Iranian Journal of Mechanical Engineering Transactions of ISME

Iranian Journal of Mechanical Engineering Transactions of ISME

Multiple cracks in a functionally graded electro-magneto- elastic rectangular plane

Authors
Rasul Bagheri 1
Mojtaba Mahmoodi Monfared 2
vali engilela 3
1 Assistant Professor, Department of Mechanical Engineering, Karaj Branch, Islamic Azad University
2 Assistant professor, Department of mechanical engineering, Islami Azad Unviversity of Hashtgerd
3 Mechatronics Faculty, Department of Mechanical Engineering, Karaj Branch, Islamic Azad University, Alborz, Iran
Abstract
In this paper, the static problem of several cracks in a functionally graded piezoelectric–piezomagnetic (FGPP) rectangular plane subjected to concentrated anti-plane mechanical and in-plane electric and magnetic fields is described. The material properties are assumed to vary continuously according to exponential functions along the transverse of the FGPP rectangular plane. The dislocation method and integral transforms technique are applied to obtain a set of Cauchy singular integral equations. Thestress, electric and magnetic intensity factors for several cracks, are obtained by using the corresponding solution to these equations. The numerical examples of mode-III problem are presented to illustrate the interesting mechanical and electromagnetic coupling phenomena induced by multicrack interactions. Finally, the effects of material nonhomogeneity constant, the cracks length, position of point load and the cracks configuration upon the stress and electromagnetic intensity factors are investigated. The obtained conclusions seem useful for design of the magnetoelectroelastic structures and devices of high performance.
Keywords
rectangular plane
Screw dislocation
Multiple cracks
field intensity factors

Subjects

[1] Gao, C.F., Tong, P., and Zhang, T.Y., “Fracture Mechanics for a Mode III Crack in a Magnetoelectroelastic”, International Journal of Solids and Structures, Vol. 41, pp. 6613–6629, (2004).
 [2] Wang, B.L., and Mai, Y.W., “Fracture of Piezoelectromagnetic Materials”, Mechanics Research Communications, Vol. 31, pp. 65–73, (2004).
 
[3] Zhong, X.C., and Li, X.F., “Magnetoelectroelastic Analysis for an Opening Crack in a Piezoelectromagnetic Solid”, European Journal of Mechanics, A/Solids, Vol. 26, pp. 405–417, (2007).
 
[4] Zhang, X.S., “A Finite Rectangular Sheet with a Pair of Edge Cracks Excited by a Normal Anti-plane Shear Wave”, Engineering Fracture Mechanics, Vol. 35, pp. 1037-1042, (1990).
 
[5] Ma, S.W., and Zhang, L.X., “A New Solution of an Eccentric Crack off the Center Line of a Rectangular Sheet for Mode-III”, Engineering Fracture Mechanics, Vol. 40, pp. 1-7, (1991).
 
[6] Lee, K.Y., and Kwon, S.M., “Analysis of Stress and Electric Fields in a Rectangular Piezoelectric Body with a Center Crack under Anti-plane Shear Loading”, International Journal of Solids and Structures, Vol. 37, pp. 4859-4869, (2000).
 
[7] Kwon, S.M., and Lee, K.Y., “Transient Response of a Rectangular Piezoelectric Medium with a Center Crack”, European Journal of Mechanics, A/Solids, Vol. 20, pp. 457-468, (2001).
 
[8] Li, X.F., and Lee, K.Y., “Electroelastic Behavior of a Rectangular Piezoelectric Ceramic with an Anti-plane Shear Crack at Arbitrary Position”, European Journal of Mechanics, A/Solids, Vol. 23, pp. 645-658, (2004).
 
[9] Zhou, Z.G., Wu, L.Z., and Wang, B., “The Behavior of a Crack in Functionally Graded Piezoelectric/Piezomagnetic Materials under Anti-plane Shear Loading”, Archive of Applied Mechanics, Vol. 74, pp. 526–535, (2005).
 
[10] Qin, Q.H., Kang, Y.L., and Hu., K.Q., “A Moving Crack in a Rectangular Magnetoelectroelastic Body”, Engineering Fracture Mechanics, Vol. 74, pp. 751-770, (2007).
 
