Effects of electric field and poling on the mode I energy release rate in cracked piezoelectric ceramics at cryogenic temperatures

We discuss the mode I energy release rate of a rectangular piezoelectric material with a crack under electromechanical loading at cryogenic temperatures. A crack was created normal or parallel to the poling direction, and electric fields were applied parallel or normal to the poling. A plane strain finite element analysis was carried out, and the effects of electric field and localized polarization switching on the energy release rate were discussed for the piezoelectric ceramics at cryogenic temperatures.     

Reduction in energy release rate for mode I fracture of a fibre with a cracked coating layer due to small-scale interfacial debonding

In order to predict the effect of small-scale interfacial debonding on the energy release rate at a crack tip for mode I fracture of a fibre with a cracked coating layer, an approximate calculation method has been presented. The relation of debonding length, thickness of the coating layer and ratio of elastic modulus of the coating layer to that of the fibre, to the energy release rate of the fibre was calculated for some examples. It was demonstrated that small-scale debonding reduces the energy release rate and, therefore, effectively prevents reduction in fibre strength.     

Effect of composition on rate dependence of ferroelastic/ferroelectric switching in perovskite ceramics

Abstract

The process of ferroelectric/ferroelastic switching is rate dependent as evidenced by the frequency dependence of the coercive field/stress in polarisation/strain–electric field/stress loops. The rate dependence of domain switching has been investigated in different compositions of ferroelectric/ferroelastic perovskites by studying their stress–strain hysteresis loops. Stress–strain loops were generated by applying a static compressive load and then superimposing cyclic compressive loads of different amplitudes and frequencies. The stress–strain loops were fitted using a Rayleigh type relationship, whose parameters characterise the intrinsic and extrinsic contributions to the strain. Using these parameters, the rate dependence of the extrinsic domain wall contribution was investigated.     

Studies of the temperature dependence of the dielectric breakdown field in molecular Langmuir films

Temperature dependence studies of the dielectric breakdown field in thin films have played a fundamental role in the theoretical development of the subject. Furthermore, owing to their potential importance in thin film dielectric devices, it has become desirable to study the breakdown characteristics of “built-up” Langmuir films at various temperatures. This paper presents a systematic study of the temperature dependence of the breakdown field in built-up Langmuir films of barium salts of fatty acids (CH₃(CH₂)_n?2COOH) of different chain lengths sandwiched between aluminium electrodes. These films have been found to be well suited for such studies. The breakdown field is found to depend weakly on temperature. A qualitative interpretation of the results is given. Our experimental findings, presented here, may prove useful in the development of dielectric devices based on these films.     

An analytical analysis of energy release rate in bonded composite joints in a mode I condition

A complete analytical solution of mode I strain energy release rate, G_I, was derived for bonded composite joints based on an augmented double cantilever beam (DCB) model. Good agreement was obtained between current and existing comparable theoretical solutions for this joint with a long adhesive bond. For a short bond length joint, the current solution can greatly reduce the degree of the mathematical singularity encountered in analyses of thick, short beams and avoid it entirely for thin, long beams. A correlation between the current theoretical and associated ASTM solutions was established. A bonded DCB laminate test case was conducted, and good agreement was obtained between the experimental and current theoretical results. Commentary was included regarding the tested critical strain energy release rate and the deduced critical adhesive peel stress.     

The energy release rate and the J-integral in nonlocal micropolar field theory

The recent theory of nonlocal micropolar continuum is used to derive explicit expressions for both the energy release rate and J-integral. It was shown that this J-integral has a physical meaning of the energy release rate and, for homogeneous body with the straight crack, is path independent. It was also shown that the influence of nonlocality is contained in J-integral which allows one to discuss several special cases.     

Changes in the activation energy and the rate of hydrogen release from neutral media due to deformation

It is shown that plastic deformations of metals govern the kinetics of hydrogen release (by decreasing the work function of escape of an electron into solution) and are a controlling factor in the processes of hydrogenation and crack growth by a hydrogen mechanism.Karpenko Physicomechanical Institute, Ukrainian Academy of Sciences, L'viv. Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 29, No. 6, pp. 16–22, November–December, 1993.     

