Existing test results show that the continuous rotation of principal strain axis in cyclic deformation leading to actuation of multi-slip systems which hinders the forming of stable dislocation substructures inside the material

during nonproportional cyclic loading. As a result

the stress response under nonproportional loading will be larger than that under proportional loading. In other words

the material shows additional hardening upon nonproportional cycling. Therefore

a new constitutive model for modeling stabilized cyclic stress-strain response is proposed to consider the effect of nonproportional additional hardening based on the general form of stress-space incremental plasticity relation. In the hardening rule of the proposed model

the evolution of the back stress is simulated by introducing the nonproportionality factor

fnp

and the additional hardening coefficient

αnp

into the basic Armstrong-Frederick model. The consistency condition is enforced to obtain the relationship between the back stress and plastic modulus. Besides

a new algorithm is proposed to calculate the nonproportionality factor on the basis of the minimum normal strain range. Procedures to determine the minimum normal strain range are presented for the general multiaxial loadings. In the proposed model

the effect of nonproportional additional hardening is reflected by introducing fnp and αnp

not only on the shape of the loading path

but also on the material and its microstructure. Meanwhile

the two drawbacks of the Armstrong-Frederick model are overcome. The proposed model requires only five material constants for estimating the stabilized response. Comparisons between test results of S460N steel and 304 stainless steel and model predictions under various loading paths show that the proposed model predicts relatively accurate stress responses under both proportional and nonproportional loading paths.