Switching Zone Research Articles

Domain Switching and Crack Tip Opening Stress Variation in Ferroelectric Ceramics

Evolution of switching zone near a crack tip in ferroelectric ceramics is calculated using the constitutive equations proposed in [1], with an assumption that switching-induced internal fields are minimized by fine domain microstructures and moving charges. A two-dimensional ferroelectric ceramic specimen that has an edge crack and that is poled perpendicular to the crack plane are subjected to external stress and electric fields. Diverse crack tip microstructures are obtained depending on both the history and the ratio of electric and stress loads. It is shown that opposite crack tip opening stresses under the same electric fields are due to opposite distributions of piezoelectric coefficients in the specimens with different crack tip microstructures.

Effect of geometry and electrical boundary conditions on R-curves for lead zirconate titanate ceramics

R-curve measurements on PZT poled in thickness direction were carried out on CT specimens under different electric boundary conditions. The effect of specimen geometry was evaluated by measuring R-curves in CT specimens of different thickness and comparing these with R-curves in bend bars. A low coercive stress is responsible for the development of a large switching zone. This switching zone is of high relevance for the computation of the actual stress intensity factor at the crack tip and for the R-curve calculation.

Toughening under non-uniform ferro-elastic domain switching

The existing models of switch-toughening seldom consider the effect of non-uniform ferro-elastic domain switching in the vicinity of a crack. To explore this issue, an evolution law for the volume fraction of the switched portion under applied electromechanical loading is established from the minimum energy principle. Based on this law, a switching model capable of dealing with the non-uniform distribution of switching strain is developed. The domain switching zone is divided into a saturated inner core and an active surrounding annulus. Mono-domain solution of ferro-elastic toughening is obtained under the model of small scale domain switching. Toughening for ferroelectrics with different poling states is estimated via Reuss type approximation. Two sets of solutions are obtained according to spherical and cylindrical inclusions. The interval of toughening defined by these two models covers the range of experimental data. The same conclusion is reached for the size of the switching zone.

Current Understanding on Fracture Behaviors of Ferroelectric/Piezoelectric Materials

The current understanding on fracture behaviors of ferroelectric/piezoelectric materials are reviewed in this article. Two main obstacles in understanding such fracture behaviors are discussed: (i) the selection of electric boundary condition on crack faces and (ii) the near-tip domain switching or nonlinear zone. Some previous controversial results in theoretical studies and experimental observations are also discussed here; particularly, the inherent load-dependence of the variable tendencies of the crack tip energy release rate against the applied electric field, on the applied mechanical loading level found recently, which reveals that the applied mechanical loading does significantly influence the role played by the applied electric field in piezoelectric fracture.

Study on lateral dynamic characteristics of vehicle/turnout system

Based on Chinese No. 12 high speed, single-way swing nose rail concrete sleeper turnout, a comprehensive vehicle/turnout system coupling dynamic model has been established in this paper, and the lateral and vertical dynamic characteristics of vehicle/turnout systems have been simulated while the car passes through the turnout zone on divergence. These dynamic characteristics show that the lateral impact and vibration of the systems caused by the wheel/rail contact and irregularity are very intensive, especially at the switch zone and nose area of the turnout, and the lateral dynamics of the turnout system, such as lateral stability, vibrating responses, impacting and the allowable passing velocity force between the wheelsets and the switch rails are much more complicated than that of the vertical ones.

Domain switching in ferroelectric single crystal/ceramics under electromechanical loading

Domain switching in PMN-PT single crystal and PZT-5 ceramics under electromechanical loading were studied in two different ways. For the single crystal, domain switching was in situ investigated with polarized light microscopy. A 90° domain-switching zone was observed near the crack tip and the size of the switching zone changed with the acuity of the crack tip. For PZT-5 ceramics, domain switching under orthogonal electromechanical loading ( E 3 and compressive stress σ 11) was studied by measuring the hysteresis loops, butterfly curves and reversed butterfly curves ( ɛ 11 versus E 3). Experimental results show that 90° domain switching is suppressed in the planes parallel to the compression direction. A domain-switching model dividing each 180° switching to two successive 90° switching was proposed to explain the experimental results.

Domain Switch Toughening in Polycrystalline Ferroelectrics

AbstractMode I steady crack growth is analyzed to determine the toughening due to domain switching in poled ferroelectric ceramics. A multi-axial, electromechanically coupled, incremental constitutive theory is applied to model the material behavior of the ferroelectric ceramic. The constitutive law is then implemented within the finite element method to study steady crack growth. The effects of mechanical and electrical poling on the fracture toughness are investigated. Results for the predicted fracture toughness, remanent strain and remanent polarization distributions, and domain switching zone shapes and sizes are presented. Finally, the model predictions are discussed in comparison to experimental observations.

