**Appendix A**

The wall thickness of the micro tube after passing through the die *t*die and the Lankford value *r* of deformation during drawing were calculated as follows.

It was assumed that the length of the micro tube after passing through the die *l*die (state (ii) in Figure 17) and the length during drawing *l*total (state (iii) in Figure 17) were the same. The length of the micro tube *l*total could be expressed as β·*l*<sup>0</sup> . Therefore, the parameter *l*die also could be expressed as β·*l*<sup>0</sup> . Equation (A1) indicates that the volume of the micro tube is constant in state (i) and (ii) in Figure 17.

$$l\_0 \cdot t\_0 \left( D\_0 - t\_0 \right) \ = \ l\_{\text{die}} \cdot t\_{\text{die}} \left( D\_{\text{die}} - t\_{\text{die}} \right) \tag{A1}$$

By replacing *l*die by β·*l*0, Equation (A2) is obtained.

$$t\_{\rm die} = \frac{1}{2} \Big| D\_{\rm die} + \sqrt{D\_{\rm die} - \frac{4t\_0(d\_0 - t\_0)}{\beta}} \Big| \tag{A2}$$

The Lankford value *r* of deformation during drawing was defined by Equation (A3). The change of the inner diameter, which was considered in Equation (2), was neglected to simplify the calculation.

$$r = \frac{\ln\left(\frac{D\_{\text{total}}}{D\_{\text{div}}}\right)}{\ln\left(\frac{t\_{\text{total}}}{t\_{\text{dis}}}\right)}\tag{A3}$$

It was assumed that the calculated Lankford value did not change significantly even if the dimensions during drawing (state (iii) in Figure 17) and the final dimensions (state (iv) in Figure 17) were the same. Therefore, by converting *D*total and *t*total into *D<sup>n</sup>* and *tn*, respectively in Equation (A3), Equation (A4) is obtained.

$$r = \frac{\ln\left(\frac{D\_n}{D\_{\rm dis}}\right)}{\ln\left(\frac{t\_n}{t\_{\rm dis}}\right)}\tag{A4}$$
