A Novel Approach for Modelling Crack Paths in Plate Structures for Dynamic Response Analysis

Abstract:

Cracks significantly affect the structural integrity and functionality of mechanical components. While most existing studies focus on identifying straight cracks using dynamic response (DR) data, the characterisation of crack paths, especially curved ones, remains limited. This gap is critical, as the path of crack propagation plays a vital role in determining the severity of structural damage, particularly in critical regions of plate structures. The large number of possible crack paths has made systematic research in this area difficult. Therefore, this study proposes a novel methodology for modelling both straight and curved crack paths in plate structures to analyse their DR using the Finite element method (FEM). Straight cracks are represented by coordinate pairs, while curved cracks are defined using second-order polynomial equations. A combination-based approach is employed to generate feasible curved paths within a bounded region, allowing variation in crack shapes, lengths, and geometries. The results demonstrate that the proposed methodology effectively reduces the total number of crack path configurations from 7140, an impractically large set for detailed analysis, to a manageable subset of 288. This reduction facilitates more efficient implementation in both numerical simulations and experimental investigations without compromising the representational diversity of crack path geometries. They also show that the crack path has a greater influence on the dynamic response than crack length, offering a more comprehensive framework for crack path identification and evaluation.

• Periodical: Key Engineering Materials (Volume 1037)
• Pages: 49-57
• DOI: https://doi.org/10.4028/p-kg5Mpj
• Online since: January 2026
• Authors: Yousef Lafi A. Alshammari*, Muhammad Khan, Feiyang He, Hilal Doganay Kati
• Keywords: Crack Path, Curved Crack, Damage, Dynamic Response, Plate, Straight Crack

References

[1] Azouz Z., Honarvar Shakibaei Asli B., Khan M. Evolution of Crack Analysis in Structures Using Image Processing Technique: A Review. Electronics. 12 September 2023; 12(18): 3862. Available at:

DOI: 10.3390/electronics12183862

[2] Alshammari YLA., He F., Alrwili AA., Khan M. Fundamental Challenges and Complexities of Damage Identification from Dynamic Response in Plate Structures. Applied Sciences. 12 September 2024; 14(18): 8230. Available at:

DOI: 10.3390/app14188230

[3] Yang Z., He F., Khan M. An Empirical Torsional Spring Model for the Inclined Crack in a 3D-Printed Acrylonitrile Butadiene Styrene (ABS) Cantilever Beam. Polymers. 18 January 2023; 15(3): 496. Available at:

DOI: 10.3390/polym15030496

[4] Zedan Khalel HH., Khan M., Starr A. Dynamic Response-Based Crack Resistance Analysis of Fibre Reinforced Concrete Specimens Under Different Temperatures and Crack Depths. Journal of Building Engineering. May 2023; 66: 105865. Available at:

DOI: 10.1016/j.jobe.2023.105865

[5] Zai BA., Khan MA., Khan SZ., Asif M., Khan KA., Saquib AN., et al. Prediction of Crack Depth and Fatigue Life of an Acrylonitrile Butadiene Styrene Cantilever Beam Using Dynamic Response. Journal of Testing and Evaluation. 1 March 2020; 48(2): 1520–1536. Available at:

DOI: 10.1520/JTE20180674

[6] Alshammari YLA., He F., Alrwili A., Aldubay-yan A., Khan M. Critical Challenges in Dynamic Response-Based Damage Detection in Plate Structures. Amsterdam: 30 th International Congress on Sound and Vibration; 2024. Available at: https://iiav.org/content/archives_icsv_last/2024_icsv30/content/papers/papers/full_paper_614_20240215140327578.pdf (Accessed: 18 June 2025)

[7] Alshammari YLA., He F., Khan MA. Modelling and Investigation of Crack Growth for 3D-Printed Acrylonitrile Butadiene Styrene (ABS) with Various Printing Parameters and Ambient Temperatures. Polymers. 29 October 2021; 13(21): 3737. Available at:

DOI: 10.3390/polym13213737

[8] Huang CS., Leissa AW. Vibration Analysis of Rectangular Plates with Side Cracks via the Ritz Method. Journal of Sound and Vibration. June 2009; 323(3–5): 974–988. Available at:

DOI: 10.1016/j.jsv.2009.01.018

[9] Huang CS., Leissa AW., Chan CW. Vibrations of Rectangular Plates with Internal Cracks or Slits. International Journal of Mechanical Sciences. June 2011; 53(6): 436–445. Available at:

DOI: 10.1016/j.ijmecsci.2011.03.006

[10] Israr A. Model for Vibration of Crack Plates for use with Damage Detection Methodologies. Journal of Space Technology. 2011. Available at: https://www.ist.edu.pk/downloads/jst/previous-issues/july-2011/3.pdf (Accessed: 10 June 2025)

[11] Ismail R., Cartmell MP. An Investigation Into the Vibration Analysis of a Plate with a Surface Crack of Variable Angular Orientation. Journal of Sound and Vibration. June 2012; 331(12): 2929–2948. Available at:

DOI: 10.1016/j.jsv.2012.02.011

[12] Bose T., Mohanty AR. Vibration Analysis of a Rectangular Thin Isotropic Plate with a Part-Through Surface Crack of Arbitrary Orientation and Position. Journal of Sound and Vibration. December 2013; 332(26): 7123–7141. Available at:

DOI: 10.1016/j.jsv.2013.08.017

[13] Beigi A., Edalat P., Khedmati MR., Fadavi M. A Numerical Investigation into the Crack Effects on the Natural Frequencies of the Plates. 2014. Available at: http://ijmt.ir/browse.php?a_code=A-10-7-2&sid=1&slc_lang=en

[14] Doğanay Katı H., Buhari J., Francese A., He F., Khan M. Numerical Analysis of Crack Path Effects on the Vibration Behaviour of Aluminium Alloy Beams and Its Identification via Artificial Neural Networks. Sensors. 30 January 2025; 25(3): 838. Available at:

DOI: 10.3390/s25030838