Crack problem in functionally graded elastic layer under single load from two surfaces

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Kalaycı O. O., Üstün A., Özşahin T. Ş.

ZAMM ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND MECHANIK, cilt.105, sa.7, ss.1-19, 2025 (SCI-Expanded)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 105 Sayı: 7
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/zamm.70143
  • Dergi Adı: ZAMM ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND MECHANIK
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-19
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this study, partial closure of the crack in the functionally graded (FG) layer under the effect of a single load from the upper and lower surfaces has been investigated with the help of elasticity theory. In the study, firstly, the stress and displacement expressions of the FG layer have been obtained by using the basic equations of elasticity theory and Fourier integral transforms. By applying the boundary conditions determined for the problem to the stress and displacement expressions, an equation system consisting of four equations with four unknowns has been obtained, and as a result of the solution of this equation system, the coefficients in the stress and displacement expressions have been obtained depending on an unknown slope function. The solution of the problem has been reduced to a singular integral equation by writing these coefficients in the boundary condition not used in obtaining the coefficients. Then, this non-dimensionalized integral equation has been converted into an algebraic equation system by Gauss–Chebyshev integration formulation, and the stress intensity factor at the crack tip has been determined depending on the unknown crack tip slope. The stress intensity factor has been calculated and investigated for different values of the layer thickness to crack closure length ratio, crack initiation and closure length ratio, load intensity factor, stiffness parameter, and Kolosov constant.