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At least 1,693 records · Page 94

The influence of cobalt, tantalum, and tungsten on the elevated temperature mechanical properties of single crystal nickel-base superalloys

The influence of composition on the tensile and creep strength of 001-line oriented nickel-base superalloy single crystals at temperatures near 1000 C was investigated. Cobalt, tantalum, and tungsten concentrations were varied according to a matrix of compositions based on the single crystal version of MAR-M247. For alloys with the baseline refractory metal level of 3 wt pct Ta and 10 wt pct W, decreases in Co level from 10 to 0 wt pct resulted in increased tensile and creep strength. Substitution of 2 wt pct W for 3 wt pct Ta resulted in decreased creep life at high stresses, but improved life at low stresses. Substitution of Ni for Ta caused large reductions in tensile strength and creep resistance, and corresponding increases in ductility. For these alloys with low Ta-plus-W totals, strength was independent of Co level. The effects of composition on properties were related to the microstructural features of the alloys. In general, high creep strength was associated with high levels of gamma-prime volume fraction, gamma-gamma-prime lattice mismatch, and solid solution hardening.

Nathal, M. V.↗

The development of gamma-gamma-prime lamellar structures in a nickel-base superalloy during elevated temperature mechanical testing

The kinetics of the formation and subsequent development of the directional coarsening of the gamma-prime precipitate in model Ni-Al-Mo-Ta superalloy single crystals are examined during tensile creep under various stress levels at 982 and 1038 C. Special attention is given to the gamma and gamma-prime relation to creep time and strain in order to trace the changing gamma-gamma-prime morphology. Directional coarsening of gamma-prime is found to begin during primary creep and its rate is shown to increase with an increase in temperature or stress level. The length of gamma-prime thickness increased linearly with time up to a plateau reached after the onset of steady state creep. The raft thickness, equal to the gamma-prime size, remained constant at this initial value up through the onset of the tertiary creep. The interlaminar spacing indicates the stability of directionally coarsened structure.

Mackay, R. A.↗

Analysis of damage in MMC components using an internal state variable model

A metal-matrix composite (MMC) model was developed which includes the concept of damage evolution. The evolution of damage is assumed to be governed by a Kachanov-type equation. This viscoplastic damage model was implemented in the finite element code, MARC. Both uniaxial (creep) and multiaxial (an internally pressurized thick-walled cylinder) problems were analyzed using this implementation. Some preliminary results are presented which consider monotonic (constant) loadings. The creep curves including damage for four fiber orientations are presented. As expected, the minimum creep occurs when load is applied in a direction parallel to the fibers. The tangential strains at the inner radius of a thick-walled MMC-cylinder for four fiber orientations are shown with damage included. The cylinder exhibits the maximum creep resistance when the fibers are oriented in the circumferential direction, perpendicular to the axis of the cylinder. Time-to-failure for the thick-walled cylinder for the same fiber orientation angles is also shown. As expected, the life of the cylinder can be increased by orientating the fibers in the circumferential direction, perpendicular to the axis of the cylinder. The results, although qualitative, indicate that significant benefits in creep-resistance and service life can be achieved by using MMC materials as structural materials for high-temperature design.

Arya, V. K.↗

Materials for a Stirling engine heater head

Work done on the 25-kW advanced Stirling conversion system (ASCS) terrestrial solar program in establishing criteria and selecting materials for the engine heater head and heater tubes is described. Various mechanisms contributing to incompatibility between materials are identified and discussed. Large thermal gradients, coupled with requirements for long life (60,000 h at temperature) and a large number of heatup and cooldown cycles (20,000) drive the design from a structural standpoint. The pressurized cylinder is checked for creep rupture, localized yielding, reverse plasticity, creep and fatigue damage, and creep ratcheting, in addition to the basic requirements for bust and proof pressure. In general, creep rupture and creep and fatigue interaction are the dominant factors in the design. A wide range of materials for the heater head and tubes was evaluated. Factors involved in the assessment were strength and effect on engine efficiency, reliability, and cost. A preliminary selection of Inconel 713LC for the heater head is based on acceptable structural properties but driven mainly by low cost. The criteria for failure, the structural analysis, and the material characteristics with basis for selection are discussed.

