Quasiharmonic elastic constants corrected for deviatoric thermal stresses

The quasiharmonic approximation (QHA), in its simplest form also called the statically constrained (SC) QHA, has been shown to be a straightforward method to compute thermoelastic properties of crystals. Recently we showed that for noncubic solids SC-QHA calculations develop deviatoric thermal stresses at high temperatures. Relaxation of these stresses leads to a series of corrections to the free energy that may be taken to any desired order, up to self-consistency. Here we show how to correct the elastic constants obtained using the SC-QHA. We exemplify the procedure by correcting to first order the elastic constants of MgSiO(3) perovskite and MgSiO(3) postperovskite, the major phases of the Earth's lower mantle. We show that this first-order correction is quite satisfactory for obtaining the aggregated elastic averages of these minerals and their velocities in the lower mantle. This type of correction is also shown to be applicable to experimental measurements of elastic constants in situations where deviatoric stresses can develop, such as in diamond-anvil cells.

Identification of Elastic, Dielectric, and Piezoelectric Constants in Piezoceramic Disks

Three-dimensional modeling of piezoelectric devices requires a precise knowledge of piezoelectric material parameters. The commonly used piezoelectric materials belong to the 6mm symmetry class, which have ten independent constants. In this work, a methodology to obtain precise material constants over a wide frequency band through finite element analysis of a piezoceramic disk is presented. Given an experimental electrical impedance curve and a first estimate for the piezoelectric material properties, the objective is to find the material properties that minimize the difference between the electrical impedance calculated by the finite element method and that obtained experimentally by an electrical impedance analyzer. The methodology consists of four basic steps: experimental measurement, identification of vibration modes and their sensitivity to material constants, a preliminary identification algorithm, and final refinement of the material constants using an optimization algorithm. The application of the methodology is exemplified using a hard lead zirconate titanate piezoceramic. The same methodology is applied to a soft piezoceramic. The errors in the identification of each parameter are statistically estimated in both cases, and are less than 0.6% for elastic constants, and less than 6.3% for dielectric and piezoelectric constants.

Mechanical properties and porosity of dental glass-ceramics hot-pressed at different temperatures

The objective of this work was to evaluate biaxial-flexural-strength (σf), Vickers hardness (HV), fracture toughness (K Ic), Young's modulus (E), Poisson's ratio (ν) and porosity (P) of two commercial glass-ceramics, Empress (E1) and Empress 2 (E2), as a function of the hot-pressing temperature. Ten disks were hot-pressed at 1065, 1070, 1075 and 1080 °C for E1; and at 910, 915, 920 and 925 °C for E2. The porosity was measured by an image analyzer software and s f was determined using the piston-on-three-balls method. K Ic and HV were determined by an indentation method. Elastic constants were determined by the pulse-echo method. For E1 samples treated at different temperatures, there were no statistical differences among the values of all evaluated properties. For E2 samples treated at different temperatures, there were no statistical differences among the values of σf, E, and ν, however HV and K Ic were significantly higher for 910 and 915 °C, respectively. Regarding P, the mean value obtained for E2 for 925 °C was significantly higher compared to other temperatures.

Internal Residual Stresses in Sintered and Commercial Low Expansion Li(2)O-Al(2)O(3)-SiO(2) Glass-Ceramics

We performed Synchrotron X-ray diffraction (XRD) analyses of internal residual stresses in monolithic samples of a newly developed Li(2)O-Al(2)O(3)-SiO(2) (LAS) glass-ceramic produced by sintering and in a commercial LAS glass-ceramic, CERAN (R), produced by the traditional crystal nucleation and growth treatments. The elastic constants were measured by instrumented indentation and a pulse-echo technique. The thermal expansion coefficient of virgilite was determined by high temperature XRD and dilatometry. The c-axis contracts with the increasing temperature whereas the a-axis does not vary significantly. Microcracking of the microstructure affects the thermal expansion coefficients measured by dilatometry and thermal expansion hysteresis is observed for the sintered glass-ceramic as well as for CERAN (R). The measured internal stress is quite low for both glass-ceramics and can be explained by theoretical modeling if the high volume fraction of the crystalline phase (virgilite) is considered. Using a modified Green model, the calculated critical (glass) island diameter for spontaneous cracking agreed with experimental observations. The experimental data collected also allowed the calculation of the critical crystal grain diameters for grain-boundary microcracking due to the anisotropy of thermal expansion of virgilite and for microcracking in the residual glass phase surrounding the virgilite particles. All these parameters are important for the successful microstructural design of sintered glass-ceramics.

