A model of grain boundary sliding during deformation

A model of slip at grain boundaries is proposed based on the concept of local melting of the grain boundary under intense external influence and by analogy with ultrathin lubrication. A discontinuous regime of slip along the grain boundaries similar to the stick-slip process in thin lubricants is described.     

The influence of a threshold stress for grain boundary sliding on constitutive response of polycrystalline Al during high temperature deformation

A continuum polycrystal plasticity model was used to estimate the influence of a threshold stress for grain boundary sliding on the relationship between macroscopic flow stress and strain rate for the aluminum alloy AA5083 when subjected to plane strain uniaxial tension at 450 °C. Under these conditions, AA5083 deforms by dislocation glide at strain rates exceeding 0.001 s⁻¹, and by grain boundary sliding at lower strain rates. The stress–strain rate response can be approximated by , where A and n depend on grain size and strain rate. We find that a threshold stress less or equal to 4 MPa has only a small influence on flow stress and stress exponent n in the dislocation creep regime (a threshold stress of 2 MPa increases n from 4.2 to 4.5), but substantially increases both flow stress and stress exponent in the grain boundary sliding regime (a threshold stress of 2 MPa increases n from 1.5 to 2.7). In addition, when the threshold stress is included, our model predicts stress versus strain rate behavior that is in good agreement with experimental measurements reported by Kulas et al. [M.A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, T.R. McNelley, Metall. Mater. Trans. A 36 (2005) 1249].     

The activation areas for grain boundary sliding

The activation areas for grain boundary sliding in Al, Pb, Sn, Zn, and Cu are compared with those for creep in the same materials. It is found that the activation area-stress relation for grain boundary sliding is similar to that for creep. This observation is consistent with a dislocation or ledge mechanism of grain boundary sliding.     

An investigation of grain boundary sliding in superplasticity at high elongations

Experiments were performed on the superplastic Zn-22% Al eutectoid alloy to determine the contribution of grain boundary sliding at both low (35%) and high (235%) elongations. The tests were conducted at two different strain rates in the superplastic Region II, and the results show that, within the accuracy of the measurements, there is a large sliding contribution at both elongations. By taking detailed measurements of both the magnitude of the sliding offset and the type of interface, it is shown that the average offsets are generally a maximum at the Zn-Zn boundaries, there is less sliding at the Zn-Al interfaces, and the offsets are a minimum at the Al-Al boundaries. In addition, the distributions of the magnitudes of the sliding offsets are similar at both the low and high elongations. It is concluded that grain boundary sliding is an important deformation process in the superplastic Region II and that it remains important even when the elongation is very high. The nature of the results indicates also that experimental observations of the deformation behaviour in superplastic materials at low elongations (up to 50%) provide meaningful information on the behaviour at much higher (superplastic) elongations.On leave from Mechanical Engineering Department, Nanjing Aeronautical Institute, Nanjing, Jiang-su 210002, People's Republic of China.     

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.     

Application of electron beam lithography to study microcreep deformation and grain boundary sliding

Electron beam lithography has been employed to study microcreep deformation and grain boundary sliding in pure copper. Fine electron-sensitive microgrids of an alloy of palladium and gold were developed on the surface of rectangular specimens. Interrupted creep tests were carried out at 723 K at two stress levels in an argon atmosphere. Creep strain and grain boundary sliding were determined by forming Moire fringes in a scanning electron microscope as well as from the displacement of the grid lines. Local distribution of creep strain inside the grains was found to be non-uniform. Grain boundary sliding exhibited a wavy behaviour.     

Deformation response of grain boundary networks at high temperature

The deformation response of random grain boundary networks as a function of temperature and strain rate is explored using molecular dynamics atomistic simulations and an embedded atom method interatomic potential. We find that deformation at higher temperatures promotes both dislocation emission and grain boundary accommodation processes. The results allow estimating the activation energies and volumes for the deformation process. We find activation energy values for the deformation process similar to those for grain boundary diffusion and activation volumes consistent with an atomic shuffling mechanism. Our results suggest a picture of the deformation process as governed by the combination of the applied stress and thermally activated processes.     

Model for grain boundary sliding and its relevance to optimal structural superplasticity

Abstract

he conclusions reached based on a grain/interphase boundary sliding controlled flow model for optimal structural superplasticity are verified using experimental data from three aluminium alloy systems. Isostructural strain rate–stress relationships could be calculated very accurately using five experimentally determined, physically meaningful constants (three of which could also be calculated from theory; two fully and one partially). The true activation energy for the rate controlling boundary sliding process, the variations of the internal stress distribution arising from sliding, the stress function that is proportional to the measured isostructural isothermal strain rate, and the apparent viscosity, were calculated. It is suggested that the basic units of microscopic boundary sliding in the three aluminium alloys examined have a common structure.

MST/3077     

Mesoscopic grain boundary sliding as the rate controlling process for high strain rate superplastic deformation

Important features observed during high strain rate superplastic deformation are enumerated. Starting from the premise that the phenomenon of structural superplasticity in different classes of materials results when grain boundary sliding that develops to a mesoscopic scale (defined to be of the order of a grain diameter or more) controls the rate of flow, the particular case of high strain rate superplasticity is explained. The rate equation developed is validated using experimental results concerning 5 alloy systems in which an ultra-fine grain size is developed by thermomechanical processing and retained in a similar condition during superplastic deformation by fine, grain boundary pinning particles and 3 alloy composites in which the volume fraction of the reinforcing constituent is significant (15–25%). It is demonstrated that the analysis results in estimates for the externally measured strain rates that are within a factor of two, in addition to providing a physically meaningful free energy of activation for the rate controlling process. This approach explains superplastic flow in different classes of materials in terms of a single rate controlling mechanism of deformation, viz., mesoscopic grain boundary sliding, with the help of a few constants that have the same values for all systems. The system-dependent variables of threshold stress needed for the onset of mesoscopic boundary sliding and free energy of activation are obtained directly from superplasticity stress–strain rate data, without external inputs.     

