Coble Creep Research Articles

Representative Volume Element Model for Quantitatively Predicting the Influence of 3d Polycrystalline Morphology on Coble Creep Deformation

Representative Volume Element Model for Quantitatively Predicting the Influence of 3d Polycrystalline Morphology on Coble Creep Deformation

Influence of grain size on the high-temperature creep behaviour of M5Framatome1 zirconium alloy under vacuum

The effect of grain size on the viscoplastic behaviour of M5Framatome zirconium alloy thin sheets was investigated at high temperature under uniaxial tension, using a variety of equiaxed microstructures with controlled grain sizes. In the α phase domain, a Coble diffusional creep regime and a dislocation creep regime were observed, in agreement with the literature. A negative sensitivity of the strain rate to temperature was highlighted in the upper part of the α+β two-phase temperature range, consistently with the literature. For the first time, a linear creep regime was evidenced in the β phase domain. In this regime, a sensitivity of the strain rate on the third power of the grain size is observed, suggesting a Coble regime with diffusion along grain boundaries. Modelling with multi-mechanism Norton power-law rate equations, including dependence on grain size and a homogenous strain-rate assumption (Taylor model), enabled to satisfactorily reproduce the experimental results over the 700–1100 °C temperature range, especially the negative sensitivity of the strain rate to temperature between 880 and 930 °C. Very good agreement was obtained with a second order self-consistent and full field homogenization schemes.

Thermodynamics-driven interfacial engineering of alloy-type anode materials

Alloy-type anodes can enable high specific capacity for Li-ion batteries, but the large volume change during cycling often causes fast-capacity fading. Here, we report a thermodynamically driven grain boundary engineering method to improve alloy-type anodes via the spontaneous formation of 2D interfacial phases (complexions). Notably, the 2.8 at% Bi-doped SnSb achieves improved cycling stability and rate capability, even though it is 99% dense and has a mean crystallite size 2.7× larger than the undoped SnSb reference sample. Cryogenic transmission electron microscopy reveals Bi segregation at grain boundaries. Thermodynamic modeling further suggests the stabilization of a nanoscale liquid-like interfacial phase. Synchrotron transmission X-ray microscopy shows the suppressed intergranular cracking upon cycling with Bi addition. It suggests that the liquid-like interfacial phase serves as a stress relief mechanism for the high volumetric expansion anode via improved grain boundary sliding and Coble creep, akin to room-temperature superplasticity observed in Sn-Bi. • Spontaneously formed liquid-like interfacial phase improves the SnSb-Bi anode • Cryogenic STEM reveals Bi segregation at SnSb grain boundaries • Transmission X-ray microscopy shows the suppressed cracking upon cycling • Liquid-like interfacial phase promotes grain boundary sliding and Coble creep Alloy-type anodes are promising for Li-ion batteries, but the large volume change during electrochemical cycling can cause fast degradation. Yan et al. report a thermodynamics-driven interfacial engineering method to improve alloy-type anodes via the spontaneous formation of liquid-like interfacial phase that promotes room temperature superplasticity to alleviate cracking.

Shear-coupled migration of grain boundaries: the key missing link in the mechanical behavior of small-grained metals?

Grain size reduction is a very efficient way to block dislocation movements and therefore create very strong metals and alloys. Not only grain boundaries are known obstacles for dislocations, but when reaching nanometer dimensions, crystallites usually become dislocation free, which imposes an additional constraint to develop plasticity. A recent effort to understand grain boundaries-based deformation mechanisms has therefore emerged. These mechanisms can be manifold, involving conservative and diffusive processes that are very poorly understood. A first approach consisting in downscaling mechanisms that are documented at large scale such as Coble creep, proved very limited. On the other hand, stress-assisted grain growth or shear-coupled grain boundary migration, that were recently observed in small-grained materials at room or low temperature may provide a crucial step to fully understand dislocation-less plasticity in nanocrystals. As this is a completely new field with many more degrees of freedom, a continuous research effort has to be carried out to link the mechanical properties of nanocrystals to these mechanisms specifically linked to grain boundaries.

