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At least 109 records · Page 6

Thermal equation of state of ice-VII revisited by single-crystal X-ray diffraction

Abstract Ice-VII is a high-pressure polymorph of H2O ice and an important mineral widely present in many planetary environments, such as in the interiors of large icy planetary bodies, within some cold subducted slabs, and in diamonds of deep origin as mineral inclusions. However, its stability at high pressures and high temperatures and thermoelastic properties are still under debate. In this study, we synthesized ice-VII single crystals in externally heated diamond-anvil cells and conducted single-crystal X-ray diffraction experiments up to 78 GPa and 1000 K to revisit the high-pressure and high-temperature phase stability and thermoelastic properties of ice-VII. No obvious unit-cell volume discontinuity or strain anomaly of the high-pressure ice was observed up to the highest achieved pressures and temperatures. The volume-pressure-temperature data were fitted to a high-temperature Birch-Murnaghan equation of state formalism, yielding bulk modulus KT0 = 21.0(4) GPa, its first pressure derivative KT0′ = 4.45(6), dK/dT = –0.009(4) GPa/K, and thermal expansion relation αT = 15(5) × 10–5 + 15(8) × 10–8 × (T – 300) K–1. The determined phase stability and thermoelastic properties of ice-VII can be used to model the inner structure of icy cosmic bodies. Combined with the thermoelastic properties of diamonds, we can reconstruct the isomeke P-T paths of ice-VII inclusions in diamond from depth, offering clues on the water-rich regions in Earth’s deep mantle and the formation environments of those diamonds.

Geochemistry & Geophysics↗

Thermographic inspection of fatigue cracks in riveted plates

A theoretical and experimental analysis of the inspection of reiveted plates using the thermoelastic effect is presented. Theoretically, a model is employed to estimate the thermoelastic response expected from a cracked and uncracked rivet hole. The stress invariant, which causes the thermoelastic response, is calculated for the cracked case using an FEM model and for the uncracked case using a theoretical approximation. The differences in the two thermal responses are reduced when the effects of optical spatial averaging, thermal conduction, and a concentric blind area representing the rivet heat are considered. It is suggested that discrimination between the cracked and uncracked cases for short cracks will improve with increasing frequency of stress oscillation. Measurements are shown for aerospace aluminum samples with and without fatigue cracks propagating from holes in a plate. The effect of mean stress on the thermoelastic response is illustrated, and the results are qualitatively compared with the finite element analysis.

Welch, Christopher S.↗

Continuum models for beam-like and plate-like lattice structures

A simple, rational approach is presented for developing continuum models for large repetitive beam-like and plate-like lattices with arbitrary configurations subjected to static, thermal and dynamic loadings. The continuum models for these structures are shear flexible beams and plates. They account for local effects in the repeating element of the actual structure and are characterized by their thermoelastic strain and kinetic energies from which the equations of motion and constitutive relations can be derived. The procedure for developing the expressions for thermoelastic strain and kinetic energies of the continuum involves introducing basic assumptions regarding the variation of the temperature, displacement and strain components in one or two directions (for plate-like and beam-like lattices) and obtaining effective thermoelastic and dynamic coefficients of the continuum in terms of material properties and geometry of the original lattice structure. The high accuracy of the continuum models developed is demonstrated by means of numerical examples.

Noor, A. K.↗

Accurate Thermal Stresses for Beams: Normal Stress

Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of the three-dimensional thermal stress problem to a two-dimensional one. Numerical results from the general theory of thermoelasticity are compared to those obtained from strength of materials. It is concluded that the theory of thermoelasticity for prismatic beams proposed in this paper can be used instead of strength of materials when precise stress results are desired.

Johnson, Theodore F.↗

Accurate Thermal Stresses for Beams: Normal Stress

Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of the three-dimensional thermal stress problem to a two-dimensional one. Numerical results from the general theory of thermoelasticity are compared to those obtained from strength of materials. It is concluded that the theory of thermoelasticity for prismatic beams proposed in this paper can be used instead of strength of materials when precise stress results are desired.

Johnson, Theodore F.↗

Mapping of Texture and Phase Fractions in Heterogeneous Stress States during Multiaxial Loading of Biomedical Superelastic NiTi

Thermoelastic deformation mechanisms in polycrystalline biomedical-grade superelastic NiTi are spatially mapped using in situ neutron diffraction during multiaxial loading and heating. The trigonal R-phase is formed from the cubic phase during cooling to room temperature and subsequently deforms in compression, tension, and torsion. The resulting R-phase variant microstructure from the variant reorientation and detwinning processes are equivalent for the corresponding strain in tension and compression, and the variant microstructure is reversible by isothermal loading. The R-phase variant microstructure is consistent between uniaxial and torsional loading when the principal stress directions of the stress state are considered (for the crystallographic directions observed here). The variant microstructure evolution is tracked and the similarity in general behavior between uniaxial and torsional loading, in spite of the implicit heterogeneous stress state associated with torsional loading, pointed to the ability of the reversible thermoelastic transformation in NiTi to accommodate stress and strain mismatch with deformation. This ability of the R-phase, despite its limited variants, to accommodate stress and strain and satisfy strain incompatibility in addition to the existing internal stresses has significance for reducing irrecoverable deformation mechanisms during loading and cycling through the phase transformation.

