Electric Field Loading Research Articles

Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: I-32 mode measurements

Relaxor PMN-0.32PT single crystals were subjected to combined stress, electric field, and thermal loading. The electric field induced polarization and strain for a series of bias stresses and the stress induced polarization and strain for a series of bias electric fields were measured. These data were used to generate three-dimensional plots of the material behavior that clearly show a phase transformation. The results demonstrate that combinations of stress and electric field drive the phase transformation and that the driving force for this transformation decreases with increasing temperature. The threshold for the phase transformation at each temperature is used to generate a stability map for the material. Material properties are calculated for the linear regions.

Ferroelectric switching: a micromechanics model versus measured behaviour

Abstract The behaviour of ferroelectric polycrystals is explored using a rate-independent crystal plasticity model with self-consistent homogenisation to capture grain–grain interactions. Dimensionless parameters are introduced that allow a simple connection to be made between material constants and the nonlinear ferroelectric behaviour. In particular, combinations of material parameters are identified that cause remanent straining to be strongly suppressed. The self-consistent scheme allows for the ferroelectric response of a composite of grains with distinct sets of switching systems to be modelled. This feature is used to explore the effect of pinned domain walls and of dielectric inclusions. The model is able to reproduce the electrical response of three materials (PZT-5H, PZT-4D and Barium Titanate) under proportional stress and electric field loading, as measured in a parallel study.

Magnetoplastic effect: Basic properties and physical mechanisms

This paper presents a review of the main results of investigations into the magnetoplastic effect, which manifests itself in motion of dislocations in crystals exposed to magnetic fields. The dependences of the mean free path of dislocations on the induction and direction of the magnetic field, the magnetic treatment time, the temperature, and the type and concentration of impurities are studied for NaCl, LiF, CsI, Zn, Al, and InSb crystals. The threshold magnetic field B c below which the effect is absent, the saturation field B 0 above which the mean free paths of dislocations remain constant with an increase in the magnetic induction B, and the critical frequency v c of rotation of a sample in the magnetic field above which the effect disappears are examined. The quantities B c , B 0, and v c are investigated as functions of the basic physical parameters. It is found that the magnetoplastic effect is highly sensitive to X-ray radiation at low doses and to simultaneous action of an electric field or mechanical loading. The hardening of NaCl(Pb) crystals in the magnetic field is revealed. The theoretical interpretation is proposed for all the findings and dependences observed.

Three dimensional analysis of the dynamic stability of piezoelectric circular cylindrical shells

Abstract Based on a three-dimensional theory, a set of Mathieu–Hill equations have been derived for the dynamic stability analysis of piezoelectric circular cylindrical shells subjected to combined periodic axial compression and radial electric field loading. Bolotin's method is employed to determine the dynamic instability regions. Obtained results show that both the piezoelectric effect and the electric field only have minor effect on the unstable region. On the contrary, the geometric parameters, the rigidity of constituent materials and the external loading play dominating role in the dynamic stability of piezoelectric shells.

Mechanical and electrostatic properties of carbon nanotubes under tensile loading and electric field

Coupled mechanical and electronic behaviours of single walled open carbon nanotubes (CNTs) under applied electric field and tensile loading are investigated by the use of quantum mechanics as well as quantum-molecular dynamics techniques based on the Roothaan–Hall equations and the Newton motion laws. Different failure mechanisms and mechanical properties are found for CNTs subjected to electric fields and that subjected to tensile load. The electric field induced breaking in CNT begins from the outmost carbon atomic layers while the tensile load breaks the nanotube near its middle at 300 K. Electronic polarization and mechanical deformation induced by an electric field can significantly change the electronic properties of a CNT. Under electric field, the CNT can be stretched but the toughness is much lower than that under mechanical loading. Applied tensile loading causes no electronic polarization even in a metallic tube but it indeed changes the energy gap of the tube, thus exhibits influence on field-emission properties of CNTs. When a tube is tensioned in an electric field, the critical tensile strength of the tube may decrease significantly with increasing intensity of electric field. The coupling of mechanical and electrical behaviours is an important characteristic of CNTs.

Ferroelectric properties of [110], [001] and [111] poled relaxor single crystals: measurements and modeling

A combination of modeling and experimental work has led to the identification of a crystal cut of PZN-4.5%PT with enhanced piezoelectric coefficients for bending mode applications d 31=690 pC/N, d 32 =−1670 pC/N and direct evidence of a rhombohedral-orthorhombic phase transformation under [110] electric field loading. A crystal variant model enables the calculation of the physical properties of the single crystals with an engineered domain state (the piezoelectric, elastic, and dielectric coefficients) from the properties of the single domain [111] poled rhombohedral phase. This work focuses on the piezoelectric coefficients. Not all of the [111] piezoelectric coefficients have been measured. The modeling approach is used to compute the missing coefficients, d 15 and d 16 of the [111] poled crystal from the [001] and [110] properties. Criteria for variant and phase evolution in the model reproduce the observed hysteresis loops, remanent strain and remanent polarization.

