Iranian Journal of Mechanical Engineering Transactions of the ISME

Iranian Journal of Mechanical Engineering Transactions of the ISME

Computation of SIF for Several Moving Cracks in an Orthotropic Layer Bonded to a Functionally Graded Piezoelectric Coating

Document Type : Research Paper

Authors
Mohammad Hassani 1
Mojtaba Mahmoudi Monfared 2
1 PhD Student, Department of Mechanical Engineering, Do.C., Islamic Azad University, Dorud, Iran
2 Associate Professor, Department of Mechanical Engineering, Has.C., Islamic Azad University, Hashtgerd, Iran
10.30506/jmee.2024.2041811.1362
Abstract
In this paper, the dynamic stress intensity factors (DSIFs) in an orthotropic strip coated by a functionally graded piezoelectric (FGP) containi8ng several moving cracks has been studied. The distributed dislocation method (DDM) is extended to construct integral equations for the several cracks. At first, the stress fields in an orthotropic strip coated by FGP containing a single dislocation are calculated. Then, by use of distributed dislocation density on the faces of cracks, systems of singular integral equations with Cauchy type singularity are obtained. Finally, the integral equations are solved with an appropriate numerical method to specify the dislocation density and then DSIFs at the crack tips. The primary objective of this paper is to investigate the effects types of loading, the position of cracks relative to each other, crack speed and nonhomogeneity parameter on the DSIFs.
Keywords
Orthotropic substrate
FGP coating
Distributed dislocation technique
Dynamic stress intensity factors
Several moving cracks

Subjects

[1] E. Carrera, S. Brischetto, and P. Nali, "Plates and Shells for Smart Structures: Classical and Advanced Theories for Modeling and Analysis," John Wiley & Sons, Ltd., 1st edition, Vo. 36, 2011, https://onlinelibrary.wiley.com/doi/book/10.1002/9781119950004.
 
[2] K. Ichikawa, "Functionally Graded Materials in the 21st Century: A Workshop on Trends and Forecasts," 1st edition,   Springer Science & Business Media, Springer US, 2001, https://link.springer.com/book/10.1007/978-1-4615-4373-2.    
 
[3] Y. Miyamoto, W. A. Kaysser, B. H. Rabin, A. Kawasaki, and R. G. Ford, "Functionally Graded Materials: Design, Processing and Applications," Springer Science & Business Media, LLC, Vol. 5, 2013, doi: 10.1007/978-1-4615-5301-4, https://link.springer.com/book/10.1007/978-1-4615-5301-4.
 
[4] L. Ma, L. Z. Wu, Z. G. Zhou, and L. C Guo, "Scattering of the Harmonic Anti-plane Shear Waves by a Crack in Functionally Graded Piezoelectric Materials," Composite Structures, Vol. 69, No. 4, pp. 436-441, 2005, https://doi.org/10.1016/j.compstruct.2004.08.001.
 
[5] X. F. Li, T. Y. Fan, and X. F. Wu, "A Moving Mode-III Crack at the Interface between Two Dissimilar Piezoelectric Materials," International Journal of Engineering Science, Vol. 38, No. 11, pp. 1219-1234, 2000, https://doi.org/10.1016/S0020-7225(99)00072-5.
 
[6] J. W. Shin, and Y. S. Lee, "A Moving Interface Crack between Two Dissimilar Functionally Graded Piezoelectric Layers under Electromechanical Loading, "International Journal of Solids and Structures, Vol. 47, No. 20, pp. 2706-2713, 2010, https://doi.org/10.1016/j.ijsolstr.2010.05.027.
 
[7] Y. Lapusta, A. Komarov, F. L. Jied, R. M. Pitti and, V. Loboda," Limited Permeable Crack Moving Along the Interface of a Piezoelectric Bi-Material," European Journal of Mechanics-A/Solids, Vol. 30, No. 5, pp. 639-649, 2011, https://doi.org/10.1016/j.euromechsol.2011.04.005.
 
[8] M. Ayatollahi, and M. M. Monfared, "Anti-plane Transient Analysis of Planes with Multiple Cracks," Mechanics of Materials, Vol. 50, pp. 36-46, 2012, https://doi.org/10.1016/j.mechmat.2012.03.002.
 
[9] M. M. Monfared, and M. Ayatollahi, "Dynamic Stress Intensity Factors of Multiple Cracks in a Functionally Graded Orthotropic Half-plane," Theoretical and Applied Fracture Mechanics, Vol. 56, No. 1, pp. 49-57, 2011, https://doi.org/10.1016/j.tafmec.2011.09.008.
 
[10] A. Hejazi, M. Ayatollahi, R. Bagheri, and M.M. Monfared, "Dislocation Technique to Obtain the Dynamic Stress Intensity Factors for Multiple Cracks in a Half-plane under Impact Load," Archive of Applied Mechanics, Vol. 84, No. 1, pp. 95-107, 2014, https://doi.org/10.1007/s00419-013-0785-y.
 
[11] N. T. Nguyen, T.Q. Bui, and T.T. Truong, "Transient Dynamic Fracture Analysis by an Extended Meshfree Method with Different Crack-tip Enrichments," Meccanica, Vol. 52, No. 10, pp. 2363–2390, 2017, https://doi.org/10.1007/s11012-016-0589-6.
 
[12] J. Rokne, B. M. Singh, and R. S. Dhaliwal, "Moving Anti-plane Shear Crack in a Piezoelectric Layer Bonded to Dissimilar Elastic Infinite Spaces," European Journal of Mechanics - A/Solids, Vol. 31, No. 1,  pp. 47-53, 2012, https://doi.org/10.1016/j.euromechsol.2011.07.002.
 
