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Probing fundamental deformation mechanisms and trends during decohesion across random high angle grain boundaries
Abstract
The influence of grain boundaries (GBs) on the mechanical behavior and deformation of crystalline materials is well documented. Specifically, intergranular failure within the microstructure often is due to GB fracture or decohesion under load. By analyzing the incipient failure response of individual GBs (e.g., decohesion), as a function of GB character, a more fundamental understanding of microstructure failure can be uncovered. Accordingly, this work leverages atomistic modeling and simulations of GBs in Al to ascertain the governing role of GB character on decohesion behavior. A range of GB characters are studied by using a newly developed GB structure database to develop trends and identify fundamental decohesion behaviors using macroscopic GB descriptors (e.g., energy, misorientation, and excess volume). However, we find that no clear correlations exist between GB decohesion and these descriptors, indicating that the origins of decohesion are missed by GB descriptors that ignore the underlying spectrum of atomic environments that compose a GB. Our results further indicate that GB decohesion behavior may be driven by atomic environments and/or dynamics specific to individual GBs, potentially independent of the macroscopic descriptions of GBs commonly employed for identification and model development.
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We report a novel crystal growth technique for manipulating the grain structure of directionally solidified bicrystals, tricrystals, and other higher order oligocrystals. Controlling both the direction of local heat flux and the thermodynamic forces acting on the grain boundary, we can continuously vary grain boundary position and orientation, a level of control not possible using traditional processing strategies. This processing method can now specify many combinations of the five crystallographic grain boundary parameters in a single specimen, meaning large portions of both the grain boundary and triple junction parameter spaces can be sampled quickly and efficiently.
We use atomistic simulations to investigate grain boundary (GB) phase transitions in el- emental body-centered cubic (bcc) metal tungsten. Motivated by recent modeling study of grain boundary phase transitions in [100] symmetric tilt boundaries in face-centered cu- bic (fcc) copper, we perform a systematic investigation of [100] and [110] symmetric tilt high-angle and low-angle boundaries in bcc tungsten. The structures of these boundaries have been investigated previously by atomistic simulations in several different bcc metals including tungsten using the the {\gamma}-surface method, which has limitations. In this work we use a recently developed computational tool based on the USPEX structure prediction code to perform an evolutionary grand canonical search of GB structure at 0 K. For high-angle [100] tilt boundaries the ground states generated by the evolutionary algorithm agree with the predictions of the {\gamma}-surface method. For the [110] tilt boundaries, the search predicts novel high-density low-energy grain boundary structures and multiple grain boundary phases within the entire misorientation range. Molecular dynamics simulation demonstrate that the new structures are more stable at high temperature. We observe first-order grain boundary phase transitions and investigate how the structural multiplicity affects the mechanisms of the point defect absorption. Specifically, we demonstrate a two-step nucleation process, when initially the point defects are absorbed through a formation of a metastable GB structure with higher density, followed by a transformation of this structure into a GB interstitial loop or a different GB phase.
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.
Nanoindentation has been recently used to measure the mechanical properties of polycrystalline graphene. However, the measured failure loads are found to be scattered widely and vary from lab to lab. We perform molecular dynamics simulations of nanoindentation on polycrystalline graphene at different sites including grain center, grain boundary (GB), GB triple junction, and holes. Depending on the relative position between the indenter tip and defects, significant scattering in failure load is observed. This scattering is found to arise from a combination of the non-uniform stress state, varied and weakened strengths of different defects, and the relative location between the indenter tip and the defects in polycrystalline graphene. Consequently, the failure behavior of polycrystalline graphene by nanoindentation is critically dependent on the indentation site, and is thus distinct from uniaxial tensile loading. Our work highlights the importance of the interaction between the indentation tip and defects, and the need to explicitly consider the defect characteristics at and near the indentation site in polycrystalline graphene during nanoindentation.
This work concerns a study of the effects of plasticity on the mechanism of intergranular cracking assisted by hydrogen induced embrittlement in an aluminium alloy. Here, tensile specimens charged with hydrogen were used to investigate quantitatively the effect of plastic deformation on the mechanism of intergranular crack initiation at the scale of the individual grains. An experimental procedure was set up to monitor the evolution of surface strain fields on in situ tested SEM notched specimens using digital image correlation techniques. In addition, measurements of the associated crystal orientation evolution at the micron scale were carried out using electron backscatter diffraction (EBSD). These measurements were then compared with finite element predictions of the local strain fields on the observed regions of the in situ specimen. The numerical predictions were obtained using a dislocation mechanics-based crystal plasticity model to describe the constitutive behaviour of each individual grain. The crystallographic grain orientations of the region of interest were discretised for the finite element analyses from EBSD maps. From this study, it was found that intergranular cracking due to hydrogen embrittlement in the Al alloy is locally triggered by high tensile grain boundary tractions, here estimated to be 170 ± 35 MPa. As importantly, the results also revealed that the conditions needed for grain boundary microcracks to initiate are greatly affected by the deformation of neighbouring grains: i.e. it was established that boundaries between two “hard” grains, inside a neighbourhood of “softer” deformed grains, are the first to fail.
