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The Mathematical Study of an Edge Crack in Two Different Specified Models under Time-Harmonic Wave Disturbance

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Mechanics of Composite Materials Aims and scope

This paper devotes to determining a stress intensity factor (SIF) at the tip of an edge crack in two models considered. Problem-1 is an orthotropic strip of a finite thickness bonded by an orthotropic half-plane, and problem-2 is an orthotropic vertical semi-infinite strip of the same thickness. Edge cracks have been invaded perpendicularly by time-harmonic elastic waves. The models considered were taken to the transformed plane by using the Fourier transform technique, where the Schmidt method is used to find the unknown coefficients. The analytical expression of the SIF is derived for both the problems. The variations of normalized SIF for the different crack lengths and thickness of the strips for the problems considered were calculated numerically, and their behaviour was depicted graphically for different particular cases.

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References

  1. I. N. Sneddon and S. C. Das, “The stress intensity factor at the tip of an edge crack in an elastic half-plane,” Int. J. Eng. Sci., 9, 25-36 (1971).

    Article  Google Scholar 

  2. D. Achenbach, L. M. Keer, and D. A. Mendelsohn, “Elastodynamic analysis of an edge crack,” J. Appl. Mech., 47, 551-556 (1980).

    Article  Google Scholar 

  3. G. D. Gupta and F. Erdogan, “The problem of edge cracks in an infinite strip,” J. Appl. Mech., 41, 1001-1006 (1974).

    Article  Google Scholar 

  4. N. Hasebe and S. Inohara, “Stress analysis of a semi-infinite plate with an oblique edge crack,” Ingenieur-Archiv, 49, 51-62 (1980).

    Article  Google Scholar 

  5. Z. H. Jin and N. Noda, “Edge crack in a nonhomogeneous half plane under thermal loading,” J. Therm. Stresses, 17, 591-599 (1994).

    Article  Google Scholar 

  6. Z. H. Jin and G. H. Paulino, “Transient thermal stress analysis of an edge crack in a functionally graded material,” Int. J. Fract., 107, 73-98 (2001).

    Article  CAS  Google Scholar 

  7. L. Guo, L.-Z. Wu, and T. Zeng, “The dynamic response of an edge cracks in a functionally graded orthotropic strip,” Mech. Res. Commun., 32, 385-400 (2005).

    Article  Google Scholar 

  8. S. Das, S. Chakraborty, N. Srikanth, and M. Gupta, “Symmetric edge cracks in an orthotropic strip under normal loading,” Int. J. Fract., 153, 77-84 (2008).

    Article  Google Scholar 

  9. S. Das, R Prasad, and S. Mukhopadhyay, “Stress intensity factor of an edge crack in composite media,” Int. J. Fract., 172, 201-207 (2011).

    Article  Google Scholar 

  10. A. Singh, S. Das, and E-M. Craciun, “Thermal stress intensity factor for an edge crack in orthotropic composite media,” Compos. B. Eng., 153, 130-136 (2018).

  11. A. Singh, S. Das, and E-M. Craciun, “Effect of thermomechanical loading on an edge crack of finite length in an infinite orthotropic strip,” Mech. Compos. Mater., 55, 285-296, (2019).

  12. W. K. Chiu, L. R. F. Rose, and B. S. Vien, “Scattering of the edge-guided wave by an edge crack at a circular hole in an isotropic plate,” Procedia Eng., 188, 309-316 (2017).

    Article  Google Scholar 

  13. G. H. Lee and H. G. Beom, “Interfacial edge crack between dissimilar orthotropic thermoelastic materials under uniform heat flow,” J. Mech. Sci. Technol., 28, 3041-3050 (2014).

    Article  Google Scholar 

  14. G. I. L’vov, “Using the concept of imposed constraints in the plasticity theory of composites,” Mech. Compos. Mater., 57, 337-348 (2021).

    Article  Google Scholar 

  15. A. I. Seyfullayev, M. A. Rustamova, and S. A. Kerimova, “A problem of fatigue fracture mechanics of a two-layer material with edge cracks,” Mech. Compos. Mater., 53, 415-424 (2017).

    Article  Google Scholar 

  16. D. N. Solovyev, S. S. Dadunashvili, A. Mironov, P. Doronkin, and D. Mironovs, “Mathematical modeling and experimental investigations of a main rotor made from layered composite materials,” Mech. Compos. Mater., 56, 103-110 (2020).

    Article  Google Scholar 

  17. H. A. Whitworth, “Modeling stiffness reduction of graphite/epoxy composite laminates,” J. Compos. Mater., 21, 362-372 (1987).

    Article  CAS  Google Scholar 

  18. N. K. Naik, P. Yernamma, N. M. Thoram, R. Gadipatri, and V. R. Kavala, “High strain rate tensile behavior of woven fabric e-glass/epoxy composite,” Polym. Test., 29, 14-22 (2010).

