Where Most People Crack Too, Up Top.

$g_T$ could be the reason why surface crack on heating.

$g_{T}$  greatest where  $x_o$  is small resulting in high curvature.

For the case of a sphere,

$g^2_{net}=g_Tsin^2(\theta)+(g_Tcos(\theta)-g)^2$

If we let,

$2g_{net}\cfrac{\partial g_{net}}{\partial\theta}=2g_Tsin(\theta)cos(\theta)-2(g_Tcos(\theta)-g)sin(\theta)=0$

$2gsin(\theta)=0$

$\theta$ = 0^o   or   90^o

Now consider,

$2(\cfrac{\partial g_{net}}{\partial\theta})^2+2g_{net}\cfrac{\partial^2 g_{net}}{\partial\theta^2}=2gcos(\theta)$

when  $\theta$ = 0 ^o

$\cfrac{\partial^2 g_{net}}{\partial\theta^2}>0$

We know that at 0^o,  $g_{net}$ is a minimum  from $\cfrac{\partial^2 g_{net}}{\partial\theta^2}$

This means, forces at the side of the surface beyond 0^o to the central line are pulling the outwards with higher strength.  This force distribution tends to open the top of the heated body where  $g_{net}$  is minimum.