Cyclic loading of thick vessels based on the Prager and Armstrong–Frederick kinematic hardening models

The aim of this paper is to relate the type of stress category in cyclic loading to ratcheting or shakedown behaviour of the structure. The kinematic hardening theory of plasticity based on the Prager and Armstrong–Frederick models is used to evaluate the cyclic loading behaviour of thick spherical and cylindrical vessels under load and deformation controlled stresses. It is concluded that kinematic hardening based on the Prager model under load and deformation controlled conditions, excluding creep, results in shakedown or reversed plasticity for spherical and cylindrical vessels with the isotropy assumption of the tension/compression curve. Under an anisotropy assumption of the tension/compression curve, this model predicts ratcheting. On the other hand, the Armstrong–Frederick model predicts ratcheting under load controlled cyclic loading and reversed plasticity for deformation controlled stress. The interesting conclusion is that the Armstrong–Frederick model is well capable to predict the experimental data under the assumed type of stresses, wherever experimental data are available.