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Analytical investigation of elastic and plastic behavior of rotating double-walled FGM-homogenous hollow shafts

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Abstract

Cylindrical rotating components have been of special interest in different industries and due to their wide applications such as grinding wheel, drive shaft; the analyses of elastic and plastic stress and strains have been an interesting topic for investigation. Therefore, in this study an analytical elastic and elasto-plastic solution to evaluate the stress field in axisymmetric thick-double-walled cylindrical hollow shafts made of functionally graded materials and homogeneous layers subjected to pressure, temperature gradient, and angular speed are presented. In the first step, by considering the combined different loading condition, a closed-form analytical thermo-elastic solution for radial and circumferential stresses as well as the normalized effective stresses are presented. Then, the starting radius of the plastic deformation by using a completely elastic solution and a failure criterion is determined. In the second stage, the relations for determining the plastic zone radius as well as the radial, circumferential, and effective stresses in both elastic and plastic zones are obtained for three types of functionally graded layers under different combined loading condition. Finally, it will be shown that by using the functionally graded layer, the stress distribution and consequently the yield pattern in the thick-double-walled cylindrical hollow shaft can be improved.

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Abbreviations

\({p}_{{i}};\,{p}_{{o}}\) :

Pressures at the inner and outer surfaces of double-walled hollow shaft, respectively

\({r}_{{1}};{r}_{{2}}{;}{r}_{{3}}\) :

Inner, interface, and outer radii of hollow shaft, respectively

\({r}_{{pf}}{;}{r}_{{ph}}\) :

radius of elasto-plastic boundary of FGM, and homogenous part, respectively

\(E_{h};\,K_{h};\,\alpha _{h};\sigma _{yh};\,\rho _{h}\) :

Module of elasticity, Thermal conductivity coefficient, thermal expansion coefficient, yield stress, and density in the homogeneous part of hollow shaft, respectively

\(E_{0f};\, K_{0f};\, \alpha _{of};\sigma _{y0f};\, \rho _{0f}\) :

Constant of Module of elasticity, Thermal conductivity coefficient, thermal expansion coefficient, yield stress, and density in power low relation, respectively

\({\upbeta ;}n_{1};n_{2};n_{3};n_{4}\) :

Power low indices for module of elasticity, thermal conductivity, thermal expansion coefficient, yield stress and density, respectively

\({T}_{{1}};\,{T}_{{2}};\,{T}_{{3}}\) :

Temperatures at the inner, interface, and outer surfaces of double-walled hollow shaft, respectively

\(\sigma _{rh}^{E};\sigma _{{\uptheta }h}^{E};\sigma _{{e}h}^{E}\) :

Elastic radial, tangential, and effective stresses in the homogeneous part of hollow shaft, respectively

\(\sigma _{{\uptheta }f}^{E};\,\sigma _{{\uptheta }f}^{E};\sigma _{{\uptheta }f}^{E}\) :

Elastic radial, tangential, and effective stresses in the FG part of hollow shaft, respectively

\(\sigma _{rh}^{p}{;}\sigma _{{\uptheta }h}^{p};\sigma _{{e}h}^{p}\) :

Plastic radial, tangential, and effective stresses in the homogeneous part of hollow shaft, respectively

\(\sigma _{rf}^{p}{;}\sigma _{{\uptheta }f}^{p};\sigma _{{e}f}^{p}\) :

Plastic radial, tangential, and effective stresses in in the FG part of hollow shaft, respectively

\(u_{f}^{E} ; u_{h}^{E}\) :

elastic radial displacement in FGM and homogeneous part, respectively

\(\varepsilon _{r};\,\varepsilon _{\theta }\) :

Strains at the radial and tangential directions, respectively

\(\vartheta _{h}\), \(\vartheta _{f}\) :

Poisson’s ratio in homogeneous and FG parts of hollow shaft, respectively

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  1. School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran

    Ali Hajisadeghian, Abolfazl Masoumi & Ali Parvizi

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  1. Ali Hajisadeghian
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Hajisadeghian, A., Masoumi, A. & Parvizi, A. Analytical investigation of elastic and plastic behavior of rotating double-walled FGM-homogenous hollow shafts. Arch Appl Mech 91, 1343–1369 (2021). https://doi.org/10.1007/s00419-020-01826-9

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