[11] Zhong, X.C., and Zhang, K.S., “Dynamic Analysis of a Penny-shaped Dielectric Crack in a Magnetoelectroelastic Solid under Impacts”, European Journal of Mechanics, A/Solids, Vol. 29, pp. 242–252, (2010).
 
[12] Zhang, P.W., “Dynamic Fracture of a Rectangular Limited-permeable Crack in Magneto-Electro-elastic Media under a Time-harmonic Elastic P-Wave”, International Journal of Solids and Structures, Vol. 48, pp. 553-566, (2011).
 
[13] Faal, R.T., Daliri, M., and Milani, A.S., “Anti-plane Stress Analysis of Orthotropic Rectangular Planes Weakened by Multiple Defects”, International Journal of Solids and Structures, Vol. 48, pp. 661–672, (2011).
 
[14] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., “Stress Analysis of a Functionally Graded Magneto-electro-elastic Strip with Multiple Moving Cracks”, Mathematics and Mechanics of Solids, Vol. 30, pp. 1-20, (2015).
 
[15] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., “Analytical Solution of Multiple Moving Cracks in Functionally Graded Piezoelectric Strip”, Applied Mathematics and Mechanics, Vol. 36, pp. 777–792, (2015).
 
[16] Ayatollahi, M., Monfared, M.M., and Nourazar, M., “Analysis of Multiple Moving Mode-III Cracks in a Functionally Graded Magnetoelectroelastic Half-plane” Journal of Intelligent Material Systems and Structures, Vol. 28, pp. 2823–2834, (2017).
 
[17] Bagheri, R., Ayatollahi, M., and Mousavi, S.M., “Analysis of Cracked Piezoelectric Layer with Imperfect Non-homogeneous Orthotropic Coating”, International Journal of Mechanical Sciences, Vol. 93, pp. 93–101, (2015).
 
[18] Faal, R.T., and Dehghan, A.A., “Mode III Stress Intensity Factors for Cracked FGM Rectangular Plane”, Engineering Fracture Mechanics, Vol. 140, pp. 17-30, (2015).
 
[19] Bleustein, J.L., “A New Surface Wave in Piezoelectric Materials”, Applied Physics Letters, Vol. 13, pp. 412-413, (1968).
 
[20] Zhou, Z.G., and Wang, B., “Two Parallel Symmetry Permeable Cracks in Functionally Graded Piezoelectric/Piezomagnetic Materials under Anti-plane Shear Loading”, International Journal of Solids and Structures, Vol. 41, pp. 4407–4422, (2004).
 
[21] Deeg, W.F., “The Analysis of Dislocation, Crack and Inclusion Problems in Piezoelectric Solids”, Ph.D. Thesis, Stanford University, San Francisco, USA, (1980).
 
[22] Pak, Y.E., “Crack Extension Force in a Piezoelectric Material”, Journal of Applied Mechanics, Vol. 57, pp. 647-653, (1990).
 
[23] Li, S., Gao, W., and Cross, L.E., “Stress and Electric Displacement Distribution Near Griffith's Type III Crack Tips in Piezoceramics”, Materials Letters, Vol. 10, pp. 219-222, (1990).
 
[24] Sosa, H.A., “Three-dimensional Eigenfunction Analysis of a Crack in a Piezoelectric Material”, International Journal of Solids and Structures, Vol. 36, pp. 1-15, (1990).
 
[25] Gao, H., Zhang, T.Y., and Tong, P., “Local and Global Energy Release Rates for an Electrically Yielded Crack in a Piezoelectric Ceramic”, Journal of Mechanics and Physics Solids, Vol. 45, pp. 491-510, (1997).
 
[26] Hills, D.A., Kelly, P.A., Dai, D.N., and Korsunsky, A.M., “Solution of Crack Problems: the Distributed Dislocation Technique”, Kluwer: Academic Publishers, (1996)
 
[27] Erdogan, F., Gupta, G. D., and Cook, T. S., “Numerical Solution of Singular Integral Equations, Method of Analysis and Solution of Crack Problems”, Edited by G. C. Sih, Noordhoof, Leyden, Holland, (1973).
Iranian Journal of Mechanical Engineering Transactions of ISME
Volume 20, Issue 3 - Serial Number 52
System Dynamics and Solid Mechanics
Autumn 2018
Pages 80-108

  • Receive Date 02 March 2017
  • Revise Date 25 June 2017
  • Accept Date 15 December 2018