An Automated Adaptive Finite Element Methodology for 2D Linear Elastic Fatigue Crack Growth Simulation

Abstract

Fatigue crack growth is a critical phenomenon in engineering structures, accounting for a significant percentage of structural failures across various industries. Accurate prediction of crack initiation, propagation paths, and fatigue life is essential for ensuring structural integrity and optimizing maintenance schedules. This paper presents a comprehensive finite element approach for simulating two-dimensional fatigue crack growth under linear elastic conditions with adaptive mesh generation. The source code for the program was developed in Fortran 95 and compiled with Visual Fortran. To achieve high-fidelity simulations, the methodology integrates several key features: it employs an automatic, adaptive meshing technique that selectively refines the element density near the crack front and areas of significant stress concentration. Specialized singular elements are used at the crack tip to ensure precise stress field representation. The direction of crack advancement is predicted using the maximum tangential stress criterion, while stress intensity factors are determined through either the displacement extrapolation technique or the J-integral method. The simulation models crack growth as a series of linear increments, with solution stability maintained by a consistent transfer algorithm and a crack relaxation method. The framework’s effectiveness is demonstrated across various geometries and loading scenarios. Through rigorous validation against both experimental data and established numerical benchmarks, the approach is proven to accurately forecast crack trajectories and fatigue life. Furthermore, the detailed description of the program’s architecture offers a foundational blueprint, serving as a valuable guide for researchers aiming to develop their specialized software for fracture mechanics analysis.