Nonlinear mathematical model of surface crack propagation: finite element calculation and fatigue life prediction

The presence of discontinuities such as holes close to propagating fatigue crack can significantly influence the crack path, leading either to deviation toward the hole or arrest at its boundary. This research presents a nonlinear mathematical model for surface crack propagation that integrates finite element calculations with fatigue life prediction under mixed-mode loading. The research focuses on the interaction between growing surface cracks and geometric discontinuities, such as holes, which can deflect crack trajectories, promote crack arrest, or alter fatigue life. Nonlinear effects, including crack-tip plasticity, crack-face contact, and large deformation, are incorporated through advanced constitutive modelling and nonlinear finite element analysis. Crack growth is modelled using Finite Element Method (FEM) withenrichment functions, enabling crack propagation without remeshing. Stress and strain fields are evaluated to obtain nonlinear fracture factors, including the J-integral, equivalent stress intensity factors, and crack tip opening displacement (CTOD). Crack initiation and growth direction are governed by the maximum circumferential stress (local symmetry) principle, while fatigue crack growth rates are predicted using Hartman-Schijve Model (HSM) coupled with equivalent nonlinear fracture parameters. Variable-amplitude loading and load-interaction effects are modeled using retardation models, applied to modified compact tension specimens for crack deviation and arrest. The results show that nonlinear effects strongly influence crack path evolution and fatigue life, with J-integral values of 3.25-4.55 kJ/m 2 , Δ√H_J of 1.66-2.00, and crack propagation angles ranging from 28° to 35° across the specimens. Predicted crack paths and fatigue lives closely match experiments, confirming the nonlinear model’s accuracy and robustness.