Numerical modeling and experimental characterization of the pyroplasticity in ceramic materials during sintering

Pasquale Bene1, a, Danilo Bardaro2,b, Daniela Bello3,c and Orazio Manni4,d 1,2,3,4Consorzio CETMA Centro di Progettazione Design & Tecnologie dei Materiali, Cittadella della

Ricerca - Brindisi (Italy) apasquale.bene@cetma.it, bdanilo.bardaro@cetma.it, cdaniela.bello@cetma.it,

dorazio.manni@cetma.it

Keywords: Ceramic materials, sintering, sanitaryware, pyroplastic deformation, FE numerical analysis, CNC manufacturing.

Abstract. The aim of the work is the study of the pyroplasticity in ceramic materials in order to simulate the deformations of complex ceramic component during sintering. A ceramic material undergoing densification can be treated as a linear viscous material. Generally, the viscosity decreases as the temperature increases, however the densification and the consequent grain growth, result in a viscosity increase. A bending creep test is proposed for measuring the change in viscosity of the ceramic material during densification. Equations, based on beam deflection theory, are derived to determine the viscosity during the whole firing cycle by measuring the deflection in the centre of specimens. In addition, dilatometric analyses are performed to measure the sintering shrinkage and the specimen density, which continuously changes during the sintering process. On the basis of an accurate experimental characterization the parameters of Maxwell viscoelastic constitutive law are derived. A numerical-experimental procedure has been adopted in order to calibrate the numerical model that, finally, has been used to predict the pyroplastic deformations of complex ceramic components.

Ceramic material behaviour during sintering

The main objectives of the study are the experimental characterization of the behaviour of ceramic materials during sintering and the development of an accurate numerical model to simulate sintering process. During sintering processes a traditional ceramic material undergoes a lot of physical and chemical transformations. From a macroscopic mechanical point of view the main interests are the shrinkage prediction and the estimation of the pyroplastic deformation under material own weight. During firing, ceramic materials, undergoing densification, exhibit a linear viscous behaviour. For a two point bend creep test, by using the beam deflection theory and the linear elastic to viscous analogy [1,2,3,4], it’s possible to derive the following relationship:

20x

4

hδ32gL5η=

ρ=

&. (1)

where η is the material viscosity, ρ the density, h the specimen thickness, g the gravity acceleration, L the span length and 0xδ =

& is the deflection rate at beam center. Dilatometric tests are used to determine material shrinkage and density evolution during the sintering cycle. Finally starting from dilatometric analyses and the previous relation, by measuring the deflection of a specimen during a pyroplastic test, the viscosity of a ceramic material during the sintering cycle can be assessed.

Advances in Science and Technology Vol. 62 (2010) pp 203-208Online available since 2010/Oct/27 at www.scientific.net© (2010) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AST.62.203

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Experimental Characterization

Experimental tests has been carried out by means of an optical instrument, Misura FLEX-ODLT, a combined equipment able to perform flexural and dilatometric tests (Fig. 1). The ceramic material under study (Vitreous China) is highly deformable. The choice of a non-contact measurement method allows to investigate the thermo-mechanical behaviour of the material without compromising the measure, so that the material is completely free to expand or contract or to deform under its own weight. In this study, the instrument has been used to perform both thermal expansion and pyroplastic deformation measurements. Dilatometric analyses have been performed to measure sintering shrinkage and density of Vitreous China during sintering.

a) b)

Fig. 1 Misura FLEX-ODLT: a) dilatometric test configuration; b) two point bend creep test configuration

Bending creep test is performed to investigate the pyroplastic behavior of Vitreous China during firing. At temperatures of about 900-1000°C the feldspar content of raw materials melts; this turns into a viscosity decrease that causes the pyroplastic deformation. On the other end, during the thermal cycle, the sintering process involves an increase of the density and as a consequence an increase of the viscosity. The aim of bending creep test is to measure the viscosity of ceramic material during densifications (Eq. 1). The standard bending creep test procedure has highlighted some drawbacks related to the viscous behavior of Vitreous china. At high temperature, due to the viscosity decrease, the specimens bond to the instrument support rods and, as a consequence, the pyroplastic properties measurements are compromised. In order to overcome the problem an experimental equipment has been designed and applied to the optical instrument. All the related information are not reported here because they are covered by industrial secret. During experimental tests the specimens are heated up to 1235 °C according to the industrial firing cycle.