Crack tip switching zone in ferroelectric ferroelastic materials

A novel liquid crystal display was utilized to monitor electric surface potentials in front of a crack tip in a ferroelectric ferroelastic material, lead zirconate titanate (PZT). The electric potential could be converted to yield the radial stress and strain distribution in front of the crack which afforded determination of the domain switching zone as well as the hardening coefficient. This zone shape as well as its evolution during crack growth was monitored. In contrast to transformation toughening materials, the crack tip process zone size was demonstrated to first increase and then decrease with increasing crack length.

On the fracture toughness of ferroelectric ceramics with electric field applied parallel to the crack front

Mode I steady crack growth is analyzed to determine the toughening due to domain switching in ferroelectric ceramics with electric field applied parallel to the crack front. A multi-axial, electromechanically coupled, incremental constitutive theory is applied to model the material behavior of the ferroelectric ceramic. The constitutive law is then implemented within the finite element method to study steady crack growth. The effects of electric field on the fracture toughness of both initially unpoled and poled materials are investigated. Results for the predicted fracture toughness, remanent strain and remanent polarization distributions, and domain switching zone shapes and sizes are presented. The effects of the plane-strain constraint and transverse stress are also established. Finally, the model predictions are discussed in comparison to recent experimental observations.

Finite element analysis of electric fracture properties in modified small punch testing of piezoceramic plates

The fracture behavior of a piezoelectric ceramic under applied electric fields has been the subject of recent studies. We have used finite element analysis to study experiments with the modified small punch (MSP) technique. Nonlinear three-dimensional finite element analysis was employed to calculate the MSP energy and maximum strain energy density. The effects of an applied electric field, 180° and 90° domain switching on the MSP energy, and maximum strain energy density are discussed, and the model predictions are compared with the results of the experiments. The polarization switching zones corresponding to combined mechanical and electrical loads are also obtained.

Conducting crack growth in ferroelectric ceramics subjected to electric loading

Crack growth with electrically conducting surfaces in ferroelectric ceramics subjected topurely electric loading is investigated. The boundary of the domain switching zone near thetip of a growing crack under small-scale conditions is determined, based on nonlinearelectric theory. The crack tip stress intensity factor induced by domain switching for theconducting crack with growth is numerically obtained. The variation of the electricalfracture toughness obtained from the result of the stress intensity factor is examined for aferroelectric material with electrical nonlinear behaviour. It is shown that theferroelectric material can be either toughened or weakened as the crack grows.Steady state crack growth in nonlinear ferroelectric materials is also discussed.

Electrical fracture toughness for a conducting crack in ferroelectric ceramics

Conducting cracks in ferroelectric ceramics under purely electrical loading are analyzed to investigate the effects of electric fields on fracture behavior. The asymptotic problem of conducting cracks in a mono-domain ferroelectric material as well as in a poly-domain ferroelectric material is considered and the relation between the crack tip stress intensity factor and the applied intensity factor of electric field under small scale conditions is investigated. In order to evaluate the crack tip stress intensity factors due to the domain switching, the shape of the domain switching zone attending the crack tip must be determined. The evaluation of the shape is carried out based on the nonlinear domain switching model. It is shown that the switching zone boundary and the crack tip stress intensity factors due to the switching depend strongly on the angle of the polarization vector and the ratio of the coercive electric field to the yield electric field. The electrical fracture toughness of unpoled poly-domain ferroelectrics is examined. Employing a Reuss type approximation, the crack tip stress intensity factors for an unpoled poly-domain material are obtained. The ratio of the critical electrical energy release rate to the critical mechanical energy release rate is obtained.

Effect of electric displacement saturation on the stress intensity factor for a crack in a ferroelectric ceramic

A crack in a ferroelectric ceramic with perfect saturation under electric loading is analyzed. The boundary of the electric displacement saturation zone ahead of the crack tip is assumed to be ellipse in shape. The shape and size of ferroelectric domain switching zone near a crack tip is determined based on the nonlinear electric theory. The stress intensity factor induced by ferroelectric domain switching under small-scale conditions is numerically obtained as a function of the electric saturation zone parameter and the ratio of the coercive electric field to the yield electric field. It is found that the stress intensity factor increases as the ratio of the semi-axes of the saturation ellipse increases.

AFM팁/강유전박막/전극 시스템에서의 스위칭 영역의 형성

A three-dimensional constitutive model for polarization switching in ferroelectric materials is used to predict the formation of switching zones in an atomic force microscopy(AFM) tip/ferroelectric thin film/bottom electrode system via finite element simulation. Initially the ferrolectric film is poled upward and the bottom electrode is grounded. A strong dc field is imposed on a fixed point of the top surface of the film through the AFM tip. A small switching zone with downward polarization is nucleated and grows with time. It is found that initially the shape of the switched zone is that of a bulgy dagger, but later turn to the shape of a reversed cup with the lower part wider than the upper part. It can also be concluded that the size of switching zones increases with the period of applied electric potential. The present results are qualitatively consistent with experimental observations.

