This paper presents a dislocation-based yield strength model for the nano-indentation size effect. The model is based on functional expressions involving the densities of statistically stored dislocations and geometrically necessary dislocations. A single-phase austenitic stainless steel (316L) and a ferrite-austenite dual-phase steel (2205) are used here as the case-study materials to validate the proposed model. Experimental testing and finite element modelling of nano-indentation of the two materials are presented. Experimental tests are performed in the indentation load range from 1000$\mathrm{ }\mathrm{\mu }\mathrm{N}$ to 10000$\mathrm{ }\mathrm{\mu }\mathrm{N}$. For 2205 steel, finite element modelling is performed using a dual-phase microstructure-based model. It is shown that, with consideration of statistically stored dislocations and geometrically necessary dislocations, finite element modelling results can reproduce measured load–displacement curves and hence, the size effect, within an error range of about 5%.

本文提出了一种基于位错的纳米压痕尺寸效应的屈服强度模型。该模型基于涉及统计存储的位错和几何上必要的位错密度的函数表达式。本文以单相奥氏体不锈钢（316L）和铁素体-奥氏体双相钢（2205）作为案例研究材料来验证所提出的模型。介绍了两种材料的纳米压痕的实验测试和有限元建模。实验测试在压痕载荷范围从1000开始$\mathrm{ }\mathrm{\mu }\mathrm{ñ}$ 至10000$\mathrm{ }\mathrm{\mu }\mathrm{ñ}$。对于2205钢，使用基于双相微结构的模型进行有限元建模。结果表明，考虑到统计存储的位错和几何上必要的位错，有限元建模结果可以重现所测得的载荷-位移曲线，从而再现尺寸效应，误差范围约为5％。