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3D printing of porcelain: finite element simulation of anisotropic sintering

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Abstract

Sintering is a key step that determines the mechanical performances and shape quality of 3D printed ceramics. In this domain, there is an increasing interest in complex thin structures and low fill density shapes. However, these complex structures may suffer from distortions by gravity forces developed on the light structure, friction with supports, shrinkage anisotropy, or thermal gradients. Finite element simulation of the sintering process is then of high importance for predicting the specimens distortions. This paper focuses on the identification of the model parameters in the special case of anisotropic sintering of porcelain with final stage swelling. This study points out the printed specimen high resistance to high temperature shear deformation due to the alignment of the printed rods. A mesoscale simulation has been carried out to explain this mechanism. The resulting model was tested for the sintering of a thin wall cup shape.

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All data is published with the paper.

Abbreviations

θ :

Porosity

\( \dot{\theta} \) :

Porosity rate (s−1)

\( \underset{\_}{\sigma } \) :

Stress tensor (N m−2)

σ eq :

Equivalent stress (N m−2)

\( \underset{\_}{\dot{\varepsilon}} \) :

Strain rate tensor (s−1)

\( {\dot{\varepsilon}}_{eq} \) :

Equivalent strain rate (s−1)

\( {\dot{\varepsilon}}_r \) :

Radial strain rate component (s−1)

\( {\dot{\varepsilon}}_z \) :

Z axis strain rate component (s−1)

\( {\dot{\varepsilon}}_{sintering} \) :

Free strain rate due to sintering (s−1)

φ :

Shear modulus

ψ :

Bulk modulus

θ c :

Critical porosity for sintering final stage

Pl :

Sintering stress (Pa)

P s :

Pore gas pressure in closed porosity (Pa)

\( \mathbbm{i} \) :

Identity tensor

α :

Surface energy (J m−2)

r :

Grain radius (m)

\( \dot{e} \) :

Trace of the strain rate tensor (s−1)

η :

Material viscosity (Pa s)

η r :

Radial component of the viscosity (Pa s)

η z :

Z component of the viscosity (Pa s)

η 0 :

Viscosity pre-exponential factor (Pa s)

η 0r :

Radial component of the viscosity pre-exponential factor (Pa s)

η 0z :

Z component of the viscosity pre-exponential factor (Pa s)

Q :

Viscosity activation energy (J mol−1)

R :

Gas constant 8.314 (J mol−1 K−1)

T :

Temperature (K)

σ yz :

YZ stress component (N m−2)

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Acknowledgements

The help and support of Jérôme Lecourt and Christelle Bilot is gratefully acknowledged.

Code availability

The simulation software Comsol Multiphysics 5.5 is a commercially licensed product of Comsol Corporation.

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Authors and Affiliations

  1. Normandie Univ, ENSICAEN, UNICAEN, CNRS, CRISMAT, 14000, Caen, France

    Charles Manière, Christelle Harnois & Sylvain Marinel

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  1. Charles Manière
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  2. Christelle Harnois
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Charles Manière: Conceptualization, supervision, modeling, writing; Christelle Harnois: conceptualization, review, and editing; Sylvain Marinel: Conceptualization, supervision, review, and editing.

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Correspondence to Charles Manière.

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Manière, C., Harnois, C. & Marinel, S. 3D printing of porcelain: finite element simulation of anisotropic sintering. Int J Adv Manuf Technol 116, 3263–3275 (2021). https://doi.org/10.1007/s00170-021-07304-y

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