Crack tip plasticity of a penny-shaped Dugdale crack in a power-law graded elastic infinite medium

The plastic zone in the vicinity of a penny-shaped Dugdale crack embedded in an inhomogeneous infinite medium is estimated, for the first time. By virtue of the Dugdale’s hypothesis along with the method of potential theory, the equation governing the size of plastic zone is derived in terms of Hypergeometric functions. The normal stress outside the plastic zone is expressed by special functions. The validity of the present solutions is examined both analytically and numerically. Systematical calculations are made to investigate the influence of some physical parameters on the size of plastic zone and the distribution of the normal stress.

► We estimated the size of plastic zone in the vicinity of a penny-shaped crack.
► Arbitrary continuous axisymmetric loads can be applied on the crack surfaces.
► Hypergeometric functions are used to describe the involved physical quantities.
► The validity of present solutions has been discussed analytically and numerically.