36 MATERIALS SCIENCE↗

Seismic Ambient Noise Analyses Reveal Changing Temperature and Water Signals to 10s of Meters Depth in the Critical Zone

The critical zone sustains terrestrial life, but we have few tools to explore it efficiently beyond the first few meters of the subsurface. Using analyses of high-frequency ambient seismic noise from densely spaced seismometers deployed in the forested Shale Hills subcatchment of the Susquehanna Shale Hills Critical Zone Observatory (SSHCZO), we show that temporal changes in seismic velocities at depths from ~1 m to tens of m can be detected. Furthermore, these changes are driven by variations at the land surface. The Moving-Window Cross-Spectral (MWCS) method was employed to measure seismic-velocity changes in coda waves at hourly resolution in 10 different frequency bands. We observed a diurnal signal, a seasonal signal, and a meteorological-event-based signal. These signals were compared to time-series measurements of precipitation, well water levels, soil moisture, soil temperature, air temperature, latent heat flux, and air pressure in the heavily instrumented catchment. Most of the velocity changes can be explained by variations in temperature that result in thermoelastic strains that propagate to depth. But some double minima in seismic velocity time-series observed after large rain events were attributed in part to the effects of water infiltration. These results show that high-frequency ambient noise data may in some locations be used to detect changes in the critical zone from ~1 to ~100 m or greater depth with hourly resolution. But interpretation of such data requires multiple environmental data sets to deconvolve the complex interrelationships among thermoelastic and hydrological effects in the subsurface critical zone.

54 ENVIRONMENTAL SCIENCES↗

Fiber coupled laser ultrasound system using a single mode hollow core fiber for excitation laser: Theory and demonstration for on-machine thickness gauging

Laser ultrasound (LU) is a technique that uses a pump laser and a probe laser to optically generate and detect elastic waves in a material. Despite its advantages over traditional contact transducer-based ultrasound, industrial adoption has been limited by complex optical setups and the inability of multi-mode fibers to deliver a stable Gaussian profile for the pump laser. Here, we report a fully fiber-coupled thermoelastic LU system that uses an anti-resonant hollow-core single-mode fiber to deliver 1 mJ nanosecond pulses of 1064 nm light, while preserving the fundamental Gaussian mode (pump laser). When combined with a fiber-coupled interferometer (probe laser), a small, flexible, and environmentally robust sensor capable of optically generating and detecting high frequency broadband ultrasound is realized. We demonstrate such an LU system implemented in situ on a four-axis precision lathe. High-resolution thickness gauging is performed, before and after precision cutting, by exciting and measuring a zero-group velocity guided wave mode. The measurements are verified with ex-situ traceable coordinate measuring machine data. Mean absolute deviations of 0.1%, of nominal thickness, before cutting, and 0.2% and 0.3%, after stepped and tapered cuts, respectively, are reported. A theoretical background for thermoelastic ultrasound generation in an elastic waveguide is also presented. Attention is given to the effect of the pump laser profile on wave generation to elucidate the importance of using single-mode laser light. The fiber-coupled system demonstrated is well-suited for use in scientific and engineering sensing applications and facilitates the adoption of LU for industrial non-destructive testing.

Engineering↗

Thermomechanical Stress and Creep-Fatigue Analysis of a High-Temperature Prototype Receiver for Heating Particles

This work presents a three-dimensional (3D) thermomechanical model of a prototype-scale enclosed light trapping solar receiver for heating particles. Results of the thermoelastic model are used to estimate receiver lifetime under maximum flux conditions. A computational fluid dynamics (CFD) model is first developed to predict the temperature fields in a multi-panel assembly under steady operating conditions. Solar flux distributions on the receiver are obtained from the software package SolTrace and applied to the 3D thermal model. The subsequent particle heating is captured through a simplified 1D energy balance. Panel reradiation is considered through a surface-to-surface radiation model and natural convection loss to the surrounding air is captured in a representative fluid domain surrounding the receiver. The resulting temperature fields from the CFD analysis are used as inputs for a thermoelastic mechanical model with representative boundary conditions. With the resultant temperature and stress fields, a creep-fatigue damage and lifetime analysis is performed using the linear damage accumulation (LDA) theory. The Manson-Coffin formula and Larson Miller correlation are used to calculate the fatigue and creep, respectively. A maximum damage (corresponding to a 30-year service life) is defined for design assessment. The model was first developed and verified in detail by comparing with published results in the literature (temperature and stress profiles and distributions, and creep/fatigue damage fractions) for tubular solar receivers with supercritical carbon dioxide as the working fluid. It was then implemented to model a planar-cavity receiver with various design parameters. Specifically, three different design geometries are considered, and the results show that a maximum temperature of approximately 1200 K could be reached for each design with the given incident solar flux, with the main difference being the distribution of these temperatures. Preliminary resulting stresses for the small-scale prototype without design optimization vary from 20 MPa to 250 MPa for each design, with the maximum stresses occurring on the front face and concave geometry on the side of the panel. In future work, the developed methodology shown here will be applied to analyze a full-scale (50-150 MWth) receiver.

