This paper discusses an in situ observation of fracture behavior around a crack tip in ferroelectric ceramics under combined electromechanical loading by use of a moiré interferometry technique.The deformation field induced by the electric field and the stress concentration near the crack tip in three-points bending experiments was measured.By analysis of the moiré images it is found that under a constant mechanical load,the electric field almost has no effect on the crack extension in the case that the directions of the poling,electric field and crack extension are perpendicular to each other.When the poling direction is parallel to the crack extension direction and perpendicular to the electric field,the strain decreases faster than that calculated by FEM with and without electrical loading as one goes away from the crack tip.In addition,as the electric field intensity increases,the strain near the crack tip increases,and the strain concentration becomes more significant.
This paper presents an efficient meshless method for analyzing cracked piezoelectric structures subjected to mechanical and electrical loading. In this method, an element free Galerkin （EFG） formulation, an enriched basic function and some special shape functions that contain discontinuous derivatives are employed. Based on the moving least squares （MLS） interpolation approach, the EFG method is one of the promising methods for dealing with problems involving progressive crack growth. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing procedure required in the conventional finite element method （FEM） is avoided. The numerical results show that the proposed method can yield an accurate near-tip stress field in an infinite piezoelectric plate containing an interior hole. In another example studying a ceramic multilayer actuator, the proposed model was found to be accurate in the simulation of stress and electric field concentrations arround the abrupt end of an internal electrode.
Xianghua GuoDaining FangAi Kah SohHyun Chui KIMJung Ju Lee
This review presents the progress and current status of the investigation on electromechanical deformation and fracture of piezo electric/ferroelectric materials. An attempt is made to summarize a few fundamental aspects, which include electromechanical constitutive relations, piezoelectric micromechanics and electric fracture and fatigue, instead of describing all technological backgrounds, basic physics, experimental findings, and theoretical developments. A number of open questions and future prospective are presented. It is hoped that this review will encourage people to join the exploration of this important and interesting field.
A nonlinear finite element （FE） model based on domain switching was proposed to study the electromechanical behavior of ferroelectric ceramics. The incremental FE formulation was improved to avoid any calculation instability. The problems of mesh sensitivity and convergence, and the efficiency of the proposed nonlinear FE technique have been assessed to illustrate the versatility and potential accuracy of the said technique. The nonlinear electromechanical behavior, such as the hysteresis loops and butterfly curves, of ferroelectric ceramics subjected to both a uniform electric field and a point electric potential has been studied numerically. The results obtained are in good agreement with those of the corresponding theoretical and experimental analyses. Furthermore, the electromechanical coupling fields near （a） the boundary of a circular hole, （b） the boundary of an elliptic hole and （c） the tip of a crack, have been analyzed using the proposed nonlinear finite element method （FEM）. The proposed nonlinear electromechanically coupled FEM is useful for the analysis of domain switching, deformation and fracture of ferroelectric ceramics.
Considering the influence of the domain switching near the tip of a crack andapplying the idea of multiscale singularity fields in piezoelectric fracture, we have obtained anempirical criterion for the crack closure. Based on the domain switching in the electric yieldregion, referring to Yang's results on the small scale yield model for the electrical fatigue crack,a model of the crack closure during electric-field-induced fatigue is developed to analyze thecrack growth. In terms of the model we have obtained the formula of the rate of the crack growthunder cyclic electric loading. Finally we compare the theoretical predictions with the results givenby Cao and Evans experimentally. It should be pointed out that the model proposed is empirical andneeds to be verified by more experimental results.
The effects of compressive stress parallel and perpendicular to the polar axis of PZT ceramics on the nonlinear electromechanical behavior of the materials has been experimentally studied. A domain-switching model that divides each 180° switching to two successive 90° switching is proposed to explain these effects. In the case of stress parallel to the polar axis, domain switching in the ceramics is approximately axisymmetric and can be simulated by an analytical model. While in the case of stress perpendicular to the polar axis, domain switching is three-dimensional and cannot be simplified. The simulated re-sults that match the experiments well show the validity of the proposed domain-switching model.
