Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials

Plane strain analytical solutions to estimate purely elastic, partially plastic and fully plastic deformation behavior of rotating functionally graded (FGM) hollow shafts are presented. The modulus of elasticity of the shaft material is assumed to vary nonlinearly in the radial direction. Tresca’s yield criterion and its associated flow rule are used to formulate three different plastic regions for an ideal plastic material. By considering different material compositions as well as a wide range of bore radii, it is demonstrated in this article that both the elastic and the elastoplastic responses of a rotating FGM hollow shaft are affected significantly by the material nonhomogeneity.

Exact solution of rotating FGM shaft problem in the elastoplastic state of stress

An analytical model is developed to study the stress response and the yielding of rotating functionally graded hollow shafts in the framework of generalized plane strain. The modulus of elasticity and the uniaxial yield limit of the shaft material are assumed to vary radially in nonlinear forms. It is shown that different modes of plasticization may take place. Analytical expressions for the critical values of the material parameters leading to different modes of plastic deformation and the corresponding elastic limit rotation speeds are derived by the use of Tresca's yield criterion.

The stress response and onset of yield of rotating FGM hollow shafts

A computational model is developed for the analysis of elastic, partially plastic and residual stress states in long functionally graded (FGM) rotating solid shafts. The modulus of elasticity, Poisson's ratio, uniaxial yield limit and density of the shaft material are assumed to vary radially in any prescribed functional forms. Small deformations and a state of generalized plane strain are presumed. Using the von Mises' yield criterion, total deformation theory and a Swift-type nonlinear hardening law, a single nonlinear equation describing elastoplastic behavior of rotating shafts is obtained. A shooting technique using Newton iterations with numerically approximated tangents is designed and used for the computer solution of the governing equation. The model is verified by comparing predictions with elastoplastic solutions of homogeneous shafts available in the literature.

A Computational Study on Functionally Graded Rotating Solid Shafts

Analytical solutions to estimating the elastoplastic response of rotating functionally graded (FGM) hollow shafts with fixed ends are presented. The modulus of elasticity, as well as the uniaxial yield limit of the shaft material, are assumed to vary nonlinearly in the radial direction. The plastic model is based on Tresca's yield criterion, its associated flow rule, and ideal plastic material behaviour. Elastic, partially plastic, fully plastic, and residual stress states are investigated. It is shown that the elastoplastic stress response of a rotating FGM hollow shaft is affected significantly by the nonhomogeneity of the material. Unlike the case of a homogeneous hollow shaft, plastic deformation may commence at the inner surface, at the outer surface, or simultaneously at both surfaces. Accordingly, each case requires different mathematical treatment to arrive at its partially plastic solution. It is also shown that, by taking a numerical limit, the complete FGM solution presented herein con...

The Stress Response of Partially Plastic Rotating FGM Hollow Shafts: Analytical Treatment for Axially Constrained Ends

The subject of this paper is the distribution of the residual stresses in an elastic-perfectly plastic solid cylinder with fixed ends after previous rotation. Special attention is paid to the occurrence of secondary plastic flow during unloading. All the results are based on Tresca yield condition and the flow rule associated with it.

Tino Lindner

Papers

Residual Stresses in an Elastic-Plastic Solid Shaft with Fixed Ends after Previous Rotation