Plane Strain Analytical Solutions to Rotating Partially Plastic Graded Hollow Shafts


Abstract: Analytical solutions for the elastoplastic deformation of rotating graded hollow shafts are presented. The modulus of elasticity of the shaft material is 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 behavior. Elastic, partially plastic, fully plastic, and residual stress states are investigated. It is observed that the elastoplastic responses of the rotating functionally graded hollow shafts are affected notably by the material nonhomogeneity. It is also observed that the fully plastic limit rotation speed of the shaft is almost independent of the variation in the modulus of elasticity of the material. The nonhomogeneous solution derived here reduces to that of a homogeneous one as the variation in the modulus of elasticity is slowed down.

Keywords: Functionally graded material, Elastoplasticity, Rotating shafts, Stress analysis, Tresca's criterion

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