Noble, J. E.↗

Mechanical behavior of high strength ceramic fibers at high temperatures

The mechanical behavior of commercially available and developmental ceramic fibers, both oxide and nonoxide, has been experimentally studied at expected use temperatures. In addition, these properties have been compared to results from the literature. Tensile strengths were measured for three SiC-based and three oxide ceramic fibers for temperatures from 25 C to 1400 C. The SiC-based fibers were stronger but less stiff than the oxide fibers at room temperature and retained more of both strength and stiffness to high temperatures. Extensive creep and creep-rupture experiments have been performed on those fibers from this group which had the best strengths above 1200 C in both single filament tests and tests of fiber bundles. The creep rates for the oxides are on the order of two orders of magnitude faster than the polymer derived nonoxide fibers. The most creep resistant filaments available are single crystal c-axis sapphire filaments. Large diameter CVD fabricated SiC fibers are the most creep and rupture resistant nonoxide polycrystalline fibers tested to date.

Tressler, R. E.↗

Rheology of water and ammonia-water ices

Creep experiments on fine-grained water and ammonia-water ices have been performed at one atmosphere and high confining pressure in order to develop constitutive relationships necessary to model tectonic processes and interpret surface features of icy moons of the outer solar system. The present series of experiments explores the effects of temperature, strain rate, grain size, and melt fraction on creep strength. In general, creep strength decreases with increasing temperature, decreasing strain rate, and increasing melt fraction. A transition from dislocation creep to diffusion creep occurs at finer grain sizes, higher temperatures, and lower strain rates.

Goldsby, D. L.↗

Modeling of Thermal Barrier Coatings

The project examined the effectiveness of studying the creep behavior of thermal barrier coating system through the use of a general purpose, large strain finite element program, NIKE2D. Constitutive models implemented in this code were applied to simulate thermal-elastic and creep behavior. Four separate ceramic-bond coat interface geometries were examined in combination with a variety of constitutive models and material properties. The reason for focusing attention on the ceramic-bond coat interface is that prior studies have shown that cracking occurs in the ceramic near interface features which act as stress concentration points. The model conditions examined include: (1) two bond coat coefficient of thermal expansion curves; (2) the creep coefficient and creep exponent of the bond coat for steady state creep; (3) the interface geometry; and (4) the material model employed to represent the bond coat, ceramic, and superalloy base.

Ferguson, B. L.↗

Cross-Effects in Microgravity Flows

Film growth by chemical/physical vapor deposition is a process of considerable interest in microgravity experiments. The absence of natural convection should allow better control of film growth processes but, in highly non-isothermal ampoules, thermal slip (creep) can become a matter of significant concern. The reported research is a theoretical and experimental investigation of the flow of gas/vapor mixtures under non-continuum conditions. The Boltzmann equation has been solved for a monatomic gas under non-condensing conditions and the various phenomenological coefficients have been computed. Computations for realistic potentials as well as for velocity and creep slip have been completed and the creep slip has been found to be dependent on the type of gas confirming the accuracy of previous variational results. The variational technique has been extended and planar flows calculated via the Burnett solutions. Velocity, diffusion and creep slips have been computed for gas mixtures and previously unknown dependencies of the creep slip on the mixture properties have been observed. Also for gas mixtures, an integral representation of the linearized Boltzmann operator has been developed for use in numerical and variational calculations for all intermolecular force laws. Two, two-bulb capillary systems have been designed, built and tested for the measurements of cross-flows; one of glass for isothermal measurements and one of stainless steel for non-isothermal measurements. Extensive data have been collected for Ar-He and N2-He mixtures at a variety of pressures and mole ratios. Viscosity, velocity slip coefficients and tangential momentum accommodation coefficients have been obtained from measurements with a spinning rotor gauge via a new theory that has been formulated for the spinning rotor gauge in the slip regime. The FIDAP fluid dynamics code has been applied to condensing flows in ampoules in the continuum regime and agreement obtained with the earlier work of Duval.

