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NASA NTRS1998

Constitutive Theory Developed for Monolithic Ceramic Materials

With the increasing use of advanced ceramic materials in high-temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior that is inherently time-dependent and that is hereditary in the sense that the current behavior depends not only on current conditions but also on the material's thermomechanical history. Most current analytical life prediction methods for both subcritical crack growth and creep models use elastic stress fields to predict the time-dependent reliability response of components subjected to elevated service temperatures. Inelastic response at high temperatures has been well documented in the materials science literature for these material systems, but this issue has been ignored by the engineering design community. From a design engineer's perspective, it is imperative to emphasize that accurate predictions of time-dependent reliability demand accurate stress field information. Ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture the creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperatures. The objective of this effort at the NASA Lewis Research Center has been to formulate a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the effort has focused on inelastic deformation behavior associated with these service conditions by developing a multiaxial viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (such as creep and stress relaxation) in monolithic structural ceramics. Using continuum principles of engineering mechanics, we derived the complete viscoplastic theory from a scalar dissipative potential function.

Janosik, Lesley A.↗

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 NTRS1986

High temperature monotonic and cyclic deformation in a directionally solidified nickel-base superalloy

Directionally solidified (DS) MAR-M246+Hf was tested in tension and fatigue, at temperatures from 20 C to 1093 C. Tests were performed on (001) oriented specimens at strain rates of 50 % and 0.5 % per minute. In tension, the yield strength was constant up to 704 C, above which the strength dropped off rapidly. A strong dependence of strength on strain rate was seen at the higher temperatures. The deformation mode was observed to change from heterogeneous to homogeneous with increasing temperature. Low Cycle Fatigue tests were done using a fully reversed waveform and total strain control. For a given plastic strain range, lives increased with increasing temperature. For a given temperature strain rate had a strong effect on life. At 704 C, decreasing strain rates decreased life, while at the higher temperatures, decreasing strain rates increased life, for a given plastic strain range. These results could be explained through considerations of the deformation modes and stress levels. At the higher temperatures, marked coarsening caused beneficial stress reductions, but oxidation limited the life. The longitudinal grain boundaries were found to influence slip behavior. The degree of secondary slip adjacent to the boundaries was found to be related to the degree of misorientation between the grains.

Huron, Eric S.↗

NASA NTRS1973

Quasi-static extension of a tensile crack contained in a viscoelastic-plastic solid

Final stretch criterion of failure is applied to the problem of quasi-static extension of a crack embedded in an elastic-plastic or viscoelastic-plastic matrix. The slow growth under subcritical conditions in a rate-sensitive Tresca solid is shown to be a superposition of creep rupture and McClintock's ductile growth. This type of growth occurs at subcritical magnitude of the imposed K-factor and can be accounted for only through a recognition of inelastic properties of solids. In the subcritical range there is no unique value for K sub c independent of geometrical configuration and flaw size. Not only the produced states of stress and strain are dependent on the loading path, but also the material resistance to fracture turns out to be a function of the history of loading that precedes catastrophic failure. A nonlinear integro-differential equation of motion is derived for a crack progressing through a viscoelastic medium with some limited ability to plastic flow. Examples of numerical integration are given incorporating both monotonic and cyclic loading programs.

Wnuk, M. P.↗

NASA NTRS2018

Plasticity and Damage Modeling of Stress Asymmetry and Dynamic Behavior of AFS Additive Manufactured Aluminum Alloy 2219