In this article, we report on the application of our spherical nanoindentation data analysis protocols to study the mechanical
response of grain boundary regions in as-cast and 30% deformed polycrystalline Fe–3%Si steel. In particular, we demonstrate
that it is possible to investigate the role of grain boundaries in the mechanical deformation of polycrystalline samples by
systematically studying the changes in the indentation stress–strain curves as a function of the distance from the grain boundary.
Such datasets, when combined with the local crystal lattice orientation information obtained using orientation imaging microscopy,
open new avenues for characterizing the mechanical behavior of grain boundaries based on their misorientation angle, dislocation
density content near the boundary, and their propensity for dislocation source/sink behavior.
Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Σ5 and Σ13 systems with a boundary plane rotated about the 100 misorientation axis, and the Σ9 and Σ11 systems rotated about the 110 misorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Σ5 and Σ13 systems in the 100 system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Σ9 and Σ11 systems in the 110 system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Σ9 (221) and Σ11 (332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index {111} and {110} planes bounding the interface region.
It is well established from molecular dynamics simulations that grain boundaries in nanocrystalline samples serve as sources of dislocations. In this work, we use molecular dynamics simulations to study the mechanisms associated with dislocation nucleation from bicrystal [0 0 1] interfaces in aluminum. Three interface misorientations are studied, including the Σ5 (3 1 0) boundary, which has a high density of coincident atomic sites. Molecular dynamics simulations show that full dislocation loops are nucleated from each interface during uniaxial tension. After the second partial dislocation is emitted, a ledge remains within the interface at the intersection of the slip plane and the bicrystal boundary. A disclination dipole model is proposed for the structure of the distorted interface accounting for local lattice rotations and the ledge at the nucleation site.
The dynamics and energetics of intergranular crack growth along a flat grain boundary in aluminum is studied by a molecular-dynamics
simulation model for crack propagation under steady-state conditions. Using the ability of the molecular-dynamics simulation
to identify atoms involved in different atomistic mechanisms, it was possible to identify the energy contribution of different
processes taking place during crack growth. The energy contributions were divided as: elastic energy—defined as the potential
energy of the atoms in fcc crystallographic state; and plastically stored energy—the energy of stacking faults and twin boundaries;
grain-boundary and surface energy. In addition, monitoring the amount of heat exchange with the molecular-dynamics thermostat
gives the energy dissipated as heat in the system. The energetic analysis indicates that the majority of energy in a fast
growing crack is dissipated as heat. This dissipation increases linearly at low speed, and faster than linear at speeds approaching
1/3 the Rayleigh wave speed when the crack tip becomes dynamically unstable producing periodic dislocation bursts until the
crack is blunted.
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The extrinsic indentation size effect (ISE) is utilized to analyze the depth-dependent hardness for Berkovich indentation of non-uniform dislocation distributions with one and two dimensional deformation gradients and is then extended to indentation results at grain boundaries. The role of the Berkovich pyramid orientation and placement relative to the grain boundary on extrinsic ISE is considered in terms of slip transmission at yield and plastic incompatibility during post-yield deformation. The results are interpreted using a local dislocation hardening mechanism originally proposed by Ashby, combined with the Hall-Petch equation. The Hall-Petch coefficient determined from the extrinsic ISE of the grain boundary is found to be consistent with the published values for pure Fe and mild steel. A simple, linear continuum strain gradient plasticity model is used to further analyze the results to include contributions from a non-uniform distribution in plastic strain and dislocation density.
Atomistic simulations are employed to demonstrate the existence of a well-defined thermodynamic phase transformation between grain boundary (GB) phases with different atomic structures. The free energy of different interface structures for an embedded-atom-method model of the Σ5(310)[001] symmetric tilt boundary in elemental Cu is computed using the nonequilibrium Frenkel-Ladd thermodynamic integration method through molecular dynamics simulations. It is shown that the free-energy curves predict a temperature-induced first-order interfacial phase transition in the GB structure in agreement with computational studies of the same model system. Moreover, the role of vibrational entropy in the stabilization of the high-temperature GB phase is clarified. The calculated results are able to determine the GB phase stability at homologous temperatures less than 0.5, a temperature range particularly important given the limitation of the methods available hitherto in modeling GB phase transitions at low temperatures. The calculation of GB free energies complements currently available 0 K GB structure search methods, making feasible the characterization of GB phase diagrams.
