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At least 19 records

High‐Pressure Phase Stability and Thermoelastic Properties of Iron Carbonitrides and Nitrogen in the Deep Earth

Abstract Iron‐dominant metallic phases are likely the primary hosts for nitrogen in the reduced deep Earth, hence the storage of nitrogen in the lower mantle and the core is governed by the behavior of the Fe‐N‐C system at high temperatures and pressures. In this study, phase transitions and thermoelastic properties of iron carbonitrides were investigated at high pressure‐temperature conditions by diamond anvil cell experiments and first‐principles calculations. Experimental data revealed no phase transition in ε ‐type Fe 4 (N 0.6 C 0.4 ) or Fe 7 (N 0.75 C 0.25 ) 3 up to 60 GPa at room temperature. At high temperature, Fe 7 (N 0.75 C 0.25 ) 3 transforms into the Fe 3 C‐type phase at ∼27 GPa, and then into the Fe 7 C 3 ‐type phase at ∼45 GPa, which is also corroborated by our theoretical calculations. We found that the phase stability of iron carbonitrides mainly depends on the N/C ratio, and the elastic properties of iron carbonitrides are dominantly affected by the Fe/(N+C) ratio. Iron carbonitrides with diverse structures may be the main host for nitrogen in the deep mantle. Some iron carbonitride inclusions in lower mantle diamonds could be the residue of the primordial mantle or originate from subducted nitrogen‐bearing materials, rather than iron‐enriched phases of the outer core. In addition, our experiments confirmed the existence of Fe 7 C 3 ‐type Fe 7 C 3 ‐Fe 7 N 3 solid solutions above 40 GPa. Fe 7 C 3 ‐type Fe 7 (C, N) 3 has comparable density and thermoelastic properties to its isostructural endmembers and may be a promising candidate constituent of the Earth's inner core.

Huang, Shengxuan↗

Thermoelastic stress - How important as a cause of earthquakes in young oceanic lithosphere?

Thermoelastic or thermal stress is a potentially important contributor to the state of stress in the oceanic lithosphere. The present paper provides several simple models for the state of thermoelastic stress in a young oceanic lithosphere, taking into account a comparison of the predictions of these models with the characteristics of near-ridge earthquakes. Attention is given to the characteristics of near-ridge earthquakes, sources of stress in an oceanic lithosphere, previous models of thermal stress, the calculation of thermal stress, and thermal stress models. A test is conducted of the hypothesis that thermoelastic stress is a significant component of the stress field in a young oceanic lithosphere. The considered models support the hypothesis that thermoelastic stress is a significant component of the stress field in a young oceanic lithosphere.

Bratt, S. R.↗

Coupled Thermoelasticity Problem for Multilayer Composite Shells of Revolution. II. Applied Problems

We deduce a system of nonclassical nonlinear differential equations of coupled thermoelasticity for multilayer composite anisotropic shells of revolution in a coordinate system connected with the lines of curvature of the reference surface. The constructed nonclassical model of deformation of a multilayer shell and the nonlinear model of distribution of heat fluxes over the thickness of the shell enable us to take into account the transverse shear strains and guarantee the validity of the conditions of thermal and mechanical conjugation of the layers and the conditions of thermomechanical loading on the faces of the shell. We deduce the linearized differential equations of the axisymmetric coupled problem of thermoelasticity for a conic reinforced multilayer shell and solve the quasistatic problem of thermoelasticity for a two-layer cylindrical shell cross-reinforced in the direction of helical lines. By using the structural approach to the formulation of the criteria of strength for composite materials, we determine the loads of the onset of fracture of the binder and reinforcing elements of a two-layer metal-composite cylindrical shell.

42 ENGINEERING↗

Thermoelastic Properties of Fe 3+ ‐Rich Jeffbenite and Application to Superdeep Diamond Barometry

Abstract Jeffbenite (Mg 3 Al 2 Si 3 O 12 ) is a tetragonal phase found in so far only in superdeep diamonds, and its thermoelastic parameters are a prerequisite for determining entrapment pressures as it is regarded as a potential indicator for superdeep diamonds. In this study, the thermoelastic properties of synthetic Fe 3+ ‐jeffbenite were measured up to 33.7 GPa and 750 K. High‐temperature static compression data were fitted, giving ( ∂K T 0 / ∂ T ) P = −0.0107 (4) GPa/K and α T = 3.50 (3) × 10 −5 K −1 . The thermoelastic properties and phase stability are applied to modeling isomekes, or P‐T paths intersecting possible conditions of entrapment in diamond. We calculate that under ideal exhumation, jeffbenite entrapped at mantle transition zone conditions will exhibit a high remnant pressure at 300 K ( P inc ) of ∼5.0 GPa. Elastic geobarometry on future finds of jeffbenite inclusions can use the new equation of state to estimate entrapment pressures for this phase with still highly uncertain stability field in the mantle.

