How to determine the maximum internal stress for a material under compression before brittle failure?

Let us consider a ceramic material, $\mathrm{Mg_2SiO_4}$ - Forsterite, with a sphere shape.

At room temperature, the ceramic sphere is "trapped" in a matrix which does not expand (null thermal expansion coefficient).

If I raise the temperature of the system (matrix + ceramic), the sphere will not be able to expand and internal stress will grow due to the resulting compression.

How would you estimate the maximum temperature, as well as the maximum internal stress associated before the ceramic sphere fails ?

• Let us see some working so far... – Solar Mike Jul 26 '18 at 4:59