Grain boundaries play a pivotal role in defect evolution and accommodation within materials. Irradiated metals have been observed to form defect denuded zones in the vicinity of grain boundaries. This is especially apparent in nanocrystalline metals, which have an increased grain boundary concentration, as compared to their polycrystalline counterparts. Importantly, the effect of individual grain boundaries on microstructural damage tolerance is related to the character or structural state of the grain boundary. In this work, the damage accommodation behavior of a variety of copper grain boundaries is studied using atomistic simulations. Damage accumulation behavior is found to reach a saturation point where both the free volume and energy of a grain boundary fluctuate within an elliptical manifold, which varies in size for different boundary characters. Analysis of the grain boundaries shows that extrinsic damage accommodation occurs due to localized atomic shuffling accompanied by free volume rearrangement within the boundary. Continuous damage accumulation leads to altered atomic structural states that oscillate around a mean non-equilibrium state, that is energetically metastable. Our results suggest that variation of grain boundary behavior, both from equilibrium and under saturation, is directly related to grain boundary equilibrium energy and some boundaries have a greater propensity to continually accommodate damage, as compared to others.
Interfaces, free or internal, greatly influence the physical properties and stability of materials microstructures. Of particular interest are the processes that occur due to anisotropic interfacial properties. In the case of grain boundaries
(GBs) in metals, several experimental observations revealed that an initially flat GB may facet into hill-and-valley structures with well defined planes and corners/edges connecting them. Herein, we present a diffuse interface model that is capable of accounting for strongly anisotropic
GB properties and capturing the formation of hill-and-valley morphologies. The hallmark of our approach is the ability to independently examine the various factors affecting GB faceting and subsequent facet coarsening. More specifically, our formulation incorporates higher order expansions to account for the excess energy due to facet junctions and their non-local interactions. As a demonstration of the modeling capability, we consider the Σ5 〈001〉 tilt GB in body-centered-cubic iron, where faceting along the {210} and {310} planes was experimentally observed. Atomistic calculations were utilized to determine the inclination-dependent GB energy, which was then used as an input in our model. Linear stability analysis and simulation results highlight the role of junction energy and associated non-local interactions on the resulting facet length scales. Broadly speaking, our modeling approach provides a general framework to examine the microstructural stability of polycrystalline systems with highly anisotropic
GBs.
Grain boundary engineered materials are of immense interest for their corrosion resistance, fracture resistance, and microstructural stability. This work contributes to a larger goal of understanding both the structure and thermodynamic properties of grain boundaries vicinal (within ±30°) to the Σ3 (111) ⟨1 -1 0⟩ (coherent-twin) boundary which are found in grain boundary engineered materials. The misoriented boundaries vicinal to the twin show structural changes at elevated temperatures. In the case of nickel this transition temperature is substantially below the melting point and at temperatures commonly reached during processing, making the existence of such boundaries very likely in applications. Thus, the thermodynamic stability of such features is throughly investigated in order to predict and fully understand the structure of boundaries vicinal to twins. Low misorientation angle grain boundaries (|θ|≲ 16°) show distinct ±⅓⟨1 1 1⟩ disconnections which accommodate misorientation in opposite senses. The two types of disconnection have differing low temperature structures which show different temperature dependent behavior with one type undergoing a structural transition at approximately 600 K. At misorientation angles greater than approximately ±16°, the discrete disconnection nature is lost as the disconnections merge into one another. Free energy calculations demonstrate that these high angle boundaries, which exhibit a transition from a planar to a faceted structure, are thermodynamically more stable in the faceted configuration.
In this work, we use novel protocols based on spherical nanoindentation and orientation imaging microscopy (OIM) to quantify the local changes in slip resistances in the grain boundary regions of deformed, polycrystalline aluminum. The new protocols involve the use of the recently developed methods for extracting indentation stress-strain (ISS) curves from raw nanoindentation data in conjunction with the measurement of local microstructure at the indentation site using OIM to study the changes in the local slip resistances as a function of distance from the grain boundaries. Eight grain boundaries were selected for this work such that they included a broad range of boundaries, including low and high (grain-to-grain misorientation) angle boundaries as well as low, moderate, and high deviations in the Taylor factors of the grains on either side of the boundary. It was concluded that there was additional hardening in the grain boundary region when a Taylor ‘soft’ grain was present next to a Taylor ‘hard’ grain. This hardening was consistently observed on the soft grain side with one exception where hardening was observed on both sides of the boundary. A positive correlation was observed between the difference in Taylor factor across the boundary and the amount of hardening on the ‘soft’ grain side. However, no correlation was observed between the grain-to-grain misorientation angle and the extent of hardening at the grain boundary.
A statistical approach combined with molecular dynamics simulations is used to study the influence of hydrogen on intergranular decohesion. This methodology is applied to a Ni σ3(112)[. 11-0] symmetric tilt grain boundary. Hydrogenated grain boundaries with different H concentrations are constructed using an energy minimization technique with initial H atom positions guided by Monte Carlo simulation results. Decohesion behavior is assessed through extraction of a traction-separation relationship during steady-state crack propagation in a statistically meaningful approach, building upon prior work employing atomistic cohesive zone volume elements (CZVEs). A sensitivity analysis is performed on the numerical approach used to extract the traction-separation relationships, clarifying the role of CZVE size, threshold parameters necessary to differentiate elastic and decohesion responses, and the numerical averaging technique. Results show that increasing H coverage at the Ni σ3(112)[. 11-0] grain boundary asymmetrically influences the crack tip velocity during propagation, leads to a general decrease in the work of separation required for crack propagation, and provides a reduction in the peak stress in the extracted traction-separation relationship. The present framework offers a meaningful vehicle to pass atomistically derived interfacial behavior to higher length scale formulations for intergranular fracture.
