Fracture analysis of multiple axisymmetric interfacial cracks in an FGM Coated orthotropic layer

Journal of Simulation and Analysis of Novel Technologies in Mechanical Engineering

مقاله 7، دوره 13، شماره 1، اردیبهشت 2021، صفحه 55-67   

نوع مقاله: Research article

نویسنده

Behrooz Momeni^*

Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad Univercity, Isfahan, Iran

چکیده

Based on the distributed dislocation technique, an analytical solution for the orthotropic layer with functionally graded material (FGM) orthotropic coating containing multiple axisymmetric interfacial cracks subjected to torsional loading is investigated. It is assumed that the material properties of the FGM orthotropic coating vary power-law form along the thickness of the layer. At first, by using the Hankel transform, the solution for Somigliana type rotational ring dislocation in the layer and its coating is obtained. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interface cracks, including penny-shaped and annular cracks. cracks with Cauchy type kernel. The integral equations are of Cauchy singular type, which are solved by Erdogan’s collocation method for dislocation density on the surface of interfacial crack and the results are used to determine stress intensity factors (SIFs) for axisymmetric interface cracks. Finally, several examples are provided to study the effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating on the SIFs for interfacial cracks.. The effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating as well as the interaction of multiple interfacial cracks on the SIFs are investigated. The results reveal that the value of the SIFs decreases with increasing the non-homogeneity parameter, orthotropy and thickness of FGM coating. The SIFs for inner tips of annular interface crack are larger than the outer tips.

کلیدواژه‌ها

Stress intensity factors؛ Torsion؛ FGM orthotropic coating؛ Axisymmetric cracks؛ Dislocation density

مراجع

[1] Delale, F., & Erdogan, F. (1988). On the mechanical modeling of the interfacial region in bonded half-planes.

[2] Ozturk, M., & Erdogan, F. (1995). An axisymmetric crack in bonded materials with a nonhomogeneous interfacial zone under torsion.

[3] Ozturk, M., & Erdogan, F. (1996). Axsiymmetric crack problem in bonded materials with a graded interfacial region. International Journal of Solids and Structures, 33(2), 193-219.

[4] Choi, H. J., Lee, K. Y., & Jin, T. E. (1998). Collinear cracks in a layered half-plane with a graded nonhomogeneous interfacial zone–Part I: Mechanical response. International journal of fracture, 94(2), 103-122.

[5] Shbeeb, N. I., & Binienda, W. K. (1999). Analysis of an interface crack for a functionally graded strip sandwiched between two homogeneous layers of finite thickness. Engineering Fracture Mechanics, 64(6), 693-720.

[6] Itou, S. (2001). Stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes. International Journal of Fracture, 110(2), 123-135.

[7] Wang, Y. S., Huang, G. Y., & Dross, D. (2003). On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: anti-plane deformation. J. Appl. Mech., 70(5), 676-680.

 [8] Jin, Z. H., & Batra, R. C. (1996). Interface cracking between functionally graded coatings and a substrate under antiplane shear. International Journal of Engineering Science, 34(15), 1705-1716.

[9] Chen, Y. F., & Erdogan, F. (1996). The interface crack problem for a nonhomogeneous coating bonded to a homogeneous substrate. Journal of the Mechanics and Physics of Solids, 44(5), 771-787.

[10] Huang, G. Y., Wang, Y. S., & Gross, D. (2002). Fracture analysis of functionally graded coatings: antiplane deformation. European Journal of Mechanics-A/Solids, 21(3), 391-400.

[11] Guo, L. C., Wu, L. Z., Ma, L., & Zeng, T. (2004). Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface-Part I: Static problem. International Journal of fracture, 127(1), 21-38.

[12] Huang, G. Y., Wang, Y. S., & Yu, S. W. (2005). A new model for fracture analysis of functionally graded coatings under plane deformation. Mechanics of materials, 37(4), 507-516.

[13] Chen, Y. J., & Chue, C. H. (2009). Mode III crack problems of two bonded functionally graded strips with internal cracks. International Journal of Solids and Structures, 46(2), 331-343.

