Effect of grain boundary sliding on shear viscosity and viscous Poisson’s ratio in macroscopic shrinkage during sintering

Wakai, Fumihiro; Nikolić, Z.

doi:10.1016/j.actamat.2010.10.021

Cited by 20 publications

(18 citation statements)

References 36 publications

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“…Modeling of the kinetics of sintering of solid aggregates in the presence of a vapor phase has continued to develop steadily during the last 20 yr . In the absence of external loading, the driving force for sintering is the partial derivative of interface energy with respect to the volume of vapor:

Σ = {()(, \frac{\partial E_{normalinterface}}{\partial V_{normalv}})}_{V_{s}}

with

E_{normalinterface} = {normalγ}_{normalsv} A_{normalsv} + {normalγ}_{normalss} A_{normalss} = {normalγ}_{normalsv} [A_{normalsv} + 2 cos (\frac{ψ}{2}) A_{normalss}]

where V v and V s are the volumes of vapor and solid, A sv and A ss are the interface areas solid/vapor and solid/solid, γ sv and γ ss are the interface tensions solid/vapor and solid/solid, which are supposed isotropic, and ψ = 2arccos (γ ss /2γ sv ) is the dihedral angle when γ sv ≥ γ ss /2.…”

Section: Introductionmentioning

confidence: 99%

“…The average grain size will be characterized by the radius R G of the sphere having the same volume as the average volume, V G , of the grains in the aggregate. Whereas Σ varies as R G −1 [according to relations and ], K varies as R G −3 in the case of a rheology controlled by grain‐boundary diffusion [see below, relations and ]. It thus follows from relation that the sintering rate

\overset{ρ}{true}

varies as R G −4 .…”

Section: Introductionmentioning

confidence: 99%

“…Section presents computational results on the evolution of sintering stress, bulk viscosity, and densification rate across the transition between the intermediate stage and the final stage. To allow comparison with results of previous models based on periodic grain arrangements, the curves are calculated for integer values of coordination number n c which do not change with relative density ρ. A very good agreement is generally demonstrated in spite of the different approximations involved.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Influence of Dihedral Angle and Grain Coordination on Densification Rate During Intermediate and Final Sintering Stages

Delannay

2015

J. Am. Ceram. Soc.

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The evolution of sintering stress, bulk viscosity, and densification rate during the intermediate stage and the final stage of sintering of random aggregates of particles is simulated using a new model able to account for the monotonous increase in the coordination number during sintering. For the intermediate stage, the representative volume element is a cone of revolution whereas, for the final stage, it is volume centered on a closed pore located at quadruple point. Care is taken to warrant the continuity between the two models at the transition between the two stages. Computations allow tracing the variation in sintering stress and bulk viscosity with relative density, coordination, and dihedral angle during the two stages, as well as at the transition between them. They show how, as a result, densification rate is enhanced by the increase in coordination. The model is assessed via comparison of the computed curves with the predictions of previous models based on periodic 3D arrangements, in which grain coordination number is constrained to jump between integer values. The agreement is generally very good in spite of the different approximations involved.

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Σ = {()(, \frac{\partial E_{normalinterface}}{\partial V_{normalv}})}_{V_{s}}

with

E_{normalinterface} = {normalγ}_{normalsv} A_{normalsv} + {normalγ}_{normalss} A_{normalss} = {normalγ}_{normalsv} [A_{normalsv} + 2 cos (\frac{ψ}{2}) A_{normalss}]

Section: Introductionmentioning

confidence: 99%

\overset{ρ}{true}

varies as R G −4 .…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Influence of Dihedral Angle and Grain Coordination on Densification Rate During Intermediate and Final Sintering Stages

Delannay

2015

J. Am. Ceram. Soc.

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“…Simulations clearly suggest that all these phenomena are sensitive to several parameters including the boundary sliding viscosity, η * . In isotropic systems, the viscous Poisson's ratio is dependent on η * . Experimentally, it will be important to develop strategies to control η * since the viscous Poisson's ratio is expected to have a profound effect on important quantities like the magnitude of the stresses generated in constrained sintering, and the axial stress needed for zero‐radial shrinkage in sinter forging .…”

Section: Discussionmentioning

confidence: 99%

“…structure changes its sign, when C 12 crosses and exceeds C 13 at η * = 0.006. The effects of η * on the viscous shear modulus and viscous Poisson's ratios have been fully analyzed for isotropic systems . We use a fixed value η * = 0.001 in the present analysis hereafter.…”

Section: Effect Of Microstructure and Microscopic Kinetics On Continumentioning

confidence: 99%

Microstructural Evolution and Anisotropic Shrinkage in Constrained Sintering and Sinter Forging

Wakai

Bordia

2012

J. Am. Ceram. Soc.

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The microstructures of sintering bodies become anisotropic in constrained sintering of a thin film on rigid substrate, as well as in stress‐assisted densifications such as sinter forging and hot pressing. The deformation and the stress states in the body have been described by general constitutive equations using sintering stress tensor and viscosity tensor. These macroscopic quantities were determined from local microstructure and microscopic kinetics for the special case of face‐centered tetragonal structure. The simulation results were applied to the cases of sinter forging and constrained sintering and qualitatively compared to the experimental results available in the literature. This model is able to predict both the evolution of the anisotropic microstructure during sintering, and also the effect of the local micro‐structure on anisotropic shrinkage.

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Mechanics of sintering for coupled grain boundary and surface diffusion

Wakai

Brakke

2011

Acta Materialia

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Effect of grain boundary sliding on shear viscosity and viscous Poisson’s ratio in macroscopic shrinkage during sintering

Cited by 20 publications

References 36 publications

Influence of Dihedral Angle and Grain Coordination on Densification Rate During Intermediate and Final Sintering Stages

Influence of Dihedral Angle and Grain Coordination on Densification Rate During Intermediate and Final Sintering Stages

Microstructural Evolution and Anisotropic Shrinkage in Constrained Sintering and Sinter Forging

Mechanics of sintering for coupled grain boundary and surface diffusion

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