# Stress And Deformation Of Titanium Tube During Drawing

Under the action of pull-out force, positive pressure and frictional force, the metal in the deformation zone is under the stress state of two-way compression and one-way pulling. Since the metal being drawn is a solid round bar, the stress is in an axisymmetric stress state, that is, the deformation state of the metal in the deformation zone is two-way compression and one-way extension. During drawing, the external forces on the metal in the deformation zone are the drawing force P, the positive pressure N and the frictional force given to the metal by the mold wall.
The stress distribution law of titanium tube during drawing is as follows:

(1) The distribution of stress along the radial and circumferential directions. Radial stress and circumferential stress gradually decrease from the surface to the center. The distribution of axial stress is reversed. The axial stress at the center is large and the axial stress on the surface is small. It can be explained as follows: In the deformation zone, radial stress acts on the outer surface of each ring of the metal. Radial stress always tries to reduce its outer surface. The farther away from the center, the greater the surface area, the greater the force required. The distribution of axial stress on the cross section can be explained by the aforementioned plastic equation. The main difference between drawn titanium tube and drawn bar is that the former has lost the condition of axisymmetric deformation, which makes its stress and deformation state different from that of drawn solid round bar. Although the core is not placed in the tube during empty drawing, its wall thickness often changes in the deformation zone. Due to different factors, the wall thickness of the tube can eventually become thinner, thicker or remain unchanged. It is very necessary to understand the change rule of the tube wall thickness during empty drawing to correctly formulate the drawing process regulations and select the tube blank size.

(2) The distribution of stress along the axial direction. The axial stress gradually increases from the entrance end to the exit end of the deformation zone, that is, the circumferential stress and radial stress gradually decrease from the entrance end to the exit end of the deformation zone. The distribution of axial stress can be explained as follows. In the process of stable drawing, the area of ​​any section in the deformation area gradually decreases as it moves toward the exit end, and the deformation volume between this section and the spherical surface at the population end of the deformation area continues to increase. In order to achieve plastic deformation, the axial stress acting on the deformed body through this section must also gradually increase. When the degree of deformation in the entire deformation zone is not large, the metal deformation resistance can be regarded as a constant. Therefore, as the axial stress increases toward the outlet end, the radial stress and the circumferential stress must gradually decrease. In actual production, observing the wear of the mold can be found that the entrance of the mold generally wears faster, and grooves often appear prematurely, which also proves that the radial stress value at the entrance is large.