Although indentation experiments have long been used to measure the hardness and Young's modulus, the utility of this technique in analyzing the complete elastic–plastic response of materials under contact loading has only been realized in the past few years – mostly due to recent advances in testing equipment and analysis protocols. This paper provides a timely review of the recent progress made in this respect in extracting meaningful indentation stress–strain curves from the raw datasets measured in instrumented spherical nanoindentation experiments. These indentation stress–strain curves have produced highly reliable estimates of the indentation modulus and the indentation yield strength in the sample, as well as certain aspects of their post-yield behavior, and have been critically validated through numerical simulations using finite element models as well as direct in situ scanning electron microscopy (SEM) measurements on micro-pillars. Much of this recent progress was made possible through the introduction of a new measure of indentation strain and the development of new protocols to locate the effective zero-point of initial contact between the indenter and the sample in the measured datasets. This has led to an important key advance in this field where it is now possible to reliably identify and analyze the initial loading segment in the indentation experiments.
Two k-sample versions of an Anderson-Darling rank statistic are proposed for testing the homogeneity of samples. Their asymptotic null distributions are derived for the continuous as well as the discrete case. In the continuous case the asymptotic distributions coincide with the (k - 1)-fold convolution of the asymptotic distribution for the Anderson-Darling one-sample statistic. The quality of this large sample approximation is investigated for small samples through Monte Carlo simulation. This is done for both versions of the statistic under various degrees of data rounding and sample size imbalances. Tables for carrying out these tests are provided, and their usage in combining independent one- or k-sample Anderson-Darling tests is pointed out. The test statistics are essentially based on a doubly weighted sum of integrated squared differences between the empirical distribution functions of the individual samples and that of the pooled sample. One weighting adjusts for the possibly different sample sizes, and the other is inside the integration placing more weight on tail differences of the compared distributions. The two versions differ mainly in the definition of the empirical distribution function. These tests are consistent against all alternatives. The use of these tests is two-fold: (a) in a one-way analysis of variance to establish differences in the sampled populations without making any restrictive parametric assumptions or (b) to justify the pooling of separate samples for increased sample size and power in further analyses. Exact finite sample mean and variance formulas for one of the two statistics are derived in the continuous case. It appears that the asymptotic standardized percentiles serve well as approximate critical points of the appropriately standardized statistics for individual sample sizes as low as 5. The application of the tests is illustrated with an example. Because of the convolution nature of the asymptotic distribution, a further use of these critical points is possible in combining independent Anderson-Darling tests by simply adding their test statistics.
The intrinsic brittleness and ductility of intergranular cracks in Cu bicrystals under quasi-static loading conditions are investigated using molecular statics simulations. Central cracks are inserted into nine Σ11 \( [1 \, 1 \, 0] \) tilt grain boundaries with different inclination angles, seven of which are asymmetric, and two of which are symmetric. On the basis of results of molecular statics simulations, critical energy release rates at material failure are calculated using the corresponding continuum counterparts with the finite element method. Simulation results are compared to predictions made on the basis of Rice’s model, and the applicable range of Rice’s model is given in terms of inclination angle. The effects of inclination angle on the mechanical properties of grain boundaries and fracture mechanisms of the corresponding intergranular cracks are analyzed in detail.
The aim of the present work was to investigate the microstructure evolution of the nanostructured Cr/CrN multilayer coatings on titanium Ti6Al4V alloy during indentation. Five types of multilayer (Cr/CrN) × 8 coatings were deposited on Ti6Al4V titanium alloy by the PVD vacuum arc method. The coatings had the same total thickness and number of constituent layers, but differed in the thickness ratio of the Cr and CrN constituent layers (QCr/CrN parameter). The indentation measurements were performed with a Berkovich indenter at loads of 100 mN, 500 mN, and 1 N. The SEM and STEM observations were focused on the cracking behaviour in the CrN layers as well as on the microstructure changes in the ductile Cr layers.
The investigations demonstrate that the applied surface treatment significantly improves the hardness of the titanium alloy. The hardness of the coatings varied in the range 10 to 35 GPa, depending on the thickness ratio of the layers. Observations performed on cross-sections through the indentation zones revealed small radial cracks, which were observed only in the CrN layers. They initiated at the interface and propagated across a given layer, to be arrested at the next interface. The STEM observations also showed microstructure changes in the Cr layers due to the accommodation of plastic deformation. The two main mechanisms of permanent deformation were observed.
Using depth-sensing indentation, a pop-in phenomenon induced by grain boundaries, namely, a sudden indenter displacement jump when indented near a grain boundary segment, was observed in polycrystalline niobium. This grain-boundary type of pop-in occurs at a larger force than the initial elasto-plastic pop-in, which is observed with and without a grain boundary nearby. The experimental results show that this pop-in effect has a close relationship with the misorientation across the grain boundary. The occurrence of this pop-in phenomenon is rationalized in terms of slip transmission across the grain boundary.
