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a b s t r a c t Circular tubes compressed into the plastic range first buckle into axisymmetric wrinkling modes. Initially the wrinkle amplitude grows with increasing load. The wrinkles gradually induce a reduction in axial rigidity eventually 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 is 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; they are then cycled axially under stress control about a compressive mean stress. This type of cycling usually results in material ratcheting or accumulation of compressive strain; here it is accompanied by accumulation of structural damage due to the 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. The rate of ratcheting and the number of cycles to failure depend on the initial compressive pre-strain and on the amplitude of the stress cycles. However, 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 a cyclic plasticity model, are presented and used to simulate the series of experiments performed successfully. A sensitivity study of the formulation to the imperfections and to key constitutive model parameters is then performed.

Multiaxial ratcheting is often simulated by use of nonlinear kinematic hardening models, while in reality materials show cyclic hardening/softening and additional hardening under nonproportional loading. The effect of isotropic hardening on ratcheting needs to be addressed in simulation. In this study, ratcheting tests are conducted on stainless steel 304 under uniaxial, torsional, and combined axial-torsional loading. The ratcheting strain is predicted based on the constitutive theory that incorporates a modified Ohno–Wang kinematic hardening rule and Tanaka’s isotropic hardening model. The results show that the main features of the stress-strain response can be simulated with the constitutive model. Ratcheting strain under axial mean stress depends highly on the loading path and load level, and the degree of cyclic changes in shear stress under torsional strain control is not as influential. The torsional ratcheting strain under mean shear stress with (or without) fully reversed axial strain cycling is found close to the axial ratcheting strain under equivalent mean stress with (or without) torsional strain cycling. In all, the experimental and predicted ratcheting strains for nonproportional paths are found in decent correlation. However, overprediction still prevails for some loading paths, and ratcheting rates deviate considerably from experimental values.

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