Novel computational method for modeling elastic–plastic stress–strain fields near cracks under cyclic loadings

Analyzing stress and strain responses near cracks is essential for fatigue crack propagation assessments, but it often requires computationally expensive Finite Element (FE) analysis. To address this issue, an enhanced framework is developed to model elastic–plastic stress and strain distributions near a crack tip. Building on previous work, the framework employs the deviatoric forms of Hencky's plasticity equations and the multiaxial Neuber method by excluding effects of hydrostatic stresses for greater accuracy. A key innovation is the introduction of a variable stress re-distribution factor, which captures spatial variations in stress re-distribution due to plastic deformation near a crack tip. This innovation replaces the earlier assumption of a constant factor by offering a more realistic representation of stress fields. The framework was verified by using non-linear FE analysis based on two distinct hardening behaviors of SAE 1045 steel plates with 2 mm and 4 mm crack lengths to evaluate the model's robustness across diverse non-linear hardening behaviors and its ability to handle varying crack sizes. The results demonstrate the framework's superior accuracy compared to the previous model. This approach provides a practical and reliable alternative to FE analysis with promising applications in fatigue life assessment and fatigue crack growth analysis under cyclic loading conditions.