The Solid State Additive Manufacturing (AM) process referred as MELD that fabricated the samples in this study, provides a new path for repairing, coating, joining and additive manufacturing metals and metal matrix composites. This research will be the first application of a physics-based microstructure dependent internal state variable (ISV) plasticity and damage material model to capture the mechanical response of an AM Aluminum Alloy (AA) 2219 via the MELD process. In this research, a microstructure-based internal state variable (ISV) plasticity-damage model was used to capture the mechanical behavior of AFS 2219 aluminum alloy. Aeroprobe Corporation, creator and patent holder for the MELD process, fabricated the material by pushing a solid filler rod of AA2219-T861 material through a hollow rotating tool onto an AA2219 T851 plate substrate. As feedstock, solid or powder precursor metals are pushed through a nonconsumable rotating cylindrical tool. Herein, added layers are deposited and metallurgically bonded to substrate material or previously deposited layers by the heat generated from the rotating tool through plastic deformation of the filler material. Once a layer has been added, the tool height increases, and starts the deposition of the next layer. This process results in beneficial properties such as grain refinement, homogenization and reduced porosity (fully dense). This process will experience temperatures similar to those in the weld nugget zone (WNZ) in friction stir welding (FSW), ranging from 0.6-0.9 Tm, with Tm being the melting point of the material. MELD is highly scalable with AA deposition rates reaching over 1000 cm3/hr, which allows for MELD being used for repairs, coatings, and building components. A motivating factor driving the research for physics-based history dependent material modeling of MELD components is the ability to accurately capture the stress-state and strain rate dependence in the material caused by variations in material microstructure from the MELD processing of new or repaired components. The ISV model incorporates microstructural content and is consistent with continuum level kinematics, kinetics, and thermodynamics. These features allow the ISV model to capture large deformations at the structural scale using the kinematic and isotropic hardening, while microscale damage is obtained from the microstructural features. The benefits of the ISV model arise from the inclusion of structure-property relationships identified from microstructural characterization and experimentation. The Bauschinger effect (BE) is an important concept, vital in the accurate prediction of cyclic stress-strain response of ductile materials such as metals. The ISV model has been successfully used to capture the behavior and damage, and the BE of different aluminum alloys and steels. The ISV model uses kinematic and isotropic hardening to help capture deformations of the material at the macro scale. To understand this hardening relationship, calculating the kinematic and isotropic hardening relationship in the material is warranted for a high-fidelity model. Electron Backscattered Diffraction (EBSD) was used to characterize the as-fabricated microstructure, where a fully-dense equiaxed grain morphology with average grain size of 2.5 μm was observed. Microhardness mapping of the as-built structures, monotonic tension and compression experiments at both quasi-static (0.001/s) strain rates, tension-followed-by-compression and compression-followed-by-tension experiments were performed to obtain the set of plasticity and damage constants necessary to capture strain rate and stress state behavior of this additive material. To calibrate the plasticity-damage model, a single set of constants were determined to capture the different stress states the MELD AA2219. One set of the constants was determined from experimental true stress-strain curves for the tension and compression data. Additionally, microstructural information and data from the open literature were used as the other model constants. This research is a first of its kind for AFS AA2219, includes correlating the ISV model to the monotonic experimental results that capture the isotropic and kinematic plasticity mechanical response.

Rivera, O. G.↗

NASA NTRS2001

Creep-Fatigue Interaction Testing

Fatigue fives in metals are nominally time independent below 0.5 T(sub Melt). At higher temperatures, fatigue lives are altered due to time-dependent, thermally activated creep. Conversely, creep rates are altered by super. imposed fatigue loading. Creep and fatigue generally interact synergistically to reduce material lifetime. Their interaction, therefore, is of importance to structural durability of high-temperature structures such as nuclear reactors, reusable rocket engines, gas turbine engines, terrestrial steam turbines, pressure vessel and piping components, casting dies, molds for plastics, and pollution control devices. Safety and lifecycle costs force designers to quantify these interactions. Analytical and experimental approaches to creep-fatigue began in the era following World War II. In this article experimental and life prediction approaches are reviewed for assessing creep-fatigue interactions of metallic materials. Mechanistic models are also discussed briefly.

Halford, Gary R.↗

NASA NTRS1992

Thermoviscoplastic analysis of engine cowl leading edge subjected to oscillating shock-shock interaction

A finite element thermoviscoplastic analysis method, which employs a unified constitutive model proposed by Bodner and Partom, is used to predict rate-dependent nonlinear structural behavior. The method is evaluated by predicting stress-strain behavior of a uniaxially loaded bar of nickel-based superalloy (B1900 + Hf) material. The method is used to predict the time-dependent thermoviscoplastic response of a B1900 + Hf leading edge subjected to oscillating shock-shock interaction loading. Viscoplastic analysis shows that the leading edge experiences significant plastic straining. The plastic region increases with cyclic loading in the high heat flux area.