Residual stresses in titanium nitride thin films obtained with step variation of substrate bias voltage during deposition

In this work, a series of depositions of titanium nitride (TiN) films on M2 and D2 steel substrates were conducted in a Triode Magnetron Sputtering chamber. The temperature; gas flow and pressure were kept constant during each run. The substrate bias was either decreased or increased in a sequence of steps. Residual stress measurements were later conducted through the grazing X-ray diffraction method. Different incident angles were used in order to change the penetration depth and to obtain values of residual stress at different film depths. A model described by Dolle was adapted as an attempt to calculate the values of residual stress at each incident angle as a function of the value from each individual layer. Stress results indicated that the decrease in bias voltage during the deposition has produced compressive residual stress gradients through the film thickness. On the other hand, much less pronounced gradients were found in one of the films deposited with increasing bias voltage. (C) 2010 Elsevier B.V. All rights reserved.

Ultrasonic material characterization using large-aperture PVDF receivers

This work describes the use of a large-aperture PVDF receiver in the measurement of liquid density and composite material elastic constants. The density measurement of several liquids is obtained with accuracy of 0.2% using a conventional NDE emitter transducer and a 70-mm-diameter, 52-mu m P(VDF-TrFE) membrane with gold electrodes. The determination of the elastic constants is based on the phase velocity measurement. Diffraction can lead to errors around 1% in velocity measurement when using alternatively the conventional pair of ultrasonic transducers (1-MHz frequency and 19-mm-diameter) operating in through-transmission mode, separated by a distance of 100 mm. This effect is negligible when using a pair of 10-MHz, 19-mm-diameter transducers. Nevertheless, the dispersion at 10 MHz can result in errors of about 0.5%, when measuring the velocity in composite materials. The use of an 80-mm diameter, 52-mu m-thick PVDF membrane receiver practically eliminates the diffraction effects in phase velocity measurement. The elastic constants of a carbon fiber reinforced polymer were determined and compared with the values obtained by a tensile test. (C) 2009 Elsevier B. V. All rights reserved.

MEASUREMENT OF ELASTIC PROPERTIES OF MATERIALS BY THE ULTRASONIC THROUGH-TRANSMISSION TECHNIQUE

The elastic mechanical behavior of elastic materials is modeled by a pair of independent constants (Young`s modulus and Poisson`s coefficient). A precise measurement for both constants is necessary in some applications, such as the quality control of mechanical elements and standard materials used for the calibration of some equipment. Ultrasonic techniques have been used because wave velocity depends on the elastic properties of the propagation medium. The ultrasonic test shows better repeatability and accuracy than the tensile and indentation test. In this work, the theoretical and experimental aspects related to the ultrasonic through-transmission technique for the characterization of elastic solids is presented. Furthermore, an amorphous material and some polycrystalline materials were tested. Results have shown an excellent repeatability and numerical errors that are less than 3% in high-purity samples.

Analysis of the tip roundness effects on the micro- and macroindentation response of elastic-plastic materials

In this work, the effects of indenter tip roundness oil the load-depth indentation curves were analyzed using finite element modeling. The tip roundness level was Studied based on the ratio between tip radius and maximum penetration depth (R/h(max)), which varied from 0.02 to 1. The proportional Curvature constant (C), the exponent of depth during loading (alpha), the initial unloading slope (S), the correction factor (beta), the level of piling-up or sinking-in (h(c)/h(max)), and the ratio h(max)/h(f) are shown to be strongly influenced by the ratio R/h(max). The hardness (H) was found to be independent of R/h(max) in the range studied. The Oliver and Pharr method was successful in following the variation of h(c)/h(max) with the ratio R/h(max) through the variation of S with the ratio R/h(max). However, this work confirmed the differences between the hardness values calculated using the Oliver-Pharr method and those obtained directly from finite element calculations; differences which derive from the error in area calculation that Occurs when given combinations of indented material properties are present. The ratio of plastic work to total work (W(p)/W(t)) was found to be independent of the ratio R/h(max), which demonstrates that the methods for the Calculation of mechanical properties based on the *indentation energy are potentially not Susceptible to errors caused by tip roundness.

