Keywords: macro-fibre composites, transverse shear actuators, effective properties characterization, finite element homogenization method.

Recent applications of piezoelectric sensors and actuators require conformability and packaging standards not found in monolithic piezoceramic patches. The so-called macro-fibre composites (MFC) have become very popular since it may combine the conformability of epoxy-matrix composites and the electromechanical energy density of piezoceramic materials [1]. These transducers are composed of machined (diced) rectangular fibres of a piezoceramic material embedded to a epoxy-based resin matrix and covered by copper electrodes and protective kapton and/or acrylic layers. The original idea [1] uses interdigitated electrodes (IDE) to induce the longitudinal or 33 mode in the fibres. More recently, an alternative design, in which the macro-fibres are oriented perpendicular to the direction of motion, was proposed [2] to induce the transverse shear mode (15 or 35). Recently, some research effort has been directed to the identification and characterization of such transducers, in longitudinal (33) or transverse (31) [3] and transverse shear (15) [4] modes. It is noticeable that the effective properties depend not only on the epoxy-to-piezoceramic volume fraction but also on the geometrical and material properties of the other layers (kapton, acrylic, electrodes). In the present work, a finite element homogenization method for a shear actuated d₁₅ MFC made of seven layers (kapton, acrylic, electrode, piezoceramic fibre and epoxy composite, electrode, acrylic, kapton) was proposed and used for the characterization of its effective material properties. The methodology was first validated for the MFC active layer only, made of the piezoceramic fibre and epoxy, through comparison with analytical results. Then, the methodology was applied to the full MFC with seven layers. It was shown that the packaging reduces significantly the shear stiffness of the piezoceramic material and, thus, leading to significantly smaller effective electromechanical coupling coefficient k₁₅ and piezoelectric stress constant e₁₅ when compared to the piezoceramic fibre properties. However, the piezoelectric charge constant d₁₅ was less affected by the softer layers required by the MFC packaging. This might indicate that this MFC design could be interesting for sensing applications but not so much for actuation. The presented results also confirmed that a higher fibre volume fraction (FVF) is desirable and a 95% FVF seems to be a good compromise.

1

W.K. Wilkie, G.R. Bryant, J.W. High, "Low-cost Piezocomposite Actuator for Structural Control Applications", In "Proceedings of SPIE's 7th International Symposium on Smart Structures and Materials", 5-9 March, Newport Beach, CA, 2000. doi:10.1117/12.388175

2

S. Raja, T. Ikeda, "Concept and Electro-elastic Modeling of Shear Actuated Fiber Composite using Micro-mechanics Approach", Journal of Intelligent Material Systems and Structures, 19, 1173-1183, 2008. doi:10.1177/1045389X07084177

3

A. Deraemaeker, H. Nasser, A. Benjeddou, A. Preumont, "Mixing Rules for the Piezoelectric Properties of Macro Fiber Composites", Journal of Intelligent Material Systems and Structures, 20(12), 1475-1482, 2009. doi:10.1177/1045389X09335615

4

A. Benjeddou, M. Al-Ajmi, "Analytical homogenizations of piezoceramic d15 shear macro-fibre composites", In M. Kuna, A. Ricoeur, (Editors), "Proceedings of the IUTAM Conference on Multiscale Modelling of Fatigue, Damage and Fracture in Smart Materials", Freiburg, Germany, Sept 1-4, 2009. doi:10.1007/978-90-481-9887-0_22

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