Search Results (8)

The influence of stress state multiaxiality on the propagation velocity of Rayleigh waves is explored through a detailed numerical study. The study uses the Murnaghan model to capture nonlinear elastodynamics in the material behavior, necessitating consideration of third-order elastic constants. Various invariant stress variables are compared for their suitability to describe the relationship between multiaxiality of the stress state and change in propagation velocity. The results are interpreted physically and provide information about the interaction between stress state multiaxiality and wave propagation. Finite element simulations are conducted using Abaqus/Explicit, with the material behavior implemented via a VUMAT user subroutine. Transformation relations for rotated axes are used to understand how the stress state affects the directional dependence of wave velocity. This study offers valuable insights into the complex relationship between stress state and Rayleigh wave propagation, essential for applications in reconstruction of residual stress fields. The results show that the change in propagation velocity is best described by models that include the principal stresses. Different stress states lead to different distortion of the propagation front. The numerical results are compared and validated with the semianalytical solution. The results show good agreement. Full article

Equation of state (EoS) parameters of hexagonal close-packed iron (hcp-Fe), the dominant core component in large terrestrial planets, is crucial for studying interior structures of super-Earths. However, EoS parameters at interior conditions of super-Earths remain poorly constrained, and extrapolating from Earth’s core conditions introduces significant uncertainties at TPa pressures. Here, we compiled experimental static and dynamic compression data and theoretical data up to 1374 GPa and 12,000 K from the literature to refine the EoS of hcp-Fe. Using the third-order Birch–Murnaghan and Mie–Grüneisen–Debye equations, we obtained V₀ (unit-cell volume) = 6.756 (10) cm³/mol, K_T0 (isothermal bulk modulus) = 174.7 (17) GPa, $K_{T0}^{\prime }$ (pressure derivative of K_T0) = 4.790 (14), θ₀ (Debye temperature) = 1209 (73) K, γ₀ (Grüneisen parameters) = 2.86 (10), and q (volume-independent constant) = 0.84 (5) at ambient conditions. These parameters were then incorporated into an interior model of CoRoT-7b and Kepler-10b, which includes four solid compositional layers (forsterite, MgSiO₃ perovskite, post-perovskite, and hcp-Fe). The model yields the core mass fractions (CMF) of 0.1709 in CoRoT-7b and 0.2216 in Kepler-10b, suggesting a Mars-like interior structure. Extrapolation uncertainties (±10–20% in density) can change CMF by −12.6 to 21.2%, highlighting the necessity of precise EoS constraints at the super-Earth interior conditions. Full article

A high-temperature equation of state (EoS) for the fcc phase of solid lead and liquid lead was developed herein using experimental data on thermodynamic properties, volumetric thermal expansion, compressibility, temperature-dependent bulk modulus, and sound velocity from ultrasonic measurements and melting curve. The whole totality of experimental data was optimized using the temperature-dependent Murnaghan EoS over a pressure range of 0–130 kbar. The temperature dependences of thermodynamic and thermophysical parameters were described herein using an expanded Einstein model. The resultant EoS describes well the whole set of available experimental data within measurement uncertainties of individual parameters. Full article

Rocksalt-type (Pb,Cd)Te belongs to IV–VI semiconductors exhibiting thermoelectric properties. With the aim of understanding of the influence of Cd substitution in PbTe on thermostructural and elastic properties, we studied PbTe and Pb_0.884Cd_0.116Te (i) at low temperatures (15 to 300 K) and (ii) at high pressures within the stability range of NaCl-type PbTe (up to 4.5 GPa). For crystal structure studies, powder and single crystal X-ray diffraction methods were used. Modeling of the data included the second-order Grüneisen approximation of the unit-cell-volume variation, V(T), the Debye expression describing the mean square atomic displacements (MSDs), <u²>(T), and Birch–Murnaghan equation of state (BMEOS). The fitting of the temperature-dependent diffraction data provided model variations of lattice parameter, the thermal expansion coefficient, and MSDs with temperature. A comparison of the MSD runs simulated for the PbTe and mixed (Pb,Cd)Te crystal leads to the confirmation of recent findings that the cation displacements are little affected by Cd substitution at the Pb site; whereas the Te displacements are markedly higher for the mixed crystal. Moreover, information about static disorder caused by Cd substitution is obtained. The calculations provided two independent ways to determine the values of the overall Debye temperature, θ_D. The resulting values differ only marginally, by no more than 1 K for PbTe and 7 K for Pb_0.884Cd_0.116Te crystals. The θ_D values for the cationic and anionic sublattices were determined. The Grüneisen parameter is found to be nearly independent of temperature. The variations of unit-cell size with rising pressure (the NaCl structure of Pb_0.884Cd_0.116Te sample was conserved), modeled with the BMEOS, provided the dependencies of the bulk modulus, K, on pressure for both crystals. The K₀ value is 45.6(2.5) GPa for PbTe, whereas that for Pb_0.884Cd_0.116Te is significantly reduced, 33.5(2.8) GPa, showing that the lattice with fractional Cd substitution is less stiff than that of pure PbTe. The obtained experimental values of θ_D and K₀ for Pb_0.884Cd_0.116Te are in line with the trends described in recently reported theoretical study for (Pb,Cd)Te mixed crystals. Full article