Analysis of the effects of conical indentation variables on the indentation response of elastic-plastic materials through factorial design of experiment

In this work, the effects of conical indentation variables on the load-depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 2(6) was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/h(max), n, theta, E, and h(max). The dimensional variables E and h(max) were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/h(max) was obtained with two different h(max) values. A set of dimensionless functions was defined to analyze the effect of the input variables: Pi(1) = P(1)/Eh(2), Pi(2) = h(c)/h, Pi(3) = H/Y, Pi(4) = S/Eh(max), Pi(6) = h(max)/h(f) and Pi(7) = W(P)/W(T). These six functions were found to depend only on the dimensionless variables studied (Y/E, R/h(max), n, theta). Another dimension less function, Pi(5) = beta, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on beta was theta. However, beta showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that beta is especially Susceptible to the error in the Calculation of the initial unloading slope.

Using the ultrasound and instrumented indentation techniques to measure the elastic modulus of engineering materials

Currently, the acoustic and nanoindentation techniques are two of the most used techniques for material elastic modulus measurement. In this article fundamental principles and limitations of both techniques are shown and discussed. Last advances in nanoindentation technique are also reviewed. An experimental study in ceramic, metallic, composite and single crystals was also done. Results shown that ultrasonic technique is capable to provide results in agreement with those reported in literature. However, ultrasonic technique does not allow measuring the elastic modulus of some small samples and single crystals. On the other hand, the nanoindentation technique estimates the elastic modulus values in reasonable agreement with those measured by acoustic methods, particularly in amorphous materials, while in some policristaline materials some deviation from expected values was obtained.

WOOD DENSITY VARIATION AND TREE RING DEMARCATION IN Gmelina arborea TREES USING X-RAY DENSITOMETRY

Due to its relationship with other properties, wood density is the main wood quality parameter. Modern, accurate methods - such as X-ray densitometry - are applied to determine the spatial distribution of density in wood sections and to evaluate wood quality. The objectives of this study were to determinate the influence of growing conditions on wood density variation and tree ring demarcation of gmelina trees from fast growing plantations in Costa Rica. The wood density was determined by X-ray densitometry method. Wood samples were cut from gmelina trees and were exposed to low X-rays. The radiographic films were developed and scanned using a 256 gray scale with 1000 dpi resolution and the wood density was determined by CRAD and CERD software. The results showed tree-ring boundaries were distinctly delimited in trees growing in site with rainfall lower than 25 10 mm/year. It was demonstrated that tree age, climatic conditions and management of plantation affects wood density and its variability. The specific effect of variables on wood density was quantified by for multiple regression method. It was determined that tree year explained 25.8% of the total variation of density and 19.9% were caused by climatic condition where the tree growing. Wood density was less affected by the intensity of forest management with 5.9% of total variation.

Variation in the wood anatomical structure of Gmelina arborea (Verbenaceae) trees at different ecological conditions in Costa Rica

The tree Gmelina arborea has been widely introduced in Costa Rica for commercial purposes. This new conditions for melina cause variations on anatomy in secondary xylem of the trees growing in plantations. The objective of the present research was to determine the variation in the anatomy of xylem caused by the ecological conduction variation. Dimensions of fiber, axial parenchyma percentage of cross sections, parameters of vessels and the ray were measured. The results showed that some anatomical characteristics remained stable despite variations of ecological conditions, especially radial parenchyma and anatomical features which were less affected by the altitude. On the other hand, the vessels, axial parenchyma and fiber were less stable because they were affected significantly by the longitude, latitude, altitude and precipitation. Latitude significantly affected vessel percentage, length and diameter of the fiber and lumen. Longitude affected vessel percentage and fiber diameter. Altitude had a significant correlation with the amount of cells at my height. Annual average precipitation affected vessel percentage and diameter, not only of the fiber, but also of the lumen. These results suggest that the new growth conditions of G. arborea trees in Costa Rica have produced an anatomic adaptation.

