Тривимірна динамічна задача теорії пружності про усталені крутні коливання біматеріалу “півпростір – шар з тріщиною”: Fìz.-mat. model. ìnf. tehnol. 2017, 25:141-150

• Дата: 2018
• Автор: Stankevych, Volodymyr
• Формат: Стаття
• Мова: Українська
• Опубліковано: Інститут прикладних проблем механіки і математики ім. Я. С. Підстригача НАН України 2018
• Теми: пружний біматеріал; півпростір; шар з тріщиною; усталені коливання; граничні інтегральні рівняння; динамічний коефіцієнт інтенсивності напружень
• Онлайн доступ: https://www.fmmit.lviv.ua/index.php/fmmit/article/view/32
• Назва журналу: Physico-mathematical modeling and informational technologies

The three-dimensional dynamic problem of an elastic bimaterial "half-space − layer with a pennyshaped crack" is considered. The cracks surface are under time-stationary torsional loads. The problem is solved by boundary integral equations (BIE) method. Using solutions of Helmholtz potentials, the problem is reduced to a system of two BIE relatively unknown crack opening function. The dependences of the dynamic stress intensity factors mode III on the frequency of the applied load, the thickness of the layer, and the ratios of the elastic parameters of the materials body are analized. References Mahamood, R. M., Akinlabi, E. T. (2017). Functionally Graded Materials. Springer International Publishing. Rekik, M., Neifar, M., El-Borgi, S. (2010). An axisymmetric problem of an embedded crack in a graded layer bonded to a homogeneous half-space. Int. J. of Solids and Struct., 47, 2043-2055. DOI https://doi.org/10.1016/j.ijsolstr.2010.04.006 Sih, G. C., Chen, E. P. (1980). Normal and Shear Impact of Layered Composite With a Crack: Dynamic Stress Intensification. Journal of Appl. Mech., 47, 351-358. DOI https://doi.org/10.1115/1.3153668 Wang, B. L., Han, J. C., Du, S. Y. (2000). Fracture mechanics for multilayers with penny-shaped cracks subjected to dynamic torsional loading. Int. J. of Eng. Science, 38, 893-901. DOI https://doi.org/10.1016/S0020-7225(99)00068-3 Ueda, S., Shindo, Y., Atsumi, A. (1983). Torsional impact response of a penny-shaped crack lying on a biomaterial interface. Eng. Fract. Mech., 18(5), 1059-1066. DOI https://doi.org/10.1016/0013-7944(83)90077-2 Sih, G. C., Chen, E. P. (1980). Axisymmetric elastodynamic response from normal and radial impact of layered composites with embedded penny-shaped cracks. Int. J. of Solids and Struct., 16, 1093-1107. DOI https://doi.org/10.1016/0020-7683(80)90065-7 Gopalakrishnan, S. (2016). Wave Propagation in Materials and Structures. CRC Press. Kennett, B. (2009). Seismic Wave propagation in stratified media. ANU E Press. Mykhas’kiv, V., Stankevych, V., Zhbadynskyi, I., Zhang, Ch. (2009). 3-D dynamic interaction between a penny-shaped crack and a thin interlayer joining two elastic half-spaces. Int. J. Fract., 159, 137–149. DOI https://doi.org/10.1007/s10704-009-9390-z Stankevych, V. Z. (2008). Stress intensity near a crack in the composition of a half space and a layer under harmonic loading. Materials Science, 44(2), 175-182. DOI https://doi.org/10.1007/s11003-008-9065-3 Stankevych, V. Z. (1995). Calculation of some two-dimensional integrals for the dynamic problems of the cracks in the half-space body. Math. Methods Phys. Mech. Fields, 39, 56–61 (in Ukrainian) Guz, A. N., Guz, I. A., Men’shikov, A. V., Men’shikov, V. A. (2013). Three dimensional problems in the dynamic fracture mechanics of materials with interface cracks (review). Int. Appl. Mech., 49(1), 1-61. DOI https://doi.org/10.1007/s10778-013-0551-4