Atomistic processes of surface-diffusion-induced abnormal softening in nanoscale metallic crystals

Ultrahigh surface-to-volume ratio in nanoscale materials, could dramatically facilitate mass transport, leading to surface-mediated diffusion similar to Coble-type creep in polycrystalline materials. Unfortunately, the Coble creep is just a conceptual model, and the associated physical mechanisms of mass transport have never been revealed at atomic scale. Akin to the ambiguities in Coble creep, atomic surface diffusion in nanoscale crystals remains largely unclear, especially when mediating yielding and plastic flow. Here, by using in situ nanomechanical testing under high-resolution transmission electron microscope, we find that the diffusion-assisted dislocation nucleation induces the transition from a normal to an inverse Hall-Petch-like relation of the strength-size dependence and the surface-creep leads to the abnormal softening in flow stress with the reduction in size of nanoscale silver, contrary to the classical “alternating dislocation starvation” behavior in nanoscale platinum. This work provides insights into the atomic-scale mechanisms of diffusion-mediated deformation in nanoscale materials, and impact on the design for ultrasmall-sized nanomechanical devices.

Contribution of the nucleation and recovery of disconnections to shear viscosity in diffusional creep

According to the principles of diffusional creep, the normal and tangent components of the velocity jumps between adjacent grains arise from, respectively, the climbing and sliding of disconnections along grain boundaries. Stationary deformation thus implies a balance between nucleation and recovery of moving disconnections. The model considers a periodic lattice of hexagonal grains with nucleation of disconnection multipoles at triple junctions. The strain energy coupled to the population of climbing disconnections is calculated by inferring that the internal strain field associated to disconnection pile-ups brings a distribution of tractions along GBs that is consistent with the field of diffusion potential gradient that drives disconnection climb. It follows that the distribution of the density of climbing disconnections is parabolic and that the dissipation due to the nucleation and recovery of climbing disconnections is equal to 50% of the dissipation arising from diffusion fluxes. These results hold for both Nabarro-Herring creep and Coble creep. The analysis of the disconnection nucleation process highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.

Contribution of the Nucleation and Recovery of Disconnections to Shear Viscosity in Diffusional Creep

According to the principles of diffusional creep, the normal and tangent components of the velocity jumps between adjacent grains arise from, respectively, the climbing and sliding of disconnections along grain boundaries. Stationary deformation thus implies a balance between nucleation and recovery of moving disconnections. The model considers a periodic lattice of hexagonal grains with nucleation of disconnection multipoles at triple junctions. The strain energy coupled to the population of climbing disconnections is calculated by inferring that the internal strain field associated to disconnection pile-ups brings a distribution of tractions along GBs that is consistent with the field of diffusion potential gradient that drives disconnection climb. It follows that the distribution of the density of climbing disconnections is parabolic and that the contribution to dissipation is equal to 50% of the contribution arising from diffusion fluxes. These results hold for both Nabarro-Herring creep and Coble creep. The analysis of the disconnection nucleation process highlights the sources of non-Newtonian behaviour and the existence of a threshold stress as an intrinsic feature of diffusional creep.

A micropolar continuum model of diffusion creep

ABSTRACT Solid polycrystalline materials undergoing diffusion creep are usually described by Cauchy continuum models with a Newtonian viscous rheology dependent on the grain size. Such a continuum lacks the rotational degrees of freedom needed to describe grain rotation. Here we provide a more general continuum description of diffusion creep that includes grain rotation, and identifies the deformation of the material with that of a micropolar (Cosserat) fluid. We derive expressions for the micropolar constitutive tensors by a homogenisation of the physics describing a discrete collection of rigid grains, demanding an equivalent dissipation between the discrete and continuum descriptions. General constitutive laws are derived for both Coble (grain-boundary diffusion) and Nabarro-Herring (volume diffusion) creep. Detailed calculations are performed for a two-dimensional tiling of irregular hexagonal grains, which illustrates a potential coupling between the rotational and translational degrees of freedom. If only the plating out or removal of material at grain boundaries is considered, the constitutive laws are degenerate: modes of deformation that involve pure tangential motion at the grain boundaries are not resisted. This degeneracy can be removed by including the resistance to grain-boundary sliding, or by imposing additional constraints on the deformation.

