Abstract: Although the strength of ultrafine-grained materials is very good, their plastic behaviour is poor. Besides, their saturation stress relates to the grain size and the strain rate. According to the above properties, based on the Johnson-Cook model which incorporates Hall-Petch relation and then combines with Armstrong-Frederick type nonlinear kinematic hardening rule, a mixed hardening constitutive equation containing isotropic hardening rule and nonlinear kinematic hardening is put forward. The mixed hardening constitutive equation considers the size effect of ultrafine-grained materials as well as the combination of work hardening effect and Bauschinger effect. After the integral algorithm of the mixed hardening constitutive equation is deduced, the analysis of numerical simulation and comparison between the numerical results and the experimental data are performed finally. The comparison result shows that the numerical simulation results are agree well with the experimental data. Hence, it is proved that the mixed hardening constitution equation is rational. Therefore, the mixed hardening constitution equation does not only rich the theory of plasticity, but also provides a certain theoretical foundation for ultrafine-grained structural components design.

Key words: grain size, integral algorithm, mixed hardening, strain rate, ultrafine-grain material