[13] J., Podgórski," The Criterion For Determining the Direction of Crack Propagation in a Random Pattern Composites," Meccanica, Vol. 52, No. 8, pp. 1923-1934, 2017,
https://doi.org/10.1007/s11012-016-0523-y.
 
[14] R. Bagheri, M. Ayatollahi, and S. M. Mousavi, "Analytical Solution of Multiple Moving Cracks in Functionally Graded Piezoelectric Strip," Applied Mathematics and Mechanics, Vol. 36, No. 6, pp. 777-792, 2015, https://doi.org/10.1007/s10483-015-1942-6.
 
[15] J. S. Lee, S. M. Kwon, K. Y. Lee, and J. H. Kwon, "Anti-plane Interfacial Yoffe-Crack between a Piezoelectric and Two Orthotropic Layers," European Journal of Mechanics - A/Solids, Vol. 21, No. 3, pp. 483-492, 2002, https://doi.org/10.1016/S0997-7538(02)01212-3.
 
[16] M. M. Monfared", Mode III SIFs for Interface Cracks in an FGM Coating-Substrate System," Structural Engineering and Mechanics, Vol. 64, No. 1, pp. 71-79, 2017,
https://doi.org/10.12989/sem.2017.64.1.071.
 
[17] M. Hassani, M. M. Monfared, and A. Salarvand, "Multiple Unequal Cracks between an FGM Orthotropic Layer and an Orthotropic Substrate under Mixed Mode Concentrated Loads," Structural Engineering and Mechanics, Vol. 86, No. 4,  pp. 535-546, 2023,  https://doi.org/10.12989/sem.2023.86.4.535.
 
[18] H. Haghiri, A. R. Fotuhi, and A.R. Shafiei, "Elastodynamic Analysis of Mode III Multiple Cracks in a Functionally Graded Orthotropic Half-plane," Theoretical and Applied Fracture Mechanics, Vol. 80, Part B, pp. 155-169, 2015, https://doi.org/10.1016/j.tafmec.2015.09.006.
[19] J. W. Shin, and Y. S. Lee, "Anti-plane Moving Crack in a Functionally Graded Piezoelectric Layer between Two Dissimilar Piezoelectric Strips," Journal of Mechanical Science and Technology, Vol. 26, No. 4, pp. 1017-1025, 2012, https://doi.org/10.1007/s12206-012-0233-x.
 
[20] K. Hu, and Z. Chen, "An Interface Crack Moving between Magnetoelectroelastic and Functionally Graded Elastic Layers, "Applied Mathematical Modelling, Vol. 38, No. 3, pp. 910-925, 2014, https://doi.org/10.1016/j.apm.2013.07.022.
 
[21] B. Jin, and Z. Zhong, "A Moving Mode-III Crack in Functionally Graded Piezoelectric Material: Permeable Problem," Mechanics Research Communications, Vol. 29, No. 4, pp. 217-224, 2002, https://doi.org/10.1016/S0093-6413(02)00259-8.
 
[22] S. K. Alavi, M. R. Ayatollahi, J. Jamali, and M. Petru, "On the Applicability of Digital Image Correlation Method in Extracting the Higher Order Terms in Stress Field around Blunt Notches," Theoretical and Applied Fracture Mechanics, Vol. 121, pp. 103436, 2022,
https://doi.org/10.1016/j.tafmec.2022.103436 .
 
[23] S. K. Alavi, M. R. Ayatollahi, M. Daneshfar, and B. Bahrami, "Experimental Stress Determination of Blunt Notches under Combinations of Modes I and II Loading," Engineering Structures, Vol. 278, pp. 115517, 2023, https://doi.org/10.1016/j.engstruct.2022.115517.
 
[24] B. Bahrami, M. R. Ayatollahi, S. K. Alavi, and L.F.M. da Silva, "On the Prediction of the Stress Field in Adhesive Joints using a Combined Analytical-Numerical Method," International Journal of Adhesion and Adhesives, Vol. 116, pp. 103151, 2022,
https://doi.org/10.1016/j.ijadhadh.2022.103151.
 
[25] S. K. Alavi, M. R. Ayatollahi, B. Bahrami, and M. Nejati, "An Analytical Stress Field for Bi-Material V-Notches with end Hole: New Solution and Effects of Higher Order Terms," Mathematics and Mechanics of Solids, Vol. 28, No. 2, pp. 464–478, 2022,  https://doi.org/10.1177/10812865221084311.
 
[26] J. L. Bleustein, "A New Surface Wave in Piezoelectric Materials," Applied Physics Letters, Vol. 13, pp. 412-413, 1968, 10.1063/1.1652495.    
 
[27] D. A. Hills, K. P. A., Dai D. N., and A. M. Korsunsky, "Solution of Crack Problems: The Distributed Dislocation Technique," Kluwer Academic Publishers, 1996,
https://link.springer.com/book/10.1007/978-94-015-8648-1.
 
[28] F. Erdogan, G. D. Gupta, and T.S. Cook, "Numerical Solution of Integral Equations," In: Sih GC, Editor. Methods of Analysis and Solution of Crack Problems. Leyden, Holland: Noordhoof; 1973, https://link.springer.com/chapter/10.1007/978-94-017-2260-5_7.
 
[29] M. Ayatollahi, R. T. Faal, and O. Tarkian, "Anti-plane Analysis of an Orthotropic Strip Weakened by Several Moving Cracks," Applied Mathematical Modellsing, Vol. 36, pp. 596-604, 2011, https://doi.org/10.1016/j.apm.2011.07.030.
Iranian Journal of Mechanical Engineering Transactions of the ISME
Volume 26, Issue 2 - Serial Number 45
September 2025
Pages 35-56