The structure of a migrating low-angle tilt grain boundary in strontium titanate

Weak beam transmission electron microscopy and stereomicroscopy have been used to characterize the three-dimensional structure of a severely deformed low-angle tilt grain boundary in a strontium titanate ceramic. Various interactions between crystal lattice dislocations and grain boundary dislocations in this boundary have been analysed. The deformed low-angle tilt grain boundary is a result of partial glide. The boundary is composed of dislocations with Burgers vectorsa [¯100] and the deformation of the boundary is interpreted as having occurred by the interactions of the boundary with crystal lattice dislocations during grain boundary migration. Observed dislocation network in the grain boundary are a result of the reactionb ₃=b₁+b₂=a [¯100]+a [00¯1]=a [¯10¯1], and the resultant dislocations are sessile. Also, many crystal lattice dislocations are pinned by the grain boundary and produce a complex dislocation structure for the boundary.M. Fujimoto is a Visiting Scientist at the Massachusetts Institute of Technology on leave from Taiyo Yuden Co., Ltd., Tokyo, Japan.     

Temperature-dependent surface diffusion near a grain boundary

Metal surface evolution is described by a nonlinear fourth-order partial differential equation for curvature-driven flow. The standard boundary conditions for grain-boundary grooving, at a grain–grain–fluid triple intersection, involve a prescribed slope at the groove axis. The well-known similarity reduction is no longer valid when the dihedral angle and surface diffusivity depend on time due to variation of the surface temperature. We adapt a nonlinear fourth-order model that can be discerned from symmetry analysis to be integrable, equivalent to the fourth-order linear diffusion equation. The connection between classical symmetries and separation of variables allows us to develop the correction to the self-similar approximation as a power series in a time-like variable.     

Heterogeneous precipitation on a low-angle grain boundary in AI-4 wt % Cu

When a (110) tilt boundary plane deviates from its symmetrical position in an AI-4wt% Cu alloy, a singleθ′ family precipitates in only one grain. An elastic calculation of the stresses applied by the dislocation wall on the {100} habit planes of the plate-shapedθ′ precipitates determines the family with the easiest nucleation; it is found to be that making the smallest angle with the boundary plane. Furthermore it is shown that the precipitate growth is favoured in one grain, thus explaining the electron microscopic observations.     

Titanium enrichment and strontium depletion near edge dislocation in strontium titanate [001]/(110) low-angle tilt grain boundary

Dislocations are linear lattice defects in a crystalline solid. Since the unusual atomistic environment of the dislocation may greatly influence various material properties, control of the composition would offer more opportunities to obtain unique one-dimensional structures. In the present study, we have characterized the structure of dislocations in a low-angle tilt grain boundary of strontium titanate (SrTiO₃). High-spatial resolution elemental mapping by electron energy loss spectroscopy combined with scanning transmission electron microscopy has enabled visualization of the enrichment of titanium (Ti) and the depletion of strontium (Sr) near the dislocation cores. The Ti enrichment and the Sr depletion have been observed at all of the dislocations, and the grain boundary is considered to be Ti excess. The extra Ti ions are located on the positions different from the normal perovskite lattice, suggesting that the local structure is largely reconstructed. It has been proposed that tensile strain at the dislocations may be a cause of the Ti enrichment.     

Deformation by grain boundary hinge-like behavior

A symmetric tilt Σ11(113) Cu grain boundary was investigated through molecular dynamics simulation. The boundary exhibited an unexpected nonlinear elastic response upon compressive loading normal to the grain boundary plane. Analysis revealed that this particular grain boundary can act as a hinge, leading to significant rotation between two crystals. The rotation induces a change in the loading direction and a subsequent decrease in strain energy due to elastic anisotropy. The geometry, anisotropy, and atomic structure of the boundary were all found to play a role in its peculiar behavior.     

Analysis of creep crack growth by grain boundary cavitation

Intergranular creep crack growth in metals at high temperatures is analysed by assuming that the crack advances when cavities coalesce on grain boundary facets approximately normal to the maximum principal tensile stress. The analyses are based on a material model that describes the nucleation and growth of grain boundary cavities, accounting for diffusive growth as well as growth by dislocation creep of the surrouding grains, and also incorporating the effect of grain boundary sliding. Plane strain center cracked panels are analysed by a numerical method that fully accounts for the development of damage in every point of the specimen, and the solutions are compared with crack growth rates predicted by a simple model based on the singular stress fields around the tip of a sharp crack. The development of crack growth rates and the general crack growth patterns predicted by this material model are determined for a range of material parameters, including cases where failure occurs at small strains as well as cases where failure occurs at large strains.

