MATHEMATICAL SIMULATION OF THE THERMAL STABILITY
OF MAGNESIUM OXIDE
A. V. Zabolotskii
Translated from Novye Ogneupory, No. 6, pp. 90 – 97, June 2011.
Original article submitted April 6, 2011.
A simulation of the behavior of nonporous single-crystal magnesium oxide under conditions of heat loading
that approach the operating conditions of casting ladles in ferrous metallurgy is performed by means of mathe-
matical methods. Both numerical and analytic methods are used for the calculations. The temperature and me-
chanical stress fields and such breakdown parameters of materials as the moment of appearance of cracks, the
thermal stability criterion (breakdown temperature drop of surface of material), etc. were determined as a re-
sult of the calculations. Results of calculations are presented and an analysis of the application of mathemati-
cal methods to the simulation of different heat treatment regimes of a material is performed.
Keywords: thermal shock, mathematical simulation, thermal stability criterion
Thermal shock, understood as a sharp variation in the
temperature of the surface of a material, is one of the basic
causes of damage and failure of refractory linings in metal-
lurgy. It may lead to breakdown of the lining at the very start
of a run of equipment. For example, inflow of cold ambient
air into lining that has been heated to the temperature of a
metallic melt will lead with a high degree of probability to
the appearance of through-the-thickness cracks in its work-
ing layer. Attempts at calculating the thermal stability of ma-
terials were begun in the late nineteenth century by
Winkelman and Schott. In the mid-1900s Kingery and
Hasselman proposed a series of thermal stability criteria that
relate the minimum drop in the temperature of the surface of
a material that lead to the appearance of cracks or breakdown
with such quantities as the ultimate strength, temperature co-
efficient of linear expansion, modulus of elasticity, Poisson
coefficient, thermal conductivity, and thermal capacity [1–3].
The most comprehensive variant of the criterion may be
represented by the following expression:
is the breakdown drop in temperature; s
ing stress (ultimate strength of material); m, Poisson coeffi-
cient, which characterizes the capacity of a material to be-
come plastically deformed under the effect of a mechanical
load; y, a coefficient that characterizes the rate of heating of
the sample; E, modulus of elasticity; a, coefficient of ther-
mal expansion; and S, form factor. With the use of this vari-
ant expression of the criterion it becomes possible to deter-
mine the breakdown temperature drop of the surface of a
sample in the case of a “sufficiently rapid” variation in the
temperature drop achieved under practical conditions, for ex-
ample, in the form of thermal shock.
The rate of variation of the temperature of a surface is
taken into account by the coefficient y, which is a function
of the Biot criterion, which in turn characterizes the relation-
ship between the rate of heat transfer to the surface and in-
side the material:
is the characteristic dimension of the sample (thick-
ness or diameter); r
, coefficient of heat transfer to surface;
and l, thermal conductivity; The coefficient y varies from 0
to 1 and is equal to 1 once the value of the Biot criterion ex
ceeds 20 .
Refractories and Industrial Ceramics Vol. 52, No. 3, September, 2011
1083-4877/11/05203-0170 © 2011 Springer Science+Business Media, Inc.
OOO Gruppa Magnezit, Russia.