4.2.4. Summary of Excessive Thinning of Outer Diameter

Figure 25 illustrates the excessive thinning of the outer diameter in the hollow sinking of a micro metal tube. The final outer diameter becomes smaller than the die diameter even when the drawing stress is in the elastic region and at any Lankford value. Furthermore, the outer diameter becomes smaller than the die diameter with an increase in the Lankford value, as shown by a theoretical formula (6). Therefore, it is considered that the micro tube yields microscopically during drawing, even under macroscopically elastic deformation behavior. The outer diameter seems to approach the die diameter during unloading more than the linear elastic strain outside the microscopic yielding region. Therefore, the dislocations generated during drawing are considered to disappear partially during unloading, which is similar to the Bauchinger effect. The unloading strain increases under the condition where few dislocations are generated during drawing, such as low drawing stress or high apparent elastic modulus of the stress-strain curve. Therefore, the final excessive thinning of the outer diameter decreases as the drawing stress decreases, or the apparent elastic modulus increases. σ

**Figure 25.** Schematic illustration of excessive thinning of the outer diameter during drawing and after unloading.

According to the above discussion, it is considered that the excessive thinning of the outer diameter can be suppressed by reducing the die half angle or the frictional force between the micro tube and the die, which results in reduced drawing stress for a particular yield stress. Furthermore, the drawing stress increases due to work hardening. However, since few dislocations are generated during the drawing of the micro tube, the drawing stress is much smaller than the yield stress because of the small size of the tube. Therefore, it is considered that work hardening of the micro tube suppresses the excessive thinning of the outer diameter.
