Boundary Diffusion Creep Research Articles

Megathrust Shear Modulated by Albite Metasomatism in Subduction Mélanges

AbstractAseismic megathrust slip downdip of the seismogenic zone is accommodated by either steady creep or episodic slow slip events (SSEs). However, the geological conditions defining the rheology of megathrust slip remain elusive. We examined exhumed subduction mélanges on Kyushu, Japan, which deformed at ∼370–500°C under greenschist to epidote‐amphibolite facies conditions, comparable to warm‐slab environments. The mélanges recorded fluid release and viscous shear localization associated with metasomatic reactions between juxtaposed metapelitic and metabasaltic rocks. Metasomatic reactions caused albitization of metapelite, resulting in depth‐dependent changes to megathrust rheology. In a mélange deformed at ∼370°C, very fine grained reaction products (metasomatic albite) facilitated grain boundary diffusion creep at stresses of ∼45 MPa, less than those in the surrounding metabasalt. Mineralogical and chemical changes during metasomatic reactions, and their field content, imply an onset of albite metasomatism at ∼350°C. Albite metasomatism therefore potentially contributed to decreased megathrust strength around the inferred thermally controlled base of the seismogenic zone. In a mélange deformed near the mantle wedge corner at ∼500°C, metasomatic reactions promoted local quartz vein formation and localized viscous shear at slow slip strain rates, during which the coarse‐grained metasomatic albite behaved as relatively rigid blocks in a viscous matrix. We suggest that albite metasomatism can facilitate changes in a megathrust slip mode with depth and may explain why slip mode changes from creep to SSEs with tremor with increasing depth.

A unifying basis for the interplay of stress and chemical processes in the Earth: support from diverse experiments

The interplay between stress and chemical processes is a fundamental aspect of how rocks evolve, relevant for understanding fracturing due to metamorphic volume change, deformation by pressure solution and diffusion creep, and the effects of stress on mineral reactions in crust and mantle. There is no agreed microscale theory for how stress and chemistry interact, so here I review support from eight different types of the experiment for a relationship between stress and chemistry which is specific to individual interfaces: (chemical potential) = (Helmholtz free energy) + (normal stress at interface) × (molar volume). The experiments encompass temperatures from -100 to 1300 degrees C and pressures from 1 bar to 1.8 GPa. The equation applies to boundaries with fluid and to incoherent solid–solid boundaries. It is broadly in accord with experiments that describe the behaviours of free and stressed crystal faces next to solutions, that document flow laws for pressure solution and diffusion creep, that address polymorphic transformations under stress, and that investigate volume changes in solid-state reactions. The accord is not in all cases quantitative, but the equation is still used to assist the explanation. An implication is that the chemical potential varies depending on the interface, so there is no unique driving force for reaction in stressed systems. Instead, the overall evolution will be determined by combinations of reaction pathways and kinetic factors. The equation described here should be a foundation for grain-scale models, which are a prerequisite for predicting larger scale Earth behaviour when stress and chemical processes interact. It is relevant for all depths in the Earth from the uppermost crust (pressure solution in basin compaction, creep on faults), reactive fluid flow systems (serpentinisation), the deeper crust (orogenic metamorphism), the upper mantle (diffusion creep), the transition zone (phase changes in stressed subducting slabs) to the lower mantle and core mantle boundary (diffusion creep).

Ductility limit diagrams for superplasticity and forging of high temperature polycrystalline materials

A mechanistic understanding of the ductility limit diagrams is of critical importance, but it still remains elusive for a multitude of high temperature materials processing techniques, such as superplastic forming and hot forging. The relevant failure modes for the former are necking at high strain rates and intergranular cavitation at low strain rates, while those for the latter include the competition between longitudinal fracture and shear band. The comparison between the Arrhenius processes for grain boundary diffusion and grain interior creep defines a length scale that dictates whether the grain boundary cavity growth is diffusive or creep-constrained. A quantitative assessment of these damage evolution processes leads to the delineation of the dominant parametric spaces for individual failure modes, and thus superplasticity and forging limit diagrams are derived and compared to available experiments in literature.

