W. B. Carlson

The packing density of binary powder mixtures

Abstract The maximum particle packing density in a binary powder system can be predicted by the Furnas model. The packing density is lower when the size ratio of coarse particles to fine particles decreases, and is also governed by the volume fraction of coarse or fine particles. Here an empirical equation is derived which describes the packing density as a function of the initial packing efficiencies of particles, the particle size ratio, and the volume fraction variations of the system.

The effect of electric field on mechanical strain and stress in flawed electroceramics

Abstract Electrically-induced strains and stresses in ceramic transducers and capacitors play an important role in the degradation and breakdown of these components. A computer program based on a finite difference numerical technique was used to model the electric potential and electric field near internal flaws in the ceramic.1 Using the piezoelectric and electrostrictive moduli of Pb(Zr, Ti)O3 and BaTiO3, maximum strains and stresses near cracks, delaminations, and voids were evaluated.2 Predictions are made concerning the nature of field-induced cracks emanating from macrodefects.

Analysis of World Oil Production Based on the Fitting of the Logistic Function and its Derivatives

Abstract Logistic functions were used to model the depletion of the uniform resource for the case of world oil production. Results are presented for various curve fits in order to determine the value of parameters that best match the historical record of world oil production. Calculations depict a range of resource limits, namely the ultimately recoverable resource (URR) and the peak year of production (PY) for both assumed URR (two parameter) models and variable URR (three parameter) models. Logistic fitting yields a minimum URR estimate of 1.3 terabarrels (TB) and a maximum of 5.2 terabarrels. The peak production years fall between the years 1989 and 2027. Probable values of URR based on the confluence of the logistic URR trend lines yields an estimate of 2.2 or 2.8 TB corresponding to peak production during year 2004 or year 2011, respectively.

The Modeling of World Oil Production Using Sigmoidal Functions—Update 2010

Abstract The depletion of the world oil resource based upon the logistic function has been updated and fitted to the recent history of oil production. The analysis uses data through the year 2009 and further introduces the asymmetric Gompertz function in order to account for additional oil resources. Results of these calculations depict a range of production rates under different resource limits. The characteristic curvature coefficients and the peak years of production are fitted to United States Geological Survey estimates of ultimately recoverable resource (URR) limits between 2.5 and 4.5 terabarrels (TB). The logistic fittings yield peak productions from 30.4 to 38.6 gigabarrels per year (GB/yr) for URRs from 2.5 to 3.0 TB in years 2008 through 2016. The lower probability of occurrence URRs (from 4.0 to 4.5 TB) inclusive of forms of oils yet to be introduced yield peak productions from 30.9 to 33.5 GB/yr during the years 2018 through 2023. The Gompertz function is used as the model for the lower probability URR production.

Multilayer capacitor margin stresses and electrode to dielectric thickness calculations

Abstract The mismatch of thermal expansion coefficients in co-fired multilayer capacitors (MLCs) leads to development of residual stress on cooling. These stresses are of a compressive nature for the multilayer stack and a tensile character for the ceramic margin. A closed-form stress calculation of the critical ratio of electrode thickness to ceramic dielectric thickness in the stack shows a limiting ratio of approximately 1:2. Design equations are given in order to calculate the multilayer electrode to dielectric thickness ratio. The required design parameters are the linear thermal expansion coefficients, the temperature difference, the Youngs moduli, the strength of the ceramic margin, and the ratio of active to inactive capacitor area.

Simulation of elastic stresses and polarization in piezoelectric ceramic by the finite difference method

Abstract Stresses and polarization within a piezoelectric ceramic have been simulated via numerical boundary-value analysis. A Finite Difference algorithm was written to calculate the elastic response by using the Airy stress function method. Tetragonal anisotropy in the elastic, dielectric, and piezoelectric properties were included in the model. A two-dimensional plane stress analysis is used to calculate the solution for the distribution of stresses within the ceramic. The method assumes that a uniform poling field provides alignment of elastic, dielectric, and piezoelectric properties along a preferred axis. Stresses may be applied at the boundary of the model in either a uniform and in a nonuniform manner to simulate forces imposed on the specimen. The elastic response and the resulting polarization and the stresses created are used to calculate the piezoelectric stress coefficients d 33 and d 31. Simulation results were compared with test data taken on a Berlincourt d 33 meter. The conclusions from ...

Testing of Piezoresistive Polyurethane-Fe3O4 Composites

The piezoresistance of Fe 3 O 4 particles encapsulated in polyurethane forming a composite material were studied for hydrostatic and uniaxial response. Electrical and mechanical properties were examined in composite disks with volume percents of Fe 3 O 4 loading between 35 and 54%. Uniaxial and hydrostatic loading tests were conducted for electrical resistance under mechanical stress. Data obtained for the uniaxially loaded samples indicate that resistance changes of 5 to 6 orders of magnitude can be tailored in polyurethane composites. Under hydrostatic loading testing indicates that resistance changes of 2 orders of magnitude can be obtained. Mounting the piezoresistors in a rigid epoxy improves the hydrostatic response of the samples allowing resistance change of up to 3 orders of magnitude. Further tests indicate a change of almost 5 orders of magnitude are possible when highly compliant lateral air gaps are incorporated into the sample.

Composite hydrophone devices coupling piezoelectricity and tensegrity

Abstract The concept of tensegrity as conceived by Buckminster Fuller has been incorporated into a passive hydrophone device. Tensegrity is described as the physical phenomenon that produces a stable geometric structure using solid compressional elements arranged in tandem with flexible tensional cables. In the devices built by the authors, six PZT 5H™ bars acting as compressional elements in the tensegrity structure have been coupled with tensional bands of either polyaramid or carbon fiber. This stable system is then wrapped with an outer layer of either polyaramid or carbon fiber and rubber film to form a sealed device, which is referred to as a piezotensegritive device in this paper. The six bars are arranged in parallel electrical connectivity for all devices described. The resonant frequency for these devices ranged from 19.5 to 20.3 kHz depending on the material used for wrapping the piezoelectric bars. These devices were also tested in a hydrostatic environment to determine the relevant piezoelectric coefficients. For devices wrapped with carbon fiber, dh peaked at ∼6000 pC/N and gh at ∼275 mVm/N. For devices wrapped with polyaramid, dh peaked at ∼2000pC/N and gh at ∼100mVm/N. Sensitivities from –182–195 db ref. 1V/µPa were calculated for these devices.

Modeling of piezoresistively-controlled electromechanical smart material

A finite element model of a proposed smart material was developed. This is an initial investigation into using a piezoresistive sensor in conjunction with a multilayer ceramic actuator and a resistor network as the control circuit. A device model, incorporating piezoresistive composites (with orders of magnitude change in resistivity) and piezoelectric actuators has also been constructed. The model accounts for all relevant material properties and configurations. The software also provides a method of optimizing geometry to obtain desired response. At present the 2-D case predicts a material package with a controllable compliance. This can be extended to a 3-D case consistent with available components.

Sensitivity of Predicted Oil Production to the Sigmoid Function

Abstract Mathematical parameters relating to the sensitivity of oil production are modeled by the standard sigmoid function. An analysis of the function is fitted to present and past production data for different ultimately recoverable reserve (URR) assumptions. The sigmoid exponent (S) and peak production year (P) are correlated to past production data in order to model near-term (10–15 year) production. Peak production rates are determined based upon the derivative of the fitted sigmoid function.