Hydrostatic Response Research Articles

A multi‐mode approach to finite, three‐dimensional, nonlinear viscoelastic behavior of polymer glasses

In this study a phenomenological constitutive model is proposed to describe the finite, nonlinear, viscoelastic behavior of glassy polymers up to the yield point. It is assumed that the deformation behavior of a glassy polymer up to the yield point is completely determined by the linear relaxation time spectrum and that the nonlinear effect of stress is to alter the intrinsic time scale of the material. A quantitative three‐dimensional constitutive equation for polycarbonate as a model polymer was obtained by approximating the linear relaxation time spectrum by eighteen Leonov modes, all exhibiting the same stress dependence. A single Leonov mode is a Maxwell model employing a relaxation time that is dependent on an equivalent stress proportional to the Von Mises stress. Furthermore, a Leonov mode separates the (elastic) hydrostatic and (viscoelastic) deviatoric stress response and accounts for the geometrical complexities associated with simultaneous elastic and plastic deformation. Using a single set of parameters, the multi‐mode Leonov model is capable of describing realistic constant strain rate experiments, including the strain rate dependent yield behavior. It is also capable of giving a quantitative description of nonlinear stress‐relaxation experiments.

A model for the hydrostatic pressure response of a 1-3 composite

An analytical model has been developed for predicting the mechanical response of a composite cylinder that is composed of a solid right circular cylinder of one material surrounded by a cylindrical tube composed of some other material. It is assumed that there is no slippage at the boundary between the two phases. The model employs, throughout, the exact equations of linear elasticity and, thus, provides a solution that is exact for the specific boundary conditions that are imposed, In this paper, the specific case of hydrostatic pressure applied to the surface of the composite cylinder is discussed, The model yields the displacement and stress fields throughout the entire structure. The model was verified by comparing the results with a finite element model at several surfaces and interfaces in the structure, The model can be readily applied to the analysis of passive composite structures as well as to some of the recent active materials such as 1-3 piezocomposites.

A design for optimizing the hydrostatic performance of 1–3 piezocomposites

Abstract Improvement in the hydrostatic performance of 1-3 piezocomposites can be obtained through amplification of the axial stress or reduction of the lateral stress in the piezoceramic phase. In the current work, a graded interlayer design is introduced which enables both reduction in lateral stress and axial stress amplification, simultaneously. The interlayer is stiffer at the edges of the rod to enhance load transfer and axial stress amplification and softer along the interior region of the rod to attenuate lateral stresses. The hydrostatic response of a composite with such a graded interlayer is evaluated using the finite-element method. The present graded interlayer design provides improved electromechanical coupling and greater design flexibility.

Relative Contribution of External Sources of Mean Sea-level Variations at Port Sudan, Red Sea

Analysis of daily mean sea level over a 6-year period (1986–91) reveals, for the first time, the presence of a semi-annual component in addition to the annual component. Their amplitudes are 6·6 and 11 cm respectively. Variances explained by the two cycles vary significantly over the study period and average 16 and 44% respectively. The annual changes are induced by the prevailing wind regime while the semi-annual variation is associated with the evaporation rate. The spectrum of evaporation shows that the semi-annual cycle is the dominant variant in the moisture flux. Water temperature and wind speed exhibit slight semi-annual variations too. On the other hand, spectral analysis of atmospheric pressure and air temperature shows that their variability is mainly due to the annual cycle. The maximum hydrostatic response of sea level is only about 15% and lags 2 days behind with atmospheric pressure. The cross-spectrum between daily residuals of sea level and those of atmospheric pressure shows that the hydrostatic response is frequency-dependent with a maximum response occurring at 0·125 cycles day −1. An autoregressive first order model [AR(1)] has been calibrated to fit the daily residuals which explains 67% of the variance.