Ductility Limit Diagrams for Superplasticity and Forging of High Temperature Polycrystalline Materials

A mechanistic understanding of the ductility limit diagrams is of critical importance, but it still remains elusive for a multitude of high temperature materials processing techniques, such as superplastic forming and hot forging. The relevant failure modes for the former are necking at high strain rates and intergranular cavitation at low strain rates, while those for the latter include the competition between longitudinal fracture and shear band. The comparison between the Arrhenius processes for grain boundary diffusion and grain interior creep defines a length scale that dictates whether the grain boundary cavity growth is diffusive or creep-constrained. A quantitative assessment of these damage evolution processes leads to the delineation of the dominant parametric spaces for individual failure modes, and thus superplasticity and forging limit diagrams are derived and compared to available experiments in literature.

Type IV failure in weldment of creep resistant ferritic alloys: II. Creep fracture and lifetime prediction

The creep rupture behavior (Type IV failure) for weldments of creep strength enhanced ferritic steel is numerically analyzed, using an integrated microstructure- and micromechanics-based finite element model. To account for the large microstructure gradients across weldments, a two-dimensional digital microstructure is constructed based on the actual observed microstructure of ferritic steel weldment by using the Voronoi-tessellation method. According to the fracture mechanism studies and literature experimental observations, the Type IV failure is identified as an intergranular creep fracture in the fine-grained or intercritical heated affected zone (FGHAZ or ICHAZ). In the present study, the following micromechanics model is employed to determine the micromechanical and microstructural origins for the failure process above, accounting for the underlying physical fracture mechanisms at different length scales, including nucleation of grain boundary cavities, their growth by competition of grain boundary diffusion and grain interior creep, viscous grain boundary sliding, and the emergence of microcracks by coalescence and their evolution to the ultimate failure. The methodology demonstrates the capabilities in modeling the Type IV failure and providing quantitative creep rupture lifetime prediction which shows an excellent agreement with long-term creep experimental data for creep strength enhanced ferritic steels and their weldments. In particular, the drop-off in time to rupture at high temperatures and low stress levels in the creep rupture curves is quantitatively predicted, and the transition of failure mechanisms from creep-controlled to diffusion-controlled creep fracture mechanism is illustrated.

Diffusion Creep and Grain Growth in Forsterite +20 vol% Enstatite Aggregates: 1. High‐Resolution Experiments and Their Data Analyses

AbstractWe conducted uniaxial compression and grain growth experiments on fine‐grained (~1 μm) forsterite +20 vol% enstatite aggregates. Based on analyses of the sensitivity of the strain rate as a function of stress, we find power law creep at low stress, Newtonian creep at intermediate stress, and again power law creep at high stress, which correspond to interface‐controlled diffusion creep, grain boundary diffusion (Coble) creep, and a dislocation‐controlled process, respectively. The creep rate of these samples is well expressed by a combination of strain rates of these three mechanisms where interface‐controlled and Coble creep rates are combined as series‐sequential processes, while the rate of the dislocation process is added with them as a parallel‐concurrent process. Mechanical data collected continuously during the application of a constant load but while slowly changing temperature were decomposed into data for every 1 °C, which allowed consideration of >600 mechanical data points from 1054 to 1370 °C. The data were analyzed using Bayesian statistics implementing a Markov chain Monte Carlo method imposed on the above constitutive equation, resulting in the best fit flow law parameters for interface‐controlled and Coble creep. Samples were annealed for 500 hr at various temperatures. A comparison of the final grain sizes as a function of temperature on an Arrhenius plot resulted in an activation energy for grain growth similar to that observed for grain boundary diffusion during Coble creep of these materials.

Diffusion Creep and Grain Growth in Forsterite +20 vol% Enstatite Aggregates: 2. Their Common Diffusional Mechanism and Its Consequence for Weak‐Temperature‐Dependent Viscosity

AbstractWe determined the rate‐controlling diffusivities for creep and grain growth of forsterite +20 vol% enstatite aggregates from the experimental results presented in Part 1 of this study. Both diffusivities exhibit similar values with similar temperature dependency, indicating that a common grain boundary diffusion process controls both creep and grain growth. This correspondence is due to the presence of pyroxene grains as a secondary phase in the olivine aggregate, which is the case for the majority of mantle‐derived rocks. As a consequence, the viscosity (η) of the material during deformation by grain boundary diffusion creep accompanied by grain growth changes with time (t) and temperature (T) as where QGB is the activation energy for grain boundary diffusion and R is gas constant. This viscosity relationship is used to interpret the very low activation energy estimated for the viscosity of the oceanic mantle lithosphere.

