Grain Boundary Diffusion Creep Research Articles

Deformation mechanism and inverse Hall – Petch behavior in nanocrystalline materials

Abstract It is widely accepted that for the very smallest grain sizes (typically below 20 – 30 nm), dislocations play no significant role in the deformation of nanocrystalline materials. However, the grain-boundary mechanisms responsible for the reported decrease in strength with decreasing grain size in this regime (the ‘inverse Hall–Petch effect’) remain unclear. Here, we demonstrate by molecular-dynamics simulation that, in the absence of both grain growth and any dislocations, nanocrystalline fcc metals deform via a mechanism involving an intricate interplay between grain-boundary sliding and grain-boundary diffusion. By quantitatively reproducing the well-known Coble-creep formula for coarse-grained materials, we show that the ‘inverse Hall–Petch effect’ arises from sliding-accommodated grain-boundary diffusion creep. Previous, apparently contradictory, suggestions that GB sliding, on the one hand, or GB-diffusion creep, on the other, are responsible for this behavior can thus be reconciled as originating from one and the same deformation mechanism. We discuss the reasons why we believe that these simulations also capture the room-temperature deformation behavior of nanocrystalline fcc metals in the absence of dislocation nucleation and microcracking.

Structure and fracture mechanism of a two-phase chromium–nickel alloy during high-temperature deformation

The structure and mechanical properties of a two-phase Kh65N33V2FT alloy has been studied after tests at room and high temperatures. The morphology of the main phases, namely, solid solutions of nickel in chromium (α) and chromium in nickel (γ), is changed depending on temperature. The lattice parameters of the main phases have been determined. The main mechanism of deformation for this alloy is shown to be grain-boundary sliding. Bulk and grain-boundary diffusion creep and self-regulating diffusion-viscous flow is possible in the γ phase during high-temperature deformation. The heat resistance of this alloy is restricted to 1000°C because of the formation of a γ-phase percolation cluster.

Rheology of two-phase systems: A microphysical and observational approach

Ductile shear zones commonly contain distinctive bands of high strain rock characterized by intimately mixed fine-grained two-phase or polyphase material. These ultramylonite bands are weaker than the surrounding material, and may play a critical role in strain localization. How such zones develop, how the phases become evenly dispersed, the bulk rheology, and the controls on grain size, are all unclear. The following generic scenario may resolve some of these questions.1) Dislocation creep and dynamic recrystallization cause grain-size reduction: commonly, the recrystallized grain sizes of the two phases differ.2) Grain size reduction causes a switch to grain-boundary diffusion creep, which requires grain-boundary sliding. Diffusion allows one phase to fill spaces that open between grains of the other: this will happen most rapidly in the finer-grained phase. The grain size of the resulting mixture is therefore controlled by that of the finer-grained phase. This leads to mixing and dispersion of the two phases, producing a fine-grained, evenly dispersed two-phase aggregate.3) The bulk rheology will be controlled by grain-boundary diffusion creep of the two phases, with the grain size controlled by the finer-grained phase.Bulk flow laws can be developed for quartz-feldspar and olivine-orthopyroxene ultramylonites based on these concepts, using appropriate mixing laws.

Ultra-high heating rate densification of nanocrystalline magnesia at high pressure and investigation on densification mechanisms

Abstract The pressure-assisted densification method based on combustion reaction heating was applied to prepare dense nanocrystalline ceramics. The densification process of magnesia compact with a particle size of 50 nm was investigated, under the pressure range of 0–170 MPa, and the temperature range of 1620–1880 K with ultra-high heating rate (above 1600 K/min). The pressure was found to have an effect on enhancing densification while suppressing grain growth, and the higher sintering temperature lead to the larger grain size and lower density of the compact. Pure magnesia nanocrystalline ceramics with a relative density of 99.1% was obtained at 1620 K and 170 MPa, and the concurrent grain growth was almost completely restrained. Furthermore, the investigation on the pressure-dependent densification mechanisms including plastic flow, diffusion and power-law creep was also carried out. The result indicated the rate-controlling mechanism was the plastic flow accommodated by grain-boundary diffusion creep.

