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At least 163 records · Page 9

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DOE OSTI2022

Evolution of tensile and shear cracking in crystalline rocks under compression

Here we performed laboratory-scale unconfined compression experiments on Barre granite specimen with a single pre-existing flaw to study the evolution of tensile and shear cracking that occurs during different stress levels. Moment tensor inversion of acoustic emission (AE) events in combination with the nonelastic strain component obtained through the 2D digital image correlation (DIC) technique are used to track the changes in the source mechanisms of the stress-induced cracks. The mode of deformation computed from the image based strain profiles, enables visual comparison of the nucleation, growth and interaction of the tensile and shear cracks with the microseismic source mechanism observed by moment tensor inversion of the AE events. Comparing the results obtained from the two techniques on the same dataset demonstrates a quantitative correlation between the acoustic and visual observations in terms of the cracking mechanisms obtained at different stages of cracking from crack initiation at the flaw tips to the failure of the rock specimen.

58 GEOSCIENCES↗

NASA NTRS1991

The effects of rotation on initially anisotropic homogeneous flows

Rotation of initially anisotropic homogeneous flows is studied using a model spectral tensor. It is shown that the anisotropy changes because of the influence of rotation through phase scrambling. Phase scrambling causes the Reynolds stresses to develop with damped oscillations. The final Reynolds stress anisotropy is found to be proportional to the initial structural tensor anisotropy. Closure models for the rapid pressure strain terms should reflect this change in anisotropy, and should drive the anisotropy to reach its final predicted state. Finally, it is shown that long-time integration using direct numerical simulations should be treated with care because phase scrambling effects on a discrete wave space can cause loss of resolution when time becomes large.

Mansour, Nagi N.↗

NASA NTRS1989

A mechanics framework for a progressive failure methodology for laminated composites

A laminate strength and life prediction methodology has been postulated for laminated composites which accounts for the progressive development of microstructural damage to structural failure. A damage dependent constitutive model predicts the stress redistribution in an average sense that accompanies damage development in laminates. Each mode of microstructural damage is represented by a second-order tensor valued internal state variable which is a strain like quantity. The mechanics framework together with the global-local strategy for predicting laminate strength and life is presented in the paper. The kinematic effects of damage are represented by effective engineering moduli in the global analysis and the results of the global analysis provide the boundary conditions for the local ply level stress analysis. Damage evolution laws are based on experimental results.

Harris, Charles E.↗

NASA NTRS1995

Modeling and simulation of a turbulent far wake

Work continued on two projects which had been started during previous years. Both projects involve calculations of the subsonic, turbulent far wake of a two-dimensional object at a Reynolds number of 1000 (based on wake momentum thickness). This flow was used as a test case for direct comparison of various turbulence models and a direct numerical simulations (DNS) of this flow were undertaken. In the turbulence model comparison studies, for any particular model tested, a unique self-similar solution was obtained far enough downstream, regardless of inlet conditions. Furthermore, different turbulence models led to different far-wake equilibrium solutions. No turbulence model could correctly predict all features of the turbulent far wake. For example, the spreading rate and turbulent shear stresses were underpredicted by all the standard models (both two-equation and full Reynolds stress models). In cases where a more correct spreading rate was achieved, it was at the expense of the turbulent kinetic energy, which was overpredicted. In general, the Algebraic Dissipation Rate Model of Gatski and Speziale, 1992, when added to any of the standard models, improved the results dramatically. Also, full Reynolds stress closure models did a much better job at predicting the shapes of both the mean and turbulence profiles, but the spreading rate was not significantly improved over that predicted by the simpler two-equation models. There are two main conclusions from these studies: First, in a comparison such as this, it is not enough to compare just one parameter, like the spreading rate. A good prediction for one parameter does not necessarily imply good predictions for all parameters in a flow. Second, since no turbulence model could correctly predict the turbulent far wake, much of the important physics of turbulent free shear flows is apparently lost by the assumptions inherent in today's methods of turbulence modeling; turbulence models must be improved. Direct simulations of this flow were begun last year in order to provide a data base through which some of the deficiencies of the existing turbulence models could be identified. Quantities such as the pressure-strain correlation, turbulent diffusion, and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. During this summer, diagnostics codes were written which will calculate the parameters mentioned above, along with other single-point and multi-point statistics. The DNS calculations are still in progress at the time of this writing. When these calculations are complete, the diagnostics codes will be applied so that the results can aid turbulence modelers. In addition, the results will show whether or not there exists a universal equilibrium turbulent far wake, independent of initial conditions.