Geology↗

Thermoelastic properties of tungsten at simultaneous high pressure and temperature

In this work, the compressional ( P ) and shear wave velocities ( S ) and unit cell volumes (densities) of polycrystalline tungsten (W) have been measured simultaneously up to 10.5 GPa and 1073 K using ultrasonic interferometry in conjunction with x-ray diffraction and x-radiography techniques. Thermoelastic properties of W were derived using different methods. We obtained the isothermal bulk modulus K T 0 = 310.3(1.5) GPa, its pressure derivative K ' T 0 = 4.4(3), its temperature derivative at constant pressure ( ∂ K T / ∂ T ) P = – 0.0138 ( 1 ) GPa K – 1 and at constant volume ( ∂ K T / ∂ T ) V = – 0.0050 GPa K – 1 , the thermal expansion α ( 0, T ) = 1.02(27) × 10 –5 + 7.39(3.2) × 10 –9 T (K –1 ), as well as the pressure derivative of thermal expansion ( ∂ α / ∂ P ) T = – 1.44 ( 1 ) × 10 – 7 K – 1 GP a – 1 based on the high-temperature Birch–Murnaghan equation of state (EOS), the Vinet EOS, and thermal pressure approach. Finite strain analysis allowed us to derive the elastic properties and their pressure/temperature derivatives independent of the choice of pressure scale. A least-squares fitting yielded K S 0 = 314.5(2.5) GPa, K S 0 ' = 4.45(9), (∂ K S /∂ T ) P = – 0.0076(6) GPa K –1 , G 0 = 162.4(9) GPa, G 0 ' = 1.8(1), (∂ G /∂ T ) P = – 0.0175(9) GPa K –1 , and α 298 K = 1.23 × 10 – 5 K – 1 . Fitting current data to the Mie–Grüneisen–Debye EOS with derived θ 0 = 383.4 K yielded γ 0 = 1.81 ( 6 ) and q = 0.3 . The thermoelastic parameters obtained from various approaches are consistent with one another and comparable with previous results within uncertainties. Our current study provides a complete and self-consistent dataset for the thermoelastic properties of tungsten at high P – T conditions, which is important to improve the theoretical modeling of these materials under dynamic conditions.

36 MATERIALS SCIENCE↗

Thermoelastic damping and its effect on flutter of stressed panels situated in a supersonic airflow

The effects of material damping on flutter of stressed rectangular panels are studied within the context of linear thermoelasticity theory. The closed-form expression for the thermoelastic (material) damping coefficient is obtained as a function of frequency, panel temperature and dimensions, and material properties. The solution of the stability boundary value problem is obtained by use of a generalized Galerkin method in the cross stream direction which reduces the governing partial differential equations to a system of ordinary differential equations in the streamwise direction. These equations are then solved exactly. Numerical results are given for the thermoelastic damping coefficients and for the flutter speeds of partially and fully clamped panels subjected to midplane stress.

Shieh, R. C.↗

Thermoelastic Stress Analysis: The Mean Stress Effect in Metallic Alloys

The primary objective of this study involved the utilization of the thermoelastic stress analysis (TSA) method to demonstrate the mean stress dependence of the thermoelastic constant. Titanium and nickel base alloys, commonly employed in aerospace gas turbines, were the materials of interest. The repeatability of the results was studied through a statistical analysis of the data. Although the mean stress dependence was well established, the ability to confidently quantify it was diminished by the experimental variations. If calibration of the thermoelastic response to mean stress can be successfully implemented, it is feasible to use the relationship to determine a structure's residual stress state.

Gyekenyesi, Andrew L.↗

Compact thermoelastic cooling system

A compact cooling system based on thermoelastic effect is provided. In one embodiment, the system comprises a pair of rollers serving as a heat sink, stress applicator and belt drive, a cold reservoir and a solid refrigerant belt coupled to the cold reservoir and to the heat sinks to pump heat from the cold reservoir to the heat sink. The refrigerant belt comprises solid thermoelastic materials capable of thermoelastic effect. The refrigerant material is mechanically compressed when entering the gap of the roller and subsequently released after passing through. When compressed the refrigerant material transforms to martensite phase and releases heat to the roller and neighboring materials. After released by the rollers, the refrigerant material transforms back to austenite and absorbs heat from the ambient atmosphere.

