Analysis of creep due to grain-boundary diffusion in hexagonal microstructures

For steady-state deformation caused by grain-boundary diffusion in hexagonal microstructures, the stress distribution on grain boundaries and the macroscopic strain rates are analysed by taking the effects of viscous grain-boundary sliding into account. The maximum normal stress and the extent of stress concentration are shown to decrease as the grain-boundary viscosity increases. For infinite viscosity and/or extremely small grain sizes, the distribution of the normal stress becomes uniform on grain boundaries. The strain rates are predicted by both the stress analysis and the energy balance method, and the two strain rates are consistent with each other. The predicted strain rates also decrease as the grain-boundary viscosity increases. The present analysis reveals that the grain-size exponent is dependent on the grain size and the grain-boundary viscosity: the exponent becomes unity for small grain sizes and/or high viscosity, while it is three for large grain sizes and/or low viscosity. Recent experimental observations that the strain rates of nano-sized grain are much lower than those predicted by grain-boundary diffusion are explained by the increasing contribution of viscous grain-boundary sliding with decreasing grain size.     

Grain-boundary diffusion in nanocrystals with a time-dependent diffusion coefficient

A solution to the equation of grain-boundary diffusion is obtained under conditions where migration of the diffusant from the boundaries into the grains is absent and the diffusion coefficient decreases with time from an increased value to a value characteristic of equilibrium grain boundaries. The specific features of the grain-boundary diffusion in nanocrystals are qualitatively analyzed in terms of this solution.     

Atomistic simulations of interactions between the 1 / 2⟨111⟩ edge dislocation and symmetric tilt grain boundaries in tungsten

The strength of polycrystals is largely controlled by the interaction between lattice dislocations and grain boundaries. The atomistic details of these interactions are difficult to discern even by advanced high-resolution microscopy methods. In this paper we present results of atomistic simulations of interactions between an edge dislocation and three symmetric tilt grain boundaries in body-centred cubic tungsten. Our simulations reveal that the outcome of the dislocation–grain-boundary interaction depends sensitively on the grain boundary structure, the geometry of the slip systems in neighbouring grains, and the precise location of the interaction within the grain boundary. A detailed analysis of the evolution of the grain boundary structures and local stress fields during dislocation absorption and transmission is provided.     

Measuring relative grain-boundary energies in block-copolymer microstructures

The (relative) energies of symmetric tilt grain boundaries in a strongly segregated lamellar block copolymer are determined by analysis of the dihedral angles at grain-boundary triple junctions. The analysis reveals two regimes: at low and intermediate misorientations (corresponding to a tilt-angle range 0≤θ≤85°) the grain-boundary energy is found to depend on the tilt angle as E(θ)～θ(x), with 2.5>x≥0. At large misorientations the grain-boundary energy is found to be independent (within the experimental uncertainty) of the angle of tilt. The transition between the two scaling regimes is accompanied by the transition of the grain-boundary structure from the chevron to the omega morphology. Grain-boundary energy and frequency are found to be inversely related, thus suggesting boundary energy to be an important parameter during grain coarsening in block-copolymer microstructures, as it is in inorganic polycrystalline microstructures.     

Thermodynamic and Kinetic Properties of Grain-Boundary Ridges on Tilt $$[11\bar 20]$$ Grain Boundaries in Zinc

Thermodynamic and kinetic properties characteristic of grain-boundary ridges on tilt \([11\bar 20]\) grain boundaries in zinc are studied experimentally. Temperatures are determined for faceting–defaceting and roughening phase transitions in grain-boundary ridges for tilt \([11\bar 20]\) grain boundaries with 35°, 57°, and 85° angles of misorientation. Mobilities and enthalpies of activation are obtained for grain-boundary ridges on the same boundaries. Parameters of inhibition are also calculated for grain-boundary ridges, according to the observed shapes of grain-boundary loops.     

Control of grain boundary microstructures in molybdenum polycrystals by thermomechanical processing of single crystals

The formation of grain structures and grain boundary microstructures in polycrystalline molybdenum, produced by thermomechanical processing from cylindrical single crystals with different initial surface normal orientations of ?110?, ?111? and ?112?, were investigated with the objective of controlling grain boundary microstructures. The polycrystalline specimens displayed different microstructures depending on the initial orientation of the single crystal and the deformed microstructure. The recrystallized microstructure was composed of some oriented-grain clusters, in which grains possessing a similar orientation were assembled. The frequency of low-angle boundaries was very high in the oriented-grain clusters. A close relationship also existed between the grain boundary character distribution (GBCD) and the triple junction distribution. Grain boundary microstructures were compared of bcc molybdenum and fcc polycrystalline materials with reference to path-dependent percolation resistance.     

