On the inelastic deformation of structures subjected to variable loading.

The modes of behaviour of a representative two-bar assembly with unequal areas and lengths under the simultaneous action of sustained mechani- al load and cyclic thermal gradient are investigated analytically. Three types of material behaviour are used: perfect plasticity, linear kinematic hardening and linear isotropic hardening. These simple models exhibit much of the behaviour of interest in design of structural components subjected to repeated thermal loads: elastic shakedown, reversed plasticity and ratcheting. The analyses provide closed form expressions for the mechanical-thermal load bounds of the various regimes of deformation. The cyclic plastic behaviour of the structure is developed and analytical results are derived for the transient and steady state values of plastic strain. The results are applicable for a wide range of geometrical, material and loading parameters. Comparisons between perfect plasticity, kinematic and isotropic hardening models provide qualitative estimates of the cyclic inelastic behaviour of actual structural components which can be simulated by means of a two-bar assembly. The results also point out those load combinations at which thermal ratcheting experiments are more likely to yield the most useful informations. In the field of new constitutive relations, a single state variable theory of inelastic deformation is developed on the basis of the Bailey-Orowan concept of creep as the outcome of two competing mechanisms: strain hardening and thermal softening. The resulting theory is capable of representing primary creep, creep recovery, there reemergence of primary creep following a sudden increase in stress, effects of rest periods and past deformation history and strain rate sensitivity. The theory is not capable, however, of reproducing the features of material behaviour under reversed loading conditions. An attempt to describe the cyclic phenomena of metals on the basis of the two-state variable concept is presented. The material behaviour is characterized by means of the current size of the yield surface and a dimensionless parameter which represents the shape of the plastic hardening curve. The transient growth laws for these two parameters are developed from phenomenological data on annealed OFHC copper. The predictions of the model are in close agreement with the experimental cyclic hardening behaviour of copper. The model is used to obtain the inelastic response of a two-bar assembly subjected to cyclic thermal load and the results are compared to the closed form solutions of linear hardening models. Finally, a modification is suggested to the structure of the proposed model in the light of recent work on the application of the state variable concept to the theory of plasticity. It is argued that the second parameter in the model should be taken as the current coordinates of the yield surface of the material.