The conditions under which the maximum (in absolute value) principal stress in a sperical shell is the hoop stress.
Description
The data are presented for a linearly elastic thick-walled spherical vessel with the inner radius r and the outer radius R under internal p_r and external p_R pressure, when both internal and external pressures are not equal to zero. The figure demonstrates the variation range of relative pressure and the ratio R/r for which the maximum (in absolute value) principal stress in the sphere both inside and outside is the circumferential one. There is nothing new, from the theoretical point of view. This is just an illustration for the analysis of Lame's problem. From this graph one can see that if at an initial time the hoop stress is the maximum in absolute value, then it remains maximum during the process of the vessel thinning (e.g., due to corrosion) up to complete dissolution.
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Steps to reproduce
The graph is built on the basis of the analysis of the solution of Lame's problem for a pressurized sphere.