Nature of creep deformation in nanocrystalline Tungsten

Because of Tungsten’s (W) use in high temperature and stress environments like next generation fusion reactors, exploring the creep deformation mechanism in this material is very essential. In this work, for the first time, nature of creep in nanocrystalline (nc) Tungsten and factors that govern the creep mechanism like grain size, temperature, and applied stress are studied through atomistic simulations. Applied stress is varied from 2.5 to 5.5 GPa on the metallic sample while the temperature is varied in the range of 1600–2200 K. Stress and temperature variance are repeated for average grain sizes of 2.38 nm, 2.86 nm, 3.57 nm, and 4.76 nm. From the simulations, it has been found that the creep mechanism in nanocrystalline Tungsten is contingent on the applied stress as the creep mechanism varies from lattice diffusion to grain boundary diffusion creep even up to dislocation-creep. Moreover, temperature and grain refinement seem to aid the creep phenomenon at nanoscale. For very large value of stress and temperature, the power-law fails to define the creep in nc-Tungsten. In order to quantify the propensity and mechanism of creep in nanocrystalline Tungsten, stress and grain size exponents are observed in addition to the time evolution of strain and mean square displacement. Finally, atomistic features of deformation are analyzed which evince the simulation results.

Polycrystal anelasticity at near‐solidus temperatures

AbstractElasticity, anelasticity, and viscosity of polycrystalline aggregates were measured at the near‐solidus temperatures ranging from below to above the solidus temperature (Tm). The result shows that the mechanical effects of the partial melting are twofold; changes just below the solidus temperature in the absence of melt and changes at the solidus temperature due to the onset of partial melting. As homologous temperature (T/Tm) increases from about 0.92 to 1, high‐frequency part of the attenuation spectrum significantly grows. Viscosity of the grain boundary diffusion creep is also reduced in this temperature range. These changes are caused by a solid‐state mechanism and have a large amplitude even for the samples which can generate very small amounts of melt at the solidus temperature. At the onset of melting, further increases in the elastic, anelastic, and viscous compliances occur. These changes are caused by the direct effects of the melt phase and are very small for the samples with very small melt fractions. Mechanical properties of a partially molten aggregate are determined by these twofold changes, and when melt fraction is small, the former changes are dominant. We performed a parameterization of the present experimental results and applied the obtained empirical formula to the seismic tomographic data in the upper mantle. The present model explains well the steep reduction of the seismic shear wave velocity in the oceanic lithosphere just below the solidus temperature.

Strain localization during high temperature creep of marble: The effect of inclusions

The deformation of rocks in the Earth's middle and lower crust is often localized in ductile shear zones. To better understand the initiation and propagation of high-temperature shear zones induced by the presence of structural and material heterogeneities, we performed deformation experiments in the dislocation creep regime on Carrara marble samples containing weak (limestone) or strong (novaculite) second phase inclusions. The samples were mostly deformed in torsion at a bulk shear strain rate of ≈1.9×10−4s−1 to bulk shear strains γ between 0.02 and 2.9 using a Paterson-type gas deformation apparatus at 900°C temperature and 400MPa confining pressure. At low strain, twisted specimens with weak inclusions show minor strain hardening that is replaced by strain weakening at γ>0.1–0.2. Peak shear stress at the imposed conditions is about 20MPa, which is ≈8% lower than the strength of intact samples. Strain progressively localized within the matrix with increasing bulk strain, but decayed rapidly with increasing distance from the inclusion tip. Microstructural analysis shows twinning and recrystallization within this process zone, with a strong crystallographic preferred orientation, dominated by {r} and (c) slip in <a>. Recrystallization-induced weakening starts at local shear strain of about 1 in the process zone, corresponding to a bulk shear strain of about 0.1. In contrast, torsion of a sample containing strong inclusions deformed at similar stress as inclusion-free samples, but do not show localization. The experiments demonstrate that the presence of weak heterogeneities initiates localized creep at local stress concentrations around the inclusion tips. Recrystallization-induced grain size reduction may only locally promote grain boundary diffusion creep. Accordingly, the bulk strength of the twisted aggregate is close to or slightly below the lower (isostress) strength bound, determined from the flow strength and volume fraction of matrix and inclusions.

