Macrocrack-Microcrack Interaction in Piezoelectric Materials, Part II: Numerical Results and Discussions

Numerical results are shown in figures and tables. The major features for the traditional stress intensity factors and the electric displacement intensity factor against the microcrack location angle and the distance of the microcrack center from the macrocrack tip are discussed. It is shown that, unlike single-crack problems, the mechanical loading and the electric loading are coupled together since the microcrack not only releases the near-tip stresses, but also disturbs the near-tip electric field. Furthermore, the influence of the electric loading on the mechanical strain energy release rate (MSERR) at the macrocrack tip is discussed in detail. It is found that the variable nature of the MSERR against the normalized electric loading is monotonic and proportional wherever the parallel microcrack is located near the macrocrack tip. However, the slope of the MSERR's curve considering microcracking diverges far from those without considering microcracking. This finding reveals that, besides the two sources of microcrack shielding discussed by Hutchinson (1987) for brittle solids, the disturbance of the near-tip electric field due to microcracking really provides another source of shielding for piezoelectric solids.