Comparison of Fatigue Crack Growth Models for Predicting Residual Life

Muhamad Husnain Mohd Noh; Mohd Akramin Mohd Romlay; Mohd Shamil Shaari; Takahashi Akiyuki

doi:10.31436/iiumej.v27i3.3409

Authors

Muhamad Husnain Mohd Noh Universiti Malaysia Pahang Al-Sultan Abdullah https://orcid.org/0000-0003-3509-3326
Mohd Akramin Mohd Romlay Universiti Malaysia Pahang Al-Sultan Abdullah https://orcid.org/0000-0002-7713-4790
Mohd Shamil Shaari Universiti Malaysia Pahang Al-Sultan Abdullah https://orcid.org/0000-0002-3721-0816
Takahashi Akiyuki Tokyo University of Science https://orcid.org/0009-0003-2848-4481

DOI:

https://doi.org/10.31436/iiumej.v27i3.3409

Keywords:

Residual life; S-version finite element model; Paris’s Law; Frost & Pook

Abstract

Fatigue is one of the most critical failure mechanisms in structural materials. Accurate prediction of fatigue crack growth and residual fatigue life is essential to ensure structural safety and reliability during design and service-life assessment. This study aims to predict the residual fatigue life of a four-point bending specimen under fatigue loading conditions using the S-version finite element model (S-version FEM). Four fatigue crack growth models are implemented within the S-version FEM framework, namely Paris’ Law, Frost and Pook, Walker, and Huang Moan models, to simulate crack propagation and estimate residual fatigue life. Experimental data from Al7075-T6 are used for validation purposes. The results indicate that the Frost and Pook model achieves an error below 20%, demonstrating acceptable engineering accuracy. In contrast, the Paris’ Law, Walker, and Huang Moan models show significantly higher deviations from the experimental results. Overall, the Frost and Pook model exhibits the best agreement with the experimental findings and provides improved predictive capability compared to the other empirical models, confirming the effectiveness of the proposed S-version FEM approach for fatigue crack growth and residual fatigue life prediction in four-point bending structures.

ABSTRAK: Retak-lesu merupakan salah satu mekanisme kegagalan paling kritikal dalam bahan struktur. Ramalan yang tepat terhadap pertumbuhan retak-lesu dan baki jangka hayat adalah penting bagi memastikan keselamatan dan kebolehpercayaan struktur dalam reka bentuk serta penilaian hayat perkhidmatan. Kajian ini bertujuan bagi meramalkan baki jangka hayat retak-lesu spesimen lenturan empat titik menggunakan model unsur terhingga S-version (S-version FEM) di bawah beban keletihan. Empat model pertumbuhan retak-lesu dijalankan dalam rangka kerja S-version FEM, iaitu Hukum Paris, Frost dan Pook, Walker, dan Huang Moan bagi mensimulasikan penyebaran retak serta menganggar baki jangka hayat retak-lesu. Data eksperimen daripada Al7075-T6 digunakan untuk tujuan pengesahan model. Keputusan menunjukkan bahawa model Frost dan Pook memberikan ralat kurang daripada 20%, sekaligus menunjukkan ketepatan kejuruteraan yang boleh diterima. Sebaliknya, model Hukum Paris, Walker, dan Huang Moan menunjukkan sisihan lebih tinggi berbanding keputusan eksperimen. Secara keseluruhan, model Frost dan Pook menunjukkan kesepadanan terbaik dengan keputusan eksperimen serta memberikan keupayaan ramalan yang lebih baik berbanding model empirik yang lain, sekaligus mengesahkan keberkesanan pendekatan S-version FEM yang dicadangkan dalam meramal pertumbuhan retak-lesu dan baki jangka hayat bagi struktur lenturan empat titik.

Downloads

Download data is not yet available.

References

A. Grbovi?, G. Kastratovi?, A. Sedmak, I. Bala?, and M. D. Popovi?, “Fatigue crack paths in light aircraft wing spars,” Int. J. Fatigue, vol. 123, pp. 96–104, 2019, doi: https://doi.org/10.1016/j.ijfatigue.2019.02.013.

