Three-dimensional numerical elastoplastic analysis of stress and strain fields near a crack tip

Abstract

The presence of crack defects is of paramount importance in structural life prediction analyses. Basic studies utilizing the Linear Elastic Fracture Mechanics approach show that the Stress Intensity Factor (SIF) largely governs Fatigue Crack Growth (FCG). However, overloads may induce material “memory effects” that delay, arrest, or accelerate the FCG rate — a behavior that cannot be described adequately using a single elastic parameter analysis. To address service-variable amplitude loadings, recent research has proposed using a prescribed stress–strain distribution as the driving force of FCG, based on the critical damage approach. Due to the assumptions made in these analytical derivations, significant equilibrium and compatibility conditions are violated in the resulting solutions, as they rely on an idealized singular stress–strain field at the crack front region. This work provides a comprehensive review of published analytical results for solutions under both elastic and elastoplastic material behavior regimens, including Williams and HRR, which assume a singular stress distribution field, and Creager–Paris, which assumes a non-singular stress field but remains within the elastic range of the material. These solutions are compared throughout the study, with results obtained from numerical analysis using a 3D finite element discretization, applying the elastoplastic von Mises yielding criterion, to model the blunt crack tip. From this comparison, we derive conclusions regarding the application limits of the theoretical models and the required scope of numerical model representation. In addition to monotonically increasing applied loads, this work also considers unloading conditions as a main contribution to the proposed numerical analysis.