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Semi-infinite moving crack under antiplane shear loading

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Abstract

The article deals with the study of a moving interfacial semi-infinite crack situated between two orthotropic strips of different composite materials. The crack surface is under the shear wave disturbance. The governing equations have been solved by applying the Fourier transform technique to get the desired standard form of the Wiener–Hopf equation, which is further solved by using the Wiener–Hopf method. The analytical asymptotic expressions for physical quantities like stress intensity factor (SIF) and crack opening displacement (COD) for the crack have been obtained. The nature of SIF and COD for different combinations of composite materials and also for various depths of the semi-infinite strips has been depicted graphically.

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References

  1. Sih, G.C., Chen, E.P.: Mechanics of Fracture 6: Cracks in Composite Materials. Martinus Nijhoff, The Hague (1981)

    Book  Google Scholar 

  2. Das, S., Patra, B.: Stress intensity factors for moving interfacial crack between bonded dissimilar fixed orthotropic layers. Comput. Struct. 69(4), 459–472 (1998)

    Article  MATH  Google Scholar 

  3. Yang, Y., Hu, Z.L., Li, X.F.: Nanoscale mode-III interface crack in a bimaterial with surface elasticity. Mech. Mater. 140, 103246 (2020)

    Article  Google Scholar 

  4. Bidadi, J., Akbardoost, J., Aliha, M.R.M.: Thickness effect on the mode III fracture resistance and fracture path of rock using endb specimens. FFEMS 43(2), 277–291 (2020)

    Google Scholar 

  5. Yoffe, E.H.: Lxxv. The moving Griffith crack. Lond. Edinb. Dublin Philos. Mag. J. Sci. 42(330), 739–750 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  6. Georgiadis H.G., Papadopoulos G.A.: Cracked orthotropic strip with clamped boundaries (1988)

  7. Wang, X., Schiavone, P.: Interaction between a completely coated semi-infinite crack and a screw dislocation. Z. Angew. Math. Phys. 70(4), 1–13 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  8. Wang, X., Peter, S.: A semi-infinite mode III crack partially penetrating a three-phase elliptical inhomogeneity. Z. Angew. Math. Phys. 72(2), 1–12 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  9. Wang, X., Peter, S.: An edge dislocation interacting with a completely coated semi-infinite crack. Z. Angew. Math. Phys. 71(5), 1–10 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  10. Trivedi, N., Das, S., Altenbach, H.: Study of collinear cracks in a composite medium subjected to time-harmonic wave disturbance. Z. Angew. Math. Mech. 101(6), e202000307 (2021)

    Article  MathSciNet  Google Scholar 

  11. Trivedi, N., Das, S., Craciun, E.M.: The mathematical study of an edge crack in two different specified models under time-harmonic wave disturbance. Mech. Compos. Mater. 58(1), 1–14 (2022)

    Article  Google Scholar 

  12. Trifunac, M.D.: Scattering of plane SH waves by a semi-cylindrical canyon. Earthq. Eng. Struct. Dyn. 1(3), 267–281 (1972)

    Article  Google Scholar 

  13. Yang, J., Qi, H.: The scattering of steady-state SH waves in a bi-material half space with multiple cylindrical elastic inclusions. Waves Random Complex Media 29(1), 162–177 (2019)

    Article  MATH  Google Scholar 

  14. Diankui, L., Hong, L.: Scattering of SH-waves by an interacting interface linear crack and a circular cavity near bimaterial interface. Acta Mech. Solida Sin. 20, 317–326 (2004)

    Article  Google Scholar 

  15. Noble, B.: Methods Based on the Wiener–Hopf Technique for the Solution of Partial Differential Equations, vol. 332. Taylor & Francis, Boca Raton (1958)

    MATH  Google Scholar 

  16. Nilsson, F.: Dynamic stress-intensity factors for finite strip problems. Int. J. Fract. Mech. 8(4), 403–411 (1972)

    Article  Google Scholar 

  17. Nilsson, F.: Erratum to Dynamic stress-intensity factors for finite strip. Int. J. Fract. 9(4), 403–411 (1973)

    Article  Google Scholar 

  18. Achenbach J.D., Gautesen A.K.: Elastodynamic stress-intensity factors for a semi-infinite crack under 3-d loading (1977)

  19. Abrahams, I.D.: On the application of the Wiener–Hopf technique to problems in dynamic elasticity. Wave Motion 36(4), 311–333 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  20. Maurya, G., Sharma, B.L.: Scattering by two staggered semi-infinite cracks on square lattice: an application of asymptotic Wiener–Hopf factorization. Z. Angew. Math. Phys. 70(5), 1–21 (2019)

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

The authors are extending their heartfelt thanks to the revered reviewers for their constructive suggestions toward the improvement of the article. The author S. Das acknowledges the project grant provided by the NBHM, DAE, Government of India through letter no. 02011/2/2022 NBHM(R.P.)/R &D II /2171.

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Trivedi, N., Das, S. Semi-infinite moving crack under antiplane shear loading. Z. Angew. Math. Phys. 73, 229 (2022). https://doi.org/10.1007/s00033-022-01857-y

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