A PARTIALLY PERMEABLE MIXED-MODE CRACK EMBEDDED IN A FUNCTIONALLY GRADED MAGNETO ELECTRO ELASTIC LAYER M. Rekik1, S. El-Borgi1,2* and Z. Ounaies3 1Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, University of Carthage, B.P. 743, La Marsa 2078, Tunisia 2Texas A&M University at Qatar, Engineering Building, Mechanical Engineering Program, PO. Box 23874 Education City, Doha, Qatar 3Department of Mechanical Engineering, The Pennsylvania State University, 157B Hammond Building, University Park, PA 16802, USA mongi.rekik@hotmail.com, sami.el_borgi@qatar.tamu.edu, zxo100@engr.psu.edu Abstract This work paper considers the problem of a partially permeable mixed-mode crack embedded in a graded magneto electro elastic layer subjected to magneto electro mechanical loads. The medium is graded in the direction orthogonal to the crack plane and is modeled as a non homogeneous medium with anisotropic constitutive laws. Using Fourier transform, the resulting magneto electro elasticity equations are converted analytically into singular integral equations which are then solved numerically to yield the crack-tip mode I and II stress, electric displacement and magnetic induction intensity factors. The main objective of this work is to study the influence of material non homogeneity, crack position and magneto electric permeabilities on the fields’ intensity factors for the purpose of gaining better understanding on the behavior of fractured graded magneto electro elastic layers. Results showed that fields’ intensity factors increase with nonhomogeneity, and decrease with magnetic and electric permeabilities, and as the crack become closer to the layer’s center. Introduction Smart structures possessing the ability of magneto electro mechanical energy conversion have found increasing application in several engineering fields such as magnetic field probes, electric packaging, acoustic, hydrophones, medical ultrasonic imaging, microwave electronics, optoelectronics, electronic instrumentation, transducers, sensors and actuators. Research has focused on the use of Functionally Graded Magneto Electro Elastic Materials (FGMEEM) in smart structures to improve their performance. But, the manufacturing of FGMEEMs may lead to cracks that can eventually propagate and cause premature failure. Therefore, it is of a great importance to study the fracture behavior of magneto electro elastic composites. A number of authors considered FGMEEM crack problems. Ma et al (2007) studied the mode III crack problem in a functionally graded magneto electro elastic strip accounting for ideal crack surface magneto electric permeability. Ma et al (2009) considered the problem of a surface crack in a functionally graded magneto electro elastic coating homogeneous elastic substrate subjected to antiplane mechanical and in plane magneto electrical loading for the ideal crack surface magneto electric permeability. Zhou et al (2004) examined the problem of two parallel symmetric permeable cracks in functionally graded materials under anti-plane shear loading. Feng et al (2007) analyzed the dynamic behavior of magneto electrically impermeable cracks in functionally graded magneto electro elastic plates. Feng et al (2006) studied the dynamic problem of a crack embedded in a graded magneto electro elastic strip assuming ideal crack surface permeability. Jun (2007) examined the scattering of harmonic anti-plane shear stress waves by a crack in functionally graded magneto electro elastic materials assuming purely permeable crack surfaces. Zhou et al (2008) solved the mode I crack problem in a FGMEEM infinite medium assuming air permeability within the crack. Li et al (2008) considered the anti-plane problem of a permeable crack intersecting the interface between two FGMEEM layers. Li et al (2008) analyzed the anti-plane problem of a crack in the interface of tow symmetrically bonded FGMEEM assuming a linear variation of the magneto electromechanical properties. Guo et al (2009) solved the anti-plane problem of a crack in bonded FGMEEM strip sandwiched between two functionally graded strips assuming ideal magneto electrical permeability on the crack faces. Rekik et al (2012) considered the problem of magneto electrically impermeable crack embedded in a graded infinite medium subjected to magneto electro mechanical loading. The present work consists of studying the plane problem of a partially magneto electrically permeable crack embedded in a graded magneto electro elastic layer. The applied magneto electro mechanical loading will give rise to coupled fields intensity factors; namely, mode I and II stress, electric
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