Influence of applied electric field on the energy release ratefor cracked PZT/elastic laminates

Since the delamination induced failure of a laminated smartstructure always occurs under the action of mechanical and electricalfields, a generalized two-dimensional model for a piezoelectric/elasticlaminate is established in order to analyze the effect of an applied electricfield on its delamination. First, based on the double Fourier series method, ageneral analytical solution of the mid-plane displacement is derived for anyboundary condition. Furthermore, the energy release rate is employed to studythe influence of the applied electric field and mechanical loading on thefracture characteristics of the piezoelectric/elastic laminate. The energyrelease rates for modes I and II fracture behavior of the PZT/elasticlaminates are calculated in detail. Such calculations indicate that it isfeasible to choose not only suitable material properties of the piezoelectricand elastic layers, but also their thicknesses, to improve the smartstructure's fracture strength within a specified range.

Towards a fracture mechanics for brittle piezoelectric and dielectric materials

A theoretical fracture mechanics for brittle piezoelectric and dielectric materials is developed consistent with standard features of elasticity and dielectricity. The influence of electric field and mechanical loading is considered in this approach and a Griffith style energy balance is used to establish the relevant energy release rates. Results are given for a finite crack in an infinite isotropic dielectric and for steady state cracking in a piezoelectric strip. In the latter problem, the effect of charge separation in the material and discharge in the crack are considered. Observations of crack behavior in piezoelectrics under combined mechanical and electrical load are discussed to assess which features of the theory are useful.

Energy density theory formulation and interpretation of cracking behavior for piezoelectric ceramics

Any attempt made to separate energy into electrical and mechanical parts may lead to inconsistencies as they do not necessarily decouple. This is illustrated by application of the energy density function in the linear theory of piezoelasticity. By assuming that a critical energy density function prevails at the onset of crack initiation, it is possible to establish the relative size of an inner and outer damage zone around the crack tip; they correspond to the ligaments at failure caused by pure electric field and pure mechanical load. On physical grounds, the relative size of these zones must depend on the relative magnitude of the mechanical and electrical load. Hence, they can vary in size depending on the electromechanical material and damage resistance properties. Numerical results are obtained for the PZT-4, PZT-5H, and P-7 piezoelectric ceramics. These two ligaments for the two damage zones may coincide for appropriate values of the applied electrical field and mechanical load. Explicit expression of the energy density factor S is derived showing the mixed mode electromechanical coupling effects. The factor S can increase or decrease depending on the direction of the applied electric field with reference to the poling direction. This is in contrast to the result obtained from the energy release rate quantity, which remains unchanged for electric field in the direction of poling or against it.

Electric-field induced crack closure in linear piezoelectric media

Electric-field induced crack closure is studied along with its significant effect on the near tip electroelastic field in linear piezoelectric materials. First, the general conditions for crack closure are given explicitly in terms of the remote loading parameters, which delimit the applicability of the conventional traction-free model for both insulating and conducting cracks. It is found that, in a poled ferroelectric, crack closure occurs for a conducting crack parallel to the poling axis under an electric field applied in the poling direction, and for an insulting crack perpendicular to the poling axis under an electric field applied opposite to the poling direction. Further, based on the assumption that the normal traction and displacement are continuous while the tangential traction vanishes along the closed crack, the mixed boundary value problems are solved and the exact solutions are obtained for both closed insulating and conducting cracks. One desirable feature of the solution is that the condition for non-positivity of the normal traction on the closed crack faces is identical to the condition for crack closure. Additionally, the present solutions predict that electric-field loading causes a non-zero mode-I stress intensity factor at a closed insulating or conducting crack. This result is in sharp contrast to the conventional traction-free crack model which predicts that an electric field cannot produce any stress intensity factor at cracks in linear piezoelectric materials.

Crack tip energy release rate for a piezoelectric compact tension specimen

A theoretical fracture mechanics for brittle piezoelectric materials is summarized consistent with standard features of elasticity and dielectricity. The influence of electric field and mechanical loading is considered in this approach and a Griffith style energy balance is used to establish the relevant energy release rates. Finite element results are given for a compact tension specimen having properties consistent with the piezoelectric material PZT-4. The influence of the crack opening displacement on the electric field adjacent to the crack is considered. Observations of fracture behavior in a compact tension specimen composed of PZT-4 obtained by Park and Sun (J. Amer. Ceram. Soc. 1995;78:1475–1480) are used to assess the relevance of the theoretical results.

Self-strained piezothermoelastic composite beam analysis using first-order shear deformation theory

Abstract The static response of beams constructed of graphite–epoxy and piezoelectric laminae (hybrid laminate) subjected to electric field and thermal (i.e. self-strained) loading is considered. Two theoretical formulations are considered: uncoupled which ignores the `direct piezoelectric effect' (induced electric field due to variation in stress), and `coupled' which includes the direct piezoelectric effect. A hierarchical finite element approximation of the governing equations using reduced material stiffness coefficients is developed. The electromagnetic potential is assumed to vary piecewise linearly through each piezoelectric lamina and the lamina surface that is in contact with a structural lamina is assumed to be grounded. Beam displacement theory is based on Reissner–Mindlin shear deformation theory. Sample problems are presented demonstrating the accuracy of the developed finite element model, and the response of hybrid laminates to self-strained loading.

