Analytical Modeling of the Damaged Zone of Pipelines Repaired with Composite Materials Systems

Abstract

The present chapter describes an applied mathematical model aimed at assessing the strength properties of a damaged area of a transmission pipeline after repair works were performed using a composite material system. In the two-dimensional case, the problem of the stress–strain state in a pipe area with a long volumetric surface defect (VSD) has been considered. We have assumed that the repair work in the damaged area of the pipeline consisted of applying polymeric filler (in order to reconstruct the external configuration of the pipe in the VSD area) and then wrapping several layers of polymeric composite material, bonded with the help of a polymeric adhesive . We have also assumed that the VSD length (longitudinal extent) is considerably greater than its width (circumferential extent), which allows us to develop a two-dimensional analytical model. In our model, the effect of the composite material was taken into account by applying, on the pipeline outside surface, an additional normal stress , which is proportional to the tensile stresses from the composite wrap . These tensile stresses, in their turn, consist first of a pretension of the wounded composite layers, and second of the stresses arising from the circumferential deformation of the pipe. Such deformation, in the simplest case, can be described using Hooke’s law, as the product between the modulus of elasticity of the composite material in the circumferential direction and the circumferential strain of the pipe at its surface. Additional studies were conducted to evaluate the stress concentration effect at the corner points of the surface. To solve this problem, the whole area of the pipe cross-section has been divided into two subareas, each of which had its own stress function. Taking into account the symmetry of the field and external loads in each area, one stress function has been built in each subregion. All boundary conditions on the inner and outer surfaces of the pipe and on the symmetry axis are satisfied exactly. To obtain a closed system of equations, it was necessary to add two equations, including the condition of equality of the bending moment in the coupling zone and the proportionality condition of the radial and tangential displacements in the vertical direction for a solid body. Finally, we have obtained a closed system of 12 linear algebraic equations whose solution allowed us to obtain all the relevant characteristics of the problem. Numerical calculations have been conducted and von Mises combined stresses analyzed in the damaged pipe area as function of the VSD depth and compared with results obtained using a finite elements model.