Simultaneous grain boundary motion,grain rotation,and sliding in a tricrystal

Grain rotation and grain boundary (GB) sliding are two important mechanisms for grain coarsening and plastic deformation in nanocrystalline materials. They are in general coupled with GB migration and the resulting dynamics, driven by capillary and external stress, is significantly affected by the presence of junctions. Our aim is to develop and apply a novel continuum theory of incoherent interfaces with junctions to derive the kinetic relations for the coupled motion in a tricrystalline arrangement. The considered tricrystal consists of a columnar grain embedded at the center of a non-planar GB of a much larger bicrystal made of two rectangular grains. We examine the shape evolution of the embedded grain numerically using a finite difference scheme while emphasizing the role of coupled motion as well as junction mobility and external stress. The shape accommodation at the GB, necessary to maintain coherency, is achieved by allowing for GB diffusion along the boundary.     

Stimulation of capillarity-driven grain boundary migration during sliding

Zinc bicrystals with originally flat 89° symmetric tilt boundary tilted at ∼45° to the tensile direction were strained at high temperature. The operation of crystallographic slip in both grains was suppressed by orientation of basal planes parallel and perpendicular to the tensile axis. The boundary migrated under the action of curvature driving force making its inclination angle close to 70° with respect to the lateral free surface. In the case of annealing with no load applied, a small boundary migration was observed at the edges of the sample. Initiation of grain-boundary sliding significantly increases the amount of boundary migration. It has been established that sliding can increase the reduced boundary mobility by more than an order of magnitude. Askar D. Mirzakhojaev—on leave from FSU-NHMFL, Tallahassee, FL 32310, USA.     

On the experimental validation of a mesoscopic grain boundary sliding-controlled flow model for structural superplasticity

Different mechanisms have been suggested by many authors as controlling the rate of superplastic flow in different materials. From the viewpoint of computational effort and aesthetics, it is highly desirable to explain the phenomenon, independent of the material/system considered, on a common basis. With this aim, a mesoscopic grain boundary sliding-controlled deformation model was proposed sometime ago as being responsible for superplastic flow in materials of different kinds. In this paper, a rigorous numerical computational procedure for the experimental validation of the model, which takes into account all the physical requirements of the model, is presented. The soundness of the new procedure is established by analysing the experimental data pertaining to many systems belonging to different classes of materials, and matching the results of the analysis with the experimental findings.     

Atomistic simulation of grain boundary sliding and migration

Interatomic potentials using Embedded Atom Method (EAM) are used in conjunction with molecular statics and dynamics calculations to study the sliding and migration of [1 1 0] symmetric tilt grain boundaries (STGB) in aluminum, under both applied displacement and force conditions. For equilibrium grain boundaries (without applied displacements and forces), three low energy configurations (corresponding to three twin structures) are found in the [1 1 0] STGB structures when grain boundary energies at 0 K are computed as a function of grain misorientation angle. Pure grain boundary sliding (GBS) without migration is simulated by applying external displacement. When forces are applied, the energy barriers are reduced consequent to the fact that grain boundary sliding of STGB is always coupled with migration. The propensity for pure GBS is evaluated by computing the energy associated with incremental equilibrium configurations during the sliding process and compared to the case when sliding is accompanied by migration. The magnitude of the energy barriers is found to be much higher in pure GBS than when migration accompanies sliding. Relations between the applied force, internal stress field, and displacement field are established and the role of grain boundary structure on the deformation process are examined. It is found that the GBS displacement is proportional to applied force, GB energy, and time.     

High temperature plastic flow and grain boundary chemistry in oxide ceramics

High temperature plastic flow or grain boundary failure in oxide ceramics such as Al₂O₃ and tetragonal ZrO₂ polycrystal (TZP) is sensitive to small levels of doping by various cations. For example, high temperature creep deformation in fine-grained, polycrystalline Al₂O₃ is highly suppressed by 0.1 mol% lanthanoid oxide or ZrO₂-doping. An elongation to failure in superplastic TZP is improved by 0.2–3 mol% GeO₂-doping. A high-resolution transmission electron microscopy (HRTEM) observation and an energy-dispersive X-ray spectroscopy (EDS) analysis revealed that the dopant cations tend to segregate along the grain boundaries in Al₂O₃ and TZP. The dopant effect is attributed to change in the grain boundary diffusivity due to the grain boundary segregation of the dopant cations. A molecular orbital calculation suggests that ionicity is one of the most important parameters to determine the high temperature flow stress, and probably, the grain boundary diffusivity in the oxide ceramics.     

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.     

Superplasticity and grain boundary sliding in rolled AZ91 magnesium alloy at high strain rates

The superplastic deformation characteristics and microstructure evolution of the rolled AZ91 magnesium alloys at temperatures ranging from 623 to 698 K (0.67–0.76 T_m) and at the high strain rates ranging from 10⁻³ to 1 s⁻¹ were investigated with the methods of OM, SEM and TEM. An excellent superplasticity with the maximum elongation to failure of 455% was obtained at 623 K and the strain rate of 10⁻³ s⁻¹ in the rolled AZ91 magnesium alloys and its strain rate sensitivity m is high, up to 0.64. The dominant deformation mechanism in high strain rate superplasticity is still grain boundary sliding (GBS), which was studied systematically in this study. The dislocation creep controlled by grain boundary diffusion was considered the main accommodation mechanism, which was observed in this study.