**5. Conclusions**

The deformation behavior causing the excessive thinning of the outer diameter in the hollow sinking of micro thin-walled tubes can be explained as follows.

(1) At any Lankford value, the micro thin-walled tube yields microscopically during drawing even under a drawing stress lower than the yield stress of the bulk metal. Therefore, the outer diameter always becomes smaller than the die diameter during drawing.

(2) The outer diameter approaches the die diameter due to the unloading strain, which is larger than the linear elastic recovery, during unloading. The unloading strain increases as the drawing stress decreases or the apparent elastic modulus of the stress-strain curve increases. Therefore, the final excessive thinning of the outer diameter decreases as the drawing stress decreases, or the apparent elastic modulus increases. From the approximated unloading behavior, it is considered that the final outer diameter matches the die diameter completely during unloading due to elastic recovery when the apparent elastic modulus is larger than a threshold value.

**Author Contributions:** Conceptualization, T.K., K.T., and S.S. (Shinsuke Suzuki). Methodology, T.K., K.T., and S.S. (Shinsuke Suzuki). Validation, T.K., H.S., S.S. (Saki Suematsu), and S.S. (Shinsuke Suzuki). Formal analysis, T.K. Investigation, T.K., H.S., S.S. (Saki Suematsu), K.T., S.K., S.G., and S.S. (Shinsuke Suzuki). Data curation, T.K., H.S., S.S. (Saki Suematsu), and S.S. (Shinsuke Suzuki). Writing—original draft preparation, T.K. Writing—review and editing, T.K., H.S., S.S. (Saki Suematsu), K.T., S.K., S.G., and S.S. (Shinsuke Suzuki). Visualization, T.K., H.S., S.S. (Saki Suematsu), and S.S. (Shinsuke Suzuki). Supervision, S.S. (Shinsuke Suzuki). Project administration, S.S. (Shinsuke Suzuki). Funding acquisition, T.K., H.S., S.S. (Saki Suematsu), and S.S. (Shinsuke Suzuki). All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was supported by JXTG Nippon Oil & Energy Corporation. Grant number is B2R50Z004300.

**Acknowledgments:** The first author performed this study as a Research Assistant of the Kagami Memorial Research Institute of Material Science and Technology of Waseda University.

**Conflicts of Interest:** The authors declare no conflict of interest.
