The conditions under which the maximum (in absolute value) principal stress in a spherical shell is the hoop stress

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 p_R / p_r and the ratio R/r for which the maximum (in absolute value) principal stress in the vessel both inside and outside is the circumferential one. The variation range for negative p_r is the same as for positive, only the hoop stress sign being opposite. 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.