Creep Behavior of 409L and 436 Ferritic Stainless Steels Applied for Automotive Exhaust System

In order to investigate the creep behavior and understand its deformation mechanism of automotive exhaust pipe materials, this study conducted creep experiments of 409L and 436 ferritic stainless steels at both 600°C and 750°C under different stress levels. After creep tests, crept specimens were analyzed on the microstructure and fracture surfaces by the use of scanning electron microscopy. From creep data, two important material coefficients, namely, M of Monkman-Grant relationship and K of Coble creep equation are calculated for predicting the material creep life. Results show the creep resistance of 436 stainless steel is better than that of 409L stainless steel, because the 436 stainless steel has more Ni, Cr, and Mo contents. As the creep mechanism, all tests show grain boundary diffusion or Coble creep is the dominate deformation mechanism, except at higher temperature 750 °C and higher stress levels.

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.

Creep and its effect on Sn whisker growth

A comprehensive quantitative whisker growth theory has been developed. In this theory whisker growth is controlled by the ratio of the long range grain boundary diffusion creep relaxation rate to the short range creep relaxation rate. The theory relies solely on solid state diffusion effects and does not require additional constraints or assumptions to explain whisker growth. It explains a number of heretofore relatively poorly explained and puzzling observations reported over the past 6 decades, including: (i) Sn films that are 1–10 μm thick are more susceptible to whisker growth than thinner or thicker films; (ii) Sn film contamination in the form of hydrocarbons, Cu, hydrogen, etc., tend to increase the whisker propensity; (iii) as-deposited Sn films tend to be more susceptible to whisker growth than fused films; (iv) postplate annealing tends to improve the whisker resistance; (v) whisker growth rate tends toward zero as the temperature exceeds 100 °C; (vi) whisker growth propensity depends upon the crystallographic orientation of the Sn film; and (vii) the large statistical variations reported in whisker density and incubation time. The theory predicts: (i) the magnitude of the as deposited film stress state is not fundamental to whisker growth; (ii) at high stresses where power law creep relaxation dominates, whiskers do not form.; (iii) whiskers occur in those regions of the film that are exposed to stresses lower than that required for power law creep; (iv) whiskers form when a quasiequilibrium stress state is achieved as the stress in the film tends toward zero; (v) anything that affects (limits or restrains) power law creep and its associated stress dissipation, such as grain boundary pinning, increases the propensity for whisker growth; (vi) pinning tends to increase the whisker propensity and increase the whisker growth rate; and (vii) films with certain crystallographic orientations and grain sizes are less prone to whisker growth, independent of the anisotropic thermomechanical properties, as a result of the anisotropic diffusion behavior of Sn.

Viscous constitutive relations of solid‐liquid composites in terms of grain boundary contiguity: 2. Compositional model for small melt fractions

We develop a compositional model for the grain boundary (GB) diffusion creep of melt‐bearing polycrystalline aggregates. This model is an extension of the GB diffusion control model by taking into account the effects of finite liquid diffusivity and finite reaction rates, which are important at small melt fractions (ϕ). For shear viscosity η, there exists a critical melt fraction ϕcη below which the rate‐limiting process changes from diffusion through GB to diffusion through the liquid, and for bulk viscosity ξ, there exists a critical melt fraction ϕcξ below which the rate‐limiting process changes from diffusion through GB to reaction at the pore surface. The implication of the model results is that different processes may limit the kinetics of bulk and shear viscosities at small ϕ. The model also predicts that stress can cause compositional and hence volumetric asymmetry in pores. As melt fraction increases from zero to the critical melt fractions, rapid decreases occur in η, from ηcc to 0.2ηcc, and in ξ, from ∞ to 0.4ηcc, where ηcc represents η for Coble creep. In the GB diffusion control model, these decreases occur discontinuously at zero melt fraction, but this singularity is removed in the compositional model. For a typical grain size in the mantle (3 mm), the critical melt fractions are estimated semiquantitatively as ϕcη = 10−4 and ϕcξ &lt; 6 × 10−8, demonstrating the significant effect of very small amount of melt on the viscosities in the mantle.