Peculiarities of the neck growth process during initial stage of spark-plasma, microwave and conventional sintering of WC spheres

This work involves an investigation of the neck growth kinetics of free-packed spherical shaped binderless tungsten carbide particles during microwave and spark-plasma sintering. The application of a classical sphere to sphere approach showed the possibility of identifying the main diffusion mechanisms operating during the initial stage of microwave sintering of tungsten carbide powder. An anomalous neck growth rate in the initial period during microwave and spark-plasma sintering processes, up to 100 times faster in comparison to conventional sintering, was also revealed. Volume diffusion was enhanced by a small amount of a liquid phase, and surface diffusion was proposed as the primary mass transport mechanism for microwave sintering. The simulation operation of grain-boundary diffusion and power law creep was responsible for neck growth during spark-plasma sintering.Numerical simulation of neck growth revealed high values of the diffusion coefficient for microwave (3.41×10−8m2s−1 at 1200°C) and spark-plasma sintering (5.41×10−8m2s−1 at 1200°C). In the case of conventional sintering, the diffusion coefficients calculated are in good agreement with values for diffusion of W and C in a W–C system (8.6×10−16m2s−1 at 1200°C).Low values of the apparent activation energy (Ea) for microwave and spark-plasma sintering (62 and 52kJmol−1) have been obtained. For conventional sintering, all data collected indicate grain-boundary diffusion as the primary sintering mechanism (272kJmol−1).

Is diffusion creep the cause for the inverse Hall–Petch effect in nanocrystalline materials?

It has previously been demonstrated by means of molecular-dynamics (MD) simulation that for the very smallest grain sizes (typically below 20–30 nm), nanocrystalline f.c.c. metals deform via grain-boundary diffusion creep, provided the applied stress is low enough to avoid microcracking and dislocation nucleation from the grain boundaries. Experimentally, however, the nature of the deformation process in this “inverse Hall–Petch” regime (in which the yield stress decreases with decreasing grain size) remains controversial. Here we illustrate by MD simulation that in the absence of grain growth a nanocrystalline model b.c.c. metal, Mo, and a model metal oxide, UO 2, also deform via diffusion creep. However, in the case of Mo both grain-boundary and lattice diffusion are observed to contribute to the creep rate; i.e., the deformation mechanism involves a combination of Coble and Nabarro-Herring creep. While our results on Mo and UO 2 are still preliminary, they lend further support to the observation of diffusion creep previously documented in f.c.c. metals and in covalently bonded Si.

Consolidation enhancement in spark-plasma sintering: Impact of high heating rates

Spark-plasma sintering (SPS) provides accelerated densification and, in many cases, limited grain growth compared to regular hot pressing and sintering. Possible mechanisms of this enhancement of the consolidation in SPS versus conventional techniques of powder processing are identified. The consolidation enhancing factors are categorized with respect to their thermal and nonthermal nature. This paper analyses the influence of a major factor of thermal nature: high heating rates. The interplay of three mechanisms of material transport during SPS is considered: surface diffusion, grain-boundary diffusion, and power-law creep. It is shown that high heating rates reduce the duration of densification-noncontributing surface diffusion, this favors powder systems’ sinterability and the densification is intensified by grain-boundary diffusion. Modeling indicates that, besides the acceleration of densification, high heating rates diminish grain growth. The impacts of high heating rates are dependent on particle sizes. Besides SPS, the obtained results are applicable to the broad spectrum of powder consolidation techniques which involve high heating rates. The conducted experiments on SPS of an aluminum alloy powder confirm the model predictions of the impact of heating rates and initial grain sizes on the shrinkage rates during the electric current-assisted consolidation. It is noted, that this study considers only one of many possible mechanisms of the consolidation enhancement during SPS, which should stimulate further efforts on the modeling of field-assisted powder processing.

