Moving Three Collinear Griffith Cracks at Orthotropic Interface
الموضوعات :
1 - Department of Civil Engineering, Indian Institute of Technology, Hyderabad, India
2 - Department of Mathematics, Jadavpur University, India
الکلمات المفتاحية: Moving Griffith crack, Crack opening displacement, Stress intensity factor, Orthotropic media, P-Wave,
ملخص المقالة :
This work deals with the interaction of P-waves between a moving central crack and a pair of outer cracks situated at the interface of an orthotropic layer and an elastic half-space. Initially, we considered a two-dimensional elastic wave equation in orthotropic medium. The Fourier transform has been applied to convert the basic problem to solve the set of four integral equations. These set of integral equations have been solved to to get the analytical expressions for the stress intensity factor (SIF) and crack opening displacements (COD) by using the finite Hilbert transform technique and Cooke’s result. The main objective of this work is to investigate the dynamic stress intensity factors and crack opening displacement at the tips of the cracks. The aims of the study of these physical quantities (SIF, COD) is the prediction of possible arrest of the cracks within a certain range of crack velocity by monitoring applied load. SIF and COD have been depicted graphically for various types of orthotropic materials. We presented a parametric study to explore the influence of crack growing and propagation. This result is very much applicable in bridges, roads, and buildings fractures.
[1] Lowengrub M., Srivastava K.N., 1968, On two coplanar Griffith cracks in an infinite elastic medium, International Journal of Engineering Science 6: 359-363.
[2] Lowengrub M., 1975, A pair of coplanar cracks at the interface of two bonded dissimilar elastic half-planes, International Journal of Engineering Science 13: 731-741.
[3] Atkinson C., List R.D., 1978, Steady-state crack propagation into media with spatially varying elastic properties, International Journal of Engineering Science 16: 717.
[4] Chen E.P., 1978, Sudden appearance of a crack in a stretched finite strip, Journal of Applied Mechanics 45: 277-280.
[5] Itou S., 1978, Dynamic stress concentration around two coplanar Griffith cracks in an infinite elastic medium, Journal of Applied Mechanics 45: 803-806.
[6] Itou S., 1980, Diffraction of an antiplane shear wave by two coplanar Griffith cracks in an infinite elastic medium, International Journal of Solids and Structure 16: 1147-1153.
[7] Srivastava K.N., Palaiya R.M., Karaulia D.S., 1980, Interaction of antiplane shear waves by a Griffith crack at the interface of two bonded dissimilar elastic half-spaces, International Journal of Fracture 16: 349-358.
[8] Rose L.R., 1986, Microcrack interaction with the main crack, International Journal of Fracture 31: 233-242.
[9] Kundu T., 1987, The transient response of two cracks at the interface of a layered half space, International Journal of Engineering Science 25(11-12): 1427-1439.
[10] Georgiadis H.G., Papadopoulos G.A., 1988, Cracked orthotropic strip with clamped boundaries, Journal of Applied Mathematics and Physics 39: 573578.
[11] Das A.N., Ghosh M.L., 1992, Two coplanar Griffith cracks moving along the interface of two dissimilar elastic medium, Engineering Fracture Mechanic 41: 59-69.
[12] Erdogan F., Wu B.,1993, Interface Crack problems in layered orthotropic materials, Journal of Mechanics Physics and Solids 41(5): 889-917.
[13] Mandal S.C., Ghosh M.L., 1994, Interaction of elastic waves with a periodic array of coplanar Griffith cracks in an orthotropic medium, International Journal of Engineering Science 32(1): 167-178.
[14] Das S., Patra B.,1996, Interaction between three-line cracks in a sandwiched orthotropic layer, Applied Mechanics and Engineering 3: 249-269.
[15] Brencich A., Carpinteri A., 1996, Interaction of the main crack with the ordered distribution of microcracks: a numerical technique by displacement discontinuity boundary elements, International Journal of Fracture 76: 373-389.
[16] Shabeeb N.I., Binienda W.K., Kreider K. L., 1999, Analysis of driving force for multiple cracks in a non-homogeneous plate, Journal of Applied Mechanics 66: 501-506.
[17] Wang C.Y., Rubio-Gonzale C., Masson J. J., 2001,The dynamics stress intensity factor for a semi-infinite crack in orthotropic materials with concentrated shear impact loads, International Journal of Solids and Structure 38: 1265-1280.
[18] Li X.F., 2001, Closed-form solution for a mode-III interface crack between two bonded dissimilar elastic layers, International Journal of Fracture 109: L3-L8.
[19] Lira-Vergara E., Rubio-Gonzalez C., 2005, Dynamic stress intensity factor of interfacial finite cracks in orthotropic materials subjected to concentrated loads, International Journal of Fracture 135: 285-309.
[20] Matbuly M.S., 2006, Analytical solution for an interfacial crack subjected to dynamic anti-plane shear loading, Acta Mechanics 163: 77-85.
[21] Das S., 2006, Interface Crack problems in layered orthotropic materials, International Journal of Solids and Structure 43: 7880-7890.
[22] Itou S., 2016, Dynamic stress intensity factors of three collinear cracks in an orthotropic plate subjected to time-harmonic disturbance, Journal of Mechanics 32(5): 491-499.
[23] Mandal P., Mandal S.C., 2017, Interface crack at orthotropic media, International Journal of Applied and Computational Mathematics 3(4): 3253-3262.
[24] Basak P., Mandal S.C., 2017, Semi-infinite moving crack in an orthotropic strip, International Journal of Solids and Structure 128: 221-230.
[25] Karan S., Basu S., Mandal S.C., 2018, Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium, Acta Mechanica 229: 1759-1772.
[26] Das S., Debnath L., 2003, Interaction between Griffith Cracks in a sandwiched orthotropic layer, Applied Mathematics Letters 16: 609-617.
[27] Bagheri R., Ayatollahi M., Mousavi M., 2015, Analytical solution of multiple moving cracks in functionally graded piezoelectric strip, Applied Mathematics and Mechanics 36(6): 777-792.
[28] Monfared M.M., Bagheri R., 2016, Multiple interacting arbitrary shaped cracks in an FGM plane, Theoretical and Applied Fracture Mechanics 86: 161-170.
[29] 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.
[30] Habib A., Rasul B., 2018, Several embedded cracks in a functionally graded piezoelectric strip under dynamic loading, Computers & Mathematics with Applications 76(3): 534-550.
[31] Monfared M.M., Bagheri R., Yaghoubi R., 2017, The mixed mode analysis of arbitrary configuration of cracks in an orthotropic FGM strip using the distributed edge dislocations, International Journal of Solids and Structures 130: 21-35.
[32] Hejazi A.A., Ayatollahi M., Bagheri R., Monfared M.M., 2013, Dislocation technique to obtain the dynamic stress intensity factors for multiple cracks in a half-plane under impact load, Archive of Applied Mechanics 84(1): 95-107.
[33] Ershad H., Bagheri R., Noroozi M., 2018, Transient response of cracked nonhomogeneous substrate with piezoelectric coating by dislocation method, Mathematics and Mechanics of Solids 23(12): 1525-1536.
[34] Bagheri R., Mirzaei A.M., 2017, Fracture analysis in an imperfect FGM orthotropic strip bonded between two magneto-electro-elastic layers, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering 43(2): 253-271.
[35] Mandal P., Mandal S.C., 2020, Sh waves interaction with crack at orthotropic interface, Waves in Random and Complex Media, DOI:10.1080/17455030.2020.1720043.
