour is assumed to be strained by a given shear strain  so that a contour of a freely sheared grain is formed. This contour is filled in by atoms of a f.c.c. lattice with [112] direction parallel to the column axis and then the grain thus formed is subjected to an elastic shear strain -. This results in a deformed grain having the original shape, on the boundaries of which precursors of EGBDs are formed. In order to prevent these precursors from spontaneous annihilation during MD relaxation, one can temporarily fix GB atoms, or apply a proper external stress, or do both. A case study is carried out using two different protocols of MD relaxation to determine atomic structures and energies of nonequilibrium GBs.

Achieving Radiation Tolerance through Non-Equilibrium Grain Boundary Structures

Many methods used to produce nanocrystalline (NC) materials leave behind non-equilibrium grain boundaries (GBs) containing excess free volume and higher energy than their equilibrium counterparts with identical 5 degrees of freedom. Since non-equilibrium GBs have increased amounts of both strain and free volume, these boundaries may act as more efficient sinks for the excess interstitials and vacancies produced in a material under irradiation as compared to equilibrium GBs. The relative sink strengths of equilibrium and non-equilibrium GBs were explored by comparing the behavior of annealed (equilibrium) and as-deposited (non-equilibrium) NC iron films on irradiation. These results were coupled with atomistic simulations to better reveal the underlying processes occurring on timescales too short to capture using in situ TEM. After irradiation, NC iron with non-equilibrium GBs contains both a smaller number density of defect clusters and a smaller average defect cluster size. Simulations showed that excess free volume contribute to a decreased survival rate of point defects in cascades occurring adjacent to the GB and that these boundaries undergo less dramatic changes in structure upon irradiation. These results suggest that non-equilibrium GBs act as more efficient sinks for defects and could be utilized to create more radiation tolerant materials in future.

Influence of grain boundary state on electrical resistivity of ultrafine grained aluminium

An ultrafine grained (UFG) structure has been obtained in commercial purity Al by high-pressure torsion (HPT). Changes in microhardness and electrical resistivity of the UFG material after annealing at various temperatures within a range of 363–673 K have been investigated in correlation with the microstructure evolution. It has been shown that annealing at 363 K leads to substantial decrease in the electrical resistivity while keeping high microhardness level and approximately the same average grain size. The contributions from the various microstructural units (vacancies, dislocations, grain boundaries (GBs)) to the electrical resistivity were analysed. It was shown for the first time that a non-equilibrium state associated with strain-distorted grain boundary (GB) structure strongly affects electrical resistivity of UFG Al. The resistivity of non-equilibrium GBs in UFG structure formed by HPT was evaluated to be at least 50% higher than the resistivity of the thermally equilibrium GBs in a coarse-grained structure.

Mechanism of hot ductility loss in C–Mn steels based on nonequilibrium grain boundary segregation of impurities

Abstract

Microstructure evolution and dislocation configurations in nanostructured Al–Mg alloys processed by high pressure torsion

Microstructure evolution and dislocation configurations in nanostructured Al–Mg alloys processed by high pressure torsion (HPT) were analyzed by transmission electron microscopy (TEM) and high-resolution TEM (HRTEM). The results show that the grains less than 100 nm have sharp grain boundaries (GBs) and are completely free of dislocations. In contrast, a high density of dislocation as high as 1017 m−2 exists within the grains larger than 200 nm and these larger grains are usually separated into subgrains and dislocation cells. The dislocations are 60° full dislocations with Burgers vectors of ½<110> and most of them appear as dipoles and loops. The microtwins and stacking faults (SFs) formed by the Shockley partials from the dissociation of both the 60° mixed dislocation and 0° screw dislocation in ultrafine grains were simultaneously observed by HRTEM in the HPT Al–Mg alloys. These results suggest that partial dislocation emissions, as well as the activation of partial dislocations could also become a deformation mechanism in ultrafine-grained aluminum during severe plastic deformation. The grain refinement mechanism associated with the very high local dislocation density, the dislocation cells and the non-equilibrium GBs, as well as the SFs and microtwins in the HPT Al–Mg alloys were proposed.

Non-equilibrium grain boundaries with excess energy in graphene

Exploring an approach to grain boundary (GB) mesoscopic structure in 3D polycrystals, we develop a model description for equilibrium and non-equilibrium states of GBs in graphene. Non-equilibrium states of GBs in graphene are analyzed for the first time. On the base of this model, dependence of total energy for symmetric GBs on the misorientation angle, E(θ), in graphene was calculated. It was found that for the same average misorientation angle the energy in a non-equilibrium state of a GB in graphene can significantly exceed the energy in the equilibrium state. In graphene, the GB energy depends to a greater extent on the deviation from the equilibrium state than on the misorientation angle. It is proposed to account for the presence of non-equilibrium GBs in the explanations of unusual physical properties of graphene.