Effects of microstructural inhomogeneity on dynamic grain growth during large-strain grain boundary diffusion-assisted plastic deformation

Mesoscale simulations of grain-boundary (GB) diffusion creep in which GB migration-induced static grain growth is suppressed were carried out based on the variational principle of dissipated power. Assuming that the boundaries exhibit no sliding resistance in response to shear stress, the variation of the normal-stress distribution and the diffusive fluxes along the grain boundaries during Coble creep were analysed. The effects of microstructural inhomogeneity, including topological and physical inhomogeneity (i.e. distributions in the grain sizes and GB diffusivities) were investigated. We find that because of the lack of GB migration as an accommodation process to relax the stress concentrations in the microstructure, a topologically inhomogeneous microstructure becomes unphysical at high strains (of typically between 50–100%). Consistent with earlier simulations by Pan and Cocks (1993 Comput. Mater. Sci. 1 95), we find that even in the absence of static grain growth an inhomogeneous microstructure exhibits dynamic grain growth induced by grain-switching induced grain-disappearance events. Our simulations also reveal that in a topologically inhomogeneous microstructure, the diffusive fluxes along any given GB can be in the same direction at both delimiting triple points; i.e. qualitatively different from a homogeneous (i.e. regular hexagonal) microstructure in which, according to Spingarn and Nix (1978 Acta Metall. 26 1389), these fluxes oppose each other.

Deformation and Diffusion Modes in Nanocrystalline Materials

An overview of theoretical models of plastic deformation and diffusion processes in nanocrystalline (nano–grained) materials is presented. The key experimentally detected facts – abnormal Hall–Petch relationship, anomalously fast diffusion, grain rotations, plastic flow localisation, high-strain–rate superplasticity, etc. – in nanocrystalline materials are discussed. Special attention is paid to theoretical models which describe such plastic deformation mechanisms (modes) as lattice dislocation slip, grain boundary (GB) sliding, GB diffusion creep, triple junction diffusion creep and rotational deformation in nanocrystalline materials with emphasis on competition and interaction between these deformation mechanisms and explanation of the key experimentally detected facts. Theoretical models of diffusion enhancement associated with transformations of GB defects in nanocrystalline materials are also considered.

The Effect of Microstructural Inhomogeneity on Grain Boundary Diffusion Creep

AbstractStress concentration at grain boundaries (GB), a phenomena arising from microstructural inhomogeneity, is an important factor in determining the mechanical properties of polycrystalline materials. In this study we use mesoscopic simulations to investigate characteristics of the deformation mechanism of grain-boundary diffusion creep (Coble creep) in a polycrystalline material. The stress distribution along the grain boundaries in a polycrystalline solid under externally applied stress is determined and the mechanism of how topological inhomogeneities introduce stress concentrations is investigated. Microstructures with inhomogeneities of various sizes and distributions are considered and their effect on the stress distribution and creep rate is quantified.

Simulation of grain-boundary diffusion creep: analysis of some new numerical techniques

We consider the simulation of deformation of polycrystalline materials by grain–boundary diffusion creep. For a given network of grain boundaries intersecting at nodes, with appropriate boundary conditions, we can calculate the rate at which material will be dissolved or deposited along each grain boundary and hence predict the rate at which each grain will move to accommodate this dissolution/deposition. We discuss two numerical methods for simulating the network changes over a finite time–interval, based on using the movement of adjacent grain boundaries over a small time–interval to estimate the velocities of the nodes. (The second of these methods has enabled us to speed up solution by 100 times in typical experiments compared with a naive forward–Euler approach.) We show that the accuracy with which the node velocities can be estimated is dependent only on the precision of the machine with which they are computed and deduce that, for all practical purposes, the lack of precise node velocity values does not detract from the quality of our solution. Finally, we consider the underlying stability of the problem under various different boundary conditions and conclude that our methods have the potential for providing useful insight into the effect of grain size and shape on deformation in polycrystalline materials.

Effects of grain growth on grain-boundary diffusion creep by molecular-dynamics simulation

Molecular-dynamics simulations are used to elucidate the effects of grain growth on grain-boundary diffusion creep and grain-boundary sliding during high-temperature deformation of a nanocrystalline Pd model microstructure. The initial microstructure consists of a 25-grain polycrystal with an average grain size of about 15 nm and a columnar grain shape. Prior to the onset of significant grain growth, the deformation proceeds via the mechanism of Coble creep accompanied by grain-boundary sliding. While grain growth is generally known to decrease the creep rate due to the increase of the average grain size, the results obtained in this study reveal an enhanced creep rate at the onset of the grain growth, when rapid grain-boundary migration occurs. The enhanced creep rate is shown to arise from topological changes during the initial growth phases, which enhance both the stress-induced grain-boundary diffusive fluxes and grain-boundary sliding. Dislocations generated as a result of grain-rotation-induced grain coalescence and grain-boundary decomposition in the vicinity of certain triple junctions also contribute to the deformation.