A high sensitivity hydrostatic piezoelectric transducer based on transverse piezoelectric mode honeycomb ceramic composites

A new piezoelectric composite transducer based on the ceramic honeycomb structure is introduced. The transducer is operated in the transverse piezoelectric (TP) d/sub 31/ mode. The ceramic honeycomb configuration enables one to fabricate a TP honeycomb transducer by either embedding a honeycomb ceramic skeleton into a soft polymer matrix to form a composite or by blocking the openings of the honeycomb cells with thin layers of epoxy to form an end-capped honeycomb structure. With the unique honeycomb configuration and TP operation mode, the piezoelectric d/sub 33/ response of the ceramic is nearly eliminated and the piezoelectric responses from the three orthogonal directions add together when the transducer is subjected to a hydrostatic pressure. As a result, the transducer exhibits exceptionally high hydrostatic piezoelectric response.

Gravity anomalies and the flexure of the lithosphere in the Karakoram, Pakistan

The negative correlation between gravity anomalies in mountain regions and the topographic height implies a mass deficency beneath the range and adjacent regions. Classical compensation schemes in which roots of constant density form at a depth proportional to the topographic height (Airy scheme) or individual columns of laterally variable density develop to a constant depth (Pratt scheme) enable only part of the anomalies to be modeled and provide a “static” description of the structure of the crust and upper mantle, regardless of the vertical and horizontal motions associated with the origin and evolution of mountain belts. Early studies of isostatic anomalies across the Karakoram range, in northern Pakistan, have shown that the region is not in isostatic equilibrium in the Airy sense and have pointed to the need of a more refined model of the forces and stresses shaping the lithosphere than classical isostasy. The concept that the lithosphere should respond by flexure to applied loads as a thin, elastic, semi‐infinite plate buoyant on a denser, inviscid fluid is used here as the basis to compute model Bouguer anomalies, estimate by least squares the deformation of the plate, and constrain some of the plate's elastic parameters. It is assumed that the forces responsible for the deformation are the topographic load, the hydrostatic response, and the elastic stresses within the plate. The plate itself is assumed to be separated into an Indian and an Asian portion, each with its own equivalent elastic thickness. At the border between the two portions an empirical infracrustal point load is assumed to act vertically. Gravity anomalies are then computed along five profiles crossing the range, as a function of the abscissa of the border point, the load acting at this point, the elastic thicknesses of the Indian and Asian portions of the plate, and the density contrast across the median section of the plate. The corresponding numerical values and associated formal uncertainties are determined by a least squares fit of the model anomalies to the observed Bouguer anomalies, along each of the five independent profiles. The postfit residuals are found to have essentially zero mean and an rms (root mean square) dispersion of the order of 20 mGal, which is consistent with the expected overall accuracy of the “observed” Bouguer anomalies interpolated to the profiles. The distribution of the post fit residuals still shows systematic components at the level of a few tens of mGal, that are likely to be caused by local, shallow geological structures. Overall the peak‐to‐peak excursion of the residual anomalies is considerably smaller than the classical isostatic anomalies for the same region. It is found that (1) the line connecting the estimated abscissas of the border points on each profile follows closely suture lines which have been independently identified from geological data and could be associated with the center of mass of the Kohistan‐Ladakh island arc considered as a buried load; (2) for all profiles the elastic thickness of the Indian plate is systematically less than for the Asian plate, typically 80–100 km for India and 100–120 km for Asia; (3) there is a tendency of the elastic thickness of both portions to increase moving NW, towards the Pamirs. The gravity data are thus consistent with a relatively rigid Asian plate in the Tarim basin, unlike the Central Himalaya where Tibet, being indented by India, has zero strength.

A new transverse piezoelectric mode 2-2 piezocomposite for underwater transducer applications

In this paper, we present a new type of 2-2 piezoelectric ceramic-polymer composite operated at the transverse piezoelectric mode (TP). The new TP mode piezocomposite has exceptionally high hydrostatic piezoelectric response, high reliability, and can be made at low cost. Based on the isostrain approximation, an analytical model is developed to analyze and optimize the effective piezoelectric and the effective elastic properties of the composite. Several composites with the new structure were fabricated and tested. The calculated and experimental results show good agreement. It is shown that a TP 2-2 composite made of PZT plates in a soft polymer matrix with elastically unidirectional face plates yields an effective hydrostatic piezoelectric coefficient d/sub h/ of 6000 (pC/N) and a hydrostatic figure of merit d/sub h/g/sub h/ higher than 30000 (10/sup -15/ m/sup 2//N). >

