On nonlinear kinematic hardening plasticity theory

Abstract

Experimental data for metals, e.g. stainless steel, at elevated temperatures show that the loop of the stress-strain curve obtained in a cyclic tension test grows in size in a bounded fashion with each successive cycle. This implies that either the material follows isotropic hardening during its initial deformation phase from the virgin state, or that the material obeys the kinematic hardening rule by maintaining constant elastic range but with continuously increasing hardening. The known experimental data seems to favor the latter assumption, in which case the classical linear kinematic hardening rule could not adequately describe the cyclic behavior of the material. It becomes necessary, therefore, to generalize the linear hardening rule to nonlinear hardening and furthermore to make the shape of the plastic portion of the stress-strain curve variable with the number of cycles. This paper presents a development of a nonlinear kinematic hardening rule which admits the use of nonlinear stress-strain curves whose shapes can be varied as functions of the number of cycles. It will be shown that the proposed rule leads to a yield surface that depends explicitly on past history in a special way. It will also be shown that, within the original framework of Prager's kinematic hardening postulate, the proposed generalization to nonlinear hardening admits radial as well as nonradial loading for initially isotropic material. A Ramberg-Osgood form of the stress-strain curve will be utilized to demonstrate the utility of the method and, by making the parameters in the stress-strain curve cycle dependent, a cyclic stress-strain curve which grows with the number of cycles can be adequately represented. Finally, an incremental stress-strain relation which can be used in structural analysis is derived on the basis of the proposed nonlinear kinematic hardening rule.