Affiliations: [a] College of Mathematics and Computer Science, Hunan
Normal University, Changsha, Hunan 410081, P.R. China | [b] School of Aerospace and Materials Engineering,
National University of Defence Technology, Changsha, Hunan 410073, P.R.
China
Abstract: The electroelastic analysis of a cracked transversely isotropic
piezoelectric layer sandwiched between two elastic layers is made under
electromechanical loading. The crack is assumed to be situated at the mid-plane
of the piezoelectric layer and penetrate through the piezoelectric layer along
the poling direction. By using an integral transform technique, the problem is
reduced to dual integral equations. Further a singular integral equation with
Cauchy kernel of the first kind is derived and solved numerically by the
Lobatto-Chebyshev collocation technique. The field intensity factors and the
energy release rate are obtained and the results indicate that they are
independent of electric loading for the case of prescribed stress, and depend
on electric loading for the case of prescribed displacement on the top and
bottom surfaces. The electric field has no any singularity near the crack tips,
while the electric displacement exhibits the same singularity as the stress
near the crack tips. Some numerical results are presented graphically to show
the influence of layer thickness-to-crack length ratio and the material
properties on the normalized energy release rate.
Keywords: crack, electroelastic field, piezoelectric layer, field intensity factors, energy release rate