Viscous constitutive relations of solid‐liquid composites in terms of grain boundary contiguity: 1. Grain boundary diffusion control model

Viscous constitutive relations of partially molten rocks deforming in the regime of grain boundary (GB) diffusion creep are derived theoretically on the basis of microstructural processes at the grain scale. The viscous constitutive relation developed in this study is based on contiguity as an internal state variable, which enables us to take into account the detailed effects of grain‐scale melt distribution observed in experiments. Compared to the elasticities derived previously for the same microstructural model, the viscosities are much more sensitive to the presence of melt and variations in contiguity. As explored in this series of three companion papers, this “contiguity” model predicts that a very small amount of melt (ϕ &lt; 0.01) significantly reduces the bulk and shear viscosities. Furthermore, a large anisotropy in viscosity is produced by anisotropy in contiguity, which occurs in deforming partially molten rocks. These results have important implications for deformation and melt extraction at small melt fractions, as well as for shear‐induced melt segregation. The viscous and elastic constitutive relations derived in terms of contiguity bridge microscopic grain‐scale and macroscopic continuum properties. These constitutive relations are essential for investigating melt migration dynamics in a forward sense on the basis of the basic equations of two‐phase dynamics and in an inverse sense on the basis of seismological observations.

Well-wetted olivine grain boundaries in partially molten peridotite in the asthenosphere

Pore morphology in partially molten peridotites strongly controls many physical properties of the Earth's deep materials. The dihedral angle of the olivine–silicate melt system is a key factor in understanding the physical behavior of the upper mantle. For a limited range of melt compositions, previous studies of wetting behavior have determined dihedral angles of 30–50°. However, the dihedral angle of partially molten peridotites should be variable under a wide range of pressure and temperature conditions, because wetting behavior depends strongly on liquid structure and composition. The dihedral angles of olivine–silicate melt in partially molten peridotite were determined at pressures of 1 to 7 GPa and temperatures between 1473 and 1993 K. The dihedral angle decreased (approaching 0°) with increasing temperature, which corresponds to completely wetted grain boundaries. This angle variation probably depends on a decrease in the solid-melt interfacial energy, which is a product of large change in melt structure. These results suggest that the presence of partial melt would have large influences on the physical properties of the upper mantle even if the melt fraction was very low. If grain boundary diffusion creep dominates in the asthenosphere, the shear strength of partially molten peridotites at asthenospheric pressure (~ 3 GPa) would be much lower than that predicted from experiments at relatively lower pressure (~ 0.3 GPa) because of the extremely low grain boundary contiguity.

Non-conservation of grain volume during diffusion creep

In theories of the diffusion creep of polycrystals it has traditionally been assumed that individual grain volumes are conserved as they change shape. However a recent application of the theory to the creep of beams under small bending moments has shown that this need not be the case (Burton, to be published). In the present paper the theory is further extended to include cases where grain volume is not conserved during creep under tension. An analysis is presented for the grain boundary diffusion creep of a uniform array of orthorhombic grains of dimensions X, Y and Z, aligned with continuous boundaries in the XZ planes and a tensile stress normal to these planes. The analysis is simplified by assuming Z»X and Y, so that diffusion occurs along boundaries in the x and y directions only. In specimens of finite size, the non-conservation of grain volume is shown to occur as an inevitable consequence of diffusion creep. Surface grains lose volume by diffusion to grains in the interior, which gain in volume. The effect diminishes with the distance of the grain from the surface. The effects are largest for grains highly elongated along the stress axis (Y/X»1), when diffusion along boundaries in the y direction is relatively low. For smaller Y/X ratios, diffusion in the y direction makes increasing contributions but grain volume is again not conserved. When the number of grains in the cross-section is large, creep rates are predicted to converge with those for an infinite array.