Dynamic bending of a symmetric piezoelectric laminated plate with a through crack

The dynamic theory of linear piezoelectricity is applied to analyze the scattering of time harmonic flexural waves by a through crack in a symmetric piezoelectric laminated plate subjected to electric field loading. An incident wave giving rise to moments symmetric about the crack plane is considered. Piezoelectric layers are added to the upper and lower surfaces. Classical lamination theory is extended to include dynamic piezoelectric effects. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations, the solution of which is then expressed in terms of a Fredholm integral equation of the second kind. The dynamic moment intensity factor vs. frequency is computed and the influence of the electric field on the normalized values is displayed graphically.

Numerical analysis of ferroelectric/ferroelastic domain switching in ferroelectric ceramics

A numerical approach predicting the behavior of ferroelectric ceramics under electric field and mechanical loading is proposed in this paper. In the model, macroscopic properties of ferroelectric ceramics are determined by microscopic structures. Ferroelectric ceramics are seen to be composed of many domains with different orientations, and domain switching is the source of the nonlinear constitutive behavior of the ferroelectric ceramics. Numerical calculations based on the model were carried out, and the computational results are compared with the experimental results, which shows the two sets of results consist with each other. The calculation approach can provide a guidance for the ceramics component design.

The strain response of piezoelectric multilayer actuators under combined action of electric field and in-plane uniform load

The driving field governed strain of lead zirconate titanate piezoelectric multilayer actuators have been made within the 107 N/m2 stress and the 3 · 106 V/m triangle-like upward-down-ward driving voltage. A slow strain component as well as a specific relaxation pattern are detected being additional to the periodic part and attributed to the trapped space charge effects favored by nonuniform electric field of the multilayer.

Bending of a Symmetric Piezothermoelastic Laminated Plate with a Through Crack

FOLLOWING the theory of linear piezoelectricity, we consider the response of a cracked composite plate with attached piezoelectric polyvinylidene fluoride layers subjected to mechanical, thermal and electric field loading. Piezoelectric layers are added to the upper and lower surfaces. Classical lamination theory is extended to include piezothermoelastic effects, and the bending problem of a symmetric piezoelectric laminated plate with a through crack is considered. Fourier transforms are used to reduce the problem to the solution of a pair of dual integral equations. The integral equations are solved exactly and the moment intensity factor is expressed in closed form.

The effect of uniaxial stress on the electro-mechanical response of 8/65/35 PLZT

8/65/35 PLZT is characterized under stress and electric field loading above the coercive field. Strain—electric-field and electric-displacement—electric-field hysteresis loops are measured at various compressive stress levels showing the effect of stress on the electro-mechanical coupling. Stress—strain curves are run at zero electric field, showing that depolarization begins at as little as 5 MPa. The limitations of linear constitutive modeling and the limitations of this composition of PLZT as an actuator material are examined. The “yield” or ferroelastic switching stress is suggested as a good criteria for assessing the capability of actuator ceramics. This parameter is an indication of the actuation limitations of the material. An equivalence of the slopes of the strain—electric-field curve at several compressive stress levels and the electric-displacement—stress curve at the same stress level is observed. This suggests that the conjugacy of the piezoelectric coefficients may hold during path dependent polarization switching.

A note on magnetoconvection in a vertical enclosure

The combined effect of viscous and ohmic dissipations on magnetoconvection in a vertical enclosure heated at the vertical side walls in the presence of applied electric field parallel to gravity and magnetic field normal to gravity is investigated. The coupled non-linear equations governing the motion are solved both analytically valid for small buoyancy parameter N and numerically valid for large N. Solutions for large N reveal a marked change in velocity profile, mass flow rate, skin friction and rate of heat transfer. These results are presented for various Hartmann number M, electric field loading parameter E and buoyancy parameter N. It is shown in the case of open circuit (i.e. E ≠ 0) that the effect of magnetic field is to increase both the velocity and temperature in contrast with the short circuit case (i.e. E = 0). The results for the case when the walls are maintained at the same temperatures (i.e. T 1 = T 2) are obtained as a particular case.

Piezothermoelastic composite plate analysis using first-order shear deformation theory

The response of composite plates constructed of graphite/epoxy laminae with an attached piezoelectric polyvinylidene fluoride layer subjected to mechanical, thermal and electric field loading is considered for various length-to-depth and aspect ratios. First-order shear deformation theory is extended to include the piezothermoelastic response of composite plate structures. Analytic results are obtained for a plate simply supported along all edges. A nine-node Lagrangian finite element formulation is established and results are presented for simply supported or fixed boundary conditions. Numerical results show that moderately thick piezothermoelastic composites are sensitive to shear deformation, but increasing plate aspect ratio reduces the shear deformation influence.

Entrance flow in a MHD channel with Hall and ion slip currents

The problem of two-dimensional MHD flow in the entrance region of a rectangular channel is solved with generalized Ohm's law under externally applied, electric field loading conditions. The magnetic Reynolds number is assumed to be small and the induced magnetic field is neglected.