Stress shielding effect in cylindrical joints with clearance using FGM

Analytical solutions are presented for the quasi-conformal contact problem with clearance between a loaded rigid pin and a circular ring made of functionally graded material (FGM), which displays a power-law radial variation of the elastic modulus within the thickness. The stress and displacement fields in the FGM ring are taken from the general solution for plane elastic problems involving FGMs in polar coordinates, analogous to Mitchell’s solution for elastic isotropic materials. The frictionless contact conditions yield a set of dual trigonometric series equations that can be reduced to a linear system of infinite equations, then solved by truncation. Due to the nonlinear nature of the advancing contact problem, an inverse method of solution is employed, namely, the contact stress distribution is derived for a set of contact angle values. The corresponding pin load is then calculated, and a nonlinear pointwise relationship is obtained between the contact angle and the pin load. We show that the contact angle can be increased by properly choosing the inhomogeneity factor of the FGM ring. Consequently, more uniform distributions can be achieved for the contact pressure and the hoop stress, thereby preventing mechanical failure in many fasteners and bolt connections. The present findings can assist mechanical engineers in designing innovative pinned connections and improving their load-bearing capacity by exploiting the FGM capabilities.