Stress concentration factors and stress-gradients due to circular holes in radially functionally graded panels subjected to anti-plane shear loading

Abstract

Closed-form expressions for the elastic fields (stresses, stress-gradients, strains, and displacements) in radially graded continua without and with circular holes are derived. The conventional definition of the stress concentration factor, which is the ratio of the maximum tangential stress on the circumference of the hole to the far-field applied traction, leads to physically unrealistic interpretations in functionally graded materials. A novel definition is derived for the stress concentration factor in graded panels. The stress concentration factor increases when the rigidity modulus progressively decreases away from the center of the hole (softening materials). The stress concentration desirably reduces in hardening materials in which the rigidity modulus progressively increases away from the hole. The gradient of the tangential stress ahead of the circular hole introduces an affected zone that is size-dependent (depends on the size of the hole, even in homogeneous media). The affected zone size decreases, while the stress-gradients increase with increase in the inhomogeneity length-scale and results in the increasing propensity of damage in softening materials. In hardening materials, the propensity of damage reduces with increase in the inhomogeneity length-scale due to the stress dilution.