Anti-plane analysis of power function curved cracks in piezoelectric composites

By proposing a new conformal mapping and using the Stroh formula, the fracture problem of a power function curved crack in an infinite piezoelectric composite is studied under anti-plane shear stress and in-plane electric load at infinity. The analytical solutions of the field intensity factors and the mechanical strain energy release rate are presented with the assumption that the surface of the crack is electrically impermeable. When the power of the curve is zero, the present results can be reduced to the solutions of a Griffith crack in an infinite piezoelectric composite. Based on the analytical solutions, it is found that the distribution of electric field is independent on the mechanics load under a fixed shape of the curve. Numerical examples are finally conducted to analyze the influences of the projected length along the x₁-axis, power and coefficient of curved cracks on the mechanical strain energy release rate. The results show that if the piezoelectric composite is subjected to the only load along the direction of x₂-axis, there exists a critical projected length along the x₁-axis which can promote the crack growth easily for given power and coefficient of curved cracks. Moreover, for given values of projected length and power of curved cracks, the smaller coefficient of curved crack is, the easier crack propagates.