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NASA NTRS1988

Unified constitutive models for high-temperature structural applications

Unified constitutive models are characterized by the use of a single inelastic strain rate term for treating all aspects of inelastic deformation, including plasticity, creep, and stress relaxation under monotonic or cyclic loading. The structure of this class of constitutive theory pertinent for high temperature structural applications is first outlined and discussed. The effectiveness of the unified approach for representing high temperature deformation of Ni-base alloys is then evaluated by extensive comparison of experimental data and predictions of the Bodner-Partom and the Walker models. The use of the unified approach for hot section structural component analyses is demonstrated by applying the Walker model in finite element analyses of a benchmark notch problem and a turbine blade problem.

Lindholm, U. S.↗

NASA NTRS1988

Life assessment of combustor liner using unified constitutive models

Hot section components of gas turbine engines are subject to severe thermomechanical loads during each mission cycle. Inelastic deformation can be induced in localized regions leading to eventual fatigue cracking. Assessment of durability requires reasonably accurate calculation of the structural response at the critical location for crack initiation. In recent years nonlinear finite element computer codes have become available for calculating inelastic structural response under cyclic loading. NASA-Lewis sponsored the development of unified constitutive material models and their implementation in nonlinear finite element computer codes for the structural analysis of hot section components. These unified models were evaluated with regard to their effect on the life prediction of a hot section component. The component considered was a gas turbine engine combustor liner. A typical engine mission cycle was used for the thermal and structural analyses. The analyses were performed on a CRAY computer using the MARC finite element code. The results were compared with laboratory test results, in terms of crack initiation lives.

Tong, M. T.↗

NASA NTRS1988

Unified constitutive model for single crystal deformation behavior with applications

Single crystal materials are being used in gas turbine airfoils and are candidates for other hot section components because of their increased temperature capabilities and resistance to thermal fatigue. Development of a constitutive model which assesses the inelastic behavior of these materials has been studied in 2 NASA programs: Life Prediction and Constitutive Models for Engine Hot Section Anisotropic Materials and Biaxial Constitutive Equation Development for Single Crystals. The model has been fit to a large body of constitutive data for single crystal PWA 1480 material. The model uses a unified approach for computing total inelastic strains (creep plus plasticity) on crystallographic slip systems reproducing observed directional and strain rate effects as a natural consequence of the summed slip system quantities. The model includes several of the effects that have been reported to influence deformation in single crystal materials, such as shear stress, latent hardening, and cross slip. The model is operational in a commercial Finite Element code and is being installed in a Boundary Element Method code.

Walker, K. P.↗

NASA NTRS1988

Isothermal and bithermal thermomechanical fatigue behavior of a NiCoCrAlY-coated single crystal superalloy

Specimens of single crystal PWA 1480 with group of zone axes (100) orientation, bare, or with NiCoCrAlY coating PWA 276, were tested in low cycle fatigue (LCF) at 650, 870, and 1050 C, and in simplified bithermal thermomechanical fatigue (TMF) tests between these temperatures. These tests were examined as a bridge between isothermal LCF and general TMF. In the bithermal test, an inelastic strain is applied at one temperature, T sub max, and reversed at T sub min. The out-of-phase (OP) test type imposing tension at T sub min and compression at T sub max received most study, since it was more damaging than the in-phase type. Specifically investigated were the effects of: inelastic strain range, the coating, delta T, T sub max, T sub min, and the environment.

Gayda, J.↗

NASA NTRS1988

Electronic excitation and quenching of atoms at insulator surfaces

A trajectory-based semiclassical method is used to study electronically inelastic collisions of gas atoms with insulator surfaces. The method provides for quantum-mechanical treatment of the internal electronic dynamics of a localized region involving the gas/surface collision, and a classical treatment of all the nuclear degrees of freedom (self-consistently and in terms of stochastic trajectories), and includes accurate simulation of the bath-temperature effects. The method is easy to implement and has a generality that holds promise for many practical applications. The problem of electronically inelastic dynamics is solved by computing a set of stochastic trajectories that on thermal averaging directly provide electronic transition probabilities at a given temperature. The theory is illustrated by a simple model of a two-state gas/surface interaction.

Swaminathan, P. K.↗

NASA NTRS1988

Anisotropic constitutive modeling for nickel base single crystal superalloys using a crystallographic approach

A micromechanical model based on crystallographic slip theory was formulated for nickel-base single crystal superalloys. The current equations include both drag stress and back stress state variables to model the local inelastic flow. Specially designed experiments have been conducted to evaluate the effect of back stress in single crystals. The results showed that (1) the back stress is orientation dependent; and (2) the back stress state variable in the inelastic flow equation is necessary for predicting anelastic behavior of the material. The model also demonstrated improved fatigue predictive capability. Model predictions and experimental data are presented for single crystal superalloy Rene N4 at 982 C.