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Résumé On analyse la croissance d'une fissure de fluage intergranulaire dans les métaux à hautes températures en supposant que la fissure progresse lorsque s'effectue une coalescence de cavités sur les faces des frontières de grains, dans une direction sensiblement normale par rapport à la tension principale maximum. L'analyse est basée sur un modèle de matériau qui décrit la nucléation et la croissance des cavités aux frontières des grains. tenant compte à la fois d'une croissance diffusive et d'une croissance associée au fluage des grains voisins, et incorporant les effets de glissement des frontières de grain. On analyse des panneaux à fissure centrale en état plan de déformation à l'aide d'une méthode numérique qui tient compte au développement de l'endommagement en chaque point de l'éprouvette. On compare les solutions avec les vitesses de propagation de fissure dérivées d'un modèle simple basé sur les champs de contraintes singulières règnant autour de l'extrémité d'une fissure aiguë. Le développement des vitesses de croissance d'une fissure, et l'aspect général de la propagation d'une fissure prédits par ce modèle ont été établis pour une large gamme de paramètres de matériau, et en considérant aussi bien les cas où se produit une rupture sous de faibles déformations, que les cas où de grandes déformations sont requises.

     

Slip behaviour near a grain boundary in high-cycle fatigue of poly-crystal copper

In order to investigate the characteristic slip behaviour near a grain boundary in high‐cycle fatigue, a high‐cycle fatigue test is carried out using a copper poly‐crystal specimen, which consists of several tens of grains. Seventeen persistent slip bands (PSBs) are observed along the grain boundaries. Their location and the activated slip system are different from those expected by the Schmid factor. After the fatigue test, the crystalline orientation and the three‐dimensional shape of each grain are specified by the repetition of polishing and observation by means of an orientation‐imaging microscope (OIM). A finite‐element method (FEM) analysis is also conducted for the specimen with the same orientation and shape of grains taking into account the anisotropy. This analysis reveals that the shear stress concentrates near the grain boundaries where the PSBs are formed. The activated slip systems predicted by the maximum resolved shear stress agree well with those observed in the fatigue experiment. Thus, the characteristic slip near the grain boundary in the poly‐crystal is governed by the concentrated resolved shear stress on the specific slip system due to the deformation constraint by neighbouring crystals.     

Misorientation measurements near grain boundary cracks after fatigue tests

Microcrack initiation and propagation in mechanical fatigued polycrystals are sensitive to crystallographic misorientation between grains. The analysis of factors affecting the propagation of microcracks requires quantitative knowledge about the crystallographic misorientations of the grain boundary segments in which microcracks have been observed. Such observations are possible using the electron back-scattering pattern technique in the scanning electron microscope. The principle of this method is explained and some examples of such investigations on nickel polycrystals in push-pull tests are presented.Published inProblemy Prochnosti, Nos. 1–2, pp. 11–25, January–February, 1995.     

Modelling of small fatigue crack growth interacting with grain boundary

The slip band at the tip of a small fatigue crack interacting with grain boundaries is modelled for four cases: a slip band not reaching the grain boundary, a slip band blocked by the grain boundary, a slip band propagated into an adjacent grain, and a slip band propagated through one and then blocked by a second grain boundary. The theory for continuously distributed dislocations is used to calculate the crack-tip sliding or opening displacement and the microscopic stress intensity factor under tensile and shear loading. Assuming that the range of the tip displacement directly determines the propagation rate of both Stage I and II cracks, prediction of the propagation behavior of a small crack is made as a function of the distance between the crack tip and the grain boundary, and of the difficulty to propagate slip into adjacent grains, as well as a function of crack length and stress level. The directions for further development of modelling are discussed.     