Melt-assisted interior to margin switch from dislocation to diffusion creep in coarse grained plagioclase: Evidence from a deformed anorthosite pluton

At Bolangir (Eastern India), massive anorthosites in the pluton interior grade into anorthosites with outward-dipping, margin-parallel foliation neighboring the pluton margin. Sheets and veins of ferrodiorites – residual melts of anorthosite crystallization – concordant and discordant to the margin-parallel foliation suggest pluton deformation at near magmatic conditions, T ∼ 950 °C and P 6–12 kbar. In the pluton interior, the larger-than-centimeter sized magmatic plagioclase grains are replaced by aggregates of smaller (100–600 μm) dynamically recrystallized internally-strained grains with un-equilibrated boundaries. Neighboring the pluton margin, poly-sized (200–2500 μm) plagioclase grains in anorthosites are of two types: strain-free rectangular-shaped plagioclase grains with high-energy An-richer margins indenting neighboring plagioclase grains formed by diffusion creep, whereas unstrained end-to-end touching euhedral plagioclase grains showing tilling represent magmatic flow textures. The pluton interior-to-margin switch in plagioclase deformation from grain boundary migration accommodated dislocation creep to grain boundary diffusion creep is attributed to the increasing melt fraction (melt/crystal ratio) during syn-deformation pluton emplacement. Plagioclase grains in the Bolangir pluton are significantly coarser compared to plagioclase aggregates (<200 μm) in experiments designed to understand deformation mechanisms. The present study demonstrates that presence of melts promoted diffusion creep over dislocation creep, albeit in larger-than-experiment plagioclase grains.

Misorientations of garnet aggregate within a vein: an example from the Sanbagawa metamorphic belt, Japan

AbstractIn this study, the chemistry and microstructure of garnet aggregates within a metamorphic vein are investigated. Garnet‐bearing veins in the Sanbagawa metamorphic belt, Japan, occur subparallel to the foliation of a host mafic schist, but some cut the foliation at low angle. Backscattered electron image and compositional mapping using EPMA and crystallographic orientation maps from electron‐backscattered diffraction (EBSD) reveal that numerous small garnet (10–100 μm diameter) coalesce to form large porphyroblasts within the vein. Individual small garnet commonly exhibits xenomorphic shape at garnet/garnet grain boundaries, whereas it is idiomorphic at garnet/quartz boundaries. EBSD microstructural analysis of the garnet porphyroblasts reveals that misorientation angles of neighbour‐pair garnet grains within the vein have a random distribution. This contrasts with previous studies that found coalescence of garnet in mica schist leads to an increased frequency of low angle misorientation boundaries by misorientation‐driven rotation. As garnet nucleated with random orientation, the difference in misorientation between the two studies is due to the difference in the extent of grain rotation. A simple kinetic model that assumes grain rotation of garnet is rate‐limited by grain boundary diffusion creep of matrix quartz, shows that (i) the substantial rotation of a fine garnet grain could occur for the conditions of the Sanbagawa metamorphism, but (ii) the rotation rate drastically decreased as garnet grains formed large clusters during growth. Therefore, the random misorientation distribution of garnet porphyroblasts in the Sanbagawa vein is interpreted as follows: (i) garnet within the vein grew so fast that substantial grain rotation did not occur through porphyroblast formation, and thus (ii) random orientations at the nucleation stage were preserved. The extent of misorientation‐driven rotation indicated by deviation from random orientation distribution may be useful to constrain the growth rate of constituent grains of porphyroblast that formed by multiple nucleation and coalescence.

Reappraisal of grain boundary diffusion creep equations for nanocrystalline materials

Grain boundary diffusion creep equations developed previously for nanocrystalline materials were reappraised in order to elicit further understanding of plastic deformation of these materials in relation to grain boundary diffusion. From a mechanistic viewpoint, the strain rate is inversely proportional to the second power of the grain size when the grain size is refined to the same order of the grain boundary thickness. The presence of the threshold stress appears to be inherent, as a relatively large volume fraction of the grain boundary region is associated with irregularities.