It has been observed that thermal effects increase the value of angular speed required to yield at the internal surface for incompressible/compressible materials. Radial stresses have a maximum value at the internal surface of the rotating disc made of incompressible materials as compared to compressible materials. With the introduction of thermal effects, radial as well as circumferential stresses must be decreased in the absence of mechanical load but when mechanical load is applied, radial as well as circumferential stresses must be increased at the internal surface of a rotating disc with a shaft. A rotating disc is likely to fracture at the bore of the radius.
The purpose of this paper is to establish the mathematical model on the elastic-plastic transitions occurring in the rotating spherical shells based on compressibility of materials. The paper investigates the elastic-plastic stresses and angular speed required to start yielding in rotating shells for compressible and incompressible materials. The paper is based on the non-linear transition theory of elastic-plastic shells given by B.R. Seth. The elastic-plastic transition obtained is treated as an asymptotic phenomenon at critical points & the solution obtained at these points generates stresses. The solution obtained does not require the use of semi-empirical yield condition like Tresca or Von Mises or other certain laws. Results are obtained numerically and depicted graphically. It has been observed that Rotating shells made of the incompressible material are on the safer side of the design as compared to rotating shells made of compressible material. The effect of density variation has been discussed numerically on the stresses. With the effect of density variation parameter, rotating spherical shells start yielding at the internal surface with the lower values of the angular speed for incompressible/compressible materials.
ABSTRACT. Seth's transition theory is applied to the problem of stresses in a solid rotating disk under heat generation subjected to variable density by infinitesimal deformation. Neither the yield criterion nor the associated flow rule is assumed here. The results obtained here are applicable to compressible materials. If the additional condition of incompressibility is imposed, then the expression for stresses corresponds to those arising from Tresca yield condition. It has been seen that circumferential stress are maximum at the outer surface for incompressible material as compare to disk made compressible materials. Density variation parameter increases the value of circumferential as well as radial stress at the outer surface of solid disk for compressible and incompressible materials. The present solution is illustrated by numerical results and is compared with heat generation case.
ABSTRACT. Steady thermal stresses in a rotating disc with shaft having density variation parameter subjected to thermal load have been derived by using Seth's transition theory. Neither the yields criterion nor the associated flow rule is assumed here. Results are depicted graphically. It has been seen that compressible material required higher percentage increased angular speed to become fully-plastic as compare to rotating disc made of incompressible material. Circumferential stresses are maximal at the outer surface of the rotating disc. With the introduction of thermal effect it decreases the value of radial and circumferential stresses at inner and outer surface for fully-plastic state.
ABSTRACT. The effect of imposing linear thermal gradient on the steady state creep behavior of a rotating functionally graded Al-SiCp disc is investigated in the present study by using Sherby's law. Mathematical model to describe steady state creep behavior in rotating disc made of isotropic Al-SiC composite in presence of linear thermal gradient in the radial direction has been formulated. The distributions of stresses and strain rates have been obtained. The creep response of a composite disc with uniform temperature has also been computed for comparison with the results obtained for thermally graded discs. The creep rates in a rotating thermally graded disc can be significantly reduced in presence of thermal gradients.
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