COMPREHENSIVE METHOD OF STUDYING AND PREDICTING
THE DEFORMATION OF CERAMIC PRODUCTS DURING SINTERING
D. V. Andreev
and A. I. Zakharov
Translated from Novye Ogneupory, No. 9, pp. 41 – 51, September, 2013.
Original article submitted July 26, 2013.
A comprehensive method is proposed for predicting the deformation of ceramic products under their own
weight (the force of gravity) during sintering. The method is based on the torsion of thin-walled tubes, fi
nite-element modeling, a calibration process that includes tests of specimens of the material in cantilever
bending, and validation of the numerical solution. The method can be used to predict the deformation of
thin-walled and solid products made of materials whose rheology is based on the mechanisms of viscous
and/or diffusion flow.
Keywords: ceramic products, prediction, modeling, finite-elements method, calibration, validation, deforma
tion, creep, viscosity.
Automated finite-element (FE) modeling is one of the
modern tools now being used to design ceramic products.
Such modeling makes it possible to predict the deformation
of semifinished products, but their use requires an adequate
rheological model of the given material and its empirical ver-
It is known that ceramic materials exhibit nonlinear
viscoelastic properties during sintering . Under static
loading, their rheology is often represented by a mathemati
cal model that combines an elastic spring with a damper in a
series connection. Under dynamic loading, the rheology of
ceramics is represented by the viscoelastic state model
(Fig. 1). Whereas the deformation e of ceramics is mainly the
result of viscous flow during static loading, this need not be
considered in the viscoelastic case. As regards the latter, the
material’s deformation can be represented as the purely vis
cous flow which it undergoes during a certain period of time
t [2, 3]. Here, it is generally assumed that the deformation
which ceramics experience due to sintering and the applied
stresses s are subject to the superposition principle  and
that these materials’ rheology can be modeled by a simple
linear-viscous constitutive relation (Newton’s law for vis
cous flow) [2 – 4]. It is noteworthy that the linear character
of this relation is consistent with diffusion-based creep mod
els — which also posit a linear relationship between stress
and deformation rate.
Among the fine-grained ceramics whose sintering in-
volves the participation of a liquid phase, materials of the
porcelain group present the greatest challenge in terms of be-
ing able to predict their deformation. The difficulty stems
from their complex variable composition and the high proba-
bility of deformation due to the presence of a large amount of
the liquid phase. During sintering, a glazed porcelain semi
finished product can be regarded as a three-layer material
that experiences a change in it properties. The semifinished
product consists of the porcelain substrate, a glaze coating,
and an intermediate layer whose mechanical and other prop
erties are appropriately anisotropic. The porcelain undergo
ing sintering is itself a complex micro-composite material
that includes a nonuniform fluid-like material and structural
units such as pores and crystalline phases [5, 6]. The ratio of
the amount of matrix to the amount of structural units in the
Refractories and Industrial Ceramics Vol. 54, No. 5, January, 2014
1083-4877/14/05405-0366 © 2014 Springer Science+Business Media New York
Russian University of Chemical Engineering, Moscow, Russia.
Fig. 1. Mechanical model of viscous behavior: the viscous element
is series-connected to a quasi-elastic coupling composed of a
damper and two elastic elements.