The rotating elastic-plastic hollow shaft conveying a hot medium

Based on Tresca’s yield criterion and the flow rule associated with it, the distribution of stress and strain in a linearly strain hardening elastic-plastic hollow shaft subject to monotonously increasing angular speed and a negative radial temperature gradient—corresponding to the flow of a hot medium—is investigated. Presupposing circular symmetry and plane strain conditions, the problem is amenable to an analytical treatment. It is found that—depending on the temperature difference between the outer and the inner surface—several qualitatively different types of solutions may occur, and a comprehensive discussion of the admissible maximum angular speeds for elastic behaviour as well as of the elastic-plastic states is performed. Moreover, the residual stresses at stand-still are studied.     

The shrink fit consisting of elastic hollow shaft and nonlinearly hardening elastic-plastic hub

Summary Based on Tresca's yield criterion and the flow rule associated to it, general expressions for stresses and displacement in a shrink fit consisting of elastic hollow inclusion and elastic-plastic hub with arbitrary nonlinear isotropic hardening are derived. For two specific hardening laws—one of Ludwik type and the other of Swift type—there follows the explicit determination of stresses and displacement together with numerical results.     

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

Summary The stress distribution in a rotating solid shaft with temperature dependent yield stress subject to a temperature cycle is investigated. It is presumed that the shaft is in a state of generalized plane strain and obeys Tresca’s yield criterion and the flow rule associated with it. Even in an initially purely elastic shaft two plastic regions with different forms of the yield condition may emerge simultaneously at the centre. However, the expansion of the plastic zone ceases soon thereafter, and an unloaded region spreads into the plastic core; the latter process is treated in an approximate way. It is shown that the stress distribution is altered significantly by the temperature cycle, hence also leading to non-zero residual stresses at stand-still. Dedicated to Professor Franz Ziegler on the occasion of his 70th birthday     

The rotating elastic-plastic shrink fit with hardening

Summary Subject of this investigation is the distribution of stress, displacement and plastic strain in a rotating shrink fit of elastic-plastic material with linear strain hardening. Special heed is given to the range of validity of the results obtained.With 7 Figures     

Mode III crack growth in linear hardening materials with strain gradient effects

The flow-theory version of couple stress strain gradient plasticity is adopted for investigating the asymptotic fields near a steadily propagating crack-tip, under Mode III loading conditions. By incorporating a material characteristic length, typically of the order of few microns for ductile metals, the adopted constitutive model accounts for the microstructure of the material and can capture the strong size effects arising at small scales. The effects of microstructure result in a substantial increase in the singularities of the skew-symmetric stress and couple stress fields, which occurs also for a small hardening coefficient. The symmetric stress field turns out to be non-singular according to the asymptotic solution for the stationary crack problem in linear elastic couple stress materials. The performed asymptotic analysis can provide useful predictions about the increase of the traction level ahead of the crack-tip due to the sole contribution of the rotation gradient, which has been found relevant and non-negligible at the micron scale.     

Mathematical simulation of temperature field in a hollow rotating cylinder with nonlinear boundary conditions

An analytical solution is obtained of the nonlinear problem on heat conduction in a hollow infinite cylinder in view of the temperature dependence of its thermophysical characteristics. Results are given of calculations of temperature field for the roll of machine for continuous casting of slabs.     

Temperature distribution in a rotating hollow cylinder

The temperature distribution in a hollow cylinder rotating with a given angular velocity is found for steady-state boundary conditions of the first kind.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 37, No. 4, pp. 705–711, October, 1979.     

The influence of the temperature on the stress‐strain curves of a bearing steel and a case hardening steel

In the present paper the influence of the temperature and strain rate on the stress strain behaviour of two different steels were investigated. Two microstructures were considered: pearlitic and austenitic. Tensile tests with the bearing steel 100Cr6 and the case hardening steel 20MnCr5 were accomplished at various temperatures. For this purpose the Ludwik equation was used to describe the stress‐strain curve. The parameter of the constitutive equation was determined for each steel and microstructure. Especially for the austenitic state the parameters of the used material law were described as a function of the temperature.     

An analysis of the flow in rotating cryogenic vapour columns with a uniform axial temperature gradient

A preliminary analysis is made on the flow of nitrogen and helium vapours in the necks of rotating cryostats. Solutions for the velocity and temperature profiles are presented for fully developed flow with a uniform axial temperature gradient and are compared with experimental observations on flow in a rotating glass dewar. The flow of cold vapour is confined to an annular boundary layer with a thickness proportional to the fourth root of the rotational Rayleigh number, while a reverse flow of warm vapour is generated on the axis.     

The temperature field in a hollow cylinder due to a source moving along a helix

We solve the problem of the temperature distribution in a hollow cylinder due to a source moving along a helix on the outer surface with boundary conditions of the second kind. The solution can be used to calculate temperature fields on a computer for various forms of processing materials.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 1, pp. 154–156, January, 1971.     

Vibration analysis of a rotating flexible shaft–disk system

Free vibrations of a spinning disk–shaft system are analysed using the finite-element method. The spinning disk is described by the Kirchhoff plate theory. The shaft is modelled by a rotating beam. Using Lagrange’s principle and including the rigid-body translation and tilting motion, equations of motion of the spinning flexible disk and shaft are derived consistently to satisfying the geometric compatibility conditions on the internal boundaries among the substructures. The finite-element method is then used to discretize the derived governing equations. The method is applied to the shaft–disk spinning system. The sensitivity to the running speed as well as the effect of both disk flexibility and boundary condition on the natural frequencies of the spinning system are numerically investigated.