Stress intensity factors for a curvilinear crack in a piecewise homogeneous anisotropic body under longitudinal shear

Keywords

anisotropy, antiplane deformation, inclusions, cracks, stress intensity factors, singular integral equation method.

Cite as

Kravets V. S., Onyshko L. Yo., and Kvasniuk О. І. Stress intensity factors for a curvilinear crack in a piecewise homogeneous anisotropic body under longitudinal shear. Physicochemical Mechanics of Materials. 2026. 62(2), 150-158.

https://doi.org/10.15407/pcmm2026.02.150

Abstract

The antiplane problem of the theory of elasticity for a piecewise homogeneous anisotropic body (matrix with an inclusion) with a smooth curvilinear crack in the matrix is considered. The constructed system of singular integral equations of the first and second kind is solved numerically by the quadrature method. The stress intensity factors (SIF) at the cracks with various shapes are calculated for a number of geometric and mechanical parameters of the problem. The influence of the shapes of the crack and inclusion contours, their mu¬tual arrangement, and the elastic constants of orthotropic materials under longitudinal shear (orthotropy levels, relative stiffnesses, angles of inclination of the matrix material ortho¬tropy axes to the shear plane) of a piecewise homogeneous body on the SIF is analyzed.

References

1. 1. G.N. Savin, Distribution of Stress Around Holes [in Russian], Naukova Dumka, Kyiv (1968).
2. S.G. Lekhnitskyi, Theory of Elasticity of an Anisotropic Body [in Russain], Nauka, Moscow (1977).
3. T. C. T. Ting, Anisotropic Elasticity. Theory and Applications, Oxford University Press., Oxford (1996).
4. V.V. Bozhidarnik, O.Ye. Andreikiv, and H.T. Sulum, Fracture Mechanics, Strength and Durability of Continuously Reinforced Composites, Vol. 2 [in Ukrainian], Nadstyrya, Lutsk (2007).
5. M.P. Savruk, and A. Kazberuk, Stress Concentration at Notches, Cham: Springer (2017). https://doi.org/10.1007/978-3-319-44555-7
6. V.N. Dolgikh, and L.A. Filshtinskyi, “Theory of linearly-reinforced composite material with anisotropic structural components,” Izvestiya Acad. Nauk USSR, Ser. Mekhanika [in Russain], Is. 6, 53-63 (12978).
7. C.Y. Dong, S.H. Lo, and Y.K. Cheung, “Stress analysis of inclusion problems of various shapes in an infinite anisotropic elastic medium,” Comput. Meth. Appl. Mech. Eng., 192, 683-696 (2003). https://doi.org/10.1016/S0045-7825(02)00579-0
8. T.C.T. Ting, and P. Schiavone, “Uniform antiplane shear stress inside an anisotropic elastic inclusion of arbitrary shape with perfect or imperfect interface bonding,” Int. J. Eng. Sci., 48, 67-77 (2010). https://doi.org/10.1016/j.ijengsci.2009.06.008
9. O. Maksymovych, and A. Podhorecki, “Determination of stresses in anisotropic plates with elastic inclusions based on singular integral equations,” Eng. Anal. Bound. Elem., 104, 364-372 (2019) https://doi.org/10.1016/j.enganabound.2019.03.039
10. M.P. Savruk, V.S. Kravets, L.Yo. Onyshko, and O.I. Kvasniuk, “Determination of the stress state of an anisotropic body with smooth curvilinear inclusions under longitudinal shear,” Mater. Sci., 59, Is. 5, 591-600 (2024). https://doi.org/10.1007/s11003-024-00815-5
11. V.S. Kravets, M.P. Savruk, L.Yo. Onyshko, and O.I. Kvasniuk, “Influence of the shape and location of orthotropic inclusion on the stress state of anisotropic body under longitudinal shear,” Mater. Sci., 60,Is. 4, 419-423 (2025). https://doi.org/10.1007/s11003-025-00901-2
12. V.N. Dolgikh, and L.A. Filshtinskyi, “Longitudinal shear of composite material with defects,” Izvestiya Acad. Nauk USSR, Ser. Mekhanika Tverdogo Tela [in Russain], Is. 4, 103-110 (1980).
13. K.M. Arkhipenko, and O.F. Kryvyi, “Crack and inclusion under complete adhesion in a piecewise homogeneous anisotropic plane,” Visnyk Odeskogo Natsionalnogo Universytetu, Ser. Matematuka. Mekhanika [in Ukrainian], 18, Is. 2, 97-104 (2013).
14. C.K. Chao, and T.F. Chiang, “Antiplane interaction of an anisotropic elliptic inclusion with an arbitrarily oriented crack,” Int. J. of Fract., 75, 229-245 (1996). https://doi.org/10.1007/BF00037084
15. M.P. Savruk, V.S. Kravets, L.Yo. Onyshko, and O.I. Kvasniuk, “Stress state of anisotropic body with smooth curvilinear inclusions and cracks under antiplane deformation,” Mater. Sci., 60, Is. 5, 640-649 (2025). https://doi.org/10.1007/s11003-025-00931-w