Can metamorphic reactions proceed faster than bulk strain?

Available constraints on metamorphic reaction rates derived from the study of natural systems are similar to, or slightly lower than, the bulk strain rates measured in the same rocks. Here, we explore whether this apparent relationship is merely coincidence or due to a more fundamental mechanistic link between reaction and strain. Grain boundary migration accommodated dislocation creep (GBMDC) or grain boundary diffusion creep (GBDC) (i.e. pressure solution), both of which involve dissolution-precipitation as we define it, will occur simultaneously with mineral reactions involving dissolution-precipitation in the presence of a non-zero deviatoric stress. The exact relationships between reaction and strain are different depending on whether GBMDC or GBDC is controlling strain, but the mechanistic link exists in both cases. We present theoretical arguments which show that bulk strain by GBMDC or GBDC, which may additionally be accommodated by processes not involving dissolution-precipitation, such as dislocation glide and climb or grain boundary sliding, should in most cases be somewhat faster than the bulk reaction rates as observed. With few exceptions, for natural metamorphic systems undergoing plastic deformation, strain rates provide an upper limit for bulk reaction rates occurring simultaneously in the same rocks. The data suggest that mineral reaction rates may typically be within one order of magnitude of the strain rate.

Deformation mechanism and inverse Hall–Petch behavior in nanocrystalline materials

Abstract It is widely accepted that for the very smallest grain sizes (typically below 20–30 nm), dislocations play no significant role in the deformation of nanocrystalline materials. However, the grain-boundary mechanisms responsible for the reported decrease in strength with decreasing grain size in this regime (the ‘inverse Hall–Petch effect’) remain unclear. Here, we demonstrate by molecular-dynamics simulation that, in the absence of both grain growth and any dislocations, nanocrystalline fcc metals deform via a mechanism involving an intricate interplay between grain-boundary sliding and grain-boundary diffusion. By quantitatively reproducing the well-known Coble-creep formula for coarsegrained materials, we show that the ‘inverse Hall–Petch effect’ arises from sliding-accommodated grain-boundary diffusion creep. Previous, apparently contradictory, suggestions that GB sliding, on the one hand, or GB-diffusion creep, on the other, are responsible for this behavior can thus be reconciled as originati...

Stress-enhanced grain growth in a nanocrystalline material by molecular-dynamics simulation

Molecular-dynamics simulations are used to elucidate the coupling between grain growth and grain-boundary diffusion creep in a polycrystal consisting of 25 grains with an average grain size of about 15 nm and a columnar grain shape. Consistent with our earlier simulations of grain-boundary diffusion creep, albeit in the absence of grain growth, we find that initially, i.e. prior to the onset of significant grain growth, the deformation proceeds via the mechanism of Coble creep. Also, consistent with our earlier grain-growth simulations in the absence of stress, two growth mechanisms are observed during the deformation: growth due to curvature-driven GB migration and growth resulting from grain rotation-induced grain coalescence. The comparison of the grain growth observed in the presence of the applied stress with that solely in response to temperature as the driving force enables us to identify the mechanisms by which external stress affects grain growth. In particular, we find that both GB migration and grain rotation are accelerated by the deformation.

Grain-boundary diffusion-controlled stress concentration in polycrystals

Mesoscopic simulations are used to elucidate the fundamental effects of microstructural inhomogeneity in polycrystalline materials on grain-boundary diffusion creep (Coble creep). Considering two-dimensional model micro-structures with a distribution in the grain sizes and grain-boundary diffusivities, we determine the stress distribution along the grain boundaries during diffusion creep. Our simulations reveal that two distinct types of microstructural inhomogeneity have similar effects on the diffusion creep. The purely topological inhomogeneities, arising from the presence of the distributions in the grain sizes and grain shapes, cause the larger grains to experience much higher stresses than the smaller grains do. Moreover, even in a topologically uniform microstructure, a distribution in the grain-boundary diffusivities can lead to even higher stress concentrations than those caused by the topological inhomogeneities alone.