Grain size, grain boundary sliding, and grain boundary interaction effects on nanocrystalline behavior

A dislocation–density grain boundary (GB) interaction scheme, a GB misorientation dependent dislocation–density relation, and a grain boundary sliding (GBS) model are presented to account for the behavior of nanocrystalline aggregates with grain sizes ranging from 25 nm to 200 nm. These schemes are coupled to a dislocation–density multiple slip crystalline plasticity formulation and specialized finite element algorithms to predict the response of nanocrystalline aggregates. These schemes are based on slip system compatibility, local resolved shear stresses, and immobile and mobile dislocation–density evolution. A conservation law for dislocation–densities is used to balance dislocation–density absorption, transmission and emission from the GB. The relation between yield stresses and grain sizes is consistent with the Hall–Petch relation. The results also indicate that GB sliding and grain-size effects affect crack behavior by local dislocation–density and slip evolution at critical GBs. Furthermore, the predictions indicate that GBS increases with decreasing grain sizes, and results in lower normal stresses in critical locations. Hence, GBS may offset strength increases associated with decreases in grain size.     

The role of partial grain boundary dislocations in grain boundary sliding and coupled grain boundary motion

We study the process of grain boundary sliding through the motion of grain boundary dislocations, utilizing molecular dynamics and embedded atom method (EAM) interatomic potentials. For a Σ = 5 [001]{310} symmetrical tilt boundary in bcc Fe, the sliding process was found to occur through the nucleation and glide of partial grain boundary dislocations, with a secondary grain boundary structure playing an important role in the sliding process. While the homogeneous nucleation of these grain boundary dislocations requires shear strain levels higher than 7%, preexisting grain boundary dislocations are shown to glide at applied shear levels of 1.5%. The glide of the dislocations results in coupled motion of the boundary in the directions parallel and perpendicular to itself. Finally, interstitial impurities and vacancies were introduced in the grain boundary to study the effects on the sliding resistance of the boundary. While vacancies and H interstitials act as preferred nucleation sites, C interstitials do not. Both hydrogen and C interstitials stop dislocation glide whereas vacancies do not. A detailed study of the dynamic properties of these dislocations is also presented.     

The role of grain boundary energy in grain boundary complexion transitions

Recent findings about the role of the grain boundary energy in complexion transitions are reviewed. Grain boundary energy distributions are most commonly evaluated using measurements of grain boundary thermal grooves. The measurements demonstrate that when a stable high temperature complexion co-exists with a metastable low temperature complexion, the stable complexion has a lower energy. It has also been found that the changes in the grain boundary energy lead to changes in the grain boundary character distribution. Finally, recent experimental observations are consistent with the theoretical prediction that higher energy grain boundaries transform at lower temperatures than relatively lower energy grain boundaries. To better control microstructures developed through grain growth, it is necessary to learn more about the mechanism and kinetics of complexion transitions.     

The influence of crystallographic orientation on crack tip displacements of microstructurally small, kinked crack crossing the grain boundary

The paper presents an analysis of the effects of grain orientations on a short, kinked surface crack in a 316L stainless steel. The kinking of the crack is assumed to take place at the boundary between two neighbouring grains. The analysis is based on a plane-strain finite element crystal plasticity model. The model consists of 212 randomly shaped, sized and oriented grains, loaded monotonically in uniaxial tension to a maximum load of 0.96R_p0.2 (240 MPa). The influence that a random grain structure imposes on a Stage I crack is assessed by calculating the crack tip opening (CTOD) displacements for bicrystal as well as for polycrystal models, considering different crystallographic orientations. Since a Stage I crack is assumed, the crack is always placed in a slip plane. Results from a bicrystal case show that the maximal CTODs are directly related to the stiffness of the grain containing the crack extension. Anisotropic elasticity and crystal plasticity both contribute to this grain stiffness, resulting in maximal CTOD when Schmid factors are the highest on two slip planes. Such crystallographic orientation results in a soft elasto-plastic response. Anisotropic elasticity can additionally increase the softness of a grain at certain crystallographic orientations. Minimal anisotropic elasticity at the crystallographic orientations with the highest Schmid factors causes the CTOD to be maximized. Presuming that the crack will preferably follow the slip plane where the crack tip opening displacement is highest, we show that the crystallographic orientation can affect the CTOD values by a factor of up to 7.7. For a given grain orientation the maximum CTOD is attained when the crack extension deflection into a second grain is between −75.141° and 34°. For the polycrystal case we show that grains beyond the first two crack-containing grains change the CTOD by a factor of up to 3.3 and that the largest CTODs are obtained when placing the crack into a slip plane with crack extension that results in a crack extension being more perpendicular to the external load.     

