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 multiparticle-
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 thermalstress
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 Rc !1.
Derived formulae are applied to the SiC–Si3N4 multiparticle-
matrix system, and calculated values of investigated
parameters are in a good agreement with those
from published experimental results.
