13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Free edge coupling effect of piezoelectric cross-ply laminated plates Chao Han1,*, Zhangjian Wu1 1 Department of MACE, The University of Manchester, M13 9PL, UK * Corresponding author: Chao.Han-2@postgrad.manchester.ac.uk Abstract Free edge effect of laminated plates has been extensively investigated in the past two decades. Due to the boundary condition limitation, very limited work on piezoelectric laminated plates with free edges was carried out. In this paper, coupled and uncoupled analytical analyses on the interlaminar stresses in the vicinity of the free edges of piezoelectric laminated plates are presented on the basis of three-dimensional elasticity and piezoelectricity. The state space equations for cross-ply piezoelectric laminates subjected to uniaxial extension are obtained by considering all independent elastic and piezoelectric constants. The equations satisfy the boundary conditions at free edges and the continuity conditions across the interfaces between plies of the laminates. Three dimensional exact solution is sought and validated by comparing present numerical results with those of existing approximate analytical and finite element models. The singularity of the interlaminar stresses near the free edges is confirmed and the electromechanical coupling effects give much higher interlaminar stresses at the free edges in comparison with those of the corresponding uncoupled cases. Keywords: piezoelectricity, laminated plate, coupling effect, interface stress, exact solution 1. Introduction In recent decades, composite materials have extensive popularity in high-performance products that demand for high-strength, lightweight among many fields. Due to the development of multifunctional structures, smart materials and structures, which can perform sensing, controlling, actuating with distinct direct and converse piezoelectric effects, are widely used in many applications such as structural vibration control, precision positioning, aerospace and nanotechnology. Piezoelectric structures are often made from multi-layered thin films of dissimilar materials in the forms of stacks. For example, a piezoelectric laminated plate with simply-supported conditions, as a multilayer stack, was investigated by many researchers such as Heyliger [1], Lee and Jiang [2], Cheng et al. [3] and Xu et al. [4]. Sheng et al. [5] presented state space solution for laminated piezoelectric plate with clamped and electric open-circuited boundary conditions. It is well-established that due to the discontinuity of material properties at the interfaces, a highly concentrated interlaminar stress field can occur in the vicinity of the free edges which will lead to interlaminar failures such as delamination or matrix cracking. Pipes and Pagano [6] presented a 3D elastic solution for the free-edge effect for a symmetric laminate strip under uniaxial tension. By using Lekhnitskii’s [7] stress potential as well as the eigenfunction technique, Wang and Choi [8] investigated the stress singularities at the free edge of laminated plate. Becker [9] presented a closed-form solution by introducing a particular warp deformation which decays rapidly towards the laminate interior to reflect the free edge effect. Most recently, analytical solutions were developed by Tahani and Nosier [10] within Reddy’s layerwise theory (LWT) to investigate the free edge effect problem of general cross-ply laminates with finite dimensions under uniform axial extension. Recently Zhang et al. [11] give the 3D analytical solution for the free edge cracking effect in composite laminates under extension and thermal loading by using state space method. Due to the piezoelectric coupling effects in piezoelectric laminated plate, the mechanical and electrical behavior becomes more complex. Thus an accurate determination of coupling effect on free edge interlaminar stresses and deformation is essential in the design of elastic and piezoelectric
RkJQdWJsaXNoZXIy MjM0NDE=