Stress intensity factors of curved crack fronts in compact tension specimens

Abstract

This study presents a response surface model for the distribution of Mode I stress intensity factors along curved crack fronts in compact tension specimens. The aim is to provide an accurate yet practical tool for describing how the crack driving force varies along three-dimensional elliptical crack fronts that commonly form during fatigue crack growth. A comprehensive dataset of stress intensity factor distributions is generated using automated finite element simulations covering a wide range of concave and convex crack front geometries. The distributions are found to follow a logarithmic form expressible with only two dimensionless geometric parameters: the relative width and aspect ratio of the crack front ellipse. A multi-surface fitting procedure is then applied to derive an algebraic representation of the dataset. The resulting three-dimensional response surface model reproduces the finite element results with high accuracy. The applicability of the model is demonstrated through experimental results obtained from nodular cast iron specimens revealing a strong environmental dependence of the crack front shape. The model supports the increasing adoption of physics-based fatigue and fracture assessments and enables inference of crack growth resistance patterns from observed fracture surfaces, among other utilities.