Creep Ovalization and Buckling of a Linear Viscoelastic Externally Pressurized Pipe

An analysis model is developed for the creep ovalization and buckling of an imperfect plastic pipe subjected to a uniform external pressure. The pipe’s cross section is assumed to have a known initial out of roundness or ovality and to be composed of a linear viscoelastic material. The governing equations are transformed using Laplace and Carson transforms. The transformed deviation of the cross section from its initial shape is inverted exactly by evaluating the Bromwich integral and approximately by the simpler direct inversion method. The two inversion methods, which yield nearly identical results, are compared with the quasi-elastic method wherein the elastic modulus in the solution to the equivalent elastic problem is replaced by the relaxation modulus. The model predictions are quite sensitive to the viscoelastic material parameters for small values of the relaxation exponent and this sensitivity has direct implications with respect to the reliability of the predicted life expectancy for the pipe. Predictions and measurements made in creep ovalization tests of a high density polyethylene (HDPE) pipe at 50°C and different pressures are compared. Very good agreement is obtained between predicted and measured response in short-term tests and in an extended test. Bi-directional shifting is used to translate inferred material parameters at 50°C to 35°C for making comparisons of predictions with measurements at the latter temperature. While the predicted ovalization overestimates the measurement, very good agreement is obtained when one material parameter is decreased by 10% and the other is increased by 7%; thereby demonstrating the sensitivity of the predictions to small changes in the material parameters for small values of the relaxation exponent. The efficacy of a simple estimate for the limiting creep buckling or collapse pressure as a function of the design life is presented and compared with measurements.