Twinning is an important deformation mechanism in hexagonal close-packed (hcp) metals such as Mg, Zr, Ti, and Be. Twinning in hcp materials is a multiscale process that depends on microstructural and mechanical response details at the mesoscale, microscale, and atomic scales. Twinning can generally be understood as a two-step process, a nucleation step followed by propagation. The nucleation of twins is governed by both material details such as the defect configurations at potential nucleation sites within grain boundaries, as well as the highly local mechanical field near grain boundaries. These two factors, the material and mechanical, must align for a successful nucleation event. In this article, we present a stochastic constitutive law for nucleation of twins and describe its implementation into a homogenized crystal plasticity simulation. Twin nucleation relies on the dissociation of grain boundary defects under stress into the required twinning partials. This dissociation is considered to follow a Poisson process where the parameters of the Poisson distribution are related to the properties of the grain boundaries. The rate of the process is a direct function of the local stress concentration at the grain boundary. These stress concentrations are randomly sampled from a distribution calibrated to full-field crystal plasticity simulations.
The competition between intergranular and intragranular fracture is investigated using a bilayer damage model, which incorporates the relevant microstructural features of aluminium alloys with precipitate free zones (PFZ) nearby the grain boundary. One layer represents the grain behaviour: due to precipitation, it presents a high yield stress and low hardening exponent. The other layer represents the PFZ which has the behaviour of a solid solution: it is much softer but with a much higher strain hardening capacity. In both layers, void growth and coalescence is modelled using an enhanced Gurson-type model incorporating the effects of the void aspect ratio and of the relative void spacing. The effects on the ductility (i) of the flow properties of each zone, (ii) of the relative thickness of the PFZ, and (iii) of the particles spacing and volume fraction in the PFZ are elucidated. Comparisons are made with experimental data. Based on the previous analysis, qualitative understanding of trends in the fracture toughness of aluminium alloys can be gained in order to provide a link with the thermal treatment process. (C) 2003 Elsevier Science Ltd. All rights reserved.
The energy of 388 grain boundaries in Al, Au, Cu and Ni were calculated using atomistic simulations. Grain boundary energies in different elements are strongly correlated. Consistent with a dislocation model for grain boundary structure, the boundary energy scales with the shear modulus. Boundaries with substantial stacking fault character scale with the stacking fault energy. There is more scatter in the data for Al, which has a high stacking fault energy, than for the low stacking fault energy elements.
Highly optimized embedded-atom-method (EAM) potentials have been developed for 14 face-centered-cubic (fcc) elements across the periodic table. The potentials were developed by fitting the potential-energy surface (PES) of each element derived from high-precision first-principles calculations. The as-derived potential-energy surfaces were shifted and scaled to match experimental reference data. In constructing the PES, a variety of properties of the elements were considered, including lattice dynamics, mechanical properties, thermal behavior, energetics of competing crystal structures, defects, deformation paths, liquid structures, and so forth. For each element, the constructed EAM potentials were tested against the experiment data pertaining to thermal expansion, melting, and liquid dynamics via molecular dynamics computer simulation. The as-developed potentials demonstrate high fidelity and robustness. Owing to their improved accuracy and wide applicability, the potentials are suitable for high-quality atomistic computer simulation of practical applications.
There is an increasing amount of interest in grain boundary engineering (GBE) to improve the properties of the grain boundary network. In general, research has concentrated on use of a grain boundary misorientation based approach, namely, the coincidence site lattice (CSL), to categorise 'special' boundaries. The present paper presents the case that the specialness of grain boundaries is based on having at least one low index plane at the boundary, rather than because the boundary is a CSL type. It is shown that grain boundary planes play a pivotal role in GBE, and hence, an approach which focuses on the plane is advocated. Some potential routes for 'grain boundary plane engineering' are discussed.
The objective of this research is to use atomistic simulations to investigate the energy and structure of symmetric and asymmetric Σ3 〈110〉 tilt grain boundaries. A nonlinear conjugate gradient algorithm was employed along with an embedded atom method potential for Cu and Al to generate the equilibrium 0 K grain boundary structures. A total of 25 〈110〉 grain boundary structures were explored to identify the various equilibrium and metastable structures. Simulation results show that the Σ3 asymmetric tilt grain boundaries in the 〈110〉 system are composed of only structural units of the two Σ3 symmetric tilt grain boundaries. The energies for the Σ3 grain boundaries are similar to previous experimental and calculated grain boundary energies. A structural unit and faceting model for Σ3 asymmetric tilt grain boundaries fits all of the calculated asymmetric grain boundary structures. The significance of these results is that the structural unit and facet description of all Σ3 asymmetric tilt grain boundaries may be predicted from the structural units of the Σ3 coherent twin and incoherent twin boundaries for both Cu and Al.
