Validation of Finite Element-Based Crack Tip Driving Force Solutions Using Fractal Analysis of Crack-Path Microfeatures

Accurate quantification of the crack tip driving force (ΔK) is fundamental to predicting the fatigue life of engineering structures. Analytical formulations of ΔK are rarely available for components with complex geometries. In such cases, finite element (FE) analysis has become a widely accepted approach for determining ΔK. In this study, an FE-based solution for the crack-tip driving force of a fatigue crack in an asymmetric L-shaped bell crank geometry, a representative complex structure, is established. The structure is fabricated from AISI 410 martensitic stainless steel. The FE-predicted ΔK_I for crack growth in the Paris regime has been independently validated using the multifractal stress-intensity-factor model. Results show that the fatigue crack in the bell crank structure is driven by a combined Mode-I (opening) and Mode-II (shearing) crack tip loading along a curved crack path trajectory, as dictated by the asymmetric stress distribution. The fatigue crack edge exhibits fractality with fractal dimensions ranging from 1.00 (Euclidean) to 1.18 over the crack length, (a-a_o) up to 9.947 mm. The FE-calculated crack tip driving forces of the bell crank structure are comparable with those computed based on the corrected crack edge fractal dimensions, thus validating the FE simulation outcomes. The resulting fatigue crack growth rates, determined from crack-tip driving forces based on validated FE-computed contour integrals, are comparable to those obtained from the ASTM standard tests.