Pandey, Ajay K.↗

NASA NTRS1999

Effects of Internal and External Hydrogen on Inconel 718

Internal hydrogen embrittlement (IHE) and hydrogen environment embrittlement (HEE) tensile and bend crack growth tests were performed on Inconel 718. For the IHE tests, the specimens were precharged to approximately 90 ppm hydrogen by exposure to 34.5 MPa H2 at 650 C. The HEE tests were performed in 34.5 MPa H2. Parameters evaluated were test temperature, strain rate for smooth and notch specimen geometries. The strain rate effect was very significant at ambient temperature for both IHE and HEE and decreased with increasing temperatures. For IHE, the strain rate effect was neglible at 260'C, and for HEE the strain rate effect was neglible at 400 C. At low temperatures, IHE was more severe than HEE, and at high temperatures HEE was more severe than IHE with a cross over temperature about 350 C. At 350 C, the equilibrium hydrogen concentration in Inconel 718 is about 50% lower than the hydrogen content of the precharged IHE specimens. Dislocation hydrogen sweeping of surface absorbed hydrogen was the likely transport mechanism for increasing the hydrogen concentration in the HEE tests sufficiently to produce the same degree of embrittlement as that of the more highly hydrogen charged IHE specimens. The main IHE fracture characteristic was formation of large, brittle flat facets, which decreased with increasing test temperature. The IHE fracture matrix surrounding the large facets ranged between brittle fine faceted to microvoid ductility depending upon strain rate, specimen geometry as well as temperature. The HEE fractures were characteristically fine featured, transgranular and brittle with a significant portion forming a "saw tooth" crystallographic pattern. Both IHE and HEE fractures were predominantly along the {1 1 1) slip and twin boundaries. With respect to embrittlement mechanism, it was postulated that dislocation hydrogen sweeping and hydrogen enhanced localized plasticity were active in HEE and IHE for concentrating hydrogen along (1 1 1) slip and twin planes. Final brittle failure occurred by hydrogen induced planer decohesion.

Walter, R. J.↗

NASA NTRS2003

1100 to 1500 K Slow Plastic Compressive Behavior of NiAl-xCr Single Crystals

The compressive properties of near <001> and <111> oriented NiAl-2Cr single crystals and near <011> oriented NiAl-6Cr samples have been measured between 1100 and 1500 K. The 2Cr addition produced significant solid solution strengthening in NiAl, and the <111> and <001> single crystals possessed similar strengths. The 6Cr crystals were not stronger than the 2Cr versions. At 1100 and 1200 K plastic flow in all three Cr-modified materials was highly dependent on stress with exponents > 10. The <011> oriented 6Cr alloy exhibited a stress exponent of about 8 at 1400 and 1500 K; whereas both <001> and <111> NiAl-2Cr crystals possessed stress exponents near 3 which is indicative of a viscous dislocation glide creep mechanism. While the Cottrell-Jaswon solute drag model predicted creep rates within a factor of 3 at 1500 K for <001>-oriented NiAl-2Cr; this mechanism greatly over predicted creep rates for other orientations and at 1400 K for <001> crystals.

Whittenberger, J. Daniel↗

NASA NTRS1984

Lubricant Rheology in Concentrated Contacts

A revue of experimental investigations of lubricant behaviour in highly stressed situations shows that a Newtonian model for lubricant rheology is insufficient for explanation of traction behaviour. The oil film build-up, on the other hand, is fairly well predicted using a Newtonian lubricant model except at high slide to roll ratios and at very high loads, where the non-Newtonian behaviour starts to be important already outside the Hertzian contact area. Two main types of experiments are reported: static and dynamic. In static experiments the pressure is typically applied to the lubricant more than a million times longer than in an EHD contact. Depending on the pressure-temperature history of the experiment the lubricant will become a crystallized or amorphous solid at high pressures. In dynamic experiments, where the pressure is applied as short time as in real EHD contacts, the oil is in an amorphous solid state. Depending on the viscosity, time-scale, elasticity of the oil and the bearing surfaces, the oil film pressure, shear strain rate and the type of lubricant, different properties of the oil are important for prediction of shear stresses in the oil. This can be seen from the different proposed models for the lubricant, where it is described as being for instance a Newtonian liquid, an elastic liquid, a plastic liquid and an elastic-plastic solid.