On the effect of remanent polarization on electro-mechanical fields near an elliptic cavity in poled or depolarized piezoelectric ceramics

In this paper the effect of remanent polarization on electric-mechanical fields near an elliptic cavity in piezoelectric ceramics is studied. The analysis is based on the application of exact electric boundary conditions at the rim of the elliptic cavity, thus avoiding the common assumption of electric impermeability. Expressions for electromechanical fields near the elliptic cavity are derived in a closed form in terms of complex potentials. The result shows that the problem of remanent polarization is similar to the problem of general strain mismatch and the effect of remanent polarization on fracture in poled or depolarized piezoelectric ceramics can not be omitted. When the permitivity of the medium in a cavity is small, the effect of remanent polarization is identical to the effect of a considerable strong positive electric field and the tangent stress at the major axial apex of the elliptical cavity is tensile. Such behavior explains why the positive electric field promotes the crack growth while the negative electric field retards the crack growth and accounts for the anisotropy of fracture toughness under mechanical loads. The results show that the effect of remanent polarization on electromechanical fields near an elliptic cavity depends not only on the geometry of the elliptic cavity, i.e. the ratio of the minor semi-axis to major semi-axis, but also on the ratio of permitivity of the medium in the cavity to permitivity of the piezoelectric ceramic.     

Characterization of a cracked specimen with full-field measurements: direct determination of the crack tip and energy release rate calculation

The crack characterization in a pre-cracked aluminum specimen is investigated in this study using the grid method. The images of this grid are analyzed to provide the crack tip location as well as the displacement and strain fields on the surface of the specimen during a tensile test. Experimental data are used to calculate the energy release rate with the compliance method A fracture analysis is also performed using the invariant M $\uptheta $ integral in which both real and virtual displacement fields are introduced. This integral is implemented in the finite element software Cast3M. Both approaches give similar results in 2D case.     

One dimensional polar mechanical and dielectric responses of the ferroelectric ceramic PZT 65/35 due to domain switching

The constitutive relations and rate laws proposed by Chen and Peercy[l] have been successfully implemented in describing the one dimensional polar mechanical and dielectric responses of the ferroelectric ceramic PZT 65/35 to a slowly varying cyclic electric field ($\text{period > 1 s}$). In particular, we are interested in the consequences of domain switching due to the applied field and the results associated with the butterfly and hysteresis loops. An extensive experimental program has been carried out to obtain simultaneous time resolved measurements of the mechanical strain, the electric displacement and the applied field. The excellent agreement between numerical and experimental results indicates that we are beginning to gain considerable insight into the fundamentals of domain switching.     

“Peak effect” in the magnetic field dependence of the transport critical-current density in high-T c superconducting ceramics

The maximum observed in the magnetic field dependence of the transport critical-current density of high-T _c superconducting ceramics was analyzed. Transport critical current and magnetization measurements performed on Bi(Pb)-Sr-Ca-Cu-O bulk sintered samples allowed us to conclude that such a maximum may result from the influence of demagnetization effects at low applied field values and an increase of the intergrannular pinning at higher fields.     

The surface effect on the strain energy release rate of buckling delamination in thin film-substrate systems

Gurtin-Murdoch continuum surface elasticity model is employed to study the buckling delamination of ultra thin film-substrate system. The effects of surface deformation and residual stress on the large deflection of ultra thin film are considered in analysis. A concept of effective bending rigidity (EBR) for ultra thin plate is proposed on the basis of Gurtin-Murdoch continuum theory and the principle of minimum potential energy. The governing equations with EBR are formally consistent with the classical plate theory, including both small deflection and large deflection. A surface effect factor is introduced to decide whether there is need to consider the surface effect or not. Combining the buckling theory and interface fracture mechanics, we obtain analytical solutions of the critical buckling load and the energy release rate of the interface crack in the film-substrate system. It is seen that the surface deformation and residual stress have significant effects on the buckling delamination of ultra thin film-substrate system.     

Fracture mechanics approach to facesheet delamination in honeycomb: measurement of energy release rate of the adhesive bond

Two types of experiments were designed and performed to evaluate the adhesive bond in honeycomb sandwich panels. The tensile bond strength between the facesheet and the core was determined through the flatwise tension test. The fracture toughness of the bond line was measured through the double cantilever beam test. Fracture toughness values varied for different facesheet thicknesses and core materials. Toughness was also different for the bag and tool sides of the panels for all specimen types.     

