Stress shielding effects in pin-loaded hole contact with clearance using FGM

An analytical solution is presented for the contact problem with clearance between a loaded rigid pin and a circular ring made of functionally graded material (FGM), which is inserted around a hole in an infinite isotropic elastic plane. It is assumed that the elastic shear modulus of the FGM ring varies continuously with the radius according to a power law, while the Poisson’s ratio is taken costant. The most general expressions for the stress and displacement fields in polar coordinates are considered, both for the FGM ring and the elastic plane. 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 nonlinearity 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. By properly tuning the variation of the material properties within the ring thickness, the contact angle can be increased. Consequently, more uniform distributions can be achieved for the contact pressure and the hoop stress along radial directions, thereby preventing mechanical failure in many fasteners and bolt connections. To compare the stress distributions in the plate with and without the FGM annular reinforcement around the hole, a new solution is worked out as a particular case for the problem of a rigid circular pin in frictionless quasi-conformal contact with a hole in an isotropic elastic plane, and the stress shielding effect consequent to the introduction of the FGM ring is clearly illustrated. The analytical results are then validated against Finite Element predictions, as well as by verifying the invariance of the sum of the classical M-integral, taken along circular contours surrounding the hole, together with an area integral that compensates for the path dependence of the M-integral in inhomogeneous elastic materials, showing very good agreement.