A closed form expression of stress intensity factor for an arbitrarily shaped planar crack in 3-D under tensile loading

A closed-form equation was developed in this work to quantify the stress intensity factor (SIF) along an arbitrarily shaped planar crack under mode-I loading by substituting the ellipse-related parameters in Irwin’s solution with geometry-related parameters $f_i$ of the crack. This allowed incorporation of the local crack curvature effect on SIF at each discrete point along the crack front and its relative weighted contribution to SIF of the neighboring crack point i, where either stress concentration or shielding took place, into computation of the SIF distribution along the crack front. Good agreement was obtained between the $K_I$ values derived in the current work and previous numerical simulation-based studies. The current method could capture the $K_I$ distributions for surface and embedded cracks having the same shape, with their maximum values being consistent with Murakami’s $\sqrt{\mathrm{area}}$ method. This solution of $K_I$ allows for highly efficient calculation of $\Delta K_I$ for quantification of the 3D growth behaviors of a fatigue crack with a complex shape, paving the way for studying the statistical nature of short fatigue crack growth.