EFFECT OF FERTILIZATION ON CELL SIZE IN WOOD OF Eucalyptus grandis Hill Ex Maiden

The use of fertilization in forest stands results in yield gains, yet little attention has been directed to its potential effects on the quality of wood produced. Information is scarce about the effect of fertilization on anatomical structures of older Eucalyptus wood. This work aims to study the effect of fertilization on tissue cell size of wood from an Eucalyptus grandis stand at age 21 years, the management system of which is based on selective thinning and fertilizer application at the start of the thinning season. Factors to consider include: presence or absence of fertilizers, two log positions and five radial (pith to bark) positions. Results led to the conclusion that fertilization significantly influenced only vessel frequency. Vessel element length was influenced by tree height. Fiber length, fiber diameter, fiber wall thickness, vessel element length, vessel diameter and vessel frequency were influenced by the radial position of the sample in relation to the log. A positive correlation was observed between fiber length, fiber diameter, fiber wall thickness, vessel element length, vessel diameter, ray width and radial position, while a negative correlation was observed between ray frequency and radial position.

Radial variation of anatomical features, wood density and decay resistance in teak (Tectona grandis) from two qualities of growing sites and two climatic regions of Costa Rica

The objective of this study was to show the radial variation of some anatomic characteristics, wood density and natural durability of teak (Tectona grandis L.F.) growing in Costa Rica. Samples of trees 13 years old were obtained from two growing sites (high and low growing) of plantations established in a humid tropical climate (CHT) and dry tropical climate (CST). The variables measured of the fibers as well as for the rays were not affected by the climate or the type of growing site, except for the length of the fibers. The fibers of teak wood from the best growing site were significantly larger. Vessels were found with a greater frequency for the CST but mostly solitary in comparison with the CBT. Average density, maximum density and the variation within the ring presented a light higher magnitude for the CST. The quality of the growing site did not affect these variables. The resistance of fungus attack was similar in the area of heartwood near the pith compared to the heartwood near the sapwood for all the conditions evaluated. Nevertheless, it was observed in some trees a similar resistance of fungus attack for areas of sapwood compared to similar areas of heartwood.

The isotropic nuclear magnetic shielding constants of acetone in supercritical water: A sequential Monte Carlo/quantum mechanics study including solute polarization

The nuclear isotropic shielding constants sigma((17)O) and sigma((13)C) of the carbonyl bond of acetone in water at supercritical (P=340.2 atm and T=673 K) and normal water conditions have been studied theoretically using Monte Carlo simulation and quantum mechanics calculations based on the B3LYP/6-311++G(2d,2p) method. Statistically uncorrelated configurations have been obtained from Monte Carlo simulations with unpolarized and in-solution polarized solute. The results show that solvent effects on the shielding constants have a significant contribution of the electrostatic interactions and that quantitative estimates for solvent shifts of shielding constants can be obtained modeling the water molecules by point charges (electrostatic embedding). In supercritical water, there is a decrease in the magnitude of sigma((13)C) but a sizable increase in the magnitude of sigma((17)O) when compared with the results obtained in normal water. It is found that the influence of the solute polarization is mild in the supercritical regime but it is particularly important for sigma((17)O) in normal water and its shielding effect reflects the increase in the average number of hydrogen bonds between acetone and water. Changing the solvent environment from normal to supercritical water condition, the B3LYP/6-311++G(2d,2p) calculations on the statistically uncorrelated configurations sampled from the Monte Carlo simulation give a (13)C chemical shift of 11.7 +/- 0.6 ppm for polarized acetone in good agreement with the experimentally inferred result of 9-11 ppm. (C) 2008 American Institute of Physics.