Thermal stresses and related phenomena in composite ceramics |
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Authors: | Ladislav Ceniga |
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Affiliation: | (1) Institute of Materials Research, Slovak Academy of Sciences, Watsonova 47, 043 53 Košice, Slovak Republic |
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Abstract: | The paper deals with elastic thermal stresses in an isotropic multi-particle-matrix system consisted of periodically distributed
spherical particles in an infinite matrix, imaginarily divided into cubic cells containing a central spherical particle. Originating
during a cooling process as a consequence of the difference in thermal expansion coefficients between the matrix and the particle,
and investigated within the cubic cell, the thermal stresses, as functions of the particle volume fraction v, being transformed for v = 0 to those of an isotropic one-particle-matrix system, are maximal at the critical particle volume fraction, representing
a considerable value related to maximal resistance of the thermal-stress strengthened multi-particle-matrix system against
mechanical loading. The thermal stresses are derived for such temperature range within which the multi-particle-matrix system
exhibits elastic deformations, considering the yield stress and the particle-matrix boundary adhesion strength. With regard
to a curve integral of the thermal-stress induced elastic energy density, critical particle radii related to crack initiation
in ideal-brittle particle and matrix, functions describing crack shapes in a plane perpendicular to the direction of crack
formation in the particle and in the matrix, and consequently dimensions of a crack in the particle and in the matrix are
derived along with the condition concerning the direction of the crack formation. Additionally, derived by two equivalent
mathematical techniques, the elastic energy gradient within the cubic cell, representing a surface integral of the thermal-stress
induced elastic energy density, is presented to derive the thermal-stress induced strengthening in the spherical particle
and in the cubic cell matrix. The former parameters for v = 0 are derived using the model of a spherical cell with the radius . Derived formulae are applied to the SiC–Si3N4 multi-particle-matrix system, and calculated values of investigated parameters are in a good agreement with those from published
experimental results. |
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Keywords: | |
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