A 3-D approach to the calculation of the energy release rate in some fracture problems

A 3-D ellipsoidal flaw model is sufficiently versatile to cover a wide variety of flaw shapes: existing 2-D flaw models are special cases. The energy release rate from an ellipsoidal flaw in an infinite medium may be calculated by both a strain method and a displacement method. Solution techniques for both tension and compression are presented. The results calculated by both methods are in excellent agreement with available explicit results. The simpler and more efficient strain method is preferred in the calculation of the energy release rate for various flaws, except for line cracks and flat cracks subject to tensile stress normal to the crack plane. The 3-D formulation has considerable promise for providing understanding of the effects of various parameters on the energy release rate under triaxial stress states.     

Spatial variations of field polarization and phase in microwavecavities: application to the cesium fountain cavity

Wall losses in microwave cavities will generate a phase difference between the components of the field, and give rise to spatial phase variations which are related to the geometry of complicated shaped metal boundaries. Such effects are important to the design of the cavities used in the field of atomic frequency standards. Past attempts at calculating spatial phase variations in microwave cavities have been either limited to 1-D models or based upon an idealized model of the cavity, which simplifies its boundary shapes and neglects the effect of the source. In this paper, a numerical implementation of an electromagnetic field approach is used to overcome these limitations. The finite element method (FEM) is used to solve the driven form of the electromagnetic wave equation. The results show good agreement with transmission line predictions for a structure having simply shaped metal walls. The spatial phase distribution is then calculated for a 2-D approximation of the fountain cavity operating in the cylindrical TE₀₁₁ mode, which has been recommended for use in a Cs fountain frequency standard. A physical interpretation of the gradient of the phase in the cavity is presented, which shows it to be proportional to power flow     

Calculation of the crack tip parameters in the holed‐cracked flattened Brazilian disk (HCFBD) specimens under wide range of mixed mode I/II loading

In this paper, the crack tip parameters including the stress intensity factors (K_I and K_II), T‐stress and the third terms of the stress field (A₃ and B₃) are determined comprehensively for a disk‐type sample named holed‐cracked flattened Brazilian disk (HCFBD) under various combinations of mode I and mode II loading. The HCFBD specimen is a circular disk containing a central hole in which the initial cracks are created radially from the hole circumference. Moreover, the ends of HCFBD are flattened for the sake of convenient loading. Performing enormous finite element analyses and calculating the stress intensity factors K_I and K_II, the states of pure mode II are determined for different configurations of HCFBD. Furthermore, the sign and magnitude of parameter A₃ which plays an important role to justify the geometry and size effects on the fracture toughness of quasi‐brittle materials are also determined for HCFBD with different geometrical ratios.     

Electric field dependence of conductivity in thin amorphous films and bulk glasses of the system Ge4Se6−xTex

The electric field dependence of the conductivity of amorphous Ge₄Se_6−xTe_x (x = 0, 0.5, 1.0 or 1.5) is strongly influenced by the way in which the samples are prepared. Bulk samples are compared with thin films of identical composition prepared by vacuum evaporation at relatively low temperature or by flash evaporation. Differences in the shape of the field dependence of the conductivity are discussed in terms of a conductivity model which takes into account the Poole-Frenkel effect with intrinsic defects of the valence alternation pair type and hopping contributions from charge transport via localized states at the band edges. It is shown that the preparation technique influences the density of intrinsic defects and localized states at the band edges resulting in a different field dependence of the conductivity.     

A computational study of the piezoelectric response due to the material effect in periodic, single island thin films and the geometric effect in periodic, bi-island thin films

The electromechanical response of a square-periodic array of circular piezoelectric (PE) thin films alternating with non-piezoelectric (NPE) films is studied in this paper. The material effects are studied for four film/substrate combinations in absence of NPE films for which it is found that if d_zxx ? d_zzz (z-axis being normal to the interfacial plane between the film and the substrate), it results in reduced substrate bending leading to reduced degradation in the electromechanical response of the thin film. The bi-island structure is studied for zinc oxide on strontium titanate, and, in general, it is seen that the NPE films not only reduce degradation of the electromechanical response of the PE films but also increase their internal stresses; the effect on the former is less than the latter. These effects are most prominent when the circular NPE thin films fill the space between the PE thin films and are elastically very stiff compared to the substrate.