13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Fracture Criteria for Piezoelectric Ceramics Leslie Banks-Sills School of Mechanical Engineering, Tel Aviv University, Ramat Aviv, 69978, Israel Division of Solid Mechanics, Lund University, Lund SE-221 00, Sweden banks@eng.tau.ac.il Abstract An analytical, numerical and experimental investigation was carried out to determine fracture criteria for piezoceramics with poling parallel and perpendicular to the crack faces. The asymptotic expressions of stress, strain, electric flux density and electric fields were derived. For a piezoelectric material, in addition to the usual three modes of fracture, there is a fourth mode associated with the electric field. The asymptotic expressions were used for determining the energy release rate and extending a conservative interaction energy or M-integral for calculating the intensity factors associated with piezoelectric material for energetically consistent boundary conditions on the crack faces. Tests were performed on four-point bend PZT-5H fracture specimens with the poling direction parallel to the crack faces. The specimens were analyzed numerically by means of the finite element method. Finally, a mixed mode fracture criterion for piezoelectric ceramics was developed. This criterion is based upon the energy release rate and two phase angles, determined from the ratio between the intensity factors KIV and KI, for the first, and KII and KI, for the second. This data and that taken from another source for poling perpendicular to the crack faces were used to produce failure criteria for each case. Keywords Conservation integrals, Four-point bend tests, Mixed mode fracture, Piezoelectric ceramics 1. Introduction Piezoelectric ceramics are in widespread use as sensors and actuators in smart structures, despite the absence of a fundamental understanding of their fracture behavior. Piezoceramics are brittle and susceptible to cracking. As a result of the importance of the reliability of these devices, there has been tremendous interest in studying the fracture and failure behavior of such materials. To understand failure mechanisms of piezoelectric materials and maintain the stability of cracked piezoelectric structures operating in an environment of combined electromechanical loading, analysis of the mechanical and electrical behavior is a prerequisite. There have been many fracture tests carried out on piezoelectric material [1–12]. Fracture criteria have been presented in [10-17]. Each of these is based on the energy release rate. In fact, in [17] the energy was separated into its mechanical and electrical parts. Assuming impermeable crack face conditions, it was concluded in [17] that crack propagation of poled piezoelectric material is governed by the mechanical energy release rate. However, crack growth driven by purely electric fields in poled ferroelectrics has been observed in experiments [18,19]. A local energy release rate criterion was presented in [14] and [15] based on electric nonlinearity caused by a domain switching zone ahead of the crack tip. Impermeable crack face boundary conditions were also assumed there. The energy release rate obtained in [13] was used in [10] as a fracture criterion for analyzing results obtained with four-point bend specimens. This expression is based upon the load and electric current measured during the experiment. For an applied field of 0.5 MV/m, the energy release rate was zero or negative, which is not physically reasonable. Fracture curves of I K versus IV K were presented in [16] using impermeable and permeable assumptions. For both
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