Ratcheting, wrinkling and collapse of tubes due to axial cycling

The first instability of circular tubes compressed into the plastic range is axisymmetric wrinkling, which is stable. Compressed further the wrinkle amplitude grows, leading to a limit load instability followed by collapse. The two instabilities can be separated by strain levels of a few percent. This work investigates whether a tube that develops small amplitude wrinkles can be subsequently collapsed by persistent cycling. The problem was first investigated experimentally using SAF 2507 super-duplex steel tubes with D/t of 28.5. The tubes are first compressed to strain levels high enough for mild wrinkles to form and then cycled axially under stress control about a compressive mean stress. This type of cycling usually results in accumulation of compressive strain; here it is accompanied by growth of the amplitude of the initial wrinkles. The tube average strain initially grows nearly linearly with the number of cycles, but as a critical value of wrinkle amplitude is approached, wrinkling localizes, the rate of ratcheting grows exponentially and the tube collapses. Similar experiments were then performed for tubes involving axial cycling under internal pressure and the combined loads cause simultaneous ratcheting in the hoop and axial directions as well as a gradual growth of the wrinkles. The rate of ratcheting and the number of cycles to collapse depend on the initial compressive pre-strain, the internal pressure, and the stress cycle parameters all of which were varied sufficiently to generate vii a sufficient data base. Interestingly, in both the pressurized and unpressurized cases collapse was found to occur when the accumulated average strain reaches the value at which the tube localizes under monotonic compression. A custom shell model of the tube with initial axisymmetric imperfections, coupled to the Dafalias-Popov two-surface nonlinear kinematic hardening model, are presented and used to simulate the experiments performed. It is demonstrated that when suitably calibrated this modeling framework reproduces the prevalent ratcheting deformations and the evolution of wrinkling including the conditions at collapse accurately for all experiments. The calibrated model is then used to evaluate the ratcheting behavior of pipes under thermal-pressure cyclic loading histories experienced by axially restrained pipelines.