Rotating elastic-plastic tube with free ends

Effect of a temperature cycle on a rotating elastic–plastic shaft

“…Although all plastic and elastic regions were derived analytically in this investigation, more details concerning the latter process were presented by Gamer, Mack and Varga [11]. An analytical solution to the rotating elastic-perfectly plastic solid shaft with axially unconstrained ends was derived by Mack [12] in 1991. On the other hand, the residual stresses in a rotating elastic-perfectly plastic solid shaft with fixed ends, which means that the long tube is constrained at both ends in the axial direction with rigid plates, were obtained by Lindner and Mack in another work [13].…”

“…Mack [15] treated the problem of rotating elastoplastic hollow shaft with free ends in 1991. In his another study [16], he investigated the unloading and the secondary flow in a rotating elastic-plastic hollow cylinder.…”

“…Therefore, Tresca's criterion claims that yielding emerges when any of the following conditions is reached [34] σ 1 − σ 3 = ±σ y , (2.7) In Figure 2.2, Tresca's yield criterion is presented as a regular hexagon in the deviatoric plane of the three-dimensional principal stress space [15]. The boundary of the hexagon marks the onset of yielding and the points outside of the hexagon represents a yielded state [3].…”

“…Another mechanical boundary condition is that axial force F z on any cross-section vanishes since the ends of the shaft are free [12] …”

“…For completeness, it is stated that the radial displacement component has to comply with the condition (see [12])…”