Simulation of Thermal Barrier Plasma-Sprayed Coatings
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SIMULATION OF THERMAL BARRIER PLASMA-SPRAYED COATINGS MAURO FERRARI
,
JOHN H. HARDING
AND MAURIZIO MARCHESE
Istituto di Meccanica Teorica e Applicata, via Ungheria 43, 33100 Udine, Italy. ** Harwell Laboratory, Theoretical Physics Division, Building 424. 4, Didcot, Oxon ORA, United Kingdom *** Dipartimento di Meccanica Strutturale e Progettazione Automatica, Universita' di Trento, Italy. ABSTRACT A general method for the analysis of the thermal stresses of plasma-sprayed thermal barrier coatings is presented. It employs a simulation technique for the reproduction of the microstructural data. Homogenization theories are used, in conjunction with symbolic analysis, in order to obtain a piece-wise homogeneous effective representation of the coating, starting from these data. The temperature portrait and the thermo-elastic fields are numerically obtained. THERMOELASTIC FIELD EQUATIONS The equilibrium equations of the general linear thermoelastic problem are :
div(Ce) + pb = div(Cs*) + pv
(1)
where C, b, and v stand for the stiffness tensor, the body force density and the velocity, respectively, while p represents the mass density and c is the symmetric part of the displacement gradient, i.e., the strain tensor. This tensor is the sum of the elastic strain e and the thermal strain c* : C =
The stress tensor stiffness C:
T
(2)
C* + e.
is related to the
elastic
strain
through
the
(3)
T =Ce
and the thermal strain is given as a* = o 6T through the thermal expansion tensor a
(4) and
the
temperature
field 6T, which may be a function of time and position.
Mat. Res. Soc. Symp. Proc. Vol. 190. 01991 Materials Research Society
difference
222
THE MODELLIL NG The finite element method was selected to determine detailed stress states in a cylindrical thermal barrier coating specimen, for the linear and uncoupled thermo-elastic case. Figure one illustrates the model geometry. When the symmetry of the configuration is considered, the problem can be reduced to a bidimensional, axisymmetric one. This approximation was adopted to keep these preliminary computations reletively fast. The geometric data of the problem are the following: the cylinder' s height and radius are 49. 5 mm, and the coating' s thickness, assumed uniform, is 0. 2 mm. The finite element mesh consists of 1661 nodal points and 1500 four-node axisymmetrical elements. A very fine mesh was introduced, to model both the ceramic-metal interface, and the ceramic coating. In these regions the elements' sizes are in the 1-2 pm range (additional refinements were found not to influence the results). For all of the following numerical studies, the reference time t = 0 was taken to be the instant, at which the spraying process ends. The corresponding ceramic state is assumed to be stress-free [1]. Two kinds of information are required, to perform the thermo-elastic computation: (1) the initial and final temperature portraits across the specimen, and (2) the thermomechanical properties. The temperature field was here calculated by standard numerical tech
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