Improving hydrostatic performance of 1-3 piezocomposites

Type 1-3 piezocomposites consist of aligned piezoelectric rods embedded in a passive polymer matrix and have better hydrostatic behavior than single-phase piezoelectric materials. The improved hydrostatic performance of 1-3 piezocomposites comes from two major effects: the axial stress amplification and the lateral stress reduction in the piezoelectric rods. An improved micromechanical model has been developed to predict the hydrostatic response of 1-3 piezocomposites and to examine the interaction between the piezoelectric rods and the polymer matrix. Effective hydrostatic piezoelectric constants for the composite are predicted and compared to those calculated using a generalized plane strain model. The influence of matrix stiffness, interlayer stiffness, rod aspect ratio, and rod volume fraction on the load transfer and the effective hydrostatic piezoelectric coefficient was investigated. The results obtained provide quantitative information on how various parameters affect the hydrostatic response of the composites.

Effects of face plates and edge strips on hydrostatic piezoelectric response of 1-3 composites

Abstract Piezoceramic-polymer composites with 1–3 connectivity provide higher hydrostatic figure of merit dhgh , and low density, which make them attractive for underwater applications. By incorporating rigid face plates on the composite electrode surfaces, the transverse piezoelectric response can be reduced effectively and dh increased significantly. When edge strips are put on the lateral dimensions, the hydrostatic response of the composite may be further improved, depending on the ratio of the sample thickness to the sample lateral dimensions and the elastic properties of the edge strips. In this work the effects of the rigid face plates and the edge strips on the piezoelectric response of 1–3 composites with different lateral dimensions were investigated. All the experimental features can be well accounted for by using the shear-coupling model developed recently by us and the isostrain model. Based on these results the relationship between the dh of the face plated 1–3 composite and the elastic prop...

Densification and Grain Growth of Porous Alumina Compacts

Densification and grain growth of porous alumina compacts during various high‐temperature processes were investigated. Experimental data were obtained for densification and grain growth of alumina powder during hot pressing. A set of constitutive equations was proposed based on the constitutive equations by Helle et al.1 for hydrostatic response and by Rahaman et al.2 for deviatoric response. Theoretical results from the proposed constitutive equations were compared with various experimental data for alumina powder compacts in the literature, including pressureless sintering, sinter forging, and hot pressing. The proposed model well predicts the densification and grain growth of alumina compacts.

Piezoelectric response of a three coaxial cylinder model

Abstract The response of a 1-1-3 transducer is modeled as three coaxial cylinders with the center cylinder as the piezoelectric element. Different combinations of properties for the outer two cylinders have been used to determine the maximum hydrostatic response. For a 20v/o PZT-5H composite with a 25v/o soft filler in a 55v/o hard tube the maximum predicted effective dh° is 110 pC/N. The maximum dh° for a 1–3 composite modeled by two coaxial cylinders is 90 pC/N while the base ceramic is 45 pC/N. A maximum effective gh° of 20 mVm/N is also predicted for the same combination of materials. The d33° and d31° moduli are maximized for soft fillers and tubes, but have values of 380 and 135 pC/N respectively for the combination of materials that maximize the dh° value. A rigid end cap attached to the ceramic, which bears the axial load, gives a five fold predicted increase in the dh° response. The d33° and d31° moduli are again maximized for soft fillers and tubes, but have values of 590 and 210 pC/N, respectively, for the combination of materials that maximize the dh° value in the above case.

Axially distorted 3-3 piezoelectric composites for hydrophone applications

Abstract Application of reticulated ceramic technology to the fabrication of 3–3 lead zirconate-titanate (PZT)/Spurr epoxy composites has been investigated. Use of this technology provides a substantial improvement in manufacturability over other methods. Directional distortion of the ceramic structure to enhance the composite's hydrostatic response is also possible. Composite fabrication is described and the effects of distortion on the piezoelectric properties are presented. The results for K33 and g33 are found to be comparable to other 3–3 PZT/epoxy composites while d33 and hydrostatic gh are reduced with density.

