Mode I Stress Intensity Factor Solutions for Cracks Emanating from a Semi-Ellipsoidal Pit.

In linear elastic fracture mechanics, the stress intensity factor describes the magnitude of the stress singularity near a crack tip caused by remote stress and is related to the rate of fatigue crack growth. The literature lacks SIF solutions for cracks emanating from a three-dimensional semi-ellipsoidal pit. This study undertakes a comprehensive parametric investigation of the Mode I stress intensity factor (KI) concerning cracks originating from a semi-ellipsoidal pit in a plate. This work utilizes finite element analysis, controlled by Python scripts, to conduct an extensive study on the effect of various pit dimensions and crack lengths on KI. Two cracks in the shape of a circular arc are introduced at the pit mouth perpendicular to the loading direction. The KI values are calculated using the displacement extrapolation method. The effect of normalized geometric parameters pit-depth-to-pit-width (a/2c), pit-depth-to-plate-thickness (a/t), and crack-radius-to-pit-depth (R/a) are investigated. The crack-radius-to-pit-depth (R/a) is found to be the dominating parameter based on correlation analysis. The data obtained from 216 FEA simulations are incorporated into a predictive model using a k-dimensional (k-d) tree and k-Nearest Neighbour (k-NN) algorithm.