Bo O Jacobson↗

NASA NTRS1991

1000 to 1200 K time-dependent compressive deformation of single-crystalline and polycrystalline B2 Ni-40Al

The 1000-K and 1200-K time-dependent deformation of 100-line-oriented and non-100-line-oriented single crystals of Ni-40Al (made by a modified Bridgman technique) was examined over a large range of strain rates (from 0.1 to 10 to the -7th per sec). The results were compared with those for polycrystalline Ni-40Al made by hot pressing XD synthesized powder. The results from measurements of slow-plastic-strain-rate properties of the two materials show that single crystals offer no strength advantage over polycrystalline material. Both forms were found to deform via a dislocation climb mechanism.

Whittenberger, J. D.↗

NASA NTRS1991

1200 and 1300 K slow plastic compression properties of Ni-50Al composites

XD synthesis, powder blending, and hot pressing techniques have been utilized to produce NiAl composites containing 4, 7.5, 15, and 25 vol pct alumina whiskers and hybrid composite materials with 15 vol pct Al2O3 + 10 or 20 vol pct, nominally 1 micron TiB2 particles. The resistance to slow plastic flow was determined at 1200 and 1300 K via compression testing in air under constant velocity conditions. The stress-strain behavior of the intermetallic composites depended on the fraction of second phases where the 4 and 7.5 percent Al2O3 materials flowed at a nominally constant stress after about 2 percent deformation, while all the other composites exhibited diffuse yielding followed by strain softening. The flow stress-strain rate properties increased with volume fraction of Al2O3 whiskers except for the 4 and 7.5 percent materials, which had similar strengths. The hybrid composite NiAl + 15Al2O3 + 10TiB2 was substantially stronger than the materials simply containing alumina. Deformation in these composites can be described by the Kelly and Street model of creep in perfectly bonded, rigid, discontinuous fiber materials.

Whittenberger, J. D.↗

NASA NTRS1986

Influence of fatigue crack wake length and state of stress on crack closure

The location of crack closure with respect to crack wake and specimen thickness under different loading conditions was determined. The rate of increase of K sub CL in the crack wake was found to be significantly higher for plasticity induced closure in comparison to roughness induced closure. Roughness induced closure was uniform throughout the thickness of the specimen while plasticity induced closure levels were 50 percent higher in the near surface region than in the midthickness. The influence of state of stress on low-high load interaction effects was also examined. Load interaction effects differed depending upon the state of stress and were explained in terms of delta K sub eff.

Telesman, J.↗

NASA NTRS1988

Influence of fatigue crack wake length and state of stress on crack closure

Telesman, Jack↗

NASA NTRS2008

Effect of Microstructure on Time Dependent Fatigue Crack Growth Behavior In a P/M Turbine Disk Alloy

A study was conducted to determine the processes which govern hold time crack growth behavior in the LSHR disk P/M superalloy. Nineteen different heat treatments of this alloy were evaluated by systematically controlling the cooling rate from the supersolvus solutioning step and applying various single and double step aging treatments. The resulting hold time crack growth rates varied by more than two orders of magnitude. It was shown that the associated stress relaxation behavior for these heat treatments was closely correlated with the crack growth behavior. As stress relaxation increased, the hold time crack growth resistance was also increased. The size of the tertiary gamma' in the general microstructure was found to be the key microstructural variable controlling both the hold time crack growth behavior and stress relaxation. No relationship between the presence of grain boundary M23C6 carbides and hold time crack growth was identified which further brings into question the importance of the grain boundary phases in determining hold time crack growth behavior. The linear elastic fracture mechanics parameter, Kmax, is unable to account for visco-plastic redistribution of the crack tip stress field during hold times and thus is inadequate for correlating time dependent crack growth data. A novel methodology was developed which captures the intrinsic crack driving force and was able to collapse hold time crack growth data onto a single curve.

Telesman, Ignacy J.↗

NASA NTRS1993

Axisymmetric micromechanics of elastic-perfectly plastic fibrous composites under uniaxial tension loading

The uniaxial response of a continuous fiber elastic-perfectly plastic composite is modeled herein as a two-element composite cylinder. An axisymmetric analytical micromechanics solution is obtained for the rate-independent elastic-plastic response of the two-element composite cylinder subjected to tensile loading in the fiber direction for the case wherein the core fiber is assumed to be a transversely isotropic elastic-plastic material obeying the Tsai-Hill yield criterion, with yielding simulating fiber failure. The matrix is assumed to be an isotropic elastic-plastic material obeying the Tresca yield criterion. It is found that there are three different circumstances that depend on the fiber and matrix properties: fiber yield, followed by matrix yielding; complete matrix yield, followed by fiber yielding; and partial matrix yield, followed by fiber yielding, followed by complete matrix yield. The order in which these phenomena occur is shown to have a pronounced effect on the predicted uniaxial effective composite response.

