一种超细晶材料的混合硬化模型及其数值模拟

针对超细晶材料强度高、塑性能力不佳以及饱和应力跟晶粒尺寸和应变率等因素有关的特点，在Johnson-Cook模型的基础上引入Hall-Petch关系式，再与Armstrong-Frederick非线性随动硬化规律进行叠加，提出一种同时包含各向同性硬化和非线性随动硬化的混合硬化模型。该数学模型不仅考虑了超细晶材料的尺寸效应，还计及了加工硬化和包辛格效应的组合效应。在推导出该混合硬化模型的积分算法的基础上进行有限元数值分析和试验数据的对比分析。对比结果表明，不同晶粒大小与不同应变率下的超细晶材料的数值仿真结果与试验数据均吻合较好，进而证明该数学模型的合理性。因此，该混合硬化模型不仅丰富了塑性力学的内容，也可为超细晶材料的结构件设计提供一定的理论依据。

A Mixed Hardening Model of Ultrafine-grained Materials and Numerical Simulation

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.