Search NASA⌕ Search

SEARCH · Search NASA

Results for “constitutive equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Numerical Simulations of Crystal Growth of an Alloy Under Microgravity Conditions

The directional solidification of a dilute binary alloy (Bi-1.0 at.%Sn)is investigated. Results are obtained at a gravity level of I pg. Computations are performed in two dimensions with a fixed, non-uniform grid. The simulation involves a solution of the species concentration equation (modified to account for solute rejection at the interface) and energy equation (modified to account for phase-change) for both the solid and liquid phases, in addition to the constitutive equations for describing convective flow in the melt. The effects of conductive heat transfer in the ampoule and in a capillary tube in the sample are included. To gauge the effects of including this growth capillary tube in the apparatus, simulations both with and without the capillary tube are presented and compared. Fully transient simulations have been performed; no simplifying steady-state approximations are used, however, the influence of solute on the melting temperature at the interface is not included. Both thermal and solutal convective cells are seen to form. Convective velocities are significantly damped inside the capillary, causing less segregation due to convection. As solidification proceeds beyond the capillary tube, longitudinal segregation arises as a result of the change in cross-sectional area of solidifying material. The magnitudes of the velocities in this cell increase significantly once the solid/liquid front passes beyond the end of the capillary tube; this causes a corresponding increase in the level of radial solute segregation in the solidified material.

Simpson, James E.↗

Transport Equations for CAD Modeling of Al(x)Ga(1-x)N/GaN HEMTs

BEMTs formed from Al(x)Ga(1-x)N/GaN heterostructures are being investigated for high RF power and efficiency around the world by many groups, both academic and industrial. In these devices, the 2DEG formation is dominated by both spontaneous and piezoelectric polarization fields, with each component having nearly the same order of magnitude. The piezoelectric portion is induced by the mechanical strain in the structure, and to analyze these devices, one must incorporate the stress/strain relationships, along with the standard semiconductor transport equations. These equations for Wurtzite GaN are not easily found in the open literature, hence this paper summarizes them, along with the constitutive equations for piezoelectric materials. The equations are cast into the format for the Wurtzite crystal class, which is the most common way GaN is grown epitaxially.

Freeman, Jon C.↗

EBS Task Force: Task 9/FEBEX Modeling Final Report: Thermo-Hydrological Modeling with PFLOTRAN

This report outlines Sandia National Laboratories modeling studies applied to Stage 1 and Stage 2 of the Full-scale Engineered Barriers Experiment in Crystalline Host Rock (FEBEX) in situ test for the SKB EBS Task Force Task 9. The FEBEX test was a full-scale test conducted over ~18 years at the Grimsel, Switzerland Underground Research Laboratory (URL) managed by NAGRA. It involved emplacing simulated waste packages, in the form of welded cylindrical heaters, inside a tunnel in crystalline granitic rock and surrounded by a bentonite barrier and cement plug. Sensors emplaced within the bentonite monitored the wetting-up, heating, and drying out of the bentonite barrier, and the large resulting data set provides an excellent opportunity for validation of multiphysics Thermal-Hydrological (TH), Thermal-Hydrologic-Chemical (THC), and Thermal-Hydrological-Mechanical (THM) modeling approaches for underground nuclear waste storage and the performance of engineered bentonite barriers. The present status of the EBS Task Force is finalizing Task 9, which follows years of modeling studies of the FEBEX test, by many notable modeling teams (Gens et al., 2009; Sanchez et al. 2010; 2012; Samper et al., 2018). These modeling studies generally use two-dimensional axisymmetric meshes, ignoring threedimensional effects, gravity and asymmetric wetting and dry out of the bentonite engineered barrier. This study investigates these effects with use of the PFLOTRAN THC code with massively parallel computational methods in modeling FEBEX Stage 1 and Stage 2 results. The PFLOTRAN numerical code is an open source, state-of-the-art, massively parallel subsurface flow and reactive transport code operating in a high-performance computing environment (Hammond et al., 2014). Section 2 describes the applied partial differential equations describing mass, momentum and energy balance used in this study, considerations derived by assuming phase equilibrium between gas and liquid phases, constitutive equations for granite, cement plug, and bentonite domains, and specific approaches for use inthe PFLOTRAN code. Section 3 describes the geometry, meshing, and model set-up. Section 4 describes modeling results, Section 5 compares modeling results to field testing data, and Section 6 gives conclusions. The Appendix provides detailed information required by the EBSTask Force for final reporting.

