%0 Journal Article
%T A Modified Strip-Yield-Saturation-Induction Model Solution for Cracked Piezoelectromagnetic Plate
%A R. R. Bhargava
%A Pooja Raj Verma
%J International Journal of Engineering Mathematics
%D 2014
%R 10.1155/2014/892576
%X A strip-yield-saturation-induction model is proposed for an impermeable crack embedded in piezoelectromagnetic plate. The developed slide-yield, saturation, and induction zones are arrested by distributing, respectively, mechanical, electrical, and magnetic loads over their rims. Two cases are considered: when saturation zone exceeds induction zone and vice-versa. It is assumed that developed slide-yield zone is the smallest because of the brittle nature of piezoelectromagnetic material. Fourier integral transform technique is employed to obtain the solution. Closed form analytic expressions are derived for developed zones lengths, crack sliding displacement, crack opening potential drop, crack opening induction drop, and energy release rate. Case study presented for BaTiO3¨CCoFe2O4 shows that crack arrest is possible under small-scale mechanical, electrical, and magnetic yielding. 1. Introduction The work on magnetoelectroelastic (MEE) fracture problem was started late back in the last century. The field is a natural extension of piezoelectric media since electricity and magnetism go in hand. Due to coupling effect of magneto-, electro-, and elastic fields, MEE materials become more popular than piezoelectric materials and serve as the excellent sensor, actuator, and transducer. Wang and Shen [1] obtained energy release rate for a mode-III magnetoelectroelastic media based on the concept of energy-momentum tensor. Based on the extended Stroh formalism combined with complex variable technique, Green¡¯s function is obtained for an infinite two-dimensional anisotropic MEE media containing an elliptic cavity which degenerates into a slit crack, by Jinxi et al. [2]. Sih and Song [3] proposed a model which showed that crack growth in a magnetoelectroelastic material could be suppressed by increasing the magnitude of piezomagnetic constants in relation to these for piezoelectricity. They [4] further derived energy density function for cracked MEE medium and studied the additional magnetic strictive effect which could influence crack initiation as applied field direction is altered. Wang and Mai [5] addressed the problem of a crack in a MEE medium possessing coupled piezoelectric, piezomagnetic, and magnetoelastic effects. Wang and Mai [6] further extended above problem to calculate a conservative integral based on governing equations for MEE media. Gao et al. [7] investigated the fracture mechanics for an elliptic cavity in a MEE solid under remotely applied uniform in-plane electromagnetic and/or antiplane mechanical loadings. Reducing cavity into a crack they
%U http://www.hindawi.com/journals/ijem/2014/892576/