Extended planar boundary inclinations in fcc single crystals and polycrystals subjected to plane strain deformation

When fcc single crystals with high-symmetry crystal orientations are deformed to moderate strains by rolling, tension or channel die compression, long dislocation boundaries inclined to the extension axis form. Similarly, long dislocation boundaries are often found in grains embedded in polycrystals deformed in the same manner. These extended planar boundaries (EPBs) are characteristically -30-40° from the extension direction and contain the transverse specimen axis. The objective of the present article is to demonstrate that EPBs formed during plane strain deformation are parallel to equivalent slip planes, a pair of hypothetical slip systems used for analyses of the strain and crystal rotation components in place of the larger number of physical slip systems. The coincidence of EPBs and equivalent slip plane inclinations is shown to account for persistent observations of EPBs in the angle range -30-40° from the rolling direction, in rolled single crystals of various initial orientations. The tendency of EPBs towards tilt or twist boundary character can also be rationalized on the basis of the equivalent slip system concept and consideration of the dislocation types available to be incorporated into EPBs.     

Heterogeneities of grain boundary arrangement in polycrystals

Data on mutual arrangements of different types of grain boundaries in polycrystals are presented. The heterogeneity in grain boundary distribution, namely, the effect of gathering low-angle or special tilt grain boundaries is found in pure aluminum thin films, in sheets of Fe-3% Si alloy and in Al₂O₃ doped with MgO or MgO and Y ₂O₃. The local texture, i.e., formation of colonies or clusters of close-oriented grains is considered as a reason of this heterogeneity. The influences of grain boundary gathering on the transport properties of polycrystals and on the crack propagation are discussed. A new concept of effective grain size is suggested to analyze the relationship between material microstructures and material properties.     

Multiscale model of deformed polycrystals. Hall-Petch problem

The paper puts forward a multiscale model of deformed polycrystals according to which the basis for self-consistent deformation of grains is rotational wave flows of planar structural transformations at their boundaries. Computer-aided engineering of grain boundaries reveals two types of rotational wave flows defined by the misorientation angle of adjacent grains. Grain boundary flows of the first type develop at low-angle boundaries and feature low curvature. These flows generate dislocations in the grain bulk and the Hall-Petch equation for them has the form σ=σ₀+kd^?1/2. Grain boundary flows of the second type develop at high-angle boundaries and feature high curvature. These flows generate curvature bands in near-boundary zones and inject them into the grain bulk, resulting in fragmentation of grains and breakdown of translation invariance. For such self-consistency of grains in a polycrystal, the Hall-Petch equation has the form σ=σ₀+kd^?1. Experimental data in support of the proposed multiscale model are presented.     

Connectivity and percolation in simulated grain-boundary networks

Random percolation theory is a common basis for modelling intergranular phenomena such as cracking, corrosion or diffusion. However, crystallographic constraints in real microstructures dictate that grain boundaries are not assembled at random. In this work a Monte Carlo method is used to construct physically realistic networks composed of high-angle grain boundaries that are susceptible to intergranular attack, as well as twin-variant boundaries that are damage resistant. When crystallographic constraints are enforced, the simulated networks exhibit triple-junction distributions that agree with experiment and reveal the non-random nature of grain-boundary connectivity. The percolation threshold has been determined for several constrained boundary networks and is substantially different from the classical result of percolation theory; compared with a randomly assembled network, about 50-75% more resistant boundaries are required to break up the network of susceptible boundaries. Triple-junction distributions are also shown to capture many details of the correlated percolation problem and to provide a simple means of ranking microstructures.     

Anisotropic rheology during grain boundary diffusion creep and its relation to grain rotation,grain boundary sliding and superplasticity

The response of periodic microstructures to deformation can be analysed rigorously and this provides guidance in understanding more complex microstructures. When deforming by diffusion creep accompanied by sliding, irregular hexagons are shown to be anisotropic in their rheology. Analytic solutions are derived in which grain rotation is a key aspect of the deformation. If grain boundaries cannot support shear stress, the polycrystal viscosity is extremely anisotropic. There are two orthogonal directions of zero strength: sliding and rotation cooperate to allow strain parallel to these directions to be accomplished without any dissolution or plating. When a linear velocity/shear stress relationship is introduced for grain boundaries, the anisotropy is less extreme, but two weak directions still exist along which polycrystal strength is controlled only by the grain boundary “viscosity”. Irregular hexagons are characterised by four parameters. A particular subset of hexagons defined by two parameters, which includes regular hexagons as well as some elongate shapes, shows singular behaviour. Grain shapes that are close to that of the subset may exhibit large grain rotation rates and have no well-defined rheology unless there is a finite grain boundary viscosity. This new analysis explains why microstructures based on irregular but near equiaxed grains show high rotation rates during diffusion creep and it provides a framework for understanding strength anisotropy during diffusion creep.     