Experimental tests results. Sintering shrinkage, measured by a dilatometric analysis, is used to determine material density

evolution during the firing process (Fig. 2 a)). From room temperature up to 800 °C the material behaviour is characterized by a density decrease due to the weight loss caused by residual water evaporation and the decomposition of organic components. At higher temperature the density increase as consequence of porosity closure (sintering).

Fig. 2 b) shows the bending creep test results obtained by means of the developed experimental methodology. Specimen deflection starts at 900 °C, as a consequence of the glass phase presence and the liquid formation due to the feldspar melting. Initially the deflection velocity is high, this is due to the low viscosity of the liquid phases; then the material densification allows the viscosity increase and finally the deflection stops during the cooling phase, at temperature of about 1100°C. The designed experimental equipment has allowed the solution of the problems related to the ceramic material characterization during sintering. Finally the developed methodology has allowed

204 12th INTERNATIONAL CERAMICS CONGRESS PART A

the determination of reliable data to be used in the numerical models able to simulate components behavior.

a)0 200 400 600 800 1000 1200 1400

1,8

1,9

2,0

2,1

2,2

2,3

2,4

dens

ity (g

/cm

3 )

T (°C) b)

0 200 400 600 800 1000 1200 1400

-6

-5

-4

-3

-2

-1

0

1

defle

ctio

n (m

m)

T (°C)

Fig. 2 a) Density evolution during sintering cycle; b) Bending creep test: deflection vs

temperature

Numerical modeling of ceramic material during sintering.

Once the experimental characterization of the material behavior is assessed through the use of simple geometry specimens, it is possible to start the numerical implementation of the finite element model that will simulate the global behavior of ceramic components having a complex geometry. In this frame, the first step is the calibration of a simple numerical model able to reproduce the experimental results. A very important aspect of the study is the definition of the material law that could simulate in a very accurate way the microstructural phenomena involved during material sintering. After a detailed study of the material models existing in the scientific literature for the simulation of sintering processes, two different paths are followed in the present work. The first consists in the use of a viscoelastic model based on the Maxwell law (Eq. 2), the second in the use of a more complex material law based on the theoretical formulation developed by Olevsky and others (Eq. 3). In the last model the increment of the viscoelastic term is a function of the hydrostatic and deviatoric value of the stress acting and it is correlated to microscopic properties (the porosity and the sintering surface energy).

Maxwell constitutive law:

TE

∆α+ησ

+σ

=ε && . (2)

Olevsky constitutive law [5.]:

ijLijijij Pe31

W)W(

δ+⎥⎦

⎤⎢⎣

⎡δ⎟

⎠⎞

⎜⎝⎛ ϕ−ψ+εφ

σ=σ & . (3)

For each case, the implementation of the previous material laws needs the use of dedicated user-subroutines, by means of Fortran programming language [6.], that could be linked to the numerical codes [7.]. Due to the complexity of the second material law, the difficulty to determine microscopic material properties and the very high time required to get a convergent solution in the non linear range, the viscoelastc Maxwell law has been preferred to determine the total deformation of complex ceramic components. The numerical results reported are all referred to this approach. Aiming to design the deformed mould shape for ceramic components, particular attention is required to invert, in an accurate way, the physical phenomena.

Advances in Science and Technology Vol. 62 205

Finally, the finite element analyses consist in: the development and the calibration of the numerical models reproducing simple geometry

tests, the reverse numerical simulation of the pyroplastic behaviour of complex ceramic

components. Simple geometry numerical simulation Fig. 3 shows the numerical results related to a simple geometry model. The numerical simulation

reproduces the bending creep test performed with the fleximeter Misura FLEX-ODLT. Constitutive law parameters implemented in Ansys numerical code are obtained starting from the experimental characterization carried out. Material parameters (viscosity, thermal expansion coefficient, Young’s modulus) are calibrated by means of a sensitivity analysis. A comparison between the experimental and the numerical displacements along the gravity direction shows a good agreement: the FE model is able to correctly predict the material deformation during the sintering cycle.