42 ENGINEERING↗

Effective Thermoelasticity of Polymer-Bonded Particle Composites with Imperfect Interfaces and Thermally Expansive Interphases

A micromechanical model for the thermoelasticity of polymer-bonded composites is presented. The model is particularly aimed at describing materials where the polymeric binder phase undergoes non-negligible thermal expansion affecting the overall thermoelastic response. Constitutive choices for modeling a mixed binder-void interphase layer are proposed, and an associated decomposition of total eigenstrains into classical, elastic imperfection (damage), and binder thermal expansivity parts is examined within the context of imperfect inter-particle interfaces. A novel temperature dependent modified Eshelby tensor is identified, making possible the development of a temperature dependent modified self-consistent homogenization scheme—what we call the M θ-SCH model. A method for distinguishing between dispersed and isolated parts of the binder and void phases in the model is also provided, along with a description of particle coating (or interphase) thickness derived from particle morphology and mesoscale effective properties. Finally, although the theory is general, its development is motivated by the need to model anisotropic and highly nonlinear observed thermal expansion behavior of the polymer bonded explosive PBX 9502, for which model simulations are performed and compared with existing measurements.

36 MATERIALS SCIENCE↗

Two-Dimensional Problem of Thermoelasticity for a Half Space in the Presence of Heat Release in a Ribbon-Shaped Domain Parallel to its Boundary

Using a logarithmic single-layer potential, thermoelastic displacement potential, Airy stress function, and Boussinesq function, we solve two-dimensional problems of stationary heat conduction and thermoelasticity under the conditions of plane deformation of a semiinfinite body in the presence of heat release in a ribbon-shaped domain parallel to its boundary (in this domain, either a temperature or a heat flux is given). The boundary of the body is kept at temperature equal to zero. We study the distribution of stresses in the domain of heat release with given heat sources of constant intensity at constant temperature.

42 ENGINEERING↗

Stability of Panels of a Thermoelastic Shell Heated at the Edge by a Mobile Point Source

The thermostability of thin-walled structures is considered by means of a thermoelasticity problem in a three-dimensional quasi-static formulation. Finite-element models of panels in the form of a circular cylinder and a plate reinforced by ribs are constructed. Numerical solutions are obtained for the stability loss of thermoelastic thin-walled reinforced structures with intense edge heating by a mobile heat source.

42 ENGINEERING↗

Magnetically induced cylindrical stress waves in a thermoelastic conductor

The problem of stress wave generation in a linear thermoelastic solid by a pulsed magnetic field is investigated both analytically and experimentally for a cylindrically symmetric conducting solid. A dynamic response analysis is developed to correlate magnetic, thermal, and stress fields in the solid with the time history of the electric current. In the experiment, a transient magnetic field was applied normal to a large conducting plate with a circular hole. Initially the field was confined to the interior of the circular hole. The field was generated by discharging a large capacitor bank through a solenoidal coil. The plane-stress cylindrical stress waves are 1-D in nature. The relative effects of the magnetic body force and thermoelastic stresses, both generated by the electromagnetic field, are assessed.

Chian, C. T.↗

Translational and extensional energy release rates (the J- and M-integrals) for a crack layer in thermoelasticity

A number of papers have been presented on the evaluation of energy release rate for thermoelasticity and corresponding J integral. Two main approaches were developed to treat energy release rate in elasticity. The first is based on direct calculation of the potential energy rate with respect to crack length. The second makes use of Lagrangian formalism. The translational and expansional energy release rates in thermoelasticity are studied by employing the formalism of irreversible thermodynamics and the Crack Layer Approach.

Chudnovsky, A.↗

A new unified architecture of thermal/structural dynamic algorithms - Applications to coupled thermoelasticity

A new unified architecture of robust thermal-structural dynamic algorithms is presented with emphasis on applications to coupled thermoelasticity. The proposed formulations are based on Lax-Wendroff/Taylor-Galerkin explicit time integration methodology. The applicability of the proposed unified architecture to interdisciplinary problems relevant to coupled dynamic thermoelasticity is demonstrated. The basic concepts and characteristic features of the unified formulations are discussed.

Tamma, Kumar K.↗