High-speed superplasticity of microcrystalline alloys under conditions of local grain boundary melting

A model is proposed for the high-speed superplasticity of materials under conditions of local grain boundary melting at temperatures close to solidus. It is shown that the local melting of grain boundaries containing segregations of impurity atoms, results in the formation of a structure consisting of liquid-phase regions and solid intergranular bridges which provide cohesion of the grains during the deformation process. The equilibrium concentration, dimensions, and activation energy for the formation of solid bridges are determined as a function of the temperature, initial impurity concentration in the boundary, and the boundary thickness. A mechanism is proposed for grain-boundary slip under conditions of local grain boundary at anomalously high strain rates. Zh. Tekh. Fiz. 68, 38–42 (December 1998)     

Microstructural evolution and grain subdivision mechanisms during severe plastic deformation of aluminum particles by ball milling

Electron backscattered diffraction technique was used to investigate the microstructure of aluminum particles deformed by high-energy ball milling. The lengths of different types of boundaries per area were calculated for different samples. The results show that the deformation mechanism and the rate of grain subdivision changed considerably as milling time increased. At the beginning of the milling, deformation banding subdivided grains and dynamic recovery formed a cellular structure of low angle boundaries. After further milling, particles were flattened; an increase in the aspect ratio of the original grains together with cold welding of the particles contributed to the formation of high angle grain boundaries (HAGBs). Lattice rotation progressively increased the misorientation of low and medium angle boundaries and transformed them to HAGBs, which resulted in formation of new small equiaxed grains by continuous dynamic recrystallization. This research shows subgrain rotation was the main mechanism for formation of new HAGBs.     

Elevated temperature directional recrystallization of high-purity nickel

Electron backscattered diffraction has been used to characterise the three different kinds of boundaries that occur in grains that are generated by secondary recrystallization during directional annealing of high-purity nickel. Boundaries between columnar grains (CC boundaries) can be twin boundaries, low-angle boundaries or high-angle grain boundaries. The frequency of low-angle CC boundaries dropped from 25% to 0% while the frequency of the high-angle CC boundaries increased from 19% to 67% when the annealing temperature was increased from 1000°C to 1200°C. The misorientation angles of boundaries between columnar grains and small equiaxed grains ahead of them (CE boundaries) was random at 1200°C but had a 40° rotation relationship about ?111? at 1000°C. It was found out that the character of the CC boundaries is determined by relative mobility of the CE boundaries, which is determined by the processing temperature rather than the energy of the CC boundaries themselves. The character of the island grain boundaries sometimes found with columnar grains was not affected by the annealing temperature or the drawing velocity.     

Grain Boundary Wetting Statistic in Zn/Ga System and its Application to Grain Boundary Energy Spectrum Estimation

The grain boundary statistic in zinc polycrystals in contact with saturated Ga(Zn) melt has been studied. The misorientation angle distributions for zinc thin foil and zinc plates were obtained. The influence of the misorientation angle value on the wetting probability p of grain boundaries was observed. The grain boundary energy distribution parameters were obtained by using the p() relationship. The dihedral angles in triple lines of non-wetted zinc samples were also measured and their distribution was used to obtain the grain boundary energy distribution function. The parameters obtained by two different methods correspond to one other.     

Geometric dynamic recrystallization of austenitic stainless steel through linear plane-strain machining

ABSTRACT

Type 316L austenitic stainless steel was severely plastically deformed at room temperature using linear plane-strain machining in a single pass that imparted shear strains up to 2.2 at strain rates up to 2?×?10³ s^?1. The resulting microstructures exhibited significant grain size refinement and improved mechanical strength where geometric dynamic recrystallization was identified as the primary microstructural recrystallization mechanism active at high strain rates. This mechanism is rarely observed in low to medium stacking fault energy materials. The critical stress required for twin initiation is raised by the combined effects of refined grain size and the increase in stacking fault energy due to the adiabatic heating of the chip, thus permitting geometric dynamic recrystallization. The suppression of martensite formation was observed and is correlated to the significant adiabatic heating and mechanical stabilisation of the austenitic stainless steel. A gradient of the amount of strain induced martensite formed from the surface towards the interior of the chip. As the strain rate is increased from 4?×?10² s^?1–2?×?10³ s^?1, a grain morphology change was observed from a population of grains with a high fraction of irregular shaped grains to one dominated by elongated grain shapes with a microstructure characterised by an enhanced density of intragranular sub-cell structure, serrated grain boundaries, and no observable twins. As strain rates were increased, the combination of reduction in strain induced martensite and non-uniform intragranular strain led to grain softening where a Hall-Petch relationship was observed with a negative strengthening coefficient of ?0.08?MPa m^1/2.     