A Study of the Impact of Graphite on the Kinetics of SPS in Nano- and Submicron WC-10%Co Powder Compositions

This study investigates the impact of carbon on the kinetics of the spark plasma sintering (SPS) of nano- and submicron powders WC-10 wt.%Co. Carbon, in the form of graphite, was introduced into powders by mixing. The activation energy of solid-phase sintering was determined for the conditions of isothermal and continuous heating. It has been demonstrated that increasing the carbon content leads to a decrease in the fraction of η-phase particles and a shift of the shrinkage curve towards lower heating temperatures. It has been established that increasing the graphite content in nano- and submicron powders has no significant effect on the SPS activation energy for “mid-range” heating temperatures, QS(I). The value of QS(I) is close to the activation energy of grain-boundary diffusion in cobalt. It has been demonstrated that increasing the content of graphite leads to a significant decrease in the SPS activation energy, QS(II), for “higher-range” heating temperatures due to lower concentration of tungsten atoms in cobalt-based γ-phase. It has been established that the sintering kinetics of fine-grained WC-Co hard alloys is limited by the intensity of diffusion creep of cobalt (Coble creep).

The role of grain boundary mobility in diffusional deformation

The model of diffusional deformation is revisited by accounting for the dependence of the diffusion potential on grain boundary curvature. The issue is developed through the analysis of two case-studies: the deformation of a lattice of columnar grains in conditions of Coble creep, and the rotation of a grain embedded in a polycrystal in conditions of either Nabarro-Herring creep or Coble creep. The analysis reveals that, unless grain boundary mobility is infinite, grain boundary curvature is dynamically induced by strain rate. A link is established between the curvature distribution and the transfer of diffusion fluxes across grain boundaries. For the two case-studies, the equation expressing the balance of grain boundary motions at steady-state is solved for calculating, within a range of grain boundary mobilities, the grain boundary profiles, the diffusion fluxes, and the contributions to power dissipation arising from curvature. The latter contributions are found to scale closely as the square of grain size. It follows that the dissipation contribution due to curvature is larger in conditions of Nabarro-Herring creep. In conditions of Coble creep, the dissipation contribution due to curvature translates into a lower bound for the apparent boundary viscosity parameter to be used in numerical simulations. This lower bound is consistent with previous identifications of the parameter in the literature. The classical model assuming flat grain boundaries with transfer of fluxes via triple junctions emerges as a particular case involving the implicit assumption of an infinite grain boundary mobility.

Atomic-scale investigation of creep behavior and deformation mechanism in nanocrystalline FeCrAl alloys

FeCrAl alloys have been proposed as nuclear fuel cladding materials in hope of offering great potential in accident tolerance for light water reactors. However, only a limited amount of data has been published on their creep properties. This work aims to provide an atomic-scale insight into the creep behavior and deformation mechanism for nanocrystalline FeCrAl alloys, using molecular dynamics method. Both primary and steady state creeps are observed in all creep curves, and tertiary creep occurs at stresses above 2.5 GPa in the time period of the present simulation. As stress increases, the creep mechanism transits from Coble creep to grain boundary sliding, and then to the synergy of grain boundary sliding and dislocation creep. The turning points are about 0.8 GPa and 1.8 GPa, respectively. The dislocation motions are controlled by viscous gliding at low temperature, and then by climbing when temperature exceeds 1000 K. Moreover, the grain size and alloy composition have little impact on the transition of creep mechanism within the present research scope. The proposed creep mechanisms are further analyzed not only from the comparison between activation energies for diffusion and creep, but also from the representative atomic snapshots.

Understanding and eliminating thermo-mechanically induced radial cracks in fully metallized through-glass via (TGV) substrates

This work aims to understand and eliminate the formation of thermo-mechanically induced radial cracks in copper (Cu) metallized through-glass via (TGV) substrates made of Corning® high purity fused silica (HPFS® fused silica), after subjection to 420 °C annealing treatment. Radial cracks were found to be formed in Cu TGV substrate during the heating step of annealing treatment process, caused by high stress buildup resulting from the large mismatch in the coefficient of thermal expansion (CTE) between the HPFS® fused silica substrate and the Cu metallization. From analytical studies, high tensile circumferential stresses were found to be the main stress component that is responsible for the formation of radial cracks during heating. From experimental studies, it was found that radial crack formation was exponentially dependent on the applied heating rate, and that faster heating rate increased the probability for their formation. However, a crack-free metallized TGV substrate was achieved when heating rates ≤6.5 °C/min was applied, thus, eliminating radial crack formation. Radial crack elimination was attributed to the significant activation of stress relaxation mechanisms in the Cu. This was confirmed by the measurement of an inverse dependence of Cu protrusion with the applied heating rate. Additionally, the Cu protrusion data confirms that the leading stress relaxation mechanisms in the Cu TGV were grain boundary sliding (GBS), plastic deformation and Coble diffusional creep.