Stouffer, D. C.↗

NASA NTRS1988

A crystallographic model for nickel base single crystal alloys

The purpose of this research is to develop a tool for the mechanical analysis of nickel-base single-crystal superalloys, specifically Rene N4, used in gas turbine engine components. This objective is achieved by developing a rate-dependent anisotropic constitutive model and implementing it in a nonlinear three-dimensional finite-element code. The constitutive model is developed from metallurgical concepts utilizing a crystallographic approach. An extension of Schmid's law is combined with the Bodner-Partom equations to model the inelastic tension/compression asymmetry and orientation-dependence in octahedral slip. Schmid's law is used to approximate the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response and strain-rate sensitivity of the single-crystal superalloys. Methods for deriving the material constants from standard tests are also discussed. The model is implemented in a finite-element code, and the computed and experimental results are compared for several orientations and loading conditions.

Dame, L. T.↗

NASA NTRS1988

Structural analysis methods development for turbine hot section components

The structural analysis technologies and activities of the NASA Lewis Research Center's gas turbine engine Hot Section Technology (HOST) Program are summarized. The technologies synergistically developed and validated include: time-varying thermal/mechanical load models; component-specific automated geometric modeling and solution strategy capabilities; advanced inelastic analysis methods; inelastic constitutive models; high-temperature experimental techniques and experiments; and nonlinear structural analysis codes. Features of the program that incorporate the new technologies and their application to hot section component analysis and design are described. Improved and, in some cases, first-time 3-D nonlinear structural analyses of hot section components of isotropic and anisotropic nickel-base superalloys are presented.

Thompson, R. L.↗

NASA NTRS1988

Thermal barrier coating life prediction model development

A life prediction model for correlating the spallation life of ceramic thermal barrier coatings is developed which includes both cyclic and time-dependent damage. The cyclic damage is related to the calculated cyclic inelastic strain range, while the time-dependent damage is related to the oxidation kinetics at the bond-ceramic interface. The cyclic inelastic strain range is calculated using a modified form of the Walker viscoplastic material model; calculation of the oxidation kinetics is based on traditional oxidation algorithms using experimentally determined parameters. The correlation between the actual and predicted spallation lives is within a factor of 3.

Cruse, T. A.↗

NASA NTRS1986

Constitutive modeling for isotropic materials

The objective of the program is to evaluate and develop existing constitutive models for use in finite-element structural analysis of turbine engine hot section components. The class of constitutive equation studied is considered unified in that all inelastic deformation including plasticity, creep, and stress relaxation are treated in a single term rather than a classical separation of plasticity (time independent) and creep (time dependent) behavior. The unified theories employed also do not utilize the classical yield surface or plastic potential concept. The models are constructed from an appropriate flow law, a scalar kinetic relation between strain rate, temperature and stress, and evolutionary equations for internal variables describing strain or work hardening, both isotropic and directional (kinematic). This and other studies have shown that the unified approach is particularly suited for determining the cyclic behavior of superalloy type blade and vane materials and is entirely compatible with three-dimensional inelastic finite-element formulations. The behavior was examined of a second nickel-base alloy, MAR-M247, and compared it with the Bodner-Partom model, further examined procedures for determining the material-specific constants in the models, and exercised the MARC code for a turbine blade under simulated flight spectrum loading. Results are summarized.

Lindholm, Ulric S.↗

NASA NTRS1986

Constitutive modeling for single crystal superalloys

The inelastic response of single crystal gamma/gamma prime superalloys is quite different from the behavior of polycrystalline nickel base superalloys. Upto a critical temperature the yield stress of single crystal alloys is a function of the material orientation relative to the direction of the applied stress and the material exhibits significant tension/compression asymmetry. This behavior is primarily due to slip on the octahedral slip system. Above the critical temperature there is a sharp drop in the yield stress, cube slip becomes more predominant and the tension/compression asymmetry is reduced. Similar orientation and tension/compression asymmetry is observed in creep and secondary creep above the critical temperature is inferred to occur by octahedral slip. There are two exceptions to this behavior. First, loading near the (111) orientation exhibits cube slip at all temperatures, and; second, loading near the (001) orientation produces only octahedral slip at all temperatures. The constitutive model is based on separating the total global strain into elastic and inelastic components. This model is developed and briefly discussed.

Stouffer, D. C.↗

NASA NTRS1988

Considerations in development and implementation of elasto-viscoplastic constitutive model for high temperature applications

The prediction of inelastic behavior of metallic materials at elevated temperatures has increased in importance in recent years. The operating conditions within the hot section of a rocket motor or a modern gas turbine engine present an extremely harsh thermomechanical environment. Large thermal transients are induced each time the engine is started or shut down. Additional thermal transients from an elevated ambient occur whenever the engine power level is adjusted to meet flight requirements. The structural elements employed in such hot sections, as well as any engine components located therein, must be capable of withstanding such extreme conditions. Failure of a component would, due to the critical nature of the hot section, lead to an immediate and catastrophic loss in power. Consequently, assuring satisfactory long term performance for such components is a major concern. Nonisothermal loading of structures often causes excursion of stress well into the inelastic range. Moreover, the influence of geometry changes on the response is also significant in most cases. Therefore, both material and geometric nonlinear effects are considered.