42 ENGINEERING↗

Rate Dependent Deformation and Strength Analysis of Polymer Matrix Composites

A research program is being undertaken to develop rate dependent deformation and failure models for the analysis of polymer matrix composite materials. In previous work in this program, strain-rate dependent inelastic constitutive equations used to analyze polymers have been implemented into a mechanics of materials based composite micromechanics method. In the current work, modifications to the micromechanics model have been implemented to improve the calculation of the effective inelastic strain. Additionally, modifications to the polymer constitutive model are discussed in which pressure dependence is incorporated into the equations in order to improve the calculation of constituent and composite shear stresses. The Hashin failure criterion is implemented into the analysis method to allow for the calculation of ply level failure stresses. The deformation response and failure stresses for two representative uniaxial polymer matrix composites, IM7/977-2 and AS4-PEEK, are predicted for varying strain rates and fiber orientations. The predicted results compare favorably to experimentally obtained values.

Goldberg, Robert K.↗

Transverse shear stiffness of laminated anisotropic shells

Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.

Cohen, G. A.↗

Computational simulation of coupled material degradation processes for probabilistic lifetime strength of aerospace materials

The research included ongoing development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects or primative variables. These primative variable may include high temperature, fatigue or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation has been randomized and is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the above described constitutive equation using actual experimental materials data together with linear regression of that data, thereby predicting values for the empirical material constraints for each effect or primative variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from the open literature for materials typically of interest to those studying aerospace propulsion system components. Material data for Inconel 718 was analyzed using the developed methodology.

Boyce, Lola↗

Computational simulation of probabilistic lifetime strength for aerospace materials subjected to high temperature, mechanical fatigue, creep, and thermal fatigue

The results of a fourth year effort of a research program conducted for NASA-LeRC by The University of Texas at San Antonio (UTSA) are presented. The research included on-going development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subjected to a number of effects or primitive variables. These primitive variables may include high temperature, fatigue, or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation was randomized and is included in the computer program, PROMISC. Also included in the research is the development of methodology to calibrate the above-described constitutive equation using actual experimental materials data together with regression analysis of that data, thereby predicting values for the empirical material constants for each effect or primitive variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from industry and the open literature for materials typically for applications in aerospace propulsion system components. Material data for Inconel 718 was analyzed using the developed methodology.

Boyce, Lola↗

Multi-fidelity modeling to predict the rheological properties of fiber suspensions

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications like biofuel production. The 3D numerical simulations of the suspension of fibers are often computationally expensive and time-consuming. Machine learning methods such as neural networks can simplify the prediction of rheological behavior; however, they require a relatively large training data set. Multi -fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified physical equations, can lead to optimized predictions. Here, we focus on a neural network with two levels of fidelity, i.e., high and low fidelity networks. To produce high-fidelity data, we perform direct numerical simulations to model the fibers as one-dimensional inextensible slender bodies that obey the Euler- Bernoulli beam equation. The Navier-Stokes equations govern the suspended fluid, and an immersed boundary method is used to couple the fluid and solid motion. The low-fidelity data is produced by using constitutive equations. Noticeable improvements have been observed in the accuracy of predicting the rheological behavior when a multi-fidelity network is used compared to the single-fidelity network.

