Theoretically, from the post "Young And On Heat", for a sphere of 1m,
\(D.\cfrac{\partial (d_s)}{\partial T}=4\pi E\cfrac{\alpha}{\rho}\Delta L\)
For a given material such that \(T_{max}<T_{melting}\),
\({\cfrac{\partial (d_s)}{\partial T}|_{T_{o}} \over\cfrac{\partial (d_s)}{\partial T}|_{T_{max}}}=\cfrac{\Delta L|_{T_{o}}}{\Delta L|_{T_{max}}}\)
and so,
\(F_{T_{max}}-F_{T_{o}}={F_{T_{max}}}\left\{1-\cfrac{L^2_e}{L^2_i}.{\cfrac{\partial (d_s)}{\partial T}|_{T_o}\over\cfrac{\partial (d_s)}{\partial T}|_{T_{max}}}\right\}\)
from the post "KaBoom", becomes,
\(F_{T_{max}}-F_{T_{o}}={F_{T_{max}}}\left\{1-\cfrac{L^2_e}{L^2_i}.\cfrac{\Delta L|_{T_{o}}}{\Delta L|_{T_{max}}}\right\}\)
this implies
\(\cfrac{L^2_e}{L^2_i}=\cfrac{\Delta L|_{T_{max}}}{\Delta L|_{T_{o}}}\)
The containment shell would have an external to internal radius ratio given by,
\(\cfrac{L_e}{L_i}=\sqrt{\cfrac{\Delta L|_{T_{max}}}{\Delta L|_{T_{o}}}}\)
for a containment without internal stress differential,
\(F_{T_{max}}-F_{T_{o}}=0\)
Big kaBoom!
