The effects of the localized edge forces have a peak near the edge point and decay drastically away from that point in an oscillating pattern. Decay length is defined as the distance from the applied force (or moment) to the point where the effect of the force (or moment) is almost completely dissipated and becomes negligible. In a real corroded area, the decay length (or angle) is influenced by normal loads, edge moments as well as the membrane forces at the boundary of the corroded spot. The actual decay angle is likely to be in between the decay angles obtained for different cases.
The decay length as calculated above is principally based on bending effects acting on spherical shells. When a spherical shell is subjected to a pure stretching membrane action, the decay length is not the same. Owing to the nature of shell behaviour, the decay length due to membrane action is much larger than that due to bending action. Results from finite element analysis (as will be discussed in Section 4.2) illustrate that for corrosion spots of very small sizes, the effects of stretching membrane action dominate the behaviour of the damaged (and surrounding) area. There is very little bulging. Instead, the component tries to ‘‘open up,’’ thereby stretching the LTA. For this behaviour, the decay angle and hence the reference volume is much larger. For larger sizes of corroded area, as mentioned earlier, the effects of bending action compared to those of membrane action are increased in defining the reference volume. Eventually a certain size of corrosion, a ‘‘crossover’’ from dominance of the stretching effects to dominance of the bending effects (bulging of the shell) occurs. The size of corrosion defining the crossover is discussed below using an approximate analysis.
Consider the limit state when plastic hinges are formed around the circular corroded area as shown in Fig. 2. If the corroded spot is not too large, the curved shell can be approximately considered to be a circular flat plate
(Fig. 3a). For a segment of a unit perimeter cut out of the circular plate (Fig. 3b), the plastic moment can be calculated by assuming that the uncorroded zone is much more rigid than the corroded part.