*2.3. Tensile Test*

Tensile tests of the starting materials and the drawn tubes were performed using a universal testing machine (Autograph AG 25 TB, Shimadzu Co., Kyoto, Japan), as shown in Figure 2. Tensile tests were performed to evaluate the followings: (1) the stress-strain curves of the starting materials and the drawn tubes, (2) the Lankford value of the starting materials at a maximum stroke, and (3) the unloading behavior of the drawn tube after reaching a drawing tension.

*ε σ*

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*β*

**Figure 2.** Schematic illustration of the method of tensile test used in this study.

The tube was grasped using a 5 kN grips set for fine wire (343-07529-01, Shimadzu Co., Kyoto, Japan). The distance between the chuck C and D was 100 mm before the test. The test speed was 5.0 mm/s. The test load was measured with a 5 kN load cell (SLBL-5kN, Shimadzu Co., Kyoto, Japan) affixed to the cross-head. The tensile test ended at a fracture point to obtain the stress-strain curves of the starting materials and the drawn tubes. The tensile tests of each material were conducted in triplicate. The nominal stress *s* was calculated by dividing the load by the initial cross-sectional area of the tube. The nominal strain *e* was calculated by dividing the stroke by the initial chuck distance. The true strain εtrue was calculated by converting the nominal strain to ln(*e* + 1). The true stress σtrue was calculated by converting the nominal stress to *s*(*e* + 1).

The Lankford value during each maximum stroke was evaluated by conducting tensile tests at maximum strokes of 10, 20, 30, 40, and 50 mm. The Lankford value *r* was calculated using Equation (2). The average values were calculated, and the standard deviations were obtained.

$$\tau = \frac{\{\ln(D\_{\text{busike}}/D\_0) + \ln(d\_{\text{busike}}/d\_0)\}/2}{\ln(t\_{\text{busike}}/t\_0)}\tag{2}$$

The parameters *D*tensile and *d*tensile are the outer diameter and inner diameter at each maximum stroke, respectively, as shown in Figure 3a. The method of measuring *D*tensile and *d*tensile is described in Section 2.4.

The loading-unloading tensile test was conducted to evaluate specimen unloading behavior. The drawn copper tube was loaded until reaching a load that corresponded to the drawing tension at a die reduction *R*<sup>e</sup> of 0.17 and drawing speed ratio β of 1.10. The cross-head was moved until the load reached 2 N during unloading. The test speed during loading and unloading was 1.0 mm/s. An equivalent strain was obtained by evaluating the change in chuck distance during loading and unloading using a digital image correlate (DIC) software GOM CorrelateTM (2019, Gesellschaft für Optische Messtechnik GmbH, Braunschweig, Germany).

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**Figure 3.** Measurement method of sample dimensions. (**a**) Dimension definition of the tube before and after the tensile test and (**b**) ellipse approximation of the outer circumference pixel.

Tensile test of the copper tube was also conducted using the draw-bench machine without the die to investigate the load measurement accuracy of the load cell affixed to the chuck of the draw-bench machine. The copper tube was chucked without setting the die. The initial chuck distance was 465 mm. The tube was stretched by moving the two chucks. The moving speeds of the chuck A and B were 3.3 mm/s and 5.0 mm/s, respectively. The stroke was calculated as the difference in the distance between the two chucks. The nominal stress was calculated by dividing the load by the initial cross-sectional area of the tube. The nominal strain was calculated by dividing the stroke by the initial chuck distance.