The structure of a 110 90° grain boundary in Au is investigated using high-resolution transmission electron microscopy (HRTEM) and atomistic simulation. It consists of coherent segments, exhibiting the extended 9R configuration described by Medlin et al. 1010.
Medlin , DL , Foiles , SM and Cohen , D . 2001 . Acta mater. , 49 : 3689 [CrossRef], [Web of Science ®], [CSA]View all references, with superimposed line defects to accommodate the coherency strain. Two types of defects are observed, crystal dislocations and disconnections, where the latter exhibit step nature in addition to dislocation character. Both types of defect are identified by HRTEM in combination with circuit mapping, and their parameters are shown to be consistent with the topological theory of interfacial defects 77.
Pond , RC . 1989 . Dislocations in Solids , Edited by: Nabarro , FRN . Vol. 8 , Elsevier Science . View all references. Moreover, the misfit-relieving function of observed defect arrays, their influence on interface orientation and the relative rotation of the adjacent crystals is elucidated. During observation, defect decomposition is observed in a manner which conserves Burgers vector and step height. One of the decomposition products is glissile, consistent with the ‘glide/climb’ rules for interfacial defects. This glissile motion is also found by atomistic simulation of the disconnection when an applied strain is imposed. The γ-surface for the interface is calculated and shows that no alternative boundary structure is stable, confirming, consistent with experimental observation, that defects separating different configurations are not feasible.
Atomistic simulations are used to investigate the structure and interfacial free volume of 〈1 1 0〉 symmetric tilt grain boundaries in copper containing the E structural unit from the Σ9(2 2 1)θ = 141.1° grain boundary. In this work, a stereologically-based methodology is used to calculate the grain boundary free volume along with the spacing and connectivity of free volume. After generating the minimum energy equilibrium grain boundary, we examine (i) the grain boundary structure, (ii) a measure of free volume associated with the grain boundary, (iii) spatial correlation functions of the distribution of free volume, and (iv) images of grain boundary free volume distribution. Using the results from these calculations, the influence of free volume spatial distribution and grain boundary structure on dislocation dissociation and nucleation is briefly discussed for boundaries with the E structural unit subjected to tensile loading normal to the interface along with the potential implications of free volume connectivity.
Atomistic simulations are used to investigate how grain boundary structure influences dislocation nucleation under uniaxial tension and compression for a specific class of symmetric tilt grain boundaries that contain the E structural unit. After obtaining the minimum energy grain boundary structure, molecular dynamics was employed based on an embedded-atom method potential for copper at 10 K. Results show several differences in dislocation nucleation with respect to uniaxial tension and compression. First, the average nucleation stress for all 〈1 1 0〉 symmetric tilt grain boundaries is over three times greater in compression than in tension for both the high strain rate and quasistatic simulations. Second, partial dislocations nucleate from the boundary on the {1 1 1} slip plane under uniaxial tension. However, partial and full dislocations nucleate from the boundary on the {1 0 0} and {1 1 1} slip planes under uniaxial compression. The full dislocation nucleation on the {1 0 0} plane for boundaries with misorientations near the coherent twin boundary is explained through the higher resolved shear stress on the {1 0 0} plane compared to the {1 1 1} plane. Last, individual dislocation nucleation mechanisms under uniaxial tension and compression are analyzed. For the vicinal twin boundary under tension, the grain boundary partial dislocation is emitted into the lattice on the same {1 1 1} plane that it dissociated onto. For compression of the vicinal twin, the 1/3〈1 1 1 〉 disconnection is removed through full dislocation emission on the {1 0 0} plane and partial dislocation emission parallel to the coherent twin boundary plane, restoring the boundary to the coherent twin. For the Σ19 boundary, the nearly simultaneous emission of numerous partial dislocations from the boundary result in the formation of the hexagonal close-packed (HCP) phase.
Grain boundary influence on material properties becomes increasingly significant as grain size is reduced to the nanoscale. Nanostructured materials produced by severe plastic deformation techniques often contain a higher percentage of high-angle grain boundaries in a non-equilibrium or energetically metastable state. Differences in the mechanical behavior and observed deformation mechanisms are common due to deviations in grain boundary structure. Fundamental interfacial attributes such as atomic mobility and energy are affected due to a higher non-equilibrium state, which in turn affects deformation response. In this research, atomistic simulations employing a biased Monte Carlo method are used to approximate representative non-equilibrium bicrystalline grain boundaries based on an embedded atom method potential, leveraging the concept of excess free volume. An advantage of this approach is that non-equilibrium boundaries can be instantiated without the need of simulating numerous defect/grain boundary interactions. Differences in grain boundary structure and deformation response are investigated as a function of non-equilibrium state using Molecular Dynamics. A detailed comparison between copper and aluminum bicrystals is provided with regard to boundary strength, observed deformation mechanisms, and stress-assisted free volume evolution during both tensile and shear simulations.