Cimbala, John M.↗

NASA NTRS1990

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Speziale, Charles G.↗

NASA NTRS1991

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

Speziale, Charles G.↗

DOE OSTI2022

Nonlinear deformation and elasticity of BCC refractory metals and alloys

Application of isotropic pressure or uniaxial strain alters the elastic properties of materials; sufficiently large strains can drive structural transformations. Linear elasticity describes stability against infinitesimal strains, while nonlinear elasticity describes the response to finite deformations. Here, it was previously shown that uniaxial strain along [100] drives refractory metals and alloys towards mechanical instabilities. These include an extensional instability, and a symmetry-breaking orthorhombic distortion caused by a Jahn-Teller-Peierls instability that splays the cubic lattice vectors. Here we analyze these transitions in depth. Eigenvalues and eigenvectors of the Wallace tensor identify and classify linear instabilities in the presence of strain. We show that both instabilities are discontinuous, leading to discrete jumps in the lattice parameters. We provide physical intuition for the instabilities by analyzing the changes in first-principles energy, stress, bond lengths, and angles upon application of strain. Electronic band structure calculations show differential occupation of bonding and antibonding orbitals, driven by the changing bond lengths and leading to the structural transformations. Strain thresholds for these instabilities depend on the valence electron count.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A finite-strain rate- and pressure-dependent constitutive framework for analyzing shock compression behavior of cemented tungsten carbides to 100 GPa

In the present study a thermodynamically-consistent finite-strain rate-and-pressure-dependent constitutive framework is implemented to analyze the shock-compression behavior of cemented tungsten carbides to 100 GPa. Central to this framework is the use of logarithmic strain with a set of invariant basis that allow the Cauchy stress tensor to be expressed as a sum of three response terms that are mutually orthogonal, thus permitting a complete separation of the deviatoric and volumetric (pressure) response. An overstress viscoplasticity model that includes strain and strain rate hardening along with thermal softening is used to represent the deviatoric response, while a complete Mie-Grüneisen equation of state (EoS) is used to obtain the pressure response. Using this formulation, the shock-induced compression behavior of cemented tungsten carbide - obtained from planar plate impact experiments using a 30 mm powder gun to peak stresses of up to ~100 GPa - is analyzed to better understand the structure of the measured shock wave profiles and the associated in-material shock quantities. Of particular interest is the evolution of material inelasticity and strength, and temperature in the tungsten carbide samples during the shock compression process.

Cemented tungsten carbide↗

DOE OSTI2020

A continuum framework for coupled solid deformation–fluid flow through anisotropic elastoplastic porous media

We present a continuum framework for coupled solid deformation–fluid flow in anisotropic elastoplastic porous media. A thermodynamic formulation of the coupled processes gives rise to an anisotropic Biot tensor that is a function of drained elastic tangent moduli tensor of the solid skeleton and the intrinsic bulk modulus of the solid constituent. Two effective stress measures emerge from the formulation, namely, σ', which is energy-conjugate to the elastic strain, and σ'', which is energy-conjugate to the plastic strain. For the special case of transverse isotropy that is commonly encountered in natural rocks, the Biot tensor can be expressed in terms of its normal and tangential components to the bedding plane, along with a microstructure tensor. Apart from its thermodynamic consistency, an advantage of this new formulation is that standard mixed finite element formulation can be employed to discretize the domain and solve initial boundary-value problems. We conduct plane strain simulations of coupled solid deformation–fluid flow in a transversely isotropic porous medium to demonstrate the impacts of material anisotropy, stress history, and the Biot tensor on the system response.

42 ENGINEERING↗

NASA NTRS1991

Explicit robust schemes for implementation of a class of principal value-based constitutive models: Theoretical development

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models is addressed. To this end, explicit forms for the corresponding material tangent stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.

Saleeb, A. F.↗

DOE OSTI2022

Characterization and visualization of grain boundary disconnections

We introduce a method to visualize dislocations along grain boundaries at the atomic level. It uses an atomic-level Nye tensor, representing the dislocation density. To calculate the Nye tensor at grain boundaries, we extend the Hartley-Mishin strain gradient calculation to the displacement shift complete lattice. We show that the method is effective in visualizing disconnections and the dislocation content of grain boundary phase junctions in body-centered cubic tungsten, as well as face-centered cubic copper. In addition, we use the method to characterize the morphology of a two-dimensional grain boundary phase nucleus in a symmetric tilt grain boundary in tungsten. This method can be applied to both bulk dislocations and grain boundary disconnections, which makes it ideal for studying the interactions and reactions of bulk dislocations with grain boundaries, and grain boundary disconnections.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Structural, Electrical, and Electromechanical Properties of Inverse Hybrid Perovskites from First-Principles: The Case of (CH 3 NH 3 ) 3 OI