M. Kikuchi, Y. Wada, and Y. Li, “Crack growth simulation in heterogeneous material by S-FEM and comparison with experiments,” Eng. Fract. Mech., vol. 167, pp. 239–247, 2016, doi: https://doi.org/10.1016/j.engfracmech.2016.03.038.

M. Aursand, P. J. Haagensen, and B. H. Skallerud, “Remaining fatigue life assessment of corroded mooring chains using crack growth modelling,” Marine Structures, vol. 90, p. 103446, 2023, doi: https://doi.org/10.1016/j.marstruc.2023.103446.

H. Okada, H. Kawai, and K. Araki, “A virtual crack closure-integral method (VCCM) to compute the energy release rates and stress intensity factors based on quadratic tetrahedral finite elements,” Eng. Fract. Mech., vol. 75, no. 15, pp. 4466–4485, 2008, doi: https://doi.org/10.1016/j.engfracmech.2008.04.014.

R. Masoudi Nejad and A. Gholami, “Fatigue crack growth and microstructural analysis of rail steel specimens under periodic overloads,” Mater. Today Commun., vol. 39, p. 108592, 2024, doi: https://doi.org/10.1016/j.mtcomm.2024.108592.

T. Wang, Z. Bahrami, G. Renaud, C. Yang, M. Liao, and Z. Liu, “A probabilistic model for fatigue crack growth prediction based on closed-form solution,” Structures, vol. 44, pp. 1583–1596, 2022, doi: https://doi.org/10.1016/j.istruc.2022.08.066.

S. O. Afolabi, B. I. Oladapo, C. O. Ijagbemi, A. O. M. Adeoye, and J. F. Kayode, “Design and finite element analysis of a fatigue life prediction for safe and economical machine shaft,” Journal of Materials Research and Technology, vol. 8, no. 1, pp. 105–111, 2019, doi: https://doi.org/10.1016/j.jmrt.2017.10.007.

W. Liang, M. Lou, C. Zhang, D. Zhao, D. Yang, and Y. Wang, “Experimental investigation and phenomenological modeling of fatigue crack growth in X80 pipeline steel under random loading,” Int. J. Fatigue, vol. 182, p. 108169, 2024, doi: https://doi.org/10.1016/j.ijfatigue.2024.108169.

C. H. Wang and C. N. Duong, “Chapter 6 - Damage tolerance and fatigue durability of scarf joints,” in Bonded Joints and Repairs to Composite Airframe Structures, C. H. Wang and C. N. Duong, Eds., Oxford: Academic Press, 2016, pp. 141–172. doi: https://doi.org/10.1016/B978-0-12-417153-4.00006-2.

H. Zhang and P. Qiao, “Virtual crack closure technique in peridynamic theory,” Comput. Methods Appl. Mech. Eng., vol. 372, p. 113318, 2020, doi: https://doi.org/10.1016/j.cma.2020.113318.

M. Goswami, S. Sharma, G. Subbarayan, S. P. A. Bordas, and S. Chattopadhyay, “Chapter Two - Historical purview and recent advances in fracture mechanics of elastomeric matrix composites,” in Advances in Applied Mechanics, vol. 56, S. P. A. Bordas, Ed., Elsevier, 2023, pp. 139–187. doi: https://doi.org/10.1016/bs.aams.2022.09.002.

B. Karihaloo and Q. Z. Xiao, “2.03 - Linear and Nonlinear Fracture Mechanics,” in Comprehensive Structural Integrity, I. Milne, R. O. Ritchie, and B. Karihaloo, Eds., Oxford: Pergamon, 2003, pp. 81–212. doi: https://doi.org/10.1016/B0-08-043749-4/02128-5.

H. Okada, H. Koya, H. Kawai, Y. Li, and K. Osakabe, “Computations of stress intensity factors for semi-elliptical cracks with high aspect ratios by using the tetrahedral finite element (fully automated parametric study),” Eng. Fract. Mech., vol. 158, pp. 144–166, 2016, doi: https://doi.org/10.1016/j.engfracmech.2016.02.049.