[14] Asadi, E., Fariborz, S. J., & Fotuhi, A. R. (2012). Anti-plane analysis of orthotropic strips with defects and imperfect FGM coating. European Journal of Mechanics-A/Solids, 34, 12-20.

[15] Cheng, Z., Gao, D., & Zhong, Z. (2012). Interface crack of two dissimilar bonded functionally graded strips with arbitrary distributed properties under plane deformations. International journal of mechanical sciences, 54(1), 287-293.

[16] Ueda, S., Shindo, Y., & Atsumi, A. (1983). Torsional impact response of a penny-shaped crack lying on a bimaterial interface. Engineering Fracture Mechanics, 18(5), 1059-1066.

[17] Itou, S. (2001). Transient dynamic stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes. International journal of solids and structures, 38(20), 3631-3645.

[18] Li, C., & Weng, G. J. (2002). Dynamic fracture analysis for a penny-shaped crack in an FGM interlayer between dissimilar half spaces. Mathematics and Mechanics of Solids, 7(2), 149-163.

[19] Guo, L. C., Wu, L. Z., Zeng, T., & Ma, L. (2004). Fracture analysis of a functionally graded coating-substrate structure with a crack perpendicular to the interface-Part II: Transient problem. International Journal of Fracture, 127(1), 39-59.

[20] Li, Y. S., Jiang, Y. Y., Ren, J. H., & Cai, Z. Y. (2011). An annular interfacial crack between dissimilar magnetoelectroelastic layers. Smart materials and structures, 20(8), 085011.

[21] Li, Y. S., Ren, J. H., Feng, W. J., & Wang, W. (2013). Dynamic fracture analysis of an annular interfacial crack between dissimilar magnetoelectroelastic layers. Archive of Applied Mechanics, 83(1), 151-170.

[22] Ren, J. H., Wang, W., Li, Y. S., & Cai, Z. Y. (2012). Transient response of an annular interfacial crack between dissimilar piezoelectric layers under mechanical and electrical impacts. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 92(6), 497-510.

[23] Singh, A., Mishra, P. K., & Das, S. (2019). Dynamic stress intensity factors of an interfacial crack in orthotropic elastic strips under impact loading conditions. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 99(1), e201800143.

[24] Xu, C., Noda, N. A., & Takase, Y. (2009). Variations of stress intensity factors of a planar interfacial crack subjected to mixed mode loading. Journal of Computational Science and Technology, 3(1), 232-241.

[25] Monfared, M. M., Ayatollahi, M., & Bagheri, R. (2016). In-plane stress analysis of dissimilar materials with multiple interface cracks. Applied Mathematical Modelling, 40(19-20), 8464-8474.

[26] Monfared, M. M. (2017). Mode III SIFs for interface cracks in an FGM coating-substrate system. Structural engineering and mechanics: An international journal, 64(1), 71-79.

[27] Ayatollahi, M., Varasteh, S., & Fartash, A. H. (2018, July). Transient analysis of multiple interface cracks in two bonded elastic and piezoelectric layers. In Fracture, Fatigue and Wear (pp. 69-77). Springer, Singapore.

[28] Fartash, A. H., Ayatollahi, M., & Bagheri, R. (2019). Transient response of dissimilar piezoelectric layers with multiple interacting interface cracks. Applied Mathematical Modelling, 66, 508-526.

[29] Asadi, E., Fariborz, S. J., & Fotuhi, A. R. (2012). Anti-plane analysis of orthotropic strips with defects and imperfect FGM coating. European Journal of Mechanics-A/Solids, 34, 12-20.

[30] Bagheri, R., Ayatollahi, M., & Mousavi, S. M. (2015). Analysis of cracked piezoelectric layer with imperfect non-homogeneous orthotropic coating. International Journal of Mechanical Sciences, 93, 93-101.

[31] Pourseifi, M., & Faal, R. T. (2015). Tension analysis of infinite solid circular cylinders with arbitrary located axisymmetric cracks. Theoretical and Applied Fracture Mechanics, 80, 182-192.

[32] Erdogan, F., Gupta, G., & Cook, T. S. (1973). Numerical solution of singular integral equations. In Methods of analysis and solutions of crack problems (pp. 368-425). Springer, Dordrecht.