Inverse-hybrid perovskites (IHPs) with large polarization have recently been predicted from first-principles computations. Here, we use one representative from the IHP class of materials, (CH 3 NH 3 ) 3 OI (MA3OI), to propose a route to the first-principles prediction of structural and electrical properties, such as polarization, polarization reversibility, and the associated coercive field for hybrid organic–inorganic perovskites. The route relies on the construction of the polarization reversal path that models experimental measurements. Such a path was found to play an important role in the ground-state search as well as in the identification of competing structural variations. The latter is believed to be the origin of the structural disorder that is characteristic of hybrid organic–inorganic perovskites. The application of such an approach to MA3OI leads to the prediction of several structural variations that are expected to result in a structurally disordered phase above 766 K and of the polar ground state with a polarization of 25.3 μC/cm 2 that is reversible with the application of an electric field. The upper estimate for the coercive field associated with homogeneous polarization reversal is 6.9 GV/m. The piezoelectric constants of MA3OI are predicted to be an order of magnitude smaller in comparison with a prototypical inorganic ferroelectric PbTiO 3 ; however, the low symmetry of the MA3OI structure yields finite values for all components of the piezoelectric tensor. The polarization in MA3OI is tunable by the epitaxial strain (11.5% change under 5% epitaxial strain), although less so as compared with PbTiO 3 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1992

LES versus DNS: A comparative study

We have performed Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) of forced isotropic turbulence at moderate Reynolds numbers. The subgrid scale model used in the LES is based on an eddy viscosity which adjusts instantaneously the energy spectrum of the LES to that of the DNS. The statistics of the large scales of the DNS (filtered DNS field or fDNS) are compared to that of the LES. We present results for the transfer spectra, the skewness and flatness factors of the velocity components, the PDF's of the angle between the vorticity and the eigenvectors of the rate of strain, and that between the vorticity and the vorticity stretching tensor. The above LES statistics are found to be in good agreement with those measured in the fDNS field. We further observe that in all the numerical measurements, the trend was for the LES field to be more gaussian than the fDNS field. Future research on this point is planned.

Shtilman, L.↗

NASA NTRS1971

On strain energy and constitutive relations for alkali metals.

An expression for the strain energy as a continuous differentiable function of the Green-Cauchy deformation tensor is obtained for the alkali metals at absolute zero temperature. The development is based on well established quantum and classical calculations of the various contributions to the crystal energy. Stress-deformation relations are next obtained. As a check on the accuracy of the strain energy, theoretical calculations of the values of the second-order elastic coefficients are obtained and compared to known experimental data. The predicted values are shown to compare quite well with the experimental values.

Eftis, J.↗

DOE OSTI2022

Ab initio calculations of third-order elastic coefficients

Third-order elasticity (TOE) theory predicts strain-induced changes in second-order elastic coefficients (SOECs) and can model elastic wave propagation in stressed media. Although third-order elastic tensors have been determined based on first principles in previous studies, their current definition is based on an expansion of thermodynamic energy in terms of the Lagrangian strain near the natural, or zero pressure, reference state. This definition is inconvenient for predictions of SOECs under significant initial stresses. Therefore, when TOE theory is necessary to study the strain dependence of elasticity, the seismological community has resorted to an empirical version of the theory. This study reviews the thermodynamic definition of the third-order elastic tensor and proposes using an “effective” third-order elastic tensor. An explicit expression for the effective third-order elastic tensor is given and verified. Additionally, we extend the ab initio approach to calculate third-order elastic tensors under finite pressure and apply it to two cubic systems, namely, NaCl and MgO. As applications and validations, we evaluate (a) strain-induced changes in SOECs and (b) pressure derivatives of SOECs based on ab initio calculations. Good agreement between third-order elasticity-based predictions and numerically calculated values confirms the validity of our theory.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Planar, longitudinal, compressive waves in solids: Thermodynamics and uniaxial strain restrictions

