Anomalies associated with energy release parameters for cracks in piezoelectric materials

For a central crack in a piezoelectric plate, the mode-I stress intensity factor (KI), electric displacement intensity factor (KD), energy release rates (G, GM) and energy density factor (S) are obtained from the finite element results. For the impermeable crack, the numerical results of KI and KD are coupled; this error is contrary to the uncoupled analytical solutions. The error has little effect on the total energy release rate G and energy density factor S, but in some cases, large errors in the mechanical energy release rate GM are observed. G is global while SED is local. Also G is negative which defies physics where energy cannot be created while crack attempts to extend as implied by G. Computations should be made for the J-integral and also show that J becomes negative. What this shows is that the global fracture energy criterion is not suitable to address the local release of energy because it includes the overall energy which are irrelevant to fracture initiation being a local behavior. In addition, the case study shows that the energy density theory is the better fracture criterion for the piezoelectric material. According to the results of S, it retards the crack growth when the external electric field and piezoelectric poling are on opposite directions. This conclusion agrees with analytical and experimental evidence in the past references.