Analytical solution for the stress fields of a hypocycloidal hole with two radial cracks in an infinite plate

Abstract

Hole structures are widely utilized in engineering applications. Edge cracks may form around holes during manufacturing or operation, potentially leading to structural failure. This study investigates the problem of unequal radial cracks emanating from a hypocycloid-shaped hole in a two-dimensional isotropic infinite plate. Using the Muskhelishvili approach and conformal mapping, a general solution is derived for cracked deltoid and astroid holes. The analytical theory is validated through finite element simulations, with numerical examples for both single-sided and double-sided radial cracks. The effects of crack length and hypocycloid geometry on the stress intensity factor (SIF) are investigated. Under uniaxial tension, an increase in crack length raises the SIF for both the corresponding and opposite crack tips. Due to geometric differences at the crack initiation location, cracks emanating from the cusps of a deltoid hole exhibit reduced sensitivity of SIF to crack length compared to cracks emanating from smoother hole edges.