Contained But Not Stressed

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!