# A Computational Framework for 2D Crack Growth Based on the Adaptive Finite Element Method
## 4 Conclusions  
In this study, two-dimensional crack growth on a rectangular structure with two holes and one central crack and on a cracked plate with four holes was studied using the developed FE source code program. The following results have been concluded from this work:  
* These examples addressed a variety of issues, including the effect of hole location on the crack-growth trajectory, mixed-mode stress intensity factors, and stress distribution. * The adaptive mesh structure was constructed using the advancing-front method, and the singularity was demonstrated by constructing quarter-point single elements around the crack tip. * The presence of a hole in close proximity to a crack that is propagating can cause the crack path to be changed. * The computed SIFs are in good agreement with the reference solutions. Figure 12: Predicted values of the \(K_{I}\) in comparison to Ansys results obtained by [6]. Figure 13: Predicted values of the \(K_{II}\) in comparison to Ansys results obtained by [6]. * The developed program can accurately simulate the crack growth of any two-dimensional linear elastic structural component, according to comparisons with several benchmark problems of crack propagation from the literature. A.M.A. ; methodology, A.M.A. ; software, A.M.A. ; validation, A.M.A. and Y.A.F. ; formal analysis, A.M.A. ; investigation, A.M.A. and Y.A.F. ; resources, A.M.A. ; data curation, A.M.A. and Y.A.F. ; writing--original draft preparation, A.M.A. ; writing--review and editing, A.M.A. and Y.A.F. ; visualization, A.M.A. and Y.A.F. ; supervision, A.M.A. ; project administration, A.M.A. and Y.A.F. ; funding acquisition, A.M.A. and Y.A.F. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable  
* _[PERSON] et al. (2000)_ [PERSON]; [PERSON]; [PERSON]; [PERSON] _The Stress Analysis of Cracks Handbook_; ASME Press: New York, NY, USA, 2000; Volume 130. * [PERSON] and [PERSON] (1993) [PERSON]; [PERSON] Stress intensity factors handbook, vol. 3. _J. Appl. Mech._**1993**, _60_, 1063. [CrossRef]
* _[PERSON] and [PERSON] (1998)_ [PERSON]; [PERSON] _Stress Intensity Factor and Limit Load Handbook_; British Energy Generation Limited Gloucester: Barnwood, UK, 1998; Volume 3. * _[PERSON] (1995)_ [PERSON]; [PERSON] On the use of displacement extrapolation to obtain crack tip singular stresses and stress intensity factors. _Eng. Fract. Mech._**1995**, _51_, 391-400. [CrossRef]
* _[PERSON] et al. (2000)_ [PERSON]; [PERSON]; [PERSON] KI evaluation by the displacement extrapolation technique. _Eng. Fract. Mech._**2000**, _66_, 243-255. [CrossRef]
* [PERSON] (1968) [PERSON] A path independent integral and the approximate analysis of strain concentration by notches and cracks. _J. Appl. Mech._**1968**, _35_, 379-386. [CrossRef]
* _[PERSON] et al. (2005)_ [PERSON]; [PERSON]; [PERSON]; [PERSON]. Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS. _Eng. Fract. Mech._**2005**, _72_, 2174-2185. [CrossRef]
* _[PERSON] (2020)_ [PERSON], [PERSON]; [PERSON] Numerical simulation of mixed-mode fatigue crack growth for compact tension shear specimen. _Adv. Mater. Sci. Eng._**2020**, _2020_, 5426831. [CrossRef]
* _[PERSON] et al. (2008)_ [PERSON]; [PERSON]; [PERSON] Finite element simulation of fatigue life estimation and crack path prediction of two-dimensional structures components. _HKIE Trans._**2008**, _15_, 1-6. [CrossRef]
* _[PERSON] et al. (2021)_ [PERSON]; [PERSON] Adaptive Finite Element Model for Simulating Crack Growth in the Presence of Holes. _Materials_**2021**, _14_, 5224. [CrossRef] [PubMedMed]
* _[PERSON] et al. (2007)_ [PERSON]; [PERSON]; [PERSON] Two-dimensional numerical estimation of stress intensity factors and crack propagation in linear elastic Analysis. _Struct. Durab. Health Mouit._**2007**, \(3\), 15. * _[PERSON] (2009)_ [PERSON]; [PERSON] Development of efficient finite element software of crack propagation simulation using adaptive mesh strategy.