Stress-Assisted Thermal Diffusion Barrier Breakdown in Ion Beam Deposited Cu/W Nano-Multilayers on Si Substrate Observed by in Situ GISAXS and Transmission EDX.

The thermal stability of Cu/W nano-multilayers deposited on a Si substrate using ion beam deposition was analyzed in situ by GISAXS and transmission EDX—a combination of methods permitting the observation of diffusion processes within buried layers. Further supporting techniques such as XRR, TEM, WAXS, and AFM were employed to develop an extensive microstructural understanding of the multilayer before and during heating. It was found that the pronounced in-plane compressive residual stress and defect population induced by ion beam deposition result in low thermal stability driven by thermally activated self-interstitial and vacancy diffusion, ultimately leading to complete degradation of the layered structure at moderate temperatures. The formation of Cu protrusions was observed, and a model was formulated for stress-assisted Cu diffusion driven by Coble creep along W grain boundaries, along with the interaction with Si substrate, which showed excellent agreement with the observed experimental data. The model provided the explanation for the experimentally observed strong correlation between thin film deposition conditions, microstructural properties, and low thermal stability that can be applied to other multilayer systems.

Valorising emissions from steel making into sustainable products

A micromechanical model is developed to predict microstructure evolution and the resultant in-plane modulus increase in a thermal barrier coating (TBC) manufactured by air plasma spray (APS). The model is based on the experimental observation that the main sintering events include the progressive healing of the inter-splat cracks and the coarsening of the columnar grains within the splats. During sintering, the splats undergo Coble creep, which relaxes the constraint on crack healing and therefore sintering. Given its columnar structure, the creep response of the splats is taken to be transversely isotropic. The proposed model is implemented numerically using finite element (FE) meshes that have been developed from cross-sectional micrographs of an as-deposited coating. This allows the evolution of microstructural features directly relevant to the performance of TBCs to be modelled, from which the overall elastic response can also be determined. The curvy nature of the nearly horizontal inter-splat cracks and the intersecting vertical intra-splat cracks explain the low in-plane modulus of the as-deposited TBC and their healing explains the evolution of in-plane modulus during sintering. The model results are validated by comparison with sintering experiments, in terms of the evolution of crack patterns and in-plane modulus. The sensitivity of the model results to the major geometrical parameters is explored and summarised in the form of a sintering map, which identifies the controlling processes as a function of the microstructural and kinetic properties. Finally, the effect of constraint on the overall sintering response is investigated.

An image-based model for the sintering of air plasma sprayed thermal barrier coatings

A micromechanical model is developed to predict microstructure evolution and the resultant in-plane modulus increase in a thermal barrier coating (TBC) manufactured by air plasma spray (APS). The model is based on the experimental observation that the main sintering events include the progressive healing of the inter-splat cracks and the coarsening of the columnar grains within the splats. During sintering, the splats undergo Coble creep, which relaxes the constraint on crack healing and therefore sintering. Given its columnar structure, the creep response of the splats is taken to be transversely isotropic. The proposed model is implemented numerically using finite element (FE) meshes that have been developed from cross-sectional micrographs of an as-deposited coating. This allows the evolution of microstructural features directly relevant to the performance of TBCs to be modelled, from which the overall elastic response can also be determined. The curvy nature of the nearly horizontal inter-splat cracks and the intersecting vertical intra-splat cracks explain the low in-plane modulus of the as-deposited TBC and their healing explains the evolution of in-plane modulus during sintering. The model results are validated by comparison with sintering experiments, in terms of the evolution of crack patterns and in-plane modulus. The sensitivity of the model results to the major geometrical parameters is explored and summarised in the form of a sintering map, which identifies the controlling processes as a function of the microstructural and kinetic properties. Finally, the effect of constraint on the overall sintering response is investigated.