Ultrasonic is one of the well-known methods for surface roughness measurement, but small roughness will only lead to a subtle variation of transmission or reflection. To explore sensitive techniques for surfaces with small roughness, nonlinear ultrasonic measurement in through-transmission and pulse-echo modes was proposed and studied based on an effective unit-cell finite element (FE) model. Higher harmonic generation in solids was realized by applying the Murnaghan hyperelastic material model. This FE model was verified by comparing the absolute value of the nonlinearity parameter with the analytical solution. Then, random surfaces with different roughness values ranging from 0 μm to 200 μm were repeatedly generated and studied in the two modes. The through-transmission mode is very suitable to measure the surfaces with roughness as small as 3% of the wavelength. The pulse-echo mode is sensitive and effective to measure the surface roughness ranging from 0.78% to 5.47% of the wavelength. This study offers a potential nondestructive testing and monitoring method for the interfaces or inner surfaces of the in-service structures. Full article

In this paper, the possibility of using nonlinear ultrasonic guided waves for early-life material degradation in metal plates is investigated through both computational modeling and study. The analysis of the second harmonics of Lamb waves in a free boundary aluminum plate, and the internal resonance conditions between the Lamb wave primary modes and the second harmonics are investigated. Subsequently, Murnaghan’s hyperelastic model is implemented in a finite element (FE) analysis to study the response of aluminum plates subjected to a 60 kHz Hanning-windowed tone burst. Different stages of material degradation are reflected as the changes in the third order elastic constants (TOECs) of the Murnaghan’s model. The reconstructed degradations match the actual ones well across various degrees of degradation. The effects of several relevant factors on the accuracy of reconstructions are also discussed. Full article

In the present study, the high-pressure high-temperature equation of the state of iridium has been determined through a combination of in situ synchrotron X-ray diffraction experiments using laser-heating diamond-anvil cells (up to 48 GPa and 3100 K) and density-functional theory calculations (up to 80 GPa and 3000 K). The melting temperature of iridium at 40 GPa was also determined experimentally as being 4260 (200) K. The results obtained with the two different methods are fully consistent and agree with previous thermal expansion studies performed at ambient pressure. The resulting thermal equation of state can be described using a third-order Birch–Murnaghan formalism with a Berman thermal-expansion model. The present equation of the state of iridium can be used as a reliable primary pressure standard for static experiments up to 80 GPa and 3100 K. A comparison with gold, copper, platinum, niobium, rhenium, tantalum, and osmium is also presented. On top of that, the radial-distribution function of liquid iridium has been determined from experiments and calculations. Full article

The density and sound velocity structure of the Earth’s interior is modeled on seismological observations and is known as the preliminary reference Earth model (PREM). The density of the core is lower than that of pure Fe, which suggests that the Earth’s core contains light elements. Carbon is one plausible light element that may exist in the core. We determined the equation of state (EOS) of Fe₃C based on in situ high-pressure and high-temperature X-ray diffraction experiments using a diamond anvil cell. We obtained the P–V data of Fe₃C up to 327 GPa at 300 K and 70–180 GPa up to around 2300 K. The EOS of nonmagnetic (NM) Fe₃C was expressed by two models using two different pressure scales and the third-order Birch–Murnaghan EOS at 300 K with the Mie–Grüneisen–Debye EOS under high-temperature conditions. The EOS can be expressed with parameters of V₀ = 148.8(±1.0) ų, K₀ = 311.1(±17.1) GPa, K₀^′ = 3.40(±0.1), γ₀ = 1.06(±0.42), and q = 1.92(±1.73), with a fixed value of θ₀ = 314 K using the KBr pressure scale (Model 1), and V₀ = 147.3(±1.0) ų, K₀ = 323.0(±16.6) GPa, K₀^′ = 3.43(±0.09), γ₀ = 1.37(±0.33), and q = 0.98(±1.01), with a fixed value of θ₀ = 314 K using the MgO pressure scale (Model 2). The density of Fe₃C under inner core conditions (assuming P = 329 GPa and T = 5000 K) calculated from the EOS is compatible with the PREM inner core. Full article