*Review* **Simulation of Quasi-Static Crack Propagation by Adaptive Finite Element Method**

**Abdulnaser M. Alshoaibi \* and Yahya Ali Fageehi**

**\*** Correspondence: alshoaibi@jazanu.edu.sa or alshoaibi@gmail.com; Tel.: +966-56-347-9523

**Abstract:** The finite element method (FEM) is a widely used technique in research, including but not restricted to the growth of cracks in engineering applications. However, failure to use fine meshes poses problems in modeling the singular stress field around the crack tip in the singular element region. This work aims at using the original source code program by Visual FORTRAN language to predict the crack propagation and fatigue lifetime using the adaptive dens mesh finite element method. This developed program involves the adaptive mesh generator according to the advancing front method as well as both the pre-processing and post-processing for the crack growth simulation under linear elastic fracture mechanics theory. The stress state at a crack tip is characterized by the stress intensity factor associated with the rate of crack growth. The quarter-point singular elements are constructed around the crack tip to accurately represent the singularity of this region. Under linear elastic fracture mechanics (LEFM) with an assumption in various configurations, the Paris law model was employed to evaluate mixed-mode fatigue life for two specimens under constant amplitude loading. The framework includes a progressive analysis of the stress intensity factors (SIFs), the direction of crack growth, and the estimation of fatigue life. The results of the analysis are consistent with other experimental and numerical studies in the literature for the prediction of the fatigue crack growth trajectories as well as the calculation of stress intensity factors.

**Keywords:** LEFM; mesh density; mixed mode stress intensity factors; fatigue crack growth; FEM

**Citation:** Alshoaibi, A.M.; Fageehi, Y.A. Simulation of Quasi-Static Crack Propagation by Adaptive Finite Element Method. *Metals* **2021**, *11*, 98. https://doi.org/10.3390/met11010098

Received: 17 December 2020 Accepted: 3 January 2021 Published: 6 January 2021

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