U. Bahr

Electrically driven cracks in piezoelectric ceramics: experiments and fracture mechanics analysis

Piezoelectric systems like multilayer actuators are susceptible to damage by crack propagation induced by strain incompatibilities. These can arise under electric fields for example between the electroded and external regions. Such incompatibilities have been realised in thin rectangular model specimens from PZT-piezoelectric ceramics with top and bottom electrodes only close to one edge. Under an electric field, controlled crack propagation has been observed in situ in an optical microscope. The crack paths are reproducible with very high accuracy. Small electrode widths lead to straight cracks with two transitions between stable and unstable crack growth regions, while large electrode widths result in curved cracks with four transitions. Fracture mechanics analysis is able to explain the different crack paths. An iteration method is developed to simulate the curved crack propagation also for strong curvature of the crack paths using the finite element method. The computed crack contours exhibit excellent quantitative agreement with the experiment with respect to their shape, the stages of stable and unstable crack propagation and the transitions between them. Finally, also the crack length as a function of the electric field can be predicted.

Crack deflection in piezoelectric ceramics

Abstract Crack deflection can occur in a specimen subject to a stress gradient of high tensile stresses near the surface which decreases with increasing depth. Such a stress gradient can be induced by strain incompatibilities. These can for example arise under electric fields between the electroded and external regions of a piezoelectric material. Such incompatibilities have been realized in thin rectangular model specimens from PZT-piezoelectric ceramics with top and bottom partial electrodes. Under an electric field, controlled crack propagation has been observed in-situ in an optical microscope. The crack paths are reproducible with very high accuracy. Small electrode widths lead to straight cracks with two transitions between stable and unstable crack growth, while large electrode widths result in curved cracks with four transitions. Poling the specimen prior to the experiment alters the crack path and introduces an anisotropy in the R-curve behavior as well as in the achievable strain mismatch. The crack path selection and crack length can be explained by means of a qualitative fracture mechanics analysis.

Threshold strength prediction for laminar ceramics from bifurcated crack path simulation

Abstract Thin compressive layers sandwiched between thicker tensile layers in laminar ceramics can stop unstable cracks. As shown by Lange and co-workers, the arrested crack propagates stably through the compressive layer under increasing load until a critical load or threshold strength is reached. In 4-point flexural loading tests, cracks can bifurcate after entering into the compressive layer. This paper presents finite element simulations of bifurcated crack paths and threshold strength prediction in two-dimensional approximation. In rather good agreement with experiments the calculated threshold strength increases with compression and is higher with bifurcated cracks than with straight cracks, and higher with loading axis parallel to the laminar plane than normal to it.

Temperature distribution in an array of moving cracks acting as heat sinks

The temperature distribution in a periodic array of parallel cracks acting as heat sinks is studied for the case of stationary crack motion by use of the Wiener–Hopf method. The problem arises in the investigation of cracks propagating into solid material, where the stresses driving crack motion are caused by heat transfer from the solid through the crack surfaces. The solution is given in terms of Fourier integrals involving infinite products. The heat-flux distribution in the vicinity of the crack tips is computed analytically from the high wavenumber asymptotics. Numerical solutions of the temperature distribution are presented for several values of the Biot and Péclet number, and the effect of varying these parameters is discussed qualitatively.