Creep crack growth by grain boundary cavitation: crack tip fields and crack growth rates under transient conditions

Transient creep crack growth due to grain boundary cavitation, and under plane strain and small scale creep conditions, is investigated. Full account is taken of the finite geometry changes accompanying crack tip blunting and the material is characterized as an elastic-power law creeping solid with an additional contribution to the creep rate arising from a given density of cavitating grain boundary facets. All voids are assumed present from the outset, distributed on a given density of cavitating grain boundary facets. Our analyses show the competing effects of stress relaxation due to creep, diffusion and crack tip blunting, and the stress increase due to crack growth. Another outcome of our analyses is the crack growth rate under various conditions of loading and for various values of material properties and for various characterizations of the failure process. Prior to crack growth, Hutchinson-Rice-Rosengren type singular fields dominate over the crack tip region, outside of a finite strain zone that has dimensions of the order of the crack opening displacement. These singular fields scale with the path integral C(t), which to a good approximation decays as K _I ²/t, with t being the elapsed time since load application and K _Ithe imposed stress intensity factor. When the crack growth rate is faster than the growth rate of the creep zone, our finite element results show that Hui-Riedel singular fields dominate over the crack tip region and the magnitude of the Hui-Riedel fields scales with the crack growth rate. For a crack that grows more slowly than the creep zone, Hutchinson-Rice-Rosengren type fields dominate over the crack tip region. In these circumstances, the crack growth rate is found to scale as C(t) to a power. Regardless of which of the two singular fields dominates for the growing crack, finite strain effects are found to be significant over a size scale of the order of the crack opening displacement at crack growth initiation. The effect of increased mesh refinement is also considered and very little mesh dependence is found.

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Résumé On étudie la croissance d'une fissure en fluage transitoire, associée à la cavitation aux frontières des grains, sous des conditions d'état plan de déformation et de fluage à petite échelle. On tient compte des modifications finies de géométrie accompagnant l'arrondisement de l'extrémité de la fissure, et le matériau suit une loi de fluage elasto-parabolique, avec une contribution additionnelle à la vitesse de fluage venant d'une densité donnée de facettes de joints de grains comportant de la cavitation. On suppose que toutes les cavités sont présentes dès le début, et qu'elles sont distribuées selon une densité déterminée de ces facettes. L'analyse montre les effets rivaux d'une relaxation des contraintes associée au fluage, à la diffusion et à l'arrondisement des extrémités de fissure, et d'une augmentation de contraintes due à la croissance de fissure. Un autre résultat de l'analyse est l'établissement de la vitesse de croissance de la fissure sous diverses conditions de mise en charge, pour diverses valeurs des propriétés du matériau, et pour divers modes de caractérisation du processus de rupture. Avant croissance de la fissure, ce sont des champs singuliers de type Hutchinson-Rice-Rosengren (HDR) qui prédominent sur la région de l'extrémité de la fissure, à l'extérieur d'une zone de déformations finies dont la taille est de l'ordre de grandeur du COD. Ces champs singulier sont proportionnels à l'intégrale de parcours C(t) laquelle, avec une bonne approximation, s'atténue en fonction de K _I ²/t, où t est le temps qui s'est écoulé depuis la mise en charge et K _Ile facteur d'intensité de contraintes imposés. Lorsque la vitesse de croissance de la fissure dépasse la vitesse de croissance de la zone en fluage, les résultats de l'analyse par éléments finis montre que ce sont les champs singuliers de Hui-Riedel qui prédominent sur la zone de l'extrémité de la fissure, et que l'amplitude de ces champs est proportionnelle à la vitesse de croissance de la fissure. Pour une fissure qui croit moins vite que la vitesse de fluage, es champs de type HRR sont prédominants et on trouve que la vitesse de croissance de la fissure est proportionelle C(t) à une certaine puissance. Quel que soit le type de champs singulier qui détermine la croissance de la fissure, on trouve que les effets de déformation finies sont significatifs sur une échelle de dimension de l'ordre du COD à l'amorçage de la fissuration. On considère également l'effet d'un affinage plus important du réseau, et l'on trouve me très faible dépendance par rapport à ce paramètre.