Piezoelectric composites of the 1–3 type used as underwater sound sources

Piezoelectric composites with 1–3 connectivity used in the thickness mode have traditionally used a relatively rigid polymer as the matrix encapsulant to force uniform surface motion. Finite element analyses are employed to show that these rigid polymers constrain the piezoelectric rod motion sufficiently to reduce rod displacements by 50% or more. The magnitude of the reduction depends upon the ceramic volume fraction, the rod aspect ratio, rod spacing, and of course the stiffness of the matrix. Further, it has been shown [W. A. Smith, ONR Tech Note (31 May 1991)] that the hydrostatic response, rather than the thickness mode alone, controls the performance of 1–3 composites used as underwater sound sources. It is shown in this paper that efficient lightweight underwater sound sources can be produced by: (1) using lightweight rigid cap plates and a very compliant matrix polymer to produce uniform surface motion comparable to the motion of the unconstrained rod, and (2) using rigid edge strips bonded to the cap plates to prevent edge motion, thereby effectively limiting the transmitting response to the thickness mode. [Work supported by ONR.]

Piezoelectric tubes and tubular composites for actuator and sensor applications

Piezoelectric actuators and sensors made with a tubular structure can provide a great agility of effective response in the radial direction. For a radially poled piezoelectric tube, the effective piezoelectric constant in that direction can be tuned to be positive, zero or negative by varying the ratio of the outer radius (Ro) to the inner radius (ro) of the tube. For a suitable ratio of Ro/ro, this effective constant can also be changed in sign or set to zero by adjusting the d.c. bias field level for tubes made of electrostrictive materials. Therefore, one can make a piezoelectric transducer with all the effective piezoelectric tensile constants having the same sign. End-capped thin-walled tubes also exhibit an exceptionally high hydrostatic response, and the small size of the tubular structure makes it very suitable for integration into a 1–3 composite which possesses low acoustic impedance and high hydrostatic response.

Modeling 1-3 composite piezoelectrics: hydrostatic response

A simple physical model of 1-3 composite piezoelectrics that was advanced for the material properties relevant to thickness-mode oscillations is extended to address the hydrostatic response. The model is valid when the lateral spatial scale of the composite is sufficiently fine that the composite can be treated as an effective homogeneous medium. Expressions are derived for the composite's material parameters in terms of the volume fraction of piezoelectric ceramic and the properties of the constituent piezoelectric ceramic and passive polymer. The results are similar to those derived by Haun and Newnham (1983, 1986) using a parallel-series connectivity model. The model is illustrated by analyzing composites made from conventional PZT5 and anisotropic modified lead titanate piezoelectric ceramics. For PZT5, the composite structure enhances its hydrostatic charge coefficient, hydrostatic voltage coefficient, hydrophone figure of merit, and hydrostatic coupling coefficient, while three of these quantities fall short of their pure ceramic values in the modified lead titanate composites. The shortfall is due to an enhanced composite that arises from lateral stress on the polymer being transferred to a longitudinal stress along the ceramic rods by the Poisson effect in the polymer, thus producing a charge through the ceramic's d(33).

Ceramic‐air composites for hydrostatic sensing

The hydrostatic response (dh) of conventional PZT ceramic is only about 10% to 30% of its biaxial (d33) response. This is expressed in dh = d33 (1–2 γ), where γ is Poisson's ratio. Higher dh values can then be obtained by lowering the Poisson's ratio of the ceramic. This can be accomplished, without lowering the d33 value significantly, by introducing into the ceramic arrays of voids, ordered in such a manner that void‐free columns of ceramic are maintained between the voids. The deposition of fugitive ink through photolithographically prepared screens onto unfired ceramic tapes, together with stacking, laminating, and subsequent firing, provide a method for the controllable preparation of PZT sensors. These not only exhibit dh values of ⩾200 pC/N, but the voids also control the capacitance, so that gh values of ⩾0.03 Vm/N are obtained. Capacitance values above 400 pf in a 0.5×0.5×0.1‐in. sensor chip permit some cable capacitance and the use of bipolar rather than of FET preamplifiers. Hydrostatic tests of such devices have shown these to be also rugged, easy to connect and use, and capable of withstanding significant hydrostatic pressures.

