Analytical solutions of mode-III lip-shape crack in piezoelectric composites

Based on the complex variable function method and the technique of conformal mapping, an anti-plane problem of lip-shape crack in piezoelectric composites was investigated under the anti-plane loading at infinity and in-plane electric loads.By using the residue theorem and Cauchy integral formula, the analytical expressions of the field intensity factors and the mechanical strain energy release rate are obtained with the assumption that the crack surfaces were electrically impermeable and electrically permeable.When the height of lip-shape crack approaches to zero, the analytical solutions of an infinitely large piezoelectric solid with a Griffith crack was obtained.Ignoring the effect of the electric field the present results can be reduced to the well-known solutions of classic material.The numerical examples are provided to show the influences of geometrical parameters and applied mechanical/electric loads on the mechanical strain energy release rate.The results indicate that an increase of the height of the lip-shape crack will retard the crack propagation and mechanical loads always accelerate the crack propagation.The influences of electric loads on the crack propagation was about boundary conditions of the lip-shape crack.