Ultralow-cobalt hard alloys obtained by spark plasma sintering

The features of spark plasma sintering (SPS) of plasma-chemical nanopowders WC-(0.3, 0.6, 1) wt.% Co were studied. The SPS process of ultralow-cobalt hard alloys can be sequentially represented as a change of the following mechanisms: rearrangement of particles at lower temperatures (Stage I) → sintering of WC-Co particles due to Coble diffusion creep of cobalt, the intensity of which is determined by the grain boundary diffusion rate (Stage II ) → sintering due to diffusion creep, the rate of which is limited by the bulk diffusion in cobalt (Stage III-1) → sintering of tungsten carbide particles along the intergranular boundaries of WC / WC under conditions of intensive grain growth (Stage III-2). Samples with a high density (96.4-98.4%) and high mechanical properties were obtained (for the WC-0.3% Co hard alloy: Hv ∼ 20.5 GPa, KIC = 7.1 MPa · m1/2).

Fundamental principles of spark plasma sintering of metals: part III – densification by plasticity and creep deformation

ABSTRACT The mechanisms of densification during spark plasma sintering (SPS) of spherical copper particles are investigated both experimentally and analytically. Experimentally measured densification rates are compared to expected contributions to densification coming from Coble creep, Nabarro-Herring creep, power-law creep, and pressure-assisted sintering described by the two-particle model. The results indicate densification by Coble creep or a low-temperature version of power-law creep in the investigated range of temperature and pressure at a relative density of 70%. The findings are supported by (i) activation energies obtained for various conditions using the Dorn-method as well as (ii) the pressure dependence of the densification rate.

The Role of Grain Boundary Curvature in Diffusional Deformation: Control of Grain Boundary Sliding by Grain Boundary Mobility

The diffusion processes involved in the accommodation of grain boundary sliding in diffusional deformation are revisited by considering the role of grain boundary curvature and of the associated grain boundary migration. A method is developed for calculating grain boundary profiles, diffusional fluxes, and the dissipation power arising from the coupling of diffusion fluxes and grain boundary migration during the quasi-steady-state stage of deformation. In conditions of dominance of Coble creep, the controlling length scale is the square root of the ratio of grain boundary diffusivity to grain boundary mobility. Zero curvature is the particular solution valid when mobility is infinite. The analysis brings the definition of a lower bound for the grain boundary viscosity parameter to be used in numerical simulations of diffusional deformation. This lower bound is consistent with previous identifications of the parameter in literature.

Ultrahigh temperature in situ transmission electron microscopy based bicrystal coble creep in zirconia I: Nanowire growth and interfacial diffusivity

This work demonstrates novel in situ transmission electron microscopy-based microscale single grain boundary Coble creep experiments used to grow nanowires through a solid-state process in cubic ZrO2 between ≈ 1200 °C and ≈ 2100 °C. Experiments indicate Coble creep drives the formation of nanowires from asperity contacts during tensile displacement, which is confirmed by phase field simulations. The experiments also facilitate efficient measurement of grain boundary diffusivity and surface diffusivity. 10 mol% Sc2O3 doped ZrO2 is found to have a cation grain boundary diffusivity of Dgb=(0.056±0.05)exp(−380,000±41,000RT)m2s−1, and surface diffusivity of Ds=(0.10±0.27)exp(−380,000±28,000RT)m2s−1.

Ultrahigh temperature in situ transmission electron microscopy based bicrystal coble creep in Zirconia II: Interfacial thermodynamics and transport mechanisms

This work uses a combination of stress dependent single grain boundary Coble creep and zero-creep experiments to measure interfacial energies, along with grain boundary point defect formation and migration volumes in cubic ZrO2. These data, along with interfacial diffusivities measured in a companion paper are then applied to analyzing two-particle sintering. The analysis presented indicates that the large activation volume, v*=vf+vmprimarily derives from a large migration volume and suggests that the grain boundary rate limiting defects are delocalized, possibly due to electrostatic interactions between charge compensating defects. The discrete nature of the sintering and creep process observed in the small-scale experiments supports the hypothesis that grain boundary dislocations serve as sources and sinks for grain boundary point defects and facilitate strain during sintering and Coble creep. Model two-particle sintering experiments demonstrate that initial-stage densification follows interface reaction rate-limited kinetics.