Hydrostatic Response of Thick Laminated Composite Cylinders

This study discusses the results of a layer-by-layer analysis of a thick-walled cross-ply graphite-epoxy cylinder subjected to external hydrostatic pressure. The analysis, which is valid away from the ends of the cylinder and is based on a generalized plane deformation elasticity solution for each layer, considers inter- and intralaminar stresses. Cylinders with 102 layers and radius to wall thickness ratios of 5 and 10 are studied. The influence of cur ing stresses are evaluated. For possible application to testing, the response of a thick lami nated ring is compared to the response of a cylinder. The idea of smearing the 102 layers into an equivalent single layer is discussed and the results of a smeared analysis are com pared with the layer-by-layer analysis. Finally, the responses of glass-epoxy and metallic cylinders are compared with the response of the graphite-epoxy cylinder. The primary findings of the study are: (1) the radial strain distribution through the thickness of the graphite-epoxy cylinder changes from extension at the inner radius to compression at the outer radius. This is different than the radial strain distributions through the glass-epoxy and metallic cylinders. The radial strains for these cylinders are everywhere extensional. (2) The magnitude of the curing stresses are much smaller than the stresses due to hydro static pressure. (3) The smearing technique works very well, the response predicted by the single-layer analysis being indistinguishable from the response predicted by the layer-by- layer analysis. (4) The high level of orthotropy of the graphite-epoxy causes a higher fiber loading than occurs for glass-epoxy. This effect could amplify any imperfections, e.g., fiber waviness, in the compressively loaded fibers and could lead to premature failure.

(Pb, Bi)(Ti, Fe, Mn)O3/Polymer 0-3 composites for hydrophone applications

The hydrostatic piezoelectric response of composite materials incorporating (Pb1-xBix)(Ti1-xFex)O3 ceramic fillers from the highly anisotropic tetragonal region of the solid solution system in the vicinity of the morphotropic phase boundary were measured and compared. The considerable difficulty in poling and, hence, the diminished piezoelectric response encountered as the composition of the filler is shifted closer to the phase boundary was determined to be largely due to the high conductivity of the BiFeO3-rich compositions. The ceramic was modified with Mn in an attempt to lower its conductivity. Composites incorporating the Mn-doped filler poled more rapidly and easily than the undoped material and ultimately achieved a hydrostatic figure of merit, dhgh, 40% better than that observed for the undoped samples. Among the samples investigated, the highest hydrostatic figures of merit were exhibited by samples containing the doped and undoped x = 0.5 fillers. The hydrostatic response remains stable over a ...

Acoustic and Elastic Properties of PZT Ceramics with Anisotropic Pores

It has been shown that anisotropic porosity in PZT reduces the d31/d33, ratio, raising the hydrostatic piezoelectric response of PZT significantly. In the present work, this behavior is related to Poisson's ratio by applying the Gibbs thermodynamic energy function, literature data for dense PZT ceramics and for materials with hexagonal crystal symmetry, and experimental results for PZT with anisotropic porosity. Acoustic as well as mechanical tests of PZT ceramics with anisotropic pores demonstrate the elastic anisotropies that cause the reduction in Poisson's ratio. The dependence of d31/d33 on Poisson's ratio is also detailed. In addition, a close relation between d31/d33 and the longitudinal acoustic velocity is demonstrated. Flexural strength tests indicate that anisotropic pores provide dhn‐enhanced PZT ceramics with significantly greater strength than isotropic pores.

Hydraulic resistance in bones of the canine shoulder

The hydraulic properties of trabecular bone were explored in both sides of normal canine shoulders by following the hydrostatic pressure response to transchondral injections of saline. In a series of isovolumetric injections at sites 9 mm beneath either joint surface, the pressure consistently rose higher and lasted longer in the humerus than it did in the scapula. Hydraulic resistance, the linear function of pressure per unit flow, averaged 8.8 times higher within the humerus than in the scapula in a second series of experiments. Hydraulic resistance fell by average factors of 9.6 in the humerus and 4.3 in the scapula when the surrounding bone was cut away to leave the injection site centered within a 1 cm ‘cube’ of trabecular bone. Direct determinations of hydraulic resistance provide a useful tool for the study of normal and abnormal physiology in trabecular bone.