0 10000 20000 30000 40000 50000

-6

-5

-4

-3

-2

-1

0

1

defle

ctio

n (m

m)

time (sec)

experimetal result numerical result

Fig. 3 Experimental and numerical results comparison Reverse numerical simulation of ceramic complex shapes The same numerical approach is used to simulate the sintering deformation of complex ceramic

shapes. In particular in this study two different geometrical models are used during the simulation and the results obtained are shown in the following figure in terms of contour levels of the total displacements (Fig. 4).

a) b) Fig. 4 Contour levels of total displacements: a) washbasin model 1; b) washbasin model 2 For the post- processing of the numerical results a macro in the APDL (Ansys Parametric Design

Language) has been developed. Because of in the finite element model no geometrical information are included, only nodes and elements are provided as input of the macro. The tool developed

206 12th INTERNATIONAL CERAMICS CONGRESS PART A

allows the creation of an STL file that is provided to CNC machines for the counter-deformed geometry production. In Fig. 5 the STL file and the resin model produced by CNC manufacturing are shown.

a) b) Fig. 5 Counter-deformed geometry of the washbasin model: a) STL file b) Resin model

produced by CNC manufacturing

The resin model is the negative of the mould. Starting from the resin model the plaster mould is produced (Fig. 6). The final product has been realized by means of the industrial process used in the ceramic sector companies (Fig. 7).

The differences between the final products and the target geometry have been measured. The results obtained are in good agreement with industry standards required. The experimental validation demonstrates the reliability of the innovative mould design methodology for the ceramic components production and its industrial application.

Fig. 6 Plaster Mould for the production of the washbasin model 1

Fig. 7 Final product

Advances in Science and Technology Vol. 62 207

Conclusions

An innovative method to design new ceramic components of complex shape is proposed. A detailed experimental characterization of the material behaviour during the sintering processes provides the data necessary for the numerical simulation of body deformations. In particular, by means of finite element analysis it’s possible to predict the pyroplastic deformations of ceramic material during sintering processes. Finally, a dedicated tool allows the creation of an STL model of the counter-deformed shape necessary for the CNC manufacturing and the mould production.

References

[1.] S.H. Lee, G. L. Messing, D. J. Green, “Bending creep test to measure the viscosity of porous materials during sintering” J. Am. Ceram. Soc., 86 [6] 877–82 (2003)

[2.] A. Mohanram, G. L. Messing, D. J. Green, “Measurement of Viscosity of Densifying Glass-Based Systems by Isothermal Cyclic Loading Dilatometry”, J. Am. Ceram. Soc., 87 [2] 192–96 (2004).

[3.] P. Z. Cai, G. L. Messing, and D. J. Green, “Determination of the Mechanical Response of Sintering Compacts by Cyclic Loading Dilatometry”, J. Am. Ceram.Soc., 80 [2] 445–452 (1997).

[4.] Sam E. Schoenberg, David J. Green, Gary L. Messing, “Effect of Green Density on the Thermomechanical Properties of a Ceramic During Sintering”, J. Am. Ceram. Soc., 89 [8] 2448–2452 (2006).

[5.] Olevsky, E.A. – “Theory of sintering: from discrete to continuum”. Mater. Sci. Eng. R, 1998, 23, 41-100

[6.] Ansys User Material Subroutine USERMAT, Mechanics Group, Development Department, Ansys, Inc. Southpointe 275 Technology Drive, Canonsburg, PA 15317 (1999)

[7.] UIDL Programmer’s Guide Ansys Release 10 Manual, Inc. Southpointe 275 Technology Drive, Canonsburg, PA 15317 (August 2005)

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during Sintering 10.4028/www.scientific.net/AST.62.203

DOI References

[1] ] S.H. Lee, G. L. Messing, D. J. Green, “Bending creep test to measure the viscosity of porous aterials

during sintering” J. Am. Ceram. Soc., 86 [6] 877–82 (2003)

doi:10.1111/j.1151-2916.2003.tb03391.x [2] ] A. Mohanram, G. L. Messing, D. J. Green, “Measurement of Viscosity of Densifying Glass- ased

Systems by Isothermal Cyclic Loading Dilatometry”, J. Am. Ceram. Soc., 87 [2] 192–96 2004).

doi:10.1111/j.1551-2916.2004.00192.x [3] ] P. Z. Cai, G. L. Messing, and D. J. Green, “Determination of the Mechanical Response of intering

Compacts by Cyclic Loading Dilatometry”, J. Am. Ceram.Soc., 80 [2] 445–452 (1997).

doi:10.1111/j.1151-2916.1997.tb02850.x [4] ] Sam E. Schoenberg, David J. Green, Gary L. Messing, “Effect of Green Density on the

hermomechanical Properties of a Ceramic During Sintering”, J. Am. Ceram. Soc., 89 [8] 2448– 452 (2006).

doi:10.1111/j.1551-2916.2006.01182.x [5] ] Olevsky, E.A. – “Theory of sintering: from discrete to continuum”. Mater. Sci. Eng. R, 1998, 3, 41-100

doi:10.1016/S0927-796X(98)00009-6