An Analytical Solution to Stress Intensity Factors of Arbitrary Elliptical Arc Crack

ABSTRACT

The accurate determination of stress intensity factors (SIFs) for curved cracks in isotropic solids is essential for assessing failure mechanisms and ensuring the structural integrity of engineering materials and rock formations. While analytical solutions for circular arc crack and symmetric elliptical arc crack have been established, an analytical treatment for an arbitrary elliptical arc crack remains lacking. This paper presents a novel analytical solution for the SIFs of an arbitrary elliptical arc crack embedded in an infinite isotropic plane subjected to uniform far‐field biaxial tension. By integrating affine transformation, conformal mapping, and complex variable methods, we derive explicit expressions for the complex potentials and the corresponding Mode‐I and Mode‐II SIFs at both crack tips. The solution is expressed in terms of four geometric parameters that uniquely define any elliptical arc crack. The accuracy and effectiveness of the proposed method are validated through comparisons with existing analytical solutions for circular arc and symmetric elliptical arc cracks, as well as finite element results for arbitrary elliptical arc cracks. The derived closed‐form expressions provide an efficient tool for parametric analysis of fracture behavior in elliptical arc crack geometries and can serve as a useful reference for validating numerical methods in isotropic fracture mechanics.