Mechanical Strain Energy Release Rate Research Articles

Multiple parallel cracks interaction problem inpiezoelectric ceramics

This paper has two goals. First, we propose the pseudo-traction–electric displacementmethod for solving the interaction problem of multiple parallel cracks in transversely isotropicpiezoelectric ceramics. Second, we present a fundamental understanding for the role that theelectric displacement loading plays in the interaction problem. Detailed comparisons between theresults under the compound mechanical–electric loading conditions and those derived underpurely mechanical loading conditions are performed. It is shown that the mechanical fractureparameters such as the stress intensity factors are no longer independent of the electric loading asthey would be in single crack problems. Quite contrary, the electric displacement loading has asignificant influence on the stress intensity factors, the total potential energy release rate and themechanical strain energy release rate. This important conclusion is mainly due to the interactioneffect, i.e., one of the multiple cracks releases the stresses and disturbs the electric fields near theother crack. It is also found that there are some special relative locations for the multiple parallelcracks at which the electric displacement loading has no effect on the Mode I stress intensityfactor. However, the mechanical strain energy release rate has no such a property.

NUMERICAL ANALYSIS OF CRACK PROPAGATION IN PIEZOELECTRIC CERAMICS

The formulation of an isoparametric displacement – electric potential finite element method that accounts for the electro‐mechanical coupling effect of piezoelectric materials is briefly presented in this paper. The crack propagation behaviour and the elasto‐electric fields near a crack tip in a PZT‐5 piezoelectric ceramic under mechanical, electrical and mechanical – electrical mixed loads are investigated using this electro‐mechanical finite element method. From the numerical results, it can be seen that crack propagation along the crack plane direction will be impeded and the crack will tend to propagate at an angle of about 84° to the crack plane under a negative electric field on the basis of the maximum stress criterion. The physical explanation of the phenomena is presented in this paper and it is shown that the mechanical strain energy release rate is not a good criterion for predicting crack propagation in the case where the ratio of the electric field to the mechanical load becomes large.

Fracture Criteria for Piezoelectric Ceramics

Fracture criteria for piezoelectric materials were investigated. Mode I and mixed mode fracture tests were performed on PZT‐4 piezoelectric ceramics to verify the validity of the mechanical strain energy release rate as a fracture criterion. Experimental results indicated that crack extension could be aided or impeded by an electric field, depending on the field direction. Further, the direction of crack extension was studied. A crack closure method, together with finite element analysis, was introduced to calculate the mechanical strain energy release rate. The maximum mechanical strain energy release rate was used to predict fracture loads under combined mechanical and electrical loads. It was found that the mechanical strain energy release rate criterion is superior to other fracture criteria and predicts fracture loads fairly accurately.

Effect of electric field on fracture of piezoelectric ceramics

Closed form solutions for all three modes of fracture for an infinite piezoelectric medium containing a center crack subjected to a combined mechanical and electrical loading were obtained. The explicit mechanical and electrical fields near the crack tip were derived, from which the strain energy release rate and the total potential energy release rate were obtained by using the crack closure integral. The suitability in using the stress intensity factor, the total energy release rate, or the mechanical strain energy release rate as the fracture criterion was discussed.

A model for transgranular stress corrosion using concepts from fracture mechanics

A model for transgranular stress corrosion in metals is developed utilising electrochemical and mechanical parameters. While the major part of the work accompanying the growth of the crack is electrochemical in origin, it is shown how this is related to the mechanical strain energy release rate, the two quantities being related through the dislocation spacing or stacking fault energy of the lattice.