Grain boundary evolution in copper bicrystals is investigated during uniaxial tension at 10 K. Grain boundary structures are generated using molecular statics employing an embedded atom method potential, followed by molecular dynamics simulation at a constant 1 × 109 s−1 strain rate. Interfacial free volume is continuously measured during boundary deformation, and its evolution is investigated both prior to and during grain boundary dislocation nucleation. Free volume provides valuable insight into atomic-scale processes associated with stress-induced grain boundary deformation. Different boundary structures are investigated in this work to analyze the role of interface structure, stress state and initial free volume on dislocation nucleation. The results indicate that the free volume influences interfacial deformation through modified atomic-scale processes, and grain boundaries containing particular free volume distributions show a greater propensity for collective atomic migration during inelastic deformation.
Extended stacking faults, with lengths of up to 10 nm, that join {1 1 1}/{1 1 2} twin-boundary junctions were observed by high-resolution transmission electron microscopy (HRTEM) in gold thin films. Circuit analysis shows that these defects possess a Burgers vector of 1/3〈1 1 1〉. In order to explain the generation of these extended defects, we consider the behavior of 1/3〈1 1 1〉 dislocations at {1 1 1}- and {1 1 2}-type twin boundaries and near {1 1 1}/{1 1 2} twin-boundary junctions using HRTEM observations and theoretical modeling. By establishing the interaction forces that lead to this defect configuration, our analysis shows that the relief of intrinsic strain at the junction corners, which results from the incompatibility of the translation states at the intersecting boundaries, is sufficient to stabilize the stacking fault extension. Because grain–boundary junctions possess intrinsic strain fields whenever they join boundaries with incompatible translation states, similar mechanisms for stacking fault emission may arise between other closely spaced grain–boundary junctions.
The Open Visualization Tool (OVITO) is a new 3D visualization software designed for post-processing atomistic data obtained from molecular dynamics or Monte Carlo simulations. Unique analysis, editing and animations functions are integrated into its easy-to-use graphical user interface. The software is written in object-oriented C++, controllable via Python scripts and easily extendable through a plug-in interface. It is distributed as open-source software and can be downloaded from the website http://ovito.sourceforge.net/.
We analyze a thin (~1nm) hexagonal-close-packed (HCP) intergranular layer at a 29° 〈110〉 tilt grain boundary in gold. Our
analysis, which is based on HRTEM observations and atomistic calculations, shows that this boundary consists of a dense array
of 60° 1/2〈110〉 crystal lattice dislocations that are distributed one to every two {111} planes. These dislocations dissociate
into paired Shockley partial dislocations, creating a stacking fault on every other plane and thereby producing the …abab…, or HCP, stacking sequence. This distribution of dislocations is consistent both with the measured intergranular misorientation
and with the calculated rigid-body translation along the tilt axis. By establishing the interfacial dislocation arrangement,
we also show how the HCP layer at the 29° boundary observed here is geometrically related to that found previously at the
80.6° Σ=43 〈110〉 boundary. This result helps to link dislocation-based descriptions for boundary structures between the
high- and low-angle misorientation regimes.
We review the application of Brandon’s criterion to identifying so-called “special” grain boundaries. The underlying principles of the Brandon criterion, and others that have followed it, are explained, and the choices of particular parameters within the criteria are considered in the light of experimental information in the literature. It is suggested that varying choices of the parameters may be appropriate for differing applications. An experimental study of the stability of CSL-related triple junctions is used to evaluate the applicability of Brandon-like criteria to these microstructural features.
The principal limitation of today’s Ni- and Fe-based superalloys continues to be their susceptibility to intergranular degradation
arising from creep, hot corrosion, and fatigue. Many precipitation-strengthened superalloys are also difficult to weld, owing
to the formation of heat-affected zone (HAZ) cracks during postweld heat treatments (PWHTs). The present work highlights significant
improvements in high-temperature intergranular degradation susceptibility and weldability arising from increasing the relative
proportion of crystallographically “special” low-Σ CSL grain boundaries in the microstructure. Susceptibility to intergranular
degradation phenomena is reduced by between 30 and 90 pct and is accompanied by decreases in the extent and length of PWHT
cracking of up to 50-fold, with virtually no compromise in mechanical (tensile) properties upon which the functionality of
these specialty materials depends. Collectively, the data presented suggest that “engineering” the crystallographic structure
of grain boundaries offers the possibility to extend superalloy lifetimes and reliability, while minimizing the need for specialized
welding techniques which can negatively impact manufacturing costs and throughput.
The fracture of grain boundaries in electron beam zone refined bi-crystals of tungsten has been investigated by propagating a crystallographic crack towards twist boundaries of controlled misorientation. Intergranular failure is interpreted by means of a Griffith type criterion for the two competing processes of fracture on the grain boundary and on the crystallographic plane in the second grain. The effects of plastic deformation, impurity segregation and lattice defects on the misorientation dependence of the crack initiation and propagation processes are discussed. The use of the value of grain boundary free energy obtained under equilibrium thermodynamic conditions cannot explain the experimental data. It is suggested that the non-equilibrium structure of the grain boundaries controlled their fracture behavior.