Loyalka, Sudarshan K.↗

NASA-UVA Light Aerospace Alloy and Structures Technology Program (LA2ST)

This report documents the progress achieved over the past 6 to 12 months on four graduate student projects conducted within the NASA-UVA Light Aerospace Alloy and Structures Technology Program. These studies were aimed specifically at light metallic alloy issues relevant to the High Speed Civil Transport. Research on Hydrogen-Enhanced Fracture of High-Strength Titanium Alloy Sheet refined successfully the high resolution R-curve method necessary to characterize initiation and growth fracture toughnesses. For solution treated and aged Low Cost Beta without hydrogen precharging, fracture is by ductile transgranular processes at 25 C, but standardized initiation toughnesses are somewhat low and crack extension is resolved at still lower K-levels. This fracture resistance is degraded substantially, by between 700 and 1000 wppm of dissolved hydrogen, and a fracture mode change is affected. The surface oxide on P-titanium alloys hinders hydrogen uptake and complicates the electrochemical introduction of low hydrogen concentrations that are critical to applications of these alloys. Ti-15-3 sheet was obtained for study during the next reporting period. Research on Mechanisms of deformation and Fracture in High-Strength Titanium Alloys is examining the microstructure and fatigue resistance of very thin sheet. Aging experiments on 0. 14 mm thick (0.0055 inch) foil show microstructural agility that may be used to enhance fatigue performance. Fatigue testing of Ti-15-3 sheet has begun. The effects of various thermo-mechanical processing regimens on mechanical properties will be examined and deformation modes identified. Research on the Effect of Texture and Precipitates on Mechanical Property Anisotropy of Al-Cu-Mg-X and Al-Cu alloys demonstrated that models predict a minor influence of stress-induced alignment of Phi, caused by the application of a tensile stress during aging, on the yield stress anisotropy of both modified AA2519 and a model Al-Cu binary alloy. This project is no longer included in the NASA-UVA LAST program. Research on the Creep Behavior and Microstructural stability of Al-Cu-Mg-Ag and Al-Cu-Li-Mg-Ag showed that the creep resistance of three candidate aluminum alloys (C415, C416 and ML377) was much superior compared to that of the current Concorde alloy, AA2618. Creep induced change in precipitates at grain boundaries was observed in the alloy which exhibits the highest creep strain of the three examined. The other two alloys developed no detectable microstructural changes at grain boundaries under the creep conditions tested.

Gangloff, Richard P.↗

Microstructure and Mechanical Properties of Extruded Gamma Met PX

A gamma TiAl alloy with a high Nb content is being assessed as a compressor blade material. The microstructure and mechanical properties of extruded Ti-45Al-X(Nb,B,C) (at %) were evaluated in both an as-extruded condition and after a lamellar heat treatment. Tensile behavior of both as-extruded and lamellar heat treated specimens was studied in the temperature range of RT to 926 C. In general, the yield stress and ultimate tensile strength reached relatively high values at room temperature and decreased with increasing deformation temperature. The fatigue strength of both microstructures was characterized at 650 C and compared to a baseline TiAl alloy and to a Ni-base superalloy. Tensile and fatigue specimens were also exposed to 800 C for 200 h in air to evaluate the alloy's environmental resistance. A decrease in ductility was observed at room temperature due to the 800 C exposure but the 650 C fatigue properties were unaffected. Compressive and tensile creep testing between 727 and 1027 C revealed that the creep deformation was reproducible and predictable. Creep strengths reached superalloy-like levels at fast strain rates and lower temperatures but deformation at slower strain rates and/or higher temperature indicated significant weakening for the as-extruded condition. At high temperatures and low stresses, the lamellar microstructure had improved creep properties when compared to the as-extruded material. Microstructural evolution during heat treatment, identification of various phases, and the effect of microstructure on the tensile, fatigue, and creep behaviors is discussed.

Draper, S. L.↗

Microstructure and Mechanical Properties of Extruded Gamma Microstructure Met PX

A gamma TiAl alloy with a high Nb content is being assessed as a compressor blade material. The microstructure and mechanical properties of extruded Ti-45Al-X(Nb,B,C) (at.%) were evaluated in both an as-extruded condition and after a lamellar heat treatment. Tensile behavior of both as-extruded and lamellar heat treated specimens was studied in the temperature range of RT to 926 C. In general, the yield stress and ultimate tensile strength reached relatively high values at room temperature and decreased with increasing deformation temperature. The fatigue strength of both microstructures was characterized at 650 C and compared to a baseline TiAl alloy and to a Ni-base superalloy. Tensile and fatigue specimens were also exposed to 800 C for 200 h in air to evaluate the alloy's environmental resistance. A decrease in ductility was observed at room temperature due to the 800 C. exposure but the 650 C fatigue properties were unaffected. Compressive and tensile creep testing between 727 and 1027 C revealed that the creep deformation was reproducible and predictable. Creep strengths reached superalloy-like levels at fast strain rates and lower temperatures but deformation at slower strain rates and/or higher temperature indicated significant weakening for the as-extruded condition. At high temperatures and low stresses, the lamellar microstructure had improved creep properties when compared to the as-extruded material. Microstructural evolution during heat treatment, identification of various phases, and the effect of microstructure on the tensile, fatigue, and creep behaviors is discussed.

