*2.1. Materials*

Stainless-steel (SUS304), commercial purity copper (C1220), and aluminum alloy (A6063) tubes with an outer diameter *D*<sup>0</sup> of 1.50 mm and a wall thickness *t*<sup>0</sup> of 0.21 mm were used as starting materials. These materials were provided after drawing with a plug by Nippon Tokushukan MFG. Co., Ltd. (Osaka, Japan). The starting materials were annealed after plug drawing to relieve internal stresses. Tables 1 and 2 show the chemical compositions of the stainless-steel and the aluminum alloy tubes, which fall within the the reference range in accordance with Japanese Industrial Standards JIS-G4305 [19] and JIS-H4080 [20], respectively. The copper tubes used in this study were the same as those used in our previous study [10], which contained 99.96 mass percent copper, 0.02 mass percent phosphorus, and 0.02 mass percent other impurities. This chemical composition was in the reference range stated in Japanese Industrial Standards JIS-H3300 [21].

**Table 1.** Chemical composition of the stainless-steel (SUS304) tube used in this study (mass percentage).


**Table 2.** Chemical composition of the aluminum alloy (A6063) tube used in this study (mass percentage).


## *2.2. Hollow Sinking*

The starting materials were drawn without an inner tool using a draw-bench machine (Factory-Automation Electronics Inc., Osaka, Japan). A schematic illustration of the draw-bench machine is shown in Figure 1. The detailed drawing procedures and drawing conditions were previously reported [10]. Table 3 shows the drawing conditions. The die reduction *R*e is defined by the outer diameter of the starting material *D*<sup>0</sup> and the die diameter *D*die, as expressed in Equation (1). −

$$R\_{\ell} = 1 - \frac{D\_{\text{die}}^2}{D\_0^2} \tag{1}$$

**Figure 1.** Schematic illustration of the draw-bench machine used in this study. The parameters *Vn*−<sup>1</sup> and *Vn* are the drawing speeds on the die's entrance and exit sides, respectively.



\* 1 : Only the tube on the exit side of the die was chucked.\*<sup>2</sup> : Both the tubes on the entrance and exit sides of the die were chucked.

A load cell (PW6CC3MB 30 kg, Hottinger Brüel & Kjær GmbH, Darmstadt, Germany) was affixed to each chuck of the draw-bench machine. The load cell on the die's exit side measured the drawing force. The drawing force was calculated as the average load within 3% of the maximum load. The drawing stress was calculated by dividing of the drawing tension by the cross-sectional area of the tube on the die's exit side. The measurement method of the cross-sectional area is described in Section 2.4.
