The plane strain corrosion problem previously analyzed by Popelar is revisited in this paper to investigate the hoop membrane stress effect on the bending behavior of corroded pipelines under internal pressure. Both the lower and the upper bounds to the pipe failure pressure are developed from the analysis results.
Metal loss due to corrosion usually results in randomly located pits, often resulting in large areas of overlapping defects on outside and/or inside surface of a pipe. The defect depths and extents are, in general, very irregular. Because of this irregular nature of metal loss, a sophisticated three dimensional finite element modeling is generally required to analyze the corroded pipe to predict its failure pressure. The finite element method is a powerful tool for three dimensional analysis. However, it should be kept in mind that the method provides a solution for the specific case considered. On the other hand, the closed form solution, while it is extremely difficult, provides an effective means of evaluating the effect of metal loss on pipe failure. To develop a closed form solution, it is necessary to idealize the shape of the metal loss region. In keeping with this objective, the plane strain corrosion problem previously analyzed by Popelar is revisited in this paper. The plane strain problem of interest is depicted in Figure 1-A which shows a single long longitudinal groove at the outside surface of the pipe. The outside (or inside) corrosion results in an eccentricity between the middle surface of the remaining pipe wall and that of the undamaged pipe wall. The issue (or concern) is that because of the eccentricity, an internal pressure induces bending moment at the interface (Ø=B) which may, when combined with the pipe hoop (membrane) stress, adversely impact the failure pressure of the corroded pipe.