In-Plane Analysis of an FGP Plane Weakened by Multiple Moving Cracks

Document Type: Research Paper


1 Department of Mechanical Engineering, Karaj Branch, Islamic Azad University, Karaj, Iran

2 Department of Mechanical Engineering, Hashtgerd Branch, Islamic Azad University, Hashtgerd, Iran



In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to in-plane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual change of the shear moduli and mass density is assumed to be same. At first, the Volterra edge dislocation solutions are employed to derive singular integral equations in the form of Cauchy singularity for an FGP plane containing multiple horizontal moving cracks. Then, these equations are solved numerically to obtain dislocation density functions on moving crack surfaces. Finally, the effects of the crack moving velocity, material properties, electromechanical coupling factor and cracks arrangement on the normalized mode I and mode II stress intensity factors and electric displacement intensity factor are studied.


[1] Ikeda T., 1996, Fundamentals of Piezoelectricit, Oxford University Press.
[2] Cheng Zh., Suia Zh., Yin H., Fenga, H., 2019, Numerical simulation of dynamic fracture in functionally graded materials using peridynamic modeling with composite weighted bonds, Engineering Analysis with Boundary Elements 105: 31-46.
[3] Hassanifard S., Mohtadi Bonab M.A., Jabbari Gh., 2013, Investigation of fatigue crack propagation in spot-welded joints based on fracture mechanics approach, Journal of Materials Engineering and Performance 22: 245-250.
[4] Mohtadi Bonab M.A., Eskandari M., Szpunar J.A., 2016, Effect of arisen dislocation density and texture components during cold rolling and annealing treatments on hydrogen induced cracking susceptibility in pipeline steel, Journal of Materials Research 31: 3390-3400.
[5] Kwon J.H., Lee K.Y., Kwon S.M., 2000, Moving crack in a piezoelectric ceramic strip under anti-plane shear loading, Mechanics Research Communications 27: 327-332.
[6] Gao C.F., Zhao Y.T., Wang M.Z., 2001, Moving antiplane crack between two dissimilar piezoelectric media, International Journal of Solids and Structures 38: 9331-9345.
[7] Li B.C., Weng G.J., 2002, Yoffe-type moving crack in a functionally graded piezoelectric material, Proceedings of the Royal Society of London 458: 381-399.
[8] Megiud S.A., Wang X.D., Jiang L.Y., 2002, On the dynamic propagation of a finite crack in functionally graded materials, Engineering Fracture Mechanics 69: 1753-1768.
[9] Wang X., Zhong Z., Wu F.L., 2003, A moving conducting crack at the interface of two dissimilar piezoelectric materials, International Journal of Solids and Structures 40: 2381-2399.
[10] Li X.F., 2003, Griffith crack moving in a piezoelectric strip, Archive of Applied Mechanics 72: 745-758.
[11] Hu K., Zhong Z., 2006, A moving mode-III crack in a functionally graded piezoelectric strip, International Journal of Mechanics and Materials in Design 2: 61-79.
[12] Piva A., Tornabene F., Viola E., 2007, Subsonic Griffith crack propagation in piezoelectric media, European Journal of Mechanics-A/Solids 26: 442-459.
[13] Yan Z., Jiang L.Y., 2009, Study of a propagating finite crack in functionally graded piezoelectric materials considering dielectric medium effect, International Journal of Solids and Structures 46: 1362-1372.
[14] Lapusta Y., Komarov A., Labesse-Jied F., MoutouPitti R., Loboda V., 2011, Limited permeable crack moving along the interface of a piezoelectric bi-material, European Journal of Mechanics-A/Solids 30: 639-649.
[15] Li Y.D., Lee K.Y., 2010, Two collinear unequal cracks in a poled piezoelectric plane: Mode I case solved by a new approach of real fundamental solutions, International Journal of Fracture 165: 47-60.
[16] Asadi E., 2011, Analysis of multiple axisymmetric annular cracks in a piezoelectric medium, European Journal of Mechanics-A/Solids 30: 844-853.
[17] Bagheri R., Ayatollahi M., Mousavi S.M., 2015, Stress analysis of a functionally graded magneto-electro-elastic strip with multiple moving cracks, Mathematics and Mechanics of Solids 22: 304-323.
[18] 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.
[19] Monfared M.M., Ayatollahi M., Bagheri R., 2016, In-plane stress analysis of dissimilar materials with multiple interface cracks, Applied Mathematical Modelling 40: 8464-8474.
[20] Wang X., Pan E., 2008, Three-dimensional quasi-steady-state problem of moving heat and diffusion sources in an infinite solid, Mechanics Research Communications 35: 475-482.
[21] Monfared M.M., Ayatollahi M., 2017, Interactions of multiple cracks in a transversely isotropic piezoelectric plane under mixed mode condition, Engineering Fracture Mechanics 180: 87-104.
[22] Bagheri R., 2017, Several horizontal cracks in a piezoelectric half-plane under transient loading, Archive of Applied Mechanics 87: 1979-1992.
[23] Delale F., Erdogan F., 1983, The crack problem for a nonhomogeneous plane, Journal of Applied Mechanics 50: 609-614.
[24] Bagheri R., Noroozi M., 2018, The linear steady state analysis of multiple moving cracks in a piezoelectric half-plane under in-plane electro-elastic loading, Theoretical and Applied Fracture Mechanics 96: 334-350.
[25] García-Sánchez F., Zhang Ch., Sládek J., Sládek V., 2007, 2D transient dynamic crack analysis in piezoelectric solids by BEM, Computational Materials Science 39: 179-186.
[26] Bagheri R., 2017, Several horizontal cracks in a piezoelectric half-plane under transient loading, Archive of Applied Mechanics 87: 1979-1992.