Investigation of Stress Concentration Factors for Functionally Graded Hollow Tubes with Curved Edges under Torsion

In this paper, a finite element (FE) model is developed to calculate stress concentration factors of functionally graded (FG) hollow tubes under torsion. First, the shear stresses in FG hollow tubes with curved edges are investigated for different curvature radius of the cross-section corners. Next, stress concentrations are evaluated at low curvature parts of the cross-sections. Due to stress concentrations in low curvature regions, more considerable shear stresses are obtained. FE results are compared with the results of an analytical method for analysis of the torsion of hollow tubes to verify the computational approaches. Except for the points of stress concentrations, in other regions, an excellent agreement is found between analytical and FE results. Therefore, in stress concentration regions, regarding the error of analytical formula in stress analysis, some correction factor is presented. These stress concentration factors are calculated for a variety of curvature radius and cross-section thicknesses. Applying the presented factors, the proposed analytical formula can be used for stress evaluations, even at stress concentration regions. Finally, the effects of changing the volume fraction of the constituent phases are investigated for a range of curvature radius of cross-section corners.