concentrated solar power↗

Solid-propellant rocket motor internal ballistic performance variation analysis, phase 2

The Monte Carlo method was used to investigate thrust imbalance and its first time derivative throughtout the burning time of pairs of solid rocket motors firing in parallel. Results obtained compare favorably with Titan 3 C flight performance data. Statistical correlations of the thrust imbalance at various times with corresponding nominal trace slopes suggest several alternative methods of predicting thrust imbalance. The effect of circular-perforated grain deformation on internal ballistics is discussed, and a modified design analysis computer program which permits such an evaluation is presented. Comparisons with SRM firings indicate that grain deformation may account for a portion of the so-called scale factor on burning rate between large motors and strand burners or small ballistic test motors. Thermoelastic effects on burning rate are also investigated. Burning surface temperature is calculated by coupling the solid phase energy equation containing a strain rate term with a model of gas phase combustion zone using the Zeldovich-Novozhilov technique. Comparisons of solutions with and without the strain rate term indicate a small but possibly significant effect of the thermoelastic coupling.

Sforzini, R. H.↗

Analysis of beam-like lattice trusses

A simple procedure is presented for predicting the thermoelastic and free vibration responses of large repetitive beam-like trusses. The procedure is based on replacing the original lattice structure by an equivalent continuum beam model and obtaining closed-form (exact) solutions for the beam model. The equivalent beam model accounts for warping and shear deformation in the plane of the cross-section and is characterized by its thermoelastic strain and kinetic energies, from which the equations of motion and constitutive relations can be derived. The high accuracy of the results obtained by the proposed approach is demonstrated by means of numerical examples.

Noor, K.↗

Transient thermal stress problem for a circumferentially cracked hollow cylinder

The paper is concerned with the transient thermal stress problem for a long hollow circular cylinder containing an internal axisymmetric circumferential edge crack that is suddenly cooled from inside. It is assumed that the transient thermal stress problem is quasi-static, i.e., the inertial effects are negligible. Also, all thermoelastic coupling effects and the possible temperature dependence of the thermoelastic constants are neglected. The problem is considered in two parts. The first part is the evaluation of transient thermal stresses in an uncracked cylinder; the second part is the isothermal perturbation problem for the cracked cylinder in which the crack surface tractions, equal and opposite to the thermal stresses obtained from the first problem, are the only external loads. The superposition of the two solutions gives results for the cracked cylinder.

Nied, H. F.↗

Development of an integrated BEM approach for hot fluid structure interaction

A comprehensive boundary element method is presented for transient thermoelastic analysis of hot section Earth-to-Orbit engine components. This time-domain formulation requires discretization of only the surface of the component, and thus provides an attractive alternative to finite element analysis for this class of problems. In addition, steep thermal gradients, which often occur near the surface, can be captured more readily since with a boundary element approach there are no shape functions to constrain the solution in the direction normal to the surface. For example, the circular disc analysis indicates the high level of accuracy that can be obtained. In fact, on the basis of reduced modeling effort and improved accuracy, it appears that the present boundary element method should be the preferred approach for general problems of transient thermoelasticity.

Dargush, G. F.↗

Thermographic characterization of stress during crack growth

A full-field-thermographic technique for imaging stress patterns in dynamically loaded structures using general purpose IR imaging and image processing hardware is described. The inspection technique is based on the thermoelastic effect. A simple geometry is examined, and the experimentally determined values for the stress invariant are shown to be consistent with theoretical and numerical calculations. The application of full-field-thermographic measurement would ensure that the observed stress field has a common sampling period, thus allowing the observation of rapidly occurring stress anomalies such as the propagation of a fatigue crack. Fatigue crack propagation in two consecutive thermoelastic stress images from an aluminum sample is shown.

Cramer, K. E.↗

Three-dimensional solutions for the thermal buckling and sensitivity derivatives of temperature-sensitive multilayered angle-ply plates

Analytic three-dimensional thermoelasticity solutions are presented for the thermal buckling of multilayered angle-ply composite plates with temperature-dependent thermoelastic properties. Both the critical temperatures and the sensitivity derivatives are computed. The sensitivity derivatives measure the sensitivity of the buckling response to variations in the different lamination and material parameters of the plate. The plates are assumed to have rectangular geometry and an antisymmetric lamination with respect to the middle plane. The temperature is assumed to be independent of the surface coordinates, but has an arbitrary symmetric variation through the thickness of the plate. The prebuckling deformations are accounted for. Numerical results are presented, for plates subjected to uniform temperature increase, showing the effects of temperature-dependent material properties on the prebuckling stresses, critical temperatures, and their sensitivity derivatives.

Noor, A. K.↗