Draper, S. L.↗

Molecular Weight Effects on the Viscoelastic Response of a Polyimide

The effect of molecular weight on the viscoelastic performance of an advanced polymer (LaRC -SI) was investigated through the use of creep compliance tests. Testing consisted of short-term isothermal creep and recovery with the creep segments performed under constant load. The tests were conducted at three temperatures below the glass transition temperature of each material with different molecular weight. Through the use of time-aging-time superposition procedures, the material constants, material master curves and aging-related parameters were evaluated at each temperature for a given molecular weight. The time-temperature superposition technique helped to describe the effect of temperature on the timescale of the viscoelastic response of each molecular weight. It was shown that the low molecular weight materials have increased creep compliance and creep compliance rate, and are more sensitive to temperature than the high molecular weight materials. Furthermore, a critical molecular weight transition was observed to occur at a weight-average molecular weight of approximately 25000 g/mol below which, the temperature sensitivity of the time-temperature superposition shift factor increases rapidly.

Nicholson, Lee M.↗

Residual Stresses Modeled in Thermal Barrier Coatings

Thermal barrier coating (TBC) applications continue to increase as the need for greater engine efficiency in aircraft and land-based gas turbines increases. However, durability and reliability issues limit the benefits that can be derived from TBC's. A thorough understanding of the mechanisms that cause TBC failure is a key to increasing, as well as predicting, TBC durability. Oxidation of the bond coat has been repeatedly identified as one of the major factors affecting the durability of the ceramic top coat during service. However, the mechanisms by which oxidation facilitates TBC failure are poorly understood and require further characterization. In addition, researchers have suspected that other bond coat and top coat factors might influence TBC thermal fatigue life, both separately and through interactions with the mechanism of oxidation. These other factors include the bond coat coefficient of thermal expansion, the bond coat roughness, and the creep behavior of both the ceramic and bond coat layers. Although it is difficult to design an experiment to examine these factors unambiguously, it is possible to design a computer modeling "experiment" to examine the action and interaction of these factors, as well as to determine failure drivers for TBC's. Previous computer models have examined some of these factors separately to determine their effect on coating residual stresses, but none have examined all the factors concurrently. The purpose of this research, which was performed at DCT, Inc., in contract with the NASA Lewis Research Center, was to develop an inclusive finite element model to characterize the effects of oxidation on the residual stresses within the TBC system during thermal cycling as well as to examine the interaction of oxidation with the other factors affecting TBC life. The plasma sprayed, two-layer thermal barrier coating that was modeled incorporated a superalloy substrate, a NiCrAlY bond coat, and a ZrO2-8 wt % Y2O3 ceramic top coat. We examined the effect on stress during burner rig thermal cycling of the following independent variables: creep in the bond coat and top coat, oxidation, bond coat coefficient of thermal expansion, number of thermal cycles, and interfacial roughness. All these factors were suspected of influencing TBC failure. The model showed that all the material properties studied had a significant effect on the coating's residual stresses if the interface of the bond coat was rough. Bond coat expansion, bond coat oxidation, and bond coat creep had the highest effect on coating stresses, and these were highly interactive. The model also showed that the mechanism of stress generation during thermal cycling changed with the number of thermal cycles. Bond coat and top coat creep dominated stress generation during early thermal cycles, greatly increasing delamination stresses at the peaks of the bond coat. Therefore, creep is the prime driver for delamination cracking early in life, but cracking is limited to the bond coat peak region. Oxidation of the bond coat, on the other hand, tended to dominate stress generation during later cycles by greatly increasing delamination stresses over bond coat valleys. These results indicate that oxidation is the driver for the continued cracking necessary to cause ceramic layer spallation.