Lee, Jong-Won↗

NASA NTRS2021

Pyrolysis Rate and Yield Strength Reduction Incarbon Fiber and Glass Fiber Composites Underreentry Heating Conditions

The behavior of composite materials, specifically carbon fiber reinforced plastic (CFRP) and glass fiber reinforced plastic (GFRP), under reentry conditions poses a problem for space debris reentry risk modeling. Since these materials pyrolyze rather than melt and their different components demise at different rates, modeling their destruction to determine ground impact risk is complex. Modern spacecraft are using these materials in ever-greater quantities owing to their superior strength-to-weight characteristics, and this has required that the orbital debris community improve its understanding of how these materials demise on reentry. The NASA Orbital Debris Program Office undertook an extensive test campaign to better understand the rate at which several types of GFRP and CFRP materials pyrolyze under reentry heating conditions and how that pyrolysis affects the ultimate strength of the material. GFRP with a polyester resin (G10/FR-4) and CFRP with epoxy, cyanate ester, vinyl ester, and phenolic resins were tested. The test campaign was carried out at the Inductively Coupled Plasma (ICP) Torch Facility at the University of Texas at Austin. Because the ICP facility operates in a shirt-sleeve environment, test samples can be changed within seconds or minutes, allowing many samples to be tested in a short period. Two heat flux rates, 20 W/m2 and 30W/m2, and two oxygen concentration conditions, 0% and 2% of atmospheric, were applied to all five types of material. To measure both the char rate and the effect of pyrolysis on the ultimate material strength, two types of test were carried out for each material: a char rate test on a ~10 mm thick sample of material and an in-situ bending stress test of a ~2 mm thick sample of material. Measurements of the char rate showed very similar average pyrolysis front velocity in epoxy resin CFRP as in G10 at 3.6 mm/min and 3.4 mm/min, respectively. However, the total mass loss rate in theG10 was nearly double that of the CFRP at 3.8 g/min and 2.2 g/min, respectively. This result represented a slow ablation rate of carbon fibers in the CFRP at the temperatures encountered in low Earth orbit reentry and a comparatively rapid removal of the glass fibers in G10 due to melting and spallation. Pyrolysis front velocity was more significantly affected by the type of plastic than the type of fiber, with the cyanate ester CFRP samples displaying an average pyrolysis front velocity of only 1.9 mm/min. Similarly, the effect of thermal exposure on the ultimate strength of the material depended heavily on the type of plastic and very little on the type of fiber in the material. Epoxy, vinyl ester, and polyester resins all behaved very similarly, with complete structural failure at between 400 J/g and 600 J/g of specific absorbed heat. Phenolic and cyanate ester resins, on the other hand, displayed a change in structural properties that was only barely measurable with the current apparatus even after the maximum exposure time tested. These data are being incorporated into a numerical model of the ablation and demise of composite materials that will be used to more accurately calculate the ground casualty risk of future spacecraft.

Benton R. Greene↗

NASA NTRS1973

Effects of thermal loading on foil and sheet composites with constituents of differing thermal expansivities.

A study was made to estimate the magnitudes of elastic stresses and elastic-plastic stresses and strains in sheet or foil laminar composites. Using a model tungsten/80Ni + 20Cr laminar composite and assuming cooling or heating through a temperature range of 80-2000 deg F (26.5-1093.5 deg C), calculated elastic stresses exceeded published or estimated strengths of the constituents. Elastic-plastic stress-strain solutions resulted in lower estimated stress levels but with the concomitant occurrence of sufficiently large strain ranges to suggest possible thermal fatigue problems. Limited experimental studies using tungsten/80Ni + 20Cr foil and sheet laminar composites, slowly cycled between 80 and 2000 deg F (26.5-1093.5 deg C) or rapidly cycled between 80 and 1600 deg F (26.5-871 deg C) produced varying degrees of observable structural damage in from 1 to 11 cycles depending upon temperature transition rate and laminae thickness; these particular results might not occur with other combinations of materials.

Hoffman, C. A.↗