Molecular dynamics (MD) simulations are used to model dislocation nucleation at or near symmetric tilt bicrystal copper interfaces with 〈1 0 0〉 or 〈1 1 0〉 misorientation axes. MD simulations indicate that orientation of the opposing lattice regions and the presence of certain structural units are two critical attributes of the interface structure that affect the stress required for dislocation nucleation. Boundaries that contain the E structural unit are found to emit dislocations at comparatively low tensile stress magnitudes. A simple model is proposed to illustrate the impact of interfacial porosity and stresses acting on the slip-plane in non-glide directions on tensile interface strength. Accounting for interfacial porosity through an average measure is found to be sufficient to model the tensile strength of boundaries with a 〈1 0 0〉 misorientation axis and many boundaries with a 〈1 1 0〉 misorientation axis.
This paper focuses on the most appropriate use of electron back-scatter diffraction (EBSD) post-acquisition analysis for categorisation of grain boundaries in polycrystals. A brief survey of the early literature shows that the most meaningful reference structure for grain boundaries in polycrystals is periodicity in the grain boundary surface, rather than the misorientation-based coincidence site lattice (CSL) and Σ notation. However, use of the CSL is convenient to the experimentalist. It is therefore suggested that wherever possible, misorientation data, obtained by EBSD mapping and classified according to CSL types, should be supplemented with other, more detailed information to aid analysis.
Atomistic simulations were used to investigate dislocation nucleation from Σ3 asymmetric (inclined) tilt grain boundaries under uniaxial tension applied perpendicular to the boundary. Molecular dynamics was employed based on embedded atom method potentials for Cu and Al at 10 K and 300 K. Results include the grain boundary structure and energy, along with mechanical properties and mechanisms associated with dislocation nucleation from these Σ3 boundaries. The stress and work required for dislocation nucleation were calculated along with elastic stiffness of the bicrystal configurations, exploring the change in response as a function of inclination angle. Analyses of dislocation nucleation mechanisms for asymmetric Σ3 boundaries in Cu show that dislocation nucleation is preceded by dislocation dissociation from the boundary. Then, dislocations preferentially nucleate in only one crystal on the maximum Schmid factor slip plane(s) for that crystal. However, this crystal is not simply predicted based on either the Schmid or non-Schmid factors. The synthesis of these results provides a better understanding of the dislocation nucleation process in these faceted, dissociated grain boundaries.
The energies of a set of 388 distinct grain boundaries have been calculated based on embedded-atom method interatomic potentials for Ni and Al. The boundaries considered are a complete catalog of the coincident site lattice boundaries constructible in a computational cell of a prescribed size. Correlations of the boundary energy with other boundary properties (disorientation angle, Σ value, excess boundary volume and proximity of boundary normals to 〈1 1 1〉) are examined. None of the usual geometric properties associated with grain boundary energy are useful predictors for this data set. The data set is incorporated as supplementary material to facilitate the search for more complex correlations. The energies of corresponding boundaries in Ni and Al are found to differ by approximately a scaling factor related to the Voigt average shear modulus or C44. Crystallographically close boundaries have similar energies; hence a table of grain boundary energies could be used for interpolation.
Atomistic calculations are used to model the nucleation of partial dislocations during a tensile deformation from bicrystal interfaces with dissociated structure. Interfaces with this type of structure occur primarily in materials with low intrinsic stacking fault energies. In this work, the initial structure of each bicrystal interface is refined using energy minimization techniques. Molecular dynamics simulations are then used to study the deformation of each interface in uniaxial tension perpendicular to the boundary plane at a constant strain rate. Analysis focuses on the evolution of the dissociated interface structure prior to the dislocation nucleation event and the resulting structure of the boundary after the emission of partial dislocations from the interface. Dislocation nucleation occurs predominantly at the dissociated interface structural unit, while the spacing between interface features is identified as an important length scale that affects the failure mode. The evolution of the dissociated interface structure and the nucleation of partial dislocations are found to be similar to results obtained in a previous atomistic study of the stress dependence of a lock formation containing a stair-rod dislocation.
Polycrystalline Ni-base superalloys are prone to time-dependent intergranular failure when the loading temperatures exceeds about 873 K. The fracture process is then controlled by oxygen grain-boundary diffusion followed by decohesion of the respective boundaries. It is shown that this kind of cracking for IN718 at 923 K in air can be reduced significantly by successive steps of deformation and annealing, which is known as grain-boundary-engineering processing. This illustrates the importance of the grain-boundary-character distribution with regard to this mode of failure, which is known as ‘dynamic embrittlement.’
Abstract Advances in automated electron diffraction techniques, microstructural modeling, and the understanding of structure-property
relationships for grain boundaries have resulted in the emergence of grain boundary engineering as a formidable tool for cost-effectively
achieving enhanced performance in commercial polycrystalline materials (i.e., metals, alloys, and ceramics). In this article,
some applications for grain boundary engineering technology that have been developed during the past several years are presented.