An analytical model based on a two-bar assembly with unequal areas and material properties is used to determine inelastic stress-strain behavior under a steady mean load and cyclic thermal loads. The study with the model extends previous study on thermal ratcheting with kinematic hardening. The model exhibits much of the behavior of interest in design of pressure vessels subject to thermal loads: elastic behavior, shakedown, ratcheting, captive plastic behavior (a special case of elastic followup), and plastic cycling. The expressions for cyclic changes in stress and cyclic inelastic strains are developed, and the mean-load and thermal-load bounds for the behavior modes are mapped.

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