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NASA NTRS2026

Development, Characterization, and Validation of Elevated-Temperature Constitutive Models: Deformation and Damage

This report provides a brief review of experimentally observed hereditary and nonhereditary material behavior along with background information on standard as well as advanced internal state variable constitutive modeling at elevated temperature. A description of exploratory, characterization, and validation testing is presented along with a detailed outline of what constitutes “sufficient” data content (i.e., quality and quantity) for developing or enhancing, characterizing, and validating a particular sophisticated nonlinear time- and history-dependent (hereditary) class of constitutive models known as GVIPS (generalized viscoplasticity with potential structure). The tests described are necessary to reveal a material’s behavior in the reversible (or viscoelastic) and irreversible (or viscoplastic) regimes, for the identification of both deformation and damage model parameters. Results presented are primarily for metallic materials. In all cases, both uniaxial and multiaxial tests are described, and the linkage between the specific tests and the parameters within the model that can be characterized from the results of these tests are also discussed. Discussion is also provided relative to the role information management must play relative to material data collection, analysis, maintenance, and dissemination. The need for such an information system is particularly important as both analyst and designer move toward utilizations of sophisticated, nonlinear time- and history dependent (hereditary) constitutive models. Lastly, the concept of state space and its utility in understanding and establishing constitutive models is addressed throughout. The intent behind this document is to help both the modeler and experimentalist understand each other’s specific points of view and provide guidance for both model development and characterization. Emphasis has been placed on providing the mechanician with information regarding how tests are performed and what issues to be aware of when interpreting results. It is hoped that experimentalists will take away a new perspective on the types of information that modelers and analysts are looking for from them.

Constitutive Modeling↗

NASA NTRS2014

Reply to Comment by Laprise on 'the Added Value to Global Model Projections of Climate Change by Dynamical Downscaling: a Case Study over the Continental U.S. Using the GISS-ModelE2 and WRF Models'

In his comment, Laprise raises several points that we agree merit consideration. His primary critique is that our study [Racherla et al., 2012] tested the ability of the WRF regional climate model to reproduce historical temperature and precipitation change relative to the driving global climate model (GCM) using only a single simulation rather than an ensemble. He asserts that the observed changes are smaller than the internal variability in the climate system (i.e., not statistically significant) and that thus a single simulation should not necessarily be able to capture the observations. Laprise points out that the statistical signal is reduced for a multi-decadal trend such as the one we analyzed in comparison with mean climatology and cites two studies showing that for particular climate parameters it can take any years for a signal to be discerned over internal variability. He states that The results of theexperiment as designed were strongly influenced by the presence of internal variability and sampling errors,which masked the rather small climate changes that may have occurred as a consequence of changes inforcing during the period considered. While Laprise discusses statistics in general terms at some length, for the actual climate trends examined in our study, he offers no evidence that the forced signal was smallcompared with internal variability. The two studies he cites [de Ela et al., 2013; Maraun, 2013] do not provide convincing evidence as they concern climate variables averaged over different times and areas. One in fact examines extreme precipitation events, which by definition are rare and thus have a lower significance level. We accept the general point that it is important to consider internal variability, and as noted in our paper we agree that an ensemble of simulations is in principle an optimal, though computationally expensive, approach. While we did not present the statistical significance of the observations in our original paper, we have now evaluated those for the regional temperature trends used in our study to evaluate the added value of WRF and thus can analyze data as to the magnitude of the trends with respect to internal variability.

climate↗

NASA NTRS1990

Materials with periodic internal structure: Computation based on homogenization and comparison with experiment

The combination of thermal and mechanical loading expected in practice means that constitutive equations of metal matrix composites must be developed which deal with time-independent and time-dependent irreversible deformation. Also, the internal state of composites is extremely complicated which underlines the need to formulate macroscopic constitutive equations with a limited number of state variables which represent the internal state at the micro level. One available method for calculating the macro properties of composites in terms of the distribution and properties of the constituent materials is the method of homogenization whose formulation is based on the periodicity of the substructure of the composite. A homogenization procedure was developed which lends itself to the use of the finite element procedure. The efficiency of these procedures, to determine the macroscopic properties of a composite system from its constituent properties, was demonstrated utilizing an aluminum plate perforated by directionally oriented slits. The selection of this problem is based on the fact that, extensive experimental results exist, the macroscopic response is highly anisotropic, and that the slits provide very high stress gradients which severely test the effectiveness of the computational procedures. Furthermore, both elastic and plastic properties were investigated so that the application to practical systems with inelastic deformation should be able to proceed without difficulty. The effectiveness of the procedures was rigorously checked against experimental results and with the predictions of approximate calculations. Using the computational results it is illustrated how macroscopic constitutive equations can be expressed in forms of the elastic and limit load behavior.

