Simple Formulae for the Stress Concentration Factor Around Spherical Cavities of Various Geometries at Surface of Well Casings and Pipelines

Well casings and pipelines in the petroleum industry are subject to severe corrosion because of their exposure to seawater and corrosive fluids that are transported. Corrosion develops pits and cavities at the surface of these structures. Under operating conditions, stress concentration around the cavities determines strength degradation of the structures. The strength deterioration can significantly shorten the life; even cause failure of the structure if this effect is not considered during the design stage. It is highly desirable to know the stress concentration factor (SCF) for both designing and evaluating tubular structures. Despite the rapid development of various numerical methods such as the finite element method, SCF analysis with any numerical method is still a tedious and time-consuming task for ordinary engineers. This paper derives simple formulae for SCF around cavities of various geometries at the surface of tubular structures. The cavity geometries considered include shallow-spherical (depth is less than the open radius), medium-spherical (depth is equal to the open radius), and deep-spherical (depth is greater than the open radius) cavities. SCF graphs are generated and results of sensitivity analyses are presented in this paper. These SCF formulae and graphs can be used in both designing and evaluating tubular structures with spherical cavities.