**4. Conclusions**

To sum up, a scaling law is proposed in this work to address the indentation depth- or loading force-dependent SRS for FCC materials, i.e., *m* = *m*<sup>0</sup> √ 1 + *h*∗/*h* or *m* = *m*<sup>0</sup> <sup>1</sup> <sup>+</sup> <sup>√</sup> *P*∗/*P*. In addition, the activation volume is found to scale with the hardness by the relation ∂ ln(*v*∗ /*b*3)/<sup>∂</sup> ln *<sup>H</sup>* = <sup>−</sup>2. The model is deduced by the consideration of a dislocation-dominant mechanism so that the mutual

interaction of GNDs at shallow indents plays a critical role in determining this scaling law. Moreover, the proposed law has been verified by comparison with different sets of experimental data.

**Author Contributions:** Conceptualization, X.X. and L.Y.; writing—original draft preparation, X.X.; writing—review and editing, H.L. and L.Y.; supervision, X.X.; project administration, X.X.; funding acquisition, H.L. and X.X. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the National Nature Science Foundation of China (NSFC) under Contract No. 11802344, 11872379 and 11805061, and the Natural Science Foundation of Hunan Province, China (Grant No. 2019JJ50809 and 2019JJ50072). Hao Liu thanks the Fundamental Research Funds for the Central Universities.

**Conflicts of Interest:** The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