Jansson, S.↗

NASA NTRS1986

A lumped parameter mathematical model for simulation of subsonic wind tunnels

Equations for a lumped parameter mathematical model of a subsonic wind tunnel circuit are presented. The equation state variables are internal energy, density, and mass flow rate. The circuit model is structured to allow for integration and analysis of tunnel subsystem models which provide functions such as control of altitude pressure and temperature. Thus the model provides a useful tool for investigating the transient behavior of the tunnel and control requirements. The model was applied to the proposed NASA Lewis Altitude Wind Tunnel (AWT) circuit and included transfer function representations of the tunnel supply/exhaust air and refrigeration subsystems. Both steady state and frequency response data are presented for the circuit model indicating the type of results and accuracy that can be expected from the model. Transient data for closed loop control of the tunnel and its subsystems are also presented, demonstrating the model's use as a control analysis tool.

Krosel, S. M.↗

NASA NTRS1982

Estimates of software size from state machine designs

The length, or size (in number of Source Lines of Code) of programs represented as state machines, it is demonstrated, can be reliably estimated in terms of the number of internal state machine variables.

Britcher, R. N.↗

NASA NTRS2026

LAI Assimilation Schedules to Constrain Uncertain Cultivars and Soils in CERES-Maize

In anticipation of large-domain crop model applications where precise local configuration and calibration is not possible, we describe benefits and potential drawbacks of employing a crop pest module to achieve leaf area index (LAI) assimilation into a high performing CERES-Maize crop model configuration at a field experiment site in Perry, Iowa. Simulation experiments explore the use of MODIS satellite-derived LAI to constrain and adjust LAI to counter imprecise cultivar and soil configurations often occurring in the absence of high-quality local information. Simulations using single-day, window, and continuous LAI replacement across 5 cultivars and 2 soil calibration approaches for nine corn rotation years from 2004 to 2020 led to different yield outcomes and reverberations throughout the field environment. Evaluating variance and mean bias, results indicate minimal interventions in early vegetative and grain-filling stages were more beneficial than use of continuous LAI adjustments, as they minimized disruptions to the internal resource balances governing plant stresses and grain production. LAI adjustment was particularly helpful in constraining growth related to uncertain thermal unit requirements and leaf tip appearance rates (P1 and PHINT cultivar parameters, respectively). Findings underscore the need to assimilate additional state variables to ensure internal biophysical coherence. This approach shows promise for applications spanning wider domains with prediction time pressure where detailed configuration, more complex assimilation methods, or recalibration of crop model parameters may not be practical.

Phenology↗

NASA NTRS1986

Effects of state recovery on creep buckling under variable loading

Structural alloys embody internal mechanisms that allow recovery of state with varying stress and elevated temperature, i.e., they can return to a softer state following periods of hardening. Such material behavior is known to strongly influence structural response under some important thermomechanical loadings, for example, that involving thermal ratchetting. The influence of dynamic and thermal recovery on the creep buckling of a column under variable loading is investigated. The column is taken as the idealized (Shanley) sandwich column. The constitutive model, unlike the commonly employed Norton creep model, incorporates a representation of both dynamic and thermal (state) recovery. The material parameters of the constitutive model are chosen to characterize Narloy Z, a representative copper alloy used in thrust nozzle liners of reusable rocket engines. Variable loading histories include rapid cyclic unloading/reloading sequences and intermittent reductions of load for extended periods of time; these are superimposed on a constant load. The calculated results show that state recovery significantly affects creep buckling under variable loading. Structural alloys embody internal mechanisms that allow recovery of state with varying stress and time.

Robinson, D. N.↗

NASA NTRS1985

Thermodynamically consistent constitutive equations for nonisothermal large strain, elasto-plastic, creep behavior

The paper is concerned with the development of constitutive relations for large nonisothermal elastic-viscoplastic deformations for metals. The kinematics of elastic-plastic deformation, valid for finite strains and rotations, is presented. The resulting elastic-plastic uncoupled equations for the deformation rate combined with use of the incremental elasticity law permits a precise and purely deductive development of elastic-viscoplastic theory. It is shown that a phenomenological thermodynamic theory in which the elastic deformation and the temperature are state variables, including few internal variables, can be utilized to construct elastic-viscoplastic constitutive equations, which are appropriate for metals. The limiting case of inviscid plasticity is examined.