Boodaghidizaji, Miad↗

Computational simulation of probabilistic lifetime strength for aerospace materials subjected to high temperature, mechanical fatigue, creep and thermal fatigue

This report presents the results of a fourth year effort of a research program, conducted for NASA-LeRC by the University of Texas at San Antonio (UTSA). The research included on-going development of methodology that provides probabilistic lifetime strength of aerospace materials via computational simulation. A probabilistic material strength degradation model, in the form of a randomized multifactor interaction equation, is postulated for strength degradation of structural components of aerospace propulsion systems subject to a number of effects or primitive variables. These primitive variables may include high temperature, fatigue or creep. In most cases, strength is reduced as a result of the action of a variable. This multifactor interaction strength degradation equation has been randomized and is included in the computer program, PROMISS. Also included in the research is the development of methodology to calibrate the above-described constitutive equation using actual experimental materials data together with regression analysis of that data, thereby predicting values for the empirical material constants for each effect or primitive variable. This regression methodology is included in the computer program, PROMISC. Actual experimental materials data were obtained from industry and the open literature for materials typically for applications in aerospace propulsion system components. Material data for Inconel 718 has been analyzed using the developed methodology.

Boyce, Lola↗

A viscous-inviscid interaction algorithm for three-dimensional turbulent subsonic aerodynamic juncture region flow

An order-of magnitude analysis of the subsonic, three-dimensional, steady time-averaged Navier-Stokes equations for semibounded aerodynamic juncture geometries yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three-dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement first-order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. The algorithm is employed to predict the three-dimensional turbulent flowfield in the juncture region formed by two intersecting parabolic arcs at a free-stream Mach-number of 0.08, and Re/C = 600,000/m.

Baker, A. J.↗

The CMC:3DPNS computer program for prediction of three-dimensional, subsonic, turbulent aerodynamic juncture region flow. Volume 1: Theoretical

An order-of-magnitude analysis of the subsonic three dimensional steady time averaged Navier-Stokes equations, for semibounded aerodynamic juncture geometries, yields the parabolic Navier-Stokes simplification. The numerical solution of the resultant pressure Poisson equation is cast into complementary and particular parts, yielding an iterative interaction algorithm with an exterior three dimensional potential flow solution. A parabolic transverse momentum equation set is constructed, wherein robust enforcement of first order continuity effects is accomplished using a penalty differential constraint concept within a finite element solution algorithm. A Reynolds stress constitutive equation, with low turbulence Reynolds number wall functions, is employed for closure, using parabolic forms of the two-equation turbulent kinetic energy-dissipation equation system. Numerical results document accuracy, convergence, and utility of the developed finite element algorithm, and the CMC:3DPNS computer code applied to an idealized wing-body juncture region. Additional results document accuracy aspects of the algorithm turbulence closure model.

Baker, A. J.↗

Constitutive modelling of single crystal and directionally solidified superalloys

The trend towards improved engine efficiency and durability places increasing demands on materials that operate in the hot section of the gas turbine engine. These demands are being met by new coatings and materials such as single crystal and directionally solidified nickel-base superalloys which have greater creep/fatigue resistance at elevated temperatures and reduced susceptibility to grain boundary creep, corrosion and oxidation than conventionally cast alloys. Work carried out as part of a research program aimed at the development of constitutive equations to describe the elevated temperature stress-strain-time behavior of single crystal and directionally solidified turbine blade superalloys is discussed. The program involves both development of suitable constitutive models and their verification through elevated temperature tension-torsion testing of single crystals of PWA 1480.

Jordan, E. H.↗

Coupled momentum balance and phase-field solver with fenicsx module

Code solves momentum balance and phase-field equations simultaneously. The differential equations are solved on a discretized domain with appropriate boundary and initial conditions using finite element method. Primary purpose of the code is to simulate brittle fracture under dynamic loading. Constitutive equations are that of linear elasticity with degradation of stress due to fracture. Small strain formulation is used.