Freborg, A. M.↗

Tensile Strength and Microstructure of Al2O3-ZrO2 Hypo-Eutectic Fibers Studied

Oxide eutectics offer high-temperature strength retention and creep resistance in oxidizing environments. Al2O3-ZrO2 eutectic strengths have been studied since the 1970's. Directionally solidified oxide eutectics exhibit improved resistance to slow crack growth and excellent strength retention at high temperatures up to 1400 C. Materials studied typically contain Y2O3 to metastably retain the high-temperature cubic and tetragonal polymorphs at room temperature. Al2O3-ZrO2 is of fundamental interest for creep studies because it combines a creep-resistant material, Al2O3, with a very low creep resistance material, ZrO2. Results on mechanical properties and microstructures of these materials will be used to define compositions for creep testing in future work. Substantial variations from the eutectic alumina to zirconia ratio can be tolerated without a loss in room-temperature strength. The effect of increasing Y2O3 addition on the room-temperature tensile strength of an Al2O3-ZrO2 material containing excess Al2O3 was examined at the NASA Glenn Research Center, where the materials were grown using Glenn's world-class laser growth facilities.

Farmer, Serene C.↗

Versatile Turbine Disk Alloy Designed and Processed for Higher Temperature Applications

Advanced turbine engine configurations using higher temperature combustor and airfoil concepts require compressor and turbine disks that can withstand temperatures higher than the 650 C typical of current engines. This requires disk alloy and processing improvements. A versatile disk alloy was needed that could be given either fine grain heat treatments for high strength and fatigue and creep resistance up to 704 C or given coarse grain heat treatments for high strength and creep and dwell crack-growth resistance at higher temperatures. This alloy could produce disks with uniform microstructures and properties, as well as with varied, optimized microstructures at disk bore and rim sections. A series of experimental disk alloys were designed and processed to give subscale disks about 13 cm in diameter and 4 cm thick. These alloys had varying levels of key elements to affect mechanical properties and change the "solvus" solution heat-treatment temperature necessary to produce coarse grain microstructures. Disks were given coarse grain heat treatments followed by rapid oil quenching and slower fan air quenching. These heat treatments were intended to simulate the cooling paths of rapidly cooled full-scale disks at the outermost rim and interior bore locations, respectively. Preliminary quench tests of tensile specimens and coin-size minidisks had indicated that alloys having high solvus temperatures were more prone to cracking during rapid quenching from coarse grain heat treatments. These findings were confirmed in the subscale disks, where such alloys did form undesirable quench cracks. Mechanical tests were performed on specimens from subscale disks given these coarse grain heat treatments, as well as on specimens given a fine grain heat treatment. Tensile, creep, and crack growth tests were performed at 704 C and higher temperatures. A versatile alloy was identified that had a low solvus temperature for resistance to quench cracking as well as an optimal combination of high levels of strengthening refractory elements that produced balanced high mechanical properties for both fine grain and coarse grain microstructures. This low-solvus, high-refractory (LSHR) alloy has been scaled-up to produce prototype full-scale turbine disks typical of regional jet turbofan engines. Disks were successfully heat treated to give uniform coarse grain and uniform fine grain microstructures. Additional disks were given a NASA dual microstructure heat treatment (DMHT) that intentionally varied the solution heat-treatment temperatures between the disk rim and bore (re f. 1). The disk rim was heated to a high enough temperature to produce a coarse grain microstructure, while the bore was maintained at a lower temperature to produce a fine grain microstructure (see the figure). This DMHT can produce optimal high strength, fatigue, and creep resistance up to 704 C in the cooler running disk bore, and high strength, creep resistance, and dwell crack growth resistance at higher temperatures for the hotter disk rim. Extensive mechanical testing is being initiated to compare the mechanical properties of the uniform and DMHT disks.