Stress Relaxation during Isothermal Annealing at Elevated Temperatures in Electroplated Cu Films

ABSTRACTDeformation mechanisms of electroplated Cu thin films on TaN/SiO2/Si were investigated by performing isothermal annealing above 200 °C. Stress relaxation behavior during isothermal annealing was analyzed by curve fitting using exponential decay equations. During heating, fast relaxation and subsequent slow relaxation processes were observed. In contrast, during cooling, only slow relaxation process was observed. Among possible mechanisms for stress relaxation, diffusion creep was found to be the most plausible mechanism based on the obtained values of the activation energy. It was suggested that the slow relaxation process observed both in the heating and in the cooling processes was attributed to a grain-boundary diffusion creep. On the other hand, the fast relaxation process observed during heating was attributed to a surface-diffusion controlled mechanism. The surface diffusion mechanism was considered to be characteristic to Cu thin films that did not form stable surface oxide.

Coble-creep response and variability of grain-boundary properties

A microstructural model of steady-state creep that couples grain-boundary transport, micromechanics, and grain sliding is employed to investigate the grain-boundary diffusional creep response of an idealized microstructure with variable boundary diffusivities. Both numerical and analytical methods were used to determine the stress state and, in some cases, the strain rate associated with an applied uniaxial, tensile stress. Various types of boundaries are considered, and the implications of our results for more general microstructures are discussed.

Grain-boundary diffusion creep in nanocrystalline palladium by molecular-dynamics simulation

Molecular-dynamics (MD) simulations of fully three-dimensional (3D), model nanocrystalline face-centered cubic metal microstructures are used to study grain-boundary (GB) diffusion creep, one mechanism considered to contribute to the deformation of nanocrystalline materials. To overcome the well-known limitations associated with the relatively short time interval used in our MD simulation (typically <10 −8 s), our simulations are performed at elevated temperatures where the distinct effects of GB diffusion are clearly identifiable. In order to prevent grain growth and thus to enable steady-state diffusion creep to be observed, our input microstructures were tailored to (1) have a uniform grain shape and a uniform grain size of nm dimensions and (2) contain only high-energy GBs which are known to exhibit rather fast, liquid-like self-diffusion. Our simulations reveal that under relatively high tensile stresses these microstructures, indeed, exhibit steady-state diffusion creep that is homogeneous, with a strain rate that agrees quantitatively with that given by the Coble-creep formula. The grain-size scaling of the Coble creep is found to decrease from d −3 to d −2 when the grain diameter becomes of the order of the GB width. For the first time a direct observation of the grain-boundary sliding as an accommodation mechanism for the Coble creep, known as Lifshitz sliding, is reported.

High-temperature creep in a Ni 2 GeO 4 : a contribution to creep systematics in spinel

High-temperature creep behavior in Ni2GeO4 spinel was investigated using synthetic polycrystalline aggregates with average grain sizes ranging from submicron to 7.4 microns. Cylindrical samples were deformed at constant load in a gas-medium apparatus at temperatures ranging from 1223 to 1523 K and stresses ranging from 40 to 320 MPa. Two deformation mechanisms were identified, characterized by the following flow laws: where σ is in MPa, d is in μm and T is in Kelvin. These flow laws suggest that deformation was accommodated by dislocation creep and grain-boundary diffusion (Coble) creep, respectively. A comparison with other spinels shows that an isomechanical group can be defined for spinels although some differences between normal and inverse spinels can be identified. When creep data for olivine and spinel are normalized and extrapolated to Earth-like conditions, spinel (ringwoodite) has a strength similar to olivine in the dislocation creep regime and is considerably stronger than olivine in the diffusion creep regime at coarse grain size. However, when grain-size reduction occurs, spinel can become weaker than olivine due to its high grain-size sensitivity (Coble creep behavior). Analysis of normalized diffusion creep data for olivine and spinel indicate that spinel is weaker than olivine at grain sizes less than 2 μm.