Elastic mechanical grain interactions in polycrystalline materials; analysis by diffraction-line broadening

Abstract

Experimental investigations have revealed that the Neerfeld–Hill and Eshelby–Kröner models, for grain interactions in massive, bulk (in particular, macroscopically isotropic) polycrystals, and a recently proposed effective grain-interaction model for macroscopically anisotropic polycrystals, as thin films, provide good estimates for the macroscopic (mechanical and) X-ray elastic constants and stress factors of such polycrystalline aggregates. These models can also be used to calculate the strain variation among the diffracting crystallites, i.e. the diffraction-line broadening induced by elastic grain interactions can thus be predicted. This work provides an assessment of diffraction-line broadening induced by elastic loading of polycrystalline specimens according to the various grain-interaction models. It is shown that the variety of environment, and thus the heterogeneity of the stress–strain states experienced by each of the individual grains exhibiting the same crystallographic orientation in a real polycrystal, cannot be accounted for by traditional grain-interaction models, where all grains of the same crystallographic orientation in the specimen frame of reference are considered to experience the same stress–strain state. A significant degree of broadening which is induced by the heterogeneity of the environments of the individual crystallites is calculated on the basis of a finite element algorithm. The obtained results have vast implication for diffraction-line broadening analysis and modelling of the elastic behaviour of massive polycrystals.     

Shape effect of elongated grains on ultrasonic attenuation in polycrystalline materials

Longitudinal and transverse wave attenuation coefficients are obtained in a simple integral form for ultrasonic waves in cubic polycrystalline materials with elongated grains. Dependences of attenuation on frequency and grain shape are described in detail. The explicit analytical solutions for ellipsoidal grains in the Rayleigh and stochastic frequency limits are given for a wave propagating in an arbitrary direction relative to ellipsoid axes. The attenuation exhibits classic frequency dependence in those frequency limits. However, the dependence on the grain shape in the stochastic limits is unexpected: it is independent of the cross-section of the ellipsoidal grains and depends only on the grain dimension in the propagation direction. In the Rayleigh region attenuation is proportional to effective volume of the ellipsoidal grain and is independent of its shape. A complex behavior of attenuation on the grain shape/size and frequency is exhibited in the transition region. The results obtained reduce to the classic dependences of attenuation on parameters for polycrystals with equiaxed grains.     

Strong pinning of triple junction migration for robust high strain nanostructures

The universality of a key recovery mechanism: triple junction migration in high strain nanostructures is revealed herein. This migration is the only means to uniformly coarsen deformed lamellar microstructures. Migration of medium to high angle geometrically necessary boundaries at triple junctions is resisted by strong pinning phenomena. Pinning by low angle dislocation boundaries is the novel mechanism that greatly adds to the solute drag of these higher angle boundaries during migration at triple junctions. Solutes furthermore cause a significant increase in the dislocation density of the low angle boundaries formed during deformation and thus greatly enhance the observed pinning. Boundary pinning by dislocation boundaries and solute drag is analysed for deformed Ni of different purities via in and ex situ electron microscopy. A kinetic model is utilised to obtain activation energies that quantitatively demonstrate the strength of this pinning. A new strategy for achieving robust nanostructured metals is developed based on solute and dislocation pinning of triple junction migration – a universal recovery mechanism in deformed lamellar microstructures.     

Orientation preferences of extended sub-granular dislocation boundaries

The orientation and disorientation of extended cell block boundaries that separate cell blocks in model rate-independent grains accommodating imposed plastic deformation by the mechanism of slip is predicted on the basis of the following three hypotheses: (1) a uniform state of stress prevails throughout the grain; (2) cell blocks are disoriented so as to minimize the power of plastic deformation; and (3) cell block boundaries are oriented so as to minimize plastic incompatibility between neighboring cell blocks. Predicted orientations and disorientations compare favorably with those reported in the experimental literature for copper and aluminum polycrystals deformed plastically in uniaxial tension. This suggests that the assumed hypotheses may represent the physical principles that determine the preferred cell block boundary orientation.