Linear and square superposition hardening models are compared for the surface nanoindentation of ion-irradiated materials. Hardening mechanisms of both dislocations and defects within the plasticity affected region (PAR) are considered. Four sets of experimental data for ion-irradiated materials are adopted to compare with theoretical results of the two hardening models. It is indicated that both models describe experimental data equally well when the PAR is within the irradiated layer; whereas, when the PAR is beyond the irradiated region, the square superposition hardening model performs better. Therefore, the square superposition model is recommended to characterize the hardening behavior of ion-irradiated materials.

比较了线性和正方形叠加硬化模型的离子辐照材料的表面纳米压痕。考虑了塑性影响区域（PAR）内位错和缺陷的硬化机制。采用四组离子辐照材料的实验数据与两种强化模型的理论结果进行比较。结果表明，当PAR处于被辐照层内时，两个模型均能很好地描述实验数据。反之，当PAR超出辐照区域时，平方叠加硬化模型的性能会更好。因此，建议使用正方形叠加模型来表征离子辐照材料的硬化行为。