Riff, R.↗

NASA NTRS1988

Effects of state recovery on creep buckling under variable loading

Robinson, D. N.↗

NASA NTRS1990

Effects of state recovery on creep buckling under variable loading

Robinson, D. N.↗

NASA NTRS1984

Calculation of nonequilibrium radiation in the flight regimes of aeroassisted orbital transfer vehicles

A computer code has been developed that calculates radiative properties of nonequilibrium air in the low-density regimes expected during the flight of aeroassisted, orbital transfer vehicles. From the given nonequilibrium thermodynamic state variables, the code calculates number densities of internal states and the accompanying emission and absorption characteristics. In addition, the code calculates the number density of the hypothetical gas in radiative equilibrium that produces the same radiation emission as the given nonequilibrium gas. Sample results are shown to demonstrate how the code predicts the nonlinear variation of radiation with density at low densities.

Park, C.↗

NASA NTRS1985

Calculation of Nonequilibrium Radiation in the Flight Regimes of Aeroassisted Orbital Transfer Vehicles

A computer code has been developed that calculates radiative properties of nonequilibrium air in the low-density regimes expected during the flight of aeroassisted, orbital transfer vehicles. From the given nonequilibrium thermodynamic state variables, the code calculates number densities of internal states and the accompanying emission and absorption characteristics. In addition, the code calculates the number density of the hypothetical gas in radiative equilibrium that produces the same radiation emission as the given nonequilibrium gas. Sample results are shown to demonstrate how the code predicts the non-linear variation of radiation with density at low densities.

Park, Chul↗

NASA NTRS2001

Thresholds in Atmosphere-Soil Moisture Interactions: Results from Climate Model Studies

The potential predictability of the effects of warm season soil moisture anomalies over the central U.S. has been investigated using a series of GCM (Global Climate Model) experiments with the NCAR (National Center for Atmospheric Research) CCM3 (Community Climate Model version 3)/LSM (Land Surface Model). Three different types of experiments have been made, all starting in either March (representing precursor conditions) or June (conditions at the onset of the warm season): (1) 'anomaly' runs with large, exaggerated initial soil moisture reductions, aimed at evaluating the physical mechanisms by which soil moisture can affect the atmosphere; (2) 'predictability' runs aimed at evaluating whether typical soil moisture initial anomalies (indicative of year-to-year variability) can have a significant effect, and if so, for how long; (3) 'threshold' runs aimed at evaluating if a soil moisture anomaly must be of a specific size (i.e., a threshold crossed) before a significant impact on the atmosphere is seen. The 'anomaly' runs show a large, long-lasting response in soil moisture and also quantities such as surface temperature, sea level pressure, and precipitation; effects persist for at least a year. The 'predictability' runs, on the other hand, show very little impact of the initial soil moisture anomalies on the subsequent evolution of soil moisture and other atmospheric parameters; internal variability is most important, with the initial state of the atmosphere (representing remote effects such as SST anomalies) playing a more minor role. The 'threshold' runs, devised to help resolve the dichotomy in 'anomaly' and 'predictability' results, suggest that, at least in CCM3/LSM, the vertical profile of soil moisture is the most important factor, and that deep soil zone anomalies exert a more powerful, long-lasting effect than do anomalies in the near surface soil zone. We therefore suggest that soil moisture feedbacks may be more important in explaining prolonged decadal to century-long droughts evident in the historic and recent prehistoric records, but less important on a seasonal to interannual time-scale.

Oglesby, Robert J.↗

NASA NTRS2013

Human and Natural Influences on the Changing Thermal Structure of the Atmosphere

Since the late 1970s, satellite-based instruments have monitored global changes in atmospheric temperature. These measurements reveal multidecadal tropospheric warming and stratospheric cooling, punctuated by short-term volcanic signals of reverse sign. Similar long- and short-term temperature signals occur in model simulations driven by human-caused changes in atmospheric composition and natural variations in volcanic aerosols. Most previous comparisons of modeled and observed atmospheric temperature changes have used results from individual models and individual observational records. In contrast, we rely on a large multimodel archive and multiple observational datasets. We show that a human-caused latitude/altitude pattern of atmospheric temperature change can be identified with high statistical confidence in satellite data. Results are robust to current uncertainties in models and observations. Virtually all previous research in this area has attempted to discriminate an anthropogenic signal from internal variability. Here, we present evidence that a human-caused signal can also be identified relative to the larger "total" natural variability arising from sources internal to the climate system, solar irradiance changes, and volcanic forcing. Consistent signal identification occurs because both internal and total natural variability (as simulated by state-of-the-art models) cannot produce sustained global-scale tropospheric warming and stratospheric cooling. Our results provide clear evidence for a discernible human influence on the thermal structure of the atmosphere.