Gabb, TImothy P.↗

Mechanical Properties and Microstructure Investigation of Lead Free Solder

While the electronics industry appears to be focusing on Sn-Ag-Cu as the alloy of choice for lead free electronics assembly, ,the exact composition varies by geographic region, supplier and user. Add to that dissolved copper and silver from the printed circuit board traces and surface finish, and there can be significant variation in the final solder joint composition. A systematic study of the mechanical and microstructural properties of Sn-Ag-Cu alloys with Ag varying from 2wt% to 4wt% and Cu varying from 0.5wt% to lSwt%, was undertaken in this research study. Different sample preparation techniques (water quenched, oil quenched and water quenched followed by reflow) were explored and the resulting microstructure compared to that of a typical reflowed lead free chip scale package (CSP) solder joint. Tensile properties (modulus, 0.2% yield strength and the ultimate tensile strength) and creep behavior of selected alloy compositions (Sn-4Ag-1 X u , Sn-4Ag-OSCu, Sn- 2Ag-1 X u , Sn-2Ag-OSCu, Sn-3.5Ag-O.SCu) were determined for three conditions: as- cast; aged for 100 hours at 125OC; and aged for 250 hours at 125OC. There was no significant difference in Young's Modulus as a function of alloy composition. After an initial decrease in modulus after 100 hours at 125"C, there was an insignificant change with further aging. The distribution of 0.2% strain yield stress and ultimate tensile strength as a function of alloy composition was more significant and decreased with aging time and temperature. The microstructures of these alloys were examined using light and scanning electron microscopy (LM and SEM) respectively and SEM based energy dispersive x-ray spectroscopy (EDS). Fracture surface and cross-section analysis were performed on the specimens after creep testing. The creep testing results and the effect of high temperature aging on mechanical properties is presented for the oil quenched samples. In general the microstructure of oil quenched specimen exhibited a eutectic region of Sn with moderately dispersed Ag3Sn intermetallic, surrounded by a dendritic Sn-rich phase. The SEM images of the fracture surface indicated the presence of a tough shear surface at the initial cavity break area and a break line in the middle of specimen along the failure direction. A hyperbolic-sine creep model was adopted and used to fit the creep experiment data. The effect on the mechanical properties by adding the quaternary element bismuth to the Sn-3.5Ag-0.8Cu alloy was measured and compared with the mechanical properties of the ternary alloys. The results of this research study provide necessary data for the modeling of solder joint reliability for a range of Sn-Ag-Cu compositions and a baseline for evaluating the effects of subsequent quaternary additions.

Wang, Qing↗

Analysis of International Space Station Materials on MISSE-3 and MISSE-4

For high-temperature applications (> 2,000 C) such as solid rocket motors, hypersonic aircraft, nuclear electric/thermal propulsion for spacecraft, and more efficient jet engines, creep becomes one of the most important design factors to be considered. Conventional creep-testing methods, where the specimen and test apparatus are in contact with each other, are limited to temperatures ~1,700 deg. C. Development of alloys for higher-temperature applications is limited by the availability of testing methods at temperatures above 2000 C. Development of alloys for applications requiring a long service life at temperatures as low as 1500 C, such as the next generation of jet turbine superalloys, is limited by the difficulty of accelerated testing at temperatures above 1700 0c. For these reasons, a new, non-contact creep-measurement technique is needed for higher temperature applications. A new non-contact method for creep measurements of ultra-high-temperature metals and ceramics has been developed and validated. Using the electrostatic levitation (ESL) facility at NASA Marshall Space Flight Center, a spherical sample is rotated quickly enough to cause creep deformation due to centrifugal acceleration. Very accurate measurement of the deformed shape through digital image analysis allows the stress exponent n to be determined very precisely from a single test, rather than from numerous conventional tests. Validation tests on single-crystal niobium spheres showed excellent agreement with conventional tests at 1985 C; however the non-contact method provides much greater precision while using only about 40 milligrams of material. This method is being applied to materials including metals and ceramics for noneroding throats in solid rockets and next-generation superalloys for turbine engines. Recent advances in the method and the current state of these new measurements will be presented.

Finckenor, Miria M.↗

Predicting Lifetime of a Thermomechanically Loaded Component

NASALIFE is a computer program for predicting the lifetime, as affected by low cycle fatigue (LCF) and creep rupture, of a structural component subject to temporally varying, multiaxial thermomechanical loads. The component could be, for example, part of an aircraft turbine engine. Empirical data from LCF tests, creep rupture tests, and static tensile tests are used as references for predicting the number of missions the component can withstand under a given thermomechanical loading condition. The user prepares an input file containing the creep-rupture and cyclic-fatigue information, temperature-dependent material properties, and mission loading and control flags. The creep rupture information can be entered in tabular form as stress versus life or by means of parameters of the Larson-Miller equation. The program uses the Walker mean-stress model to adjust predicted life for ranges of the ratio between the maximum and minimum stresses. Data representing complex load cycles are reduced by the rainflow counting method. Miner's rule is utilized to combine the damage at different load levels. Finally, the program determines the total damage due to creep and combines it with the fatigue damage due to the cyclic loading and predicts the approximate number of missions a component can endure before failing.

Murthy, Pappu L. N.↗