Zecevic, Milovan↗

Experimental Determination of Constitutive Response of Alloy 800H in Support of Viscoplastic Constitutive Model Development for ASME Section III, Division 5, Class A Applications

In FY 2022, a development effort was initiated at the US Department of Energy’s Argonne National Laboratory (Argonne) and Oak Ridge National Laboratory (ORNL) to develop the Alloy 800H viscoplastic constitutive model so that inelastic analysis methods can support high-temperature gas-cooled reactor (HTGR) designs. The viscoplastic constitutive equations will be developed at Argonne. The ORNL effort focuses on generating test data from various high-temperature experiments with specially designed loading histories to probe Alloy 800H’s constitutive response.

36 MATERIALS SCIENCE↗

Application of symbolic computations to the constitutive modeling of structural materials

In applications involving elevated temperatures, the derivation of mathematical expressions (constitutive equations) describing the material behavior can be quite time consuming, involved and error-prone. Therefore intelligent application of symbolic systems to faciliate this tedious process can be of significant benefit. Presented here is a problem oriented, self contained symbolic expert system, named SDICE, which is capable of efficiently deriving potential based constitutive models in analytical form. This package, running under DOE MACSYMA, has the following features: (1) potential differentiation (chain rule), (2) tensor computations (utilizing index notation) including both algebraic and calculus; (3) efficient solution of sparse systems of equations; (4) automatic expression substitution and simplification; (5) back substitution of invariant and tensorial relations; (6) the ability to form the Jacobian and Hessian matrix; and (7) a relational data base. Limited aspects of invariant theory were also incorporated into SDICE due to the utilization of potentials as a starting point and the desire for these potentials to be frame invariant (objective). The uniqueness of SDICE resides in its ability to manipulate expressions in a general yet pre-defined order and simplify expressions so as to limit expression growth. Results are displayed, when applicable, utilizing index notation. SDICE was designed to aid and complement the human constitutive model developer. A number of examples are utilized to illustrate the various features contained within SDICE. It is expected that this symbolic package can and will provide a significant incentive to the development of new constitutive theories.

Arnold, Steven M.↗

A procedure for utilization of a damage-dependent constitutive model for laminated composites

Described here is the procedure for utilizing a damage constitutive model to predict progressive damage growth in laminated composites. In this model, the effects of the internal damage are represented by strain-like second order tensorial damage variables and enter the analysis through damage dependent ply level and laminate level constitutive equations. The growth of matrix cracks due to fatigue loading is predicted by an experimentally based damage evolutionary relationship. This model is incorporated into a computer code called FLAMSTR. This code is capable of predicting the constitutive response and matrix crack damage accumulation in fatigue loaded laminated composites. The structure and usage of FLAMSTR are presented along with sample input and output files to assist the code user. As an example problem, an analysis of crossply laminates subjected to two stage fatigue loading was conducted and the resulting damage accumulation and stress redistribution were examined to determine the effect of variations in fatigue load amplitude applied during the first stage of the load history. It was found that the model predicts a significant loading history effect on damage evolution.

Lo, David C.↗

Constitutive modeling of superalloy single crystals with verification testing

The goal is the development of constitutive equations to describe the elevated temperature stress-strain behavior of single crystal turbine blade alloys. The program includes both the development of a suitable model and verification of the model through elevated temperature-torsion testing. A constitutive model is derived from postulated constitutive behavior on individual crystallographic slip systems. The behavior of the entire single crystal is then arrived at by summing up the slip on all the operative crystallographic slip systems. This type of formulation has a number of important advantages, including the prediction orientation dependence and the ability to directly represent the constitutive behavior in terms which metallurgists use in describing the micromechanisms. Here, the model is briefly described, followed by the experimental set-up and some experimental findings to date.

Jordan, Eric↗

Rheological properties of nondilute suspensions of deformable particles

The creeping flow equations have been solved to account for effects of shear on drop shape when the influence of neighboring drops is considered. A cell model is used to account for finite concentrations of the dispersed phase. From these results a constitutive equation is derived and implications for several flows are discussed. The shape and orientation of drops are computed and compared with existing data. Finally, dynamic viscosity and rigidity are obtained for nondilute suspensions of viscoelastic particles in an oscillatory shear flow.-

Choi, S. J.↗