    Article  CAS  Google Scholar 

  19. X. Jia, Z. Zeng, G. Li, D. Hui, X. Yang, and S. Wang, “Enhancement of ablative and interfacial bonding properties of EPDM composites by incorporating epoxy phenolic resin,” Compos. B. Eng., 54, 234-240 (2013).

    Article  CAS  Google Scholar 

  20. L. Z. Linganiso and R. D. Anandjiwala, “Fibre-reinforced laminates in aerospace engineering,” in: Advanced Composite Materials for Aerospace Engineering, Ch. 4, Woodhead Publishing (2016), pp. 101-127.

  21. C. Miao and H. V. Tippur, “Effect of loading rate on fracture behavior of carbon fiber reinforced polymer composites,” In Challenges in Mechanics of Time Dependent Materials, Fracture, Fatigue, Failure and Damage Evolution, Ch. 4, Springer, Cham (2020), pp. 21-28.

  22. M. Y. Yuhazri, A. J. Zulfikar, and A. Ginting, “Fiber reinforced polymer composite as a strengthening of concrete structures: A review,” IOP Conf. Ser.: Mater. Sci. Eng., 1003, 012135 (2020).

    Article  CAS  Google Scholar 

  23. W. Xu, C. Zhang, X. R. Wu, and Y. Yu, “Weight function method and its application for orthotropic single edge notched specimens,” Compos. Struct., 252, 112695 (2020).

    Article  Google Scholar 

  24. V. Petrova and S. Schmauder, “A theoretical model for the study of thermal fracture of functionally graded thermal barrier coatings with a system of edge and internal cracks,” Theor. Appl. Fract. Mech., 108, 102605 (2020).

    Article  Google Scholar 

  25. S. Itou, “Dynamic stress intensity factors of three collinear cracks in an orthotropic plate subjected to time-harmonic disturbance,” J. Mech., 32, 491-499 (2016).

    Article  Google Scholar 

  26. N. Trivedi, S. Das, and H. Altenbach, “Study of collinear cracks in a composite medium subjected to time-harmonic wave disturbance,” Z Angew Math Mech., 101, e202000307 (2021).

    Article  Google Scholar 

  27. T. Sadowski and A. Neubrand, “Estimation of the crack length after thermal shock in FGM strip,” Int. J. Fract., 127, L135-L140 (2004).

    Article  CAS  Google Scholar 

  28. I. V. Ivanov, T. Sadowski, and D. Pietras, “Crack propagation in functionally graded strip under thermal shock,” Eur. Phys. J. Spec. Top., 222, 1587-1595 (2013).

    Article  Google Scholar 

  29. V. N. Burlayenko, H. Altenbach, T. Sadowski, S. D. Dimitrova and A. Bhaskar, “Modelling functionally graded materials in heat transfer and thermal stress analysis by means of graded finite elements,” Appl. Math. Model., 45, 422-438 (2017).

    Article  Google Scholar 

  30. A. V. Kondratiev, V. E. Gaidachuk, and M. E. Kharchenko, “Relationships between the ultimate strengths of polymer composites in static bending, compression, and tension,” Mech. Compos. Mater., 55, 259-266 (2019).

    Article  Google Scholar 

  31. G. I. L’vov and O. A. Kostromitskaya, “Numerical Modeling of Plastic Deformation of Unidirectionally Reinforced Composites,” Mech. Compos. Mater., 56, 1-14 (2020).

    Article  Google Scholar 

  32. W. F. Yau, “Axisymmetric slipless indentation of an infinite, elastic cylinder,” SIAM J. Appl. Math., 15, 219-227 (1967).

    Article  Google Scholar 

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Acknowledgement

The authors extend their heartfelt thanks to the reviewers for their constructive suggestions towards the betterment of the manuscript.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India

    N. Trivedi, S. Das & E.-M. Craciun

  2. Faculty of Mechanical, Industrial, and Maritime Engineering, “Ovidius” University of Constanta, Bd. Mamaia 124, 900527, Constanta, Romania

    N. Trivedi, S. Das & E.-M. Craciun

Authors
  1. N. Trivedi
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  2. S. Das
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  3. E.-M. Craciun
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Correspondence to E.-M. Craciun.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 58, No. 1, pp. 3-20, January-February, 2021. Russian DOI: https://doi.org/10.22364/mkm.58.1.01.

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Trivedi, N., Das, S. & Craciun, EM. The Mathematical Study of an Edge Crack in Two Different Specified Models under Time-Harmonic Wave Disturbance. Mech Compos Mater 58, 1–14 (2022). https://doi.org/10.1007/s11029-022-10007-4

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  • DOI: https://doi.org/10.1007/s11029-022-10007-4

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