Strip-Saturation Model Solution for A Transversely Cracked Piezoelectric Strip

A crack arrest model is proposed for a long, narrow, transversely cracked piezoceramic strip. The strip is poled. The infinite boundary of the strip is prescribed four different sets of mechanical and electrical load conditions. Consequently the crack yields. Under small-scale yielding the crack is assumed to open in a self-similar fashion. Assuming the material of the strip to be electrically more brittle, ahead of each tip of the crack a saturation zone is encountered first. The present investigations are carried at this level. To arrest the crack from further opening, the rims of developed zones are subjected to normal, cohesive, unidirectional (normal to the length of the crack), in-plane saturation limit electrical displacement. Framing a mathematical model for the above, Fourier integral technique is then employed to solve the problem. This yields dual Fredholm integral equation of second kind, which in turn is solved numerically. The results obtained are applied to calculate the quantities affecting crack arrest viz. crack opening displacement, crack growth rate, saturation zone length. Case study has been presented for BaTiO3, PZT-4 and PZT-5H strips. The variation of crack opening displacement, crack growth rate has been plotted versus strip width, saturation zone length and ceramic material properties. The results obtained could be applied to all crystals possessing symmetry of hexagonal crystal of 6mm class with respect to principal axes. Proposed model ascertains that it is possible to arrest crack opening.