Grain Boundary Structure of Al–Mg Alloys Processed by High Pressure Torsion

The structure of dislocation and grain boundary(GB) in nanostructured Al–Mg alloys processed by high pressure torsion(HPT) was characterized by means of transmission electron microscopy(TEM) and high-resolution TEM(HRTEM).The results show that the grains less than 100 nm have sharp GBs and are completely free of dislocations.In contrast,a high density of dislocation as high as 1017m- 2 exists within the grains larger than 200 nm and these larger grains are usually separated into subgrains and dislocation cells.These dislocations appear as dipoles and loops.Different GB structures including low/high angle non- equilibrium GBs,low angle equilibrium GBs and high angle Σ 9 equilibrium boundaries are characterized by HRTEM.The roles of the very high local dislocation density,the dislocation cells and the non-equilibrium GBs in grain refinement during HPT are analyzed and the refinement mechanisms associated with these structural features have been proposed.

Unified mechanism of intergranular embrittlement based on non-equilibrium grain boundary segregation

The review is aimed at presenting a unified approach in understanding the mechanism of non-equilibrium grain boundary segregation, which can satisfactorily describe the three types of intergranular embrittlement, namely, reverse temper embrittlement of steels, intergranular corrosion embrittlement of stainless steels and intermediate temperature embrittlement of metals and alloys. The review starts with a broad perspective of non-equilibrium grain boundary segregation, including thermally induced non-equilibrium grain boundary segregation and stress induced non-equilibrium grain-boundary segregation. Next, it focuses on the recent progress made in the non-equilibrium grain boundary segregation, including (1) critical time, (2) segregation peak temperature, (3) segregation peak temperature movement for thermally induced and stress induced non-equilibrium grain boundary segregation, and (4) the effect of temperature difference on thermally-induced non-equilibrium grain boundary segregation. Next, the attention is focused on the grain boundary coverage of elements and intergranular embrittlement phenomena. Three types of intergranular embrittlement is analysed in terms of (1) the ductility healing effect induced by the critical time, (2) embrittlement peak or ductility trough induced by the segregation peak temperature, (3) embrittlement peak or ductility trough movement induced by the segregation peak temperature movement and (4) widening and deepening of ductility trough induced by differences in temperature. These experimental phenomena concerning the three types of intergranular embrittlement are consistent with the models of thermally induced and stress induced non-equilibrium grain boundary segregations of impurities, instead of precipitation or equilibrium grain boundary segregation. Towards the end, we visit the subject of grain boundary segregation and associated embrittlement process from the viewpoint of fracture resistance and briefly discuss different perspectives that are of practical significance.

Structure evolution and thermal stability of SMAT-derived nanograined layer on Ti–25Nb–3Mo–3Zr–2Sn alloy at elevated temperatures

A nanocrystalline layer, which consists of pure β phase with average grain size of about 30nm on Ti–25Nb–3Mo–3Zr–2Sn alloy, was fabricated by surface mechanical attrition treatment (SMAT). The microstructure evolution, phase transitions and thermal stability of the nanocrystalline layer during isochronal annealing at temperatures of 300–600°C were investigated by XRD and TEM. During annealing, the nanocrystalline layer underwent recovery, recrystallization and significant grain growth. Recovery occurs at temperatures from 300 to 400°C resulting in strain relaxation, dislocation annihilation and a very limited growth of β grains dominated by re-ordering of grain boundaries (GBs). α Precipitates start to precipitate along the β GBs at 350°C, which exhibit equiaxed morphology with size less than 10nm. Recrystallization proceeds at a higher temperature up to 450°C leading to a reduction of β grain size. Due to the pinning effect of the α precipitates, β grains sizes can be maintained less than 100nm until the annealing temperature increased to 550°C, e.g., 0.41 Tm (melting temperature in K), above which significant grain growth occurs to overstep nanocystalline scale, and the growth activation energy of β grains is calculated as 40.8kJ/mol. The abnormal low value is caused by the nonequilibrium GBs of β grains in the as-SMATed surface layer, which increase atomic mobility even in the presence of pinning effect of the α precipitates on the β GBs.