Santer, Benjamin D.↗

NASA NTRS1992

Impact damage resistance of composite fuselage structure, part 1

The impact damage resistance of laminated composite transport aircraft fuselage structures was studied experimentally. A statistically based designed experiment was used to examine numerous material, laminate, structural, and extrinsic (e.g., impactor type) variables. The relative importance and quantitative measure of the effect of each variable and variable interactions on responses including impactor dynamic response, visibility, and internal damage state were determined. The study utilized 32 three-stiffener panels, each with a unique combination of material type, material forms, and structural geometry. Two manufacturing techniques, tow placement and tape lamination, were used to build panels representative of potential fuselage crown, keel, and lower side-panel designs. Various combinations of impactor variables representing various foreign-object-impact threats to the aircraft were examined. Impacts performed at different structural locations within each panel (e.g., skin midbay, stiffener attaching flange, etc.) were considered separate parallel experiments. The relationship between input variables, measured damage states, and structural response to this damage are presented including recommendations for materials and impact test methods for fuselage structure.

Dost, E. F.↗

NASA NTRS1995

The microscopic state of the solar wind: Links between composition, velocity distributions, waves and turbulence

An overview is given of the microscopic state of the solar wind with emphasis on recent Ulysses high-latitude observations and previous Helios in-ecliptic observations. The possible links between composition, ionization state. velocity distribution functions of electrons, protons and heavy ions. kinetic plasma waves and MHD-scale turbulence are elaborated. Emphasis is placed on a connection of interplanetary kinetic-scale phenomena with their generating microscopic processes in the corona. The fast streams seem to consist of mesoscale pressure-balanced plasma filaments and magnetic flux tubes, reminiscent of the supergranular-size structures building the open corona, from which copious Alfven waves emanate. The wind from the magnetically structured and active corona shows developed compressive turbulence and considerable abundance and ionization state variations. Some modelling attempts to explain the observed element fractionation are briefly reviewed. The causes of the nonthermal particle features. such as proton-ion differential streaming, ion beams. temperature anisotropies, and skewed distributions associated with collisionless heat conduction, are ultimately to be searched in the fact, that the corona is never quiescent but fundamentally variable in space and time. Consequently, the radial evolution of the internal state of the wind resembles at all latitudes a complicated relaxation process, in the course of which the free (in comparison with LTE conditions) particle kinetic energy is converted into plasma waves and MHD turbulence on a wide range of scales. This leads to intermittent wave-particle interactions and unsteady anomalous transport, mixed with the weak effects of the rare Coulomb collisions. Spherical expansion and large-scale inhomogeneity forces the wind to attain microscopically a complex internal state of dynamic statistical equilibrium.

Marsch, E.↗

NASA NTRS2013

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.

Modeling↗

NASA NTRS2003

Computations of Internal and External Axisymmetric Nozzle Aerodynamics at Transonic Speeds

Computational Fluid Dynamics (CFD) analyses of axisymmetric circular-arc boattail nozzles have been completed in support of NASA's Next Generation Launch Technology Program to investigate the effects of high-speed nozzle geometries on the nozzle internal flow and the surrounding boattail regions. These computations span the very difficult transonic flight regime, with shock-induced separations and strong adverse pressure gradients. External afterbody and internal nozzle pressure distributions computed with the Wind code are compared with experimental data. A range of turbulence models were examined in Wind, including an Explicit Algebraic Stress model (EASM). Computations on two nozzle geometries have been completed at freestream Mach numbers ranging from 0.6 to 0.9, driven by nozzle pressure ratios (NPR) ranging from 2.9 to 5. Results obtained on converging-only geometry indicate reasonable agreement to experimental data, with the EASM and Shear Stress Transport (SST) turbulence models providing the best agreement. Calculations completed on a converging-diverging geometry involving large-scale internal flow separation did not converge to a true steady-state solution when run with variable timestepping (steady-state). Calculations obtained using constant timestepping (time-accurate) indicate less variations in flow properties compared with steady-state solutions. This failure to converge to a steady-state solution was found to be the result of difficulties in using variable time-stepping with large-scale separations present in the flow. Nevertheless, time-averaged boattail surface pressure coefficient and internal nozzle pressures show fairly good agreement with experimental data. The SST turbulence model demonstrates the best over-all agreement with experimental data.

Dalbello, Teryn↗