*2.4. Dimension and Surface Quality Measurement*

Cross sections of the drawn and tensile-tested tubes at each maximum stroke were polished and observed using a three-dimensional microscope (VHX-5000, Keyence, Miyagi, Japan). The outer diameter *D* and the inner diameter *d* of the tensile-tested and drawn tubes were measured by an image analysis as the following method. The pixels of the outer and inner circumference of the tube image were read using a proprietary programming language, MATLABTM (R2020a, Mathworks, Natick, MA, USA). A tube cross-section outline of the image became elliptical when the tube was cut diagonally. The minor axis of the ellipse was closest to the true diameter of the tubes. Therefore, ellipses were drawn by ellipse approximation of each circumference pixel, as shown in Figure 3b. The outer or inner diameter of the tube was measured as the minor axis of this ellipse. The wall thickness *t* was calculated as (*D* − *d*)/2. The cross-sectional area was calculated as π*t*(*D* − *t*). The outer diameters of the drawn tube on the die's entrance and exit sides were measured using a micrometer (MDC-25M, Mitutoyo, Kanagawa, Japan) at four points. The average values were calculated, and the standard deviations were obtained.

Maps of the height of the uneven outer surface of the drawn tubes *h* were obtained using a laser microscope (VK9510, Keyence, Miyagi, Japan). The height from an arbitrary position of the uneven outer surface of the tube *H* was measured, excepting abnormally high or low value. The average values *H*ave of the *H* were calculated. The height of the outer uneven surface of the tube *h* was calculated as the difference between the height from the arbitrary position *H* and the average height *H*ave as *H* − *H*ave.