W. Xiang, M. Chen, Y. Tian, and B. Liu, “Application of a hierarchical quadrature element method to interface crack analysis in bi-material systems,” Eng. Fract. Mech., vol. 300, p. 109983, 2024, doi: https://doi.org/10.1016/j.engfracmech.2024.109983.

P. Paris and F. Erdogan, “A critical analysis of crack propagation laws,” 1963.

O. E. Wheeler, “Spectrum loading and crack growth,” 1972.

R. G. Forman, “Study of fatigue crack initiation from flaws using fracture mechanics theory,” Eng. Fract. Mech., vol. 4, no. 2, pp. 333–345, 1972, doi: https://doi.org/10.1016/0013-7944(72)90048-3.

K. Walker, “The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum,” 1970.

N. E. Frost, L. P. Pook, and K. Denton, “A fracture mechanics analysis of fatigue crack growth data for various materials,” Eng. Fract. Mech., vol. 3, no. 2, pp. 109–126, 1971, doi: https://doi.org/10.1016/0013-7944(71)90003-8.

T. Wang, Z. Bahrami, G. Renaud, C. Yang, M. Liao, and Z. Liu, “A probabilistic model for fatigue crack growth prediction based on closed-form solution,” Structures, vol. 44, pp. 1583–1596, 2022, doi: https://doi.org/10.1016/j.istruc.2022.08.066.

M. R. M. Akramin, M. S. Marizi, M. N. M. Husnain, and M. Shamil Shaari, “Analysis of Surface Crack using Various Crack Growth Models,” J. Phys. Conf. Ser., vol. 1529, no. 4, p. 042074, 2020, doi: 10.1088/1742-6596/1529/4/042074.

W. J. Wang and M.-S. Yim, “A fatigue crack growth prediction model for cracked specimen under variable amplitude loading,” Int. J. Fatigue, vol. 168, p. 107387, 2023, doi: https://doi.org/10.1016/j.ijfatigue.2022.107387.

V. Ribeiro et al., “Fatigue crack growth modelling by means of the strain energy density-based Huffman model considering the residual stress effect,” Eng. Fail. Anal., vol. 140, p. 106543, 2022, doi: https://doi.org/10.1016/j.engfailanal.2022.106543.

N. Pugno, M. Ciavarella, P. Cornetti, and A. Carpinteri, “A generalized Paris’ law for fatigue crack growth,” J. Mech. Phys. Solids, vol. 54, no. 7, pp. 1333–1349, 2006, doi: https://doi.org/10.1016/j.jmps.2006.01.007.

V. Ribeiro, J. Correia, G. Lesiuk, A. Gonçalves, A. De Jesus, and F. Berto, “Application and discussion of various crack closure models to predict fatigue crack growth in 6061-T651 aluminium alloy,” Int. J. Fatigue, vol. 153, p. 106472, 2021, doi: https://doi.org/10.1016/j.ijfatigue.2021.106472.

M. F. V Montezuma, E. P. De Deus, C. O. F. T. Rüchert, M. C. De Carvalho, and M. A. E Silva Filho, “Numerical-experimental procedure for predicting fatigue life in SAE AMS 7475-T7351 aluminum alloy considering the effect of stress ratio,” An. Acad. Bras. Cienc., vol. 96, 2024, doi: 10.1590/0001-3765202420231400.

Y. Li, H. Wang, and D. Gong, “The interrelation of the parameters in the Paris equation of fatigue crack growth,” Eng. Fract. Mech., vol. 96, pp. 500–509, 2012, doi: 10.1016/j.engfracmech.2012.08.016.

Y. Li and J. Jia, “A modified walker’s equation in fatigue crack growth,” Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University, vol. 26, no. 2, pp. 221–224, 2008, [Online]. Available: https://www.scopus.com/inward/record.uri?eid=2-s2.0-44849123145&partnerID=40&md5=a11aa8b7e0638602de90c8576fa4c368

P.-T. Guan, C.-Y. Lü, X.-T. Tang, J.-W. Zhu, Z.-Y. Ding, and Z.-L. Gao, “Study on fatigue crack growth behavior of q345r steel under multiple overloads,” Gongcheng Lixue/Engineering Mechanics, vol. 34, no. 7, pp. 224-231and240, 2017, doi: 10.6052/j.issn.1000-4750.2016.02.0113.