Effect of electric fields on fracture behavior of ferroelectric ceramics

The asymptotic problem of a semi-infinite crack perpendicular to the poling direction in a ferroelectric ceramic subjected to combined electric and mechanical loading is analyzed to investigate effect of electric fields on fracture behavior. Electromechanical coupling induced by the piezoelectric effect is neglected in this paper. The shape and size of the switching zone is shown to depend strongly on the relative magnitude between the applied electric field and stress field as well as on the ratio of the coercive electric field to the yield electric field. A universal relation between the crack tip stress intensity factor and the applied intensity factors of stress and electric field under small-scale conditions is obtained from the solution of the switching zone. It is found that the ratio of the coercive electric field to the yield electric field plays a significant role in determining the enhancement or reduction of the crack tip stress intensity factor. The fracture toughness variation of ferroelectrics under combined electric and mechanical loading is also discussed.

R-curves of lead zirconate titanate (PZT)

Abstract R -curves were measured for ferroelectric ceramic lead zirconate titanate (PZT) using surface cracks in flexure (SCF) in a single composition of unpoled, ferroelastic PZT. The effects of several parameters on the R -curves were experimentally determined. These included grain size, indentation load, polishing away the residual stress zone associated with the Knoop indentation, and thermal depolarization after indentation. The larger grain size resulted in a higher plateau value of the R -curve, a result consistent with the larger amount of ferroelastic switching observed in the stress/strain curve. Increasing the indentation load from 10 to 50 N resulted in larger initial crack sizes. This had some effect on the early part of the R -curve, but did not much affect the plateau value. Polishing away the residual stress zone eliminated the residual stress contribution of the Knoop indentation to the stress intensity factor. This resulted in the most accurate measurement of the intrinsic toughness (0.4 MPa m 1/2 ). Thermal depolarization to remove any potential ferroelastic crack tip switching zone associated with the indentation had little or no effect on the measured R -curves.

Indentation-induced cracking and 90° domain switching pattern in barium titanate ferroelectric single crystals under different poling

We report different domain switching patterns and indenting crack orientations under Vicker's indentation for BaTiO 3 single crystals poled in different directions. For BaTiO 3 single crystal cut and poled in [001] direction, the short indenting cracks emanate not only from the diagonals of the indentation, but also from 〈110〉 directions due to the structure mismatch along the boundaries between two adjacent domain switching zones of equivalent spreading. For single crystal cut along [100] and poled in [001] direction, we found that much shorter cracks are induced if one diagonal of the indent is put 45° (termed 45° indent), instead of 0° (termed 0° indent), away from the poling direction. It shows that 45° indents favor the formation of 90° a– c domain switching just around the indents. Driven by the structure mismatch, cracks prefer to emanate along the boundary of two adjacent domain switching zones, or from the boundary dividing the domain switch zone and non-switching zone.

Uncoupled, asymptotic mode III and mode E crack tip solutions in non-linear ferroelectric materials

Complete asymptotic solutions for the mode III, longitudinal or anti-plane shear, and mode E applied electric field with conducting or insulating crack cases are presented for idealized ferroelectric switching materials. The mathematical procedure required to solve these problems has been presented by Rice (J. Appl. Mech. 34 (1967) 287). The constitutive behavior of the material is specified by an initial linear response, a segment of non-hardening switching behavior, i.e. perfect plasticity in the mechanical case, and finally a region where lock-up occurs. The crack tip solution is characterized by an outer solution with a standard r −1/2 singularity that is not centered on the crack tip, a switching zone with the solution given by a simple radial slip line field, and an inner lock-up region which surrounds the crack tip.

Indentation-induced domain switching in Pb(Mg 1/3Nb 2/3)O 3–PbTiO 3 crystal

Response of ferroelectric domains to mechanical stresses was studied on a <010> oriented piezoelectric 0.65Pb(Mg 1/3Nb 2/3)O 3–0.35PbTiO 3 (0.65PMN–0.35PT) crystal. Stress-induced domain switching was observed in the stress field of a microindentation and was confined to butterfly-shaped switching zones which extended preferentially along the <101> directions. Based on a critical shear stress criterion, a stress analysis was made to determine the condition for the 90° domain switching. The analysis predicted a hyperbolic contour for the switching-zone boundary, in agreement with the experimental observations.

A New Method for Suppressing Chattering in Variable Structure Feedback Control Systems

High-frequency chattering of sliding controller in variable structure system is undesirable in practice. A new method for suppressing chattering is presented in this paper. A proper zone for switching control is definded in the vicinity of ordinary switching hyperplane. This switching zone shrinks to the origin as the state variable converges to zero. The switching function is modified by certain integral transformation. Sustained oscillation is avoided and the global asymptotic stability is guaranteed. Simulations confirm the theoretical analysis.