A New Investigation of Plastic Limit of Repaired Steel Pipe Elbow With Bonded Composite Wrap Subjected to Internal Pressure

Abstract This work provide a thorough examination of the J-integral and plastic limit load for a circumferential through-wall fracture in an elbow reinforced with a bonded composite wrap under internal pressure. A three-dimensional (3D) finite element (FE) method is employed to evaluate the ductility of the structure and predict its failure behavior under varying conditions. The analysis systematically investigates the influence of key parameters, including the elbow angle (ψ), structural thickness (er), the ratio (Rm/t), and pipe material properties. The results are compared against existing analytical solutions in the literature, which are derived from detailed 3D FE limit analysis and are considered to provide reliable benchmarks. These solutions contribute valuable insights for the plastic analysis of pressurized pipes and the estimation of nonlinear fracture mechanics parameters using the reference stress method. To quantify the variability in the pressure limit, a probabilistic approach is employed using the Monte Carlo method. Structural failure probability is assessed by accounting for both model uncertainty and statistical variability in the input data. Three probability distribution functions—the ninth-order polynomial, the Lorentzian, and the Gaussian—are examined to characterize the uncertainty. Among these, the Gaussian distribution proves to be the most suitable for approximating the probability density function, offering a reliable estimate of the mean pressure limit. The study highlights that uncertainty in the pressure limit parameter significantly affects failure probability and contributes to a reduction in the overall structural lifespan. These findings provide essential guidance for the design and reliability assessment of composite-reinforced pressurized piping systems.