Riff, Richard↗

NASA NTRS1987

Mechanics of materials model

The Mechanics of Materials Model (MOMM) is a three-dimensional inelastic structural analysis code for use as an early design stage tool for hot section components. MOMM is a stiffness method finite element code that uses a network of beams to characterize component behavior. The MOMM contains three material models to account for inelastic material behavior. These include the simplified material model, which assumes a bilinear stress-strain response; the state-of-the-art model, which utilizes the classical elastic-plastic-creep strain decomposition; and Walker's viscoplastic model, which accounts for the interaction between creep and plasticity that occurs under cyclic loading conditions.

Meister, Jeffrey P.↗

NASA NTRS1989

Structural analysis methods development for turbine hot section components

This paper summarizes the structural analysis technologies and activities of the NASA Lewis Research Center's gas turbine engine Hot Section Technology (HOST) program. The technologies synergistically developed and validated include: mechanical load models; component-specific automated geometric modeling and solution strategy capabilities; advanced inelastic analysis methods; inelastic constitutive models; high-temperature experimental techniques and experiments; and nonlinear structural analysis codes. Features of the program that incorporate the new technologies and their application to hot section component analysis and design are described. Improved and, in some cases, first-time three-dimensional non-linear structural analyses of hot section components of isotropic and anisotropic nickel-base superalloys are presented.

R L Thompson↗

NASA NTRS1988

Exposure time considerations in high temperature low cycle fatigue

The Conventional Strainrange Partitioning (CSRP) method for High-Temperature, Low-Cycle Fatigue (HTLCF) life prediction has its origins in the modeling of first-order, creep-fatigue waveform effects while treating as second-order effects, the influence of metallurgical or environmental time dependencies. Procedures are proposed to include the latter explicitly in the inelastic strainrange-life relations. For brevity, only the CP life relation will be presented in detail. The exposure-time effect within the CP inelastic strainrange (tensile creep reversed by compressive plasticity) was determined by tensile stresshold-time experiments for 316 SS at 816 C. Reductions in CP cyclic life of a factor of about two were observed with an increase in exposure time or a corresponding decrease in creep rate by a factor of about 100. The CP life relation has been modified to be expressed in terms of either Steady State Creep Rate (SSCR) or Exposure Time (ET). The applicability and accuracy of the time-dependent CP life relations is demonstrated by conducting verification experiments involving complex hysteresis loops. Metallographic examination revealed time-dependent degradation attributable to oxide formation and precipitation of carbides along grain boundaries.

Kalluri, S.↗

NASA NTRS1989

Angular dependent transport of auroral electrons in the upper atmosphere

The transport of auroral electrons through the upper atmosphere is analyzed. The transport equation is solved using a discrete-ordinate method, including elastic and inelastic scattering of electrons (resulting in changes of pitch angle) and degradation in energy as the electrons penetrate into the atmosphere. The transport equation is solved numerically for the electron intensity as a function of altitude, pitch angle, and energy. In situ measurements of the pitch angle and energy distribution of precipitating electrons over an auroral arc provide boundary conditions for the calculation. Model calculations were carried out with various different phase functions for elastic and inelastic collisions to attempt changing the angular scattering, but the observed pitch angle distributions remain unexplained. It is suggested that mechanisms other than collisional scattering influence the angular distribution of auroral electrons at or below 300 km altitude in the low-energy domain.

Lummerzheim, D.↗

NASA NTRS1988

Isothermal and 'bithermal' thermomechanical fatigue behavior of a NiCoCrAlY-coated single crystal superalloy

Specimens of single crystal PWA 1480 with group of zone axes (100) orientation, bare, or with NiCoCrAlY coating PWA 276, were tested in low cycle fatigue (LCF) at 650, 870, and 1050 C, and in simplified bithermal thermomechanical fatigue (TMF) tests between these temperatures. These tests were examined as a bridge between isothermal LCF and general TMF. In the bithermal test, and inelastic strain is applied at one temperature, T sub max, and reversed at T sub min. The out-of-phase (OP) test type imposing tension at T sub min and compression at T sub max received most study, since it was more damaging than the in-phase type. Specifically investigated were the effects of: inelastic strain range, the coating, delta T, T sub max, T sub min, and the environment.

Gayda, J.↗

NASA NTRS1990

Determination of molecular spectroscopic parameters and energy-transfer rates by double-resonance spectroscopy

The spectroscopy of small to medium-size polyatomic molecules can be extremely complex, especially in higher-lying overtone and combination vibrational levels. The high density of levels also complicates the understanding of inelastic collision processes, which is required to model energy transfer and collision broadening of spectral lines. Both of these problems can be addressed by double-resonance spectroscopy, i.e., time-resolved pump-probe measurements using microwave, infrared, near-infrared, and visible-wavelength sources. Information on excited-state spectroscopy, transition moments, inelastic energy transfer rates and propensity rules, and pressure-broadening parameters may be obtained from such experiments. Examples are given for several species of importance in planetary atmospheres, including ozone, silane, ethane, and ammonia.

Steinfeld, J. I.↗