B. K. C. Yuen and F. Taheri, “Proposed modifications to the Wheeler retardation model for multiple overloading fatigue life prediction,” Int. J. Fatigue, vol. 28, no. 12, pp. 1803–1819, 2006, doi: 10.1016/j.ijfatigue.2005.12.007.

K. Tanaka, “4.04 - Fatigue Crack Propagation,” in Comprehensive Structural Integrity, I. Milne, R. O. Ritchie, and B. Karihaloo, Eds., Oxford: Pergamon, 2003, pp. 95–127. doi: https://doi.org/10.1016/B0-08-043749-4/04089-1.

M. Shaari, A. K. Ariffin, A. Takahashi, S. Abdullah, M. Kikuchi, and M. R. M. Akramin, “Fatigue crack growth analysis on square prismatic with embedded cracks under tension loading,” JOURNAL OF MECHANICAL ENGINEERING AND SCIENCES, vol. 14, pp. 2511–2525, Mar. 2017, doi: 10.15282/jmes.11.1.2017.10.0231.

H. Okada, M. Higashi, M. Kikuchi, Y. Fukui, and N. Kumazawa, “Three dimensional virtual crack closure-integral method (VCCM) with skewed and non-symmetric mesh arrangement at the crack front,” Eng. Fract. Mech., vol. 72, no. 11, pp. 1717–1737, 2005, doi: https://doi.org/10.1016/j.engfracmech.2004.12.005.

D. Broek, Elementary engineering fracture mechanics. Springer Netherlands, 1982. [Online]. Available: https://books.google.com.my/books?id=LC4E7OjnhuEC

G. Chell, “Developments in fracture mechanics,” 1979. [Online]. Available: https://api.semanticscholar.org/CorpusID:137575003

M. Xinting, L. Guoxu, P. Jian, T. Ping, Z. Jinbo, and L. Jian, “Study on the I-II mixed mode fatigue crack growth behavior of TC4 titanium alloy,” Theoretical and Applied Fracture Mechanics, vol. 138, p. 104985, 2025, doi: https://doi.org/10.1016/j.tafmec.2025.104985.

M.-S. Lee and M.-H. Kim, “A new fatigue crack growth model considering underloads and overloads history together with stress ratio,” International Journal of Naval Architecture and Ocean Engineering, vol. 14, p. 100481, 2022, doi: https://doi.org/10.1016/j.ijnaoe.2022.100481.

J. Cong, Z. Liu, S. Zhou, S. Gao, and X. Zhu, “Predicting fatigue life and crack growth rate of TC4 titanium alloy based on PINN before and after ultrasonic impact treatment,” Eng. Fail. Anal., vol. 166, p. 108875, 2024, doi: https://doi.org/10.1016/j.engfailanal.2024.108875.

M. S. Shaari, M. R. M. Akramin, A. K. Ariffin, S. Abdullah, and M. Kikuchi, “Fatigue crack growth behaviour of semi-elliptical surface cracks for an API 5L X65 gas pipeline under tension,” IOP Conf. Ser. Mater. Sci. Eng., vol. 308, no. 1, p. 012041, 2018, doi: 10.1088/1757-899X/308/1/012041.

F. Y. Chin, M. S. Shaari, A. Takahashi, M. R. M. Akramin, and S. Urai, “Fatigue Crack Growth Behavior of AlSi10Mg Material Produced by Direct Metal Laser Sintering Using S-Version Finite Element Method,” Journal of Failure Analysis and Prevention, vol. 23, no. 2, pp. 601–608, 2023, doi: 10.1007/s11668-023-01643-6.

M. R. M. Akramin, A. K. Ariffin, M. Kikuchi, and S. Abdullah, “Sampling method in probabilistic S-version finite element analysis for initial flaw size,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 39, no. 1, pp. 357–365, 2017, doi: 10.1007/s40430-016-0549-z.