The illustration below is an extract from the German pressure vessel code, ADM.  It plots the inside and outside stress in both the hoop and longitudinal direction; starting from the centre of the spherical portion, travelling left across the head, around the knuckle and down the cylindrical shell. 

The peak stress levels in the knuckle region can be up to three times the design stress of the material; this is permitted as these stresses only cover a small area and support is provided from neighbouring material subject to much lower stress levels.  However, these peak stresses can give rise to catastrophic failure if attachments or nozzles are welded into, or onto the knuckle region, without careful consideration.  It should also be noted that these peak stresses extend beyond the knuckle into the spherical and cylindrical sections of the vessel.