A new tri-axial pressure-based constitutive expression has been found using Cauchy's stress tensor. This stress state emphasizes pressure and shear stress. The description is a pressure plus an effective shear stress allowing for a constitutive law based on atomic solid-state phase changes in crystalline cells due to pressure plus shear-based dislocation motion commonly associated with plasticity. Pressure has a new role in the material's constitutive response as it is separated from plasticity. The thermo-mechanical system describes third-order Gibbs’ expressions without specific volume restrictions placed upon the material. Isothermally, the ratio of heat to shear work in elastic copper is shown to approach zero at a very low temperature and become larger than one as temperature approaches melting. Wave compression models investigated are elastic and plastic: in fully elastic materials, the planar wave is restricted by Poisson's effect although plastic shear changes this constraint. Plastic deformation, dominated by dissipative shear stresses in uniaxial strain, heats the material while excluding phase changes from hydrostatic pressures. The material properties per se across Hugoniot shocks are described with entropy concepts. Shock waves are exceedingly complex since the constitutive laws are linked at extreme temperatures, pressures, and shear stresses. Isothermal, isentropic, isochoric, and iso-shear conditions are used throughout with Jacobian algebra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

On the development of explicit robust schemes for implementation of a class of hyperelastic models in large-strain analysis of rubbers

The issue of developing effective and robust schemes to implement a class of the Ogden-type hyperelastic constitutive models, for large-strain analysis of rubber-like materials, is addressed. To this end, explicit forms for the corresponding material tangent-stiffness tensors are developed, and these are valid for the entire deformation range; i.e., with both distinct as well as repeated principal-stretch values. Throughout the analysis the various implications of the underlying property of separability of the strain-energy functions are exploited, thus leading to compact final forms of the tensor expressions. In particular, this facilitated the treatment of the complex cases of uncoupled volumetric/deviatoric formulations for incompressible materials, which are becoming increasingly popular in recent years. The forms derived are also amenable for use with symbolic-manipulation packages for systematic code generation.

Saleeb, A. F.↗

DOE OSTI2021

Geodyn Material Library: Pseudocap models for dry porous tocks

This report describes the second edition of the Pseudocap Strength models for porous rocks implemented in GEODYN material library. The first model was developed in 2007 and calibrated for concrete. Then, the model parameters were calibrated based on triaxial tests reported for limestones and sandstones of various porosities. In these models some key parameters were chosen as functions of the reference porosity,Φ. Since then multiple modifications were implemented in the model, therefore, it has been recalibrated for some common porous materials such as limestones, sandstones, alluvium, tuffs and granite. Two types of models are described in this repot. The first type (called Pseudocap Model or PM) is for rocks from a specific location. Parameters were calibrated for several specific geologic materials. The second type (called Generic Pseudocap Model or GPM) is useful for the sites where only basic information (rock type, porosity) is available. Generic models include built-in correlations between porosities and other mechanical properties observed for certain rock types. The models of both types were validated by comparing not only to quasi-static triaxial tests for these materials but also to shock Hugoniot data and spherical explosion data for some materials. All models were derived in the frame of isotropic plasticity. They are designed to be used in explicit finite element/difference codes. Tangent stiffness tensor is not provided but can be calculated numerically for the model to be used in implicit finite element codes. For an isotropic material the stress can be decomposed into volumetric and deviatoric parts. The volumetric part is modeled using an Equation of state (EOS) which calculates the pressure and the bulk sound speed as functions of the internal specific energy and density. Here a simple, Mie-Gruneisen EOS is presented, but tabulated EOS (LEOS) provided by the library can be used as well. The stress is limited by the yield surface which depends on three invariants of the stress tensor and specific internal energy. In addition, to capture the strain-rate dependence a simple multiplier is used for the yield surface which depends on the equivalent plastic strain rate. The failure surface (the ultimate yield, Y f , defined later) is chosen in the Hoek-Brown form, commonly used in rock mechanics. It includes measurable parameters such as Unconfined Compressive Strength (UCS) as well as scale parameters characterizing the quality of the rock such as GSI (Geologic Strength Index). Thus, even though the model is calibrated for small samples it offers a way to extrapolate the strength to the field scale using geological characterization of the rock mass. The model captures effects of brittle-ductile transition in rocks by introducing a cap multiplier to the yield function. The rate of dilatancy (bulking) is proportional to the slope of the yield surface affected by the cap. Therefore, it takes place only at low confinements when the pressure is less than the brittle-ductile transition pressure, P BD . On the contrary, the porous compaction takes place at pressures higher than P BD . The cap moves as the porosity is compacted or new porosity is generated due to dilatancy. The porous compaction is modeled using an evolution equation which includes deviatoric stress so that the onset of compaction corresponds to the cap surface. The model captures effects of shear-enhanced compaction which is an important for porous rocks. Section 2 describes the modeling framework and Section 3 presents the model calibration procedure. Section 4 compares experimental data for various rocks versus model predictions. The model parameters used for this comparison are given in Appendix. The files with material constants are available with the latest GEODYN material library distribution.

58 GEOSCIENCES↗