Statistical modeling of von-Mises and Tresca stress in internally corroded steel pipe subjected to internal hydrostatic pressure

In the present work, a statistical modeling of the % increase in von-Mises and Tresca stress was done for a structural steel pipe containing a quarter-ellipsoidal internal corrosion defect subjected to internal hydrostatic pressure. An analytical solution was developed considering the internal corrosion defect length (z), width (x), depth (y), and internal hydrostatic pressure (P) as independent variables. The finite element analysis (FEA) simulated dataset was used for modeling. The analytical equations demonstrated high predictive accuracy, with coefficients of determination (R²) of 98.64% for von Mises stress and 98.38% for Tresca stress. The stress distribution from FEA was nearly similar quantitatively for both stresses; however, their patterns exhibited noticeable differences in their respective profiles inside and outside of the curvature of the internal corrosion defect. The contour plots for the percentage increase in von-Mises and Tresca stresses revealed both elastic and plastic regimes. The maximum percentage increase in von Mises stress remained slightly below the ultimate tensile strength of the specimen. In contrast, the contour plots for Tresca stress indicated a limited region in which the stress exceeded the ultimate tensile strength. For the linear effect, the geometrical variable x (width of the internal corrosion defect) exhibited a negative T-value, indicating that an increase in x reduces the percentage increase in both von Mises and Tresca stresses. The significance of standardized effects for von-Mises stress was in the order of P > y > z > x > zy> yp> zz> xy> xP> zP> xx. However, for the Tresca stress, the order was P > y > x > z > zy> yp> xy> zz> xP> zP> xx. The steel pipe with an internal corrosion defect of minimum length (z = 30 mm), maximum width (x = 134 mm), and minimum depth (y = 0.5 mm) exhibited the lowest von Mises and Tresca stresses. However, the maximum stresses were observed for a defect with maximum length (z = 454 mm), minimum width (x = 26 mm), and maximum depth (y = 1.5 mm).