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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Determination of convergence rates across the Ventura Basin, Southern California, using GPS and historical triangulation

Comparison of angles from historical triangulation observations dating as far back as 1932 with Global Positions System (GPS) measurements taken in 1987 indicates that rapid convergence may be taking place on decade timescales in the central and eastern part of the Ventura basin, an east-west trending trough bounded by thrust faults. Changes in angles over this time were analyzed using Prescott's modified Frank's method and in terms of a model which assumes that the regions to the north and south of the basin are rigid blocks undergoing relative motion. For the two block model, inversion of the observed angle changes over the last 28 years for the relative motion vector leads to north-south convergence across the basin of 30 + or - 5 mm/yr, with a left lateral component of 10 + or - 1 mm/yr in the Fillmore-Santa Paula area in the central part of the basin. The modified Frank's method yields strain rates of approximately 2 microrad/yr in both the east and central parts of the basin for measurements spanning the 1971 San Fernando earthquake. Assuming no east-west strain yeilds north-south compression of approximately 3.5 + or - .2 cm/yr. Comparison of triangulation data prior to the earthquake shows no strain outside the margin of error. The convergence rates determined by geodetic techniques are consistent with geologic observations in the area. Such large geodetic deformation rates, with no apparent near-surface creep on the major thrust, can be understood if these faults become subhorizontal at relatively shallow depths and if the subhorizontal portions of the faults are creeping. An alternative explanation of the large displacement rates might be that the pumping of oil in the vicinity of the benchmarks caused large horizontal motions, although it is unlikely that meter scale horizontal motions are due to oil withdrawal. These and other hypotheses are evaluated to better constrain the tectonics of this active region.

Donnellan, Andrea↗
NASA NTRS1994

Effects of physical aging on long-term creep of polymers and polymer matrix composites

For many polymeric materials in use below the glass transition temperature, the long term viscoelastic behavior is greatly affected by physical aging. To use polymer matrix composites as critical structural components in existing and novel technological applications, this long term behavior of the material system must be understood. Towards that end, this study applied the concepts governing the mechanics of physical aging in a consistent manner to the study of laminated composite systems. Even in fiber-dominated lay-ups the effects of physical aging are found to be important in the long-term behavior of the composite. The basic concepts describing physical aging of polymers are discussed. Several aspects of physical aging which have not been previously documented are also explored in this study, namely the effects of aging into equilibrium and a relationship to the time-temperature shift factor. The physical aging theory is then extended to develop the long-term compliance/modulus of a single lamina with varying fiber orientation. The latter is then built into classical lamination theory to predict long-time response of general oriented lamina and laminates. It is illustrated that the long term response can be counterintuitive, stressing the need for consistent modeling efforts to make long term predictions of laminates to be used in structural situations.

Brinson, L. Catherine↗
NASA NTRS1993

An extended UTD analysis for the scattering and diffraction from cubic polynomial strips

Spline and polynomial type surfaces are commonly used in high frequency modeling of complex structures such as aircraft, ships, reflectors, etc. It is therefore of interest to develop an efficient and accurate solution to describe the scattered fields from such surfaces. An extended Uniform Geometrical Theory of Diffraction (UTD) solution for the scattering and diffraction from perfectly conducting cubic polynomial strips is derived and involves the incomplete Airy integrals as canonical functions. This new solution is universal in nature and can be used to effectively describe the scattered fields from flat, strictly concave or convex, and concave convex boundaries containing edges. The classic UTD solution fails to describe the more complicated field behavior associated with higher order phase catastrophes and therefore a new set of uniform reflection and first-order edge diffraction coefficients is derived. Also, an additional diffraction coefficient associated with a zero-curvature (inflection) point is presented. Higher order effects such as double edge diffraction, creeping waves, and whispering gallery modes are not examined. The extended UTD solution is independent of the scatterer size and also provides useful physical insight into the various scattering and diffraction processes. Its accuracy is confirmed via comparison with some reference moment method results.

Constantinides, E. D.↗
NASA NTRS2016

Environmental Barrier Coating Development for SiC/SiC Ceramic Matrix Composites: Recent Advances and Future Directions

This presentation briefly reviews the SiC/SiC major environmental and environment-fatigue degradations encountered in simulated turbine combustion environments, and thus NASA environmental barrier coating system evolution for protecting the SiC/SiC Ceramic Matrix Composites for meeting the engine performance requirements. The presentation will review several generations of NASA EBC materials systems, EBC-CMC component system technologies for SiC/SiC ceramic matrix composite combustors and turbine airfoils, highlighting the temperature capability and durability improvements in simulated engine high heat flux, high pressure, high velocity, and with mechanical creep and fatigue loading conditions. This paper will also focus on the performance requirements and design considerations of environmental barrier coatings for next generation turbine engine applications. The current development emphasis is placed on advanced NASA candidate environmental barrier coating systems for SiC/SiC CMCs, their performance benefits and design limitations in long-term operation and combustion environments. The efforts have been also directed to developing prime-reliant, self-healing 2700F EBC bond coat; and high stability, lower thermal conductivity, and durable EBC top coats. Major technical barriers in developing environmental barrier coating systems, the coating integrations with next generation CMCs having the improved environmental stability, erosion-impact resistance, and long-term fatigue-environment system durability performance will be described. The research and development opportunities for turbine engine environmental barrier coating systems by utilizing improved compositions, state-of-the-art processing methods, and simulated environment testing and durability modeling will be briefly discussed.

Environmental Barrier Coatings↗
NASA NTRSDate not supplied

Energy landscape in Ni-Co-Cr and related alloys

Among multi-principal element alloys, the NiCoCr middle-entropy alloy has an outstanding combination of strength and ductility at both low and elevated temperatures. Equiatomic NiCoCr is a single-phase alloy with the face centered cubic (fcc) crystal structure. A low stacking fault energy in the fcc matrix is a cause of a relatively low creep in this alloy. The hexagonal close-packed (hcp) structure differs from the fcc by a stacking of atomic layers. The energy difference between the hcp and fcc structures is known to correlate with the stacking fault energy in the fcc phase. We compute formation and relative structural energies versus composition in the Ni-Co-Cr ternary and related quaternary systems, discuss possibilities of compositional adjustments, and compare theoretical predictions with experiment. We acknowledge funding by NASA’s Aeronautics Research Mission Directorate (ARMD) via Transformational Tools and Technologies (TTT) Project.

Multiscale↗
NASA NTRS2012

The Economics of NASA Mission Cost Reserves

Increases in NASA mission costs are well-noted but not well-understood, and there is little evidence that they are decreasing in frequency or amount over time. The need to control spending has led to analysis of the causes and magnitude of historical mission overruns, and many program control efforts are being implemented to attempt to prevent or mitigate the problem (NPR 7120). However, cost overruns have not abated, and while some direct causes of increased spending may be obvious (requirements creep, launch delays, directed changes, etc.), the underlying impetus to spend past the original budget may be more subtle. Gaining better insight into the causes of cost overruns will help NASA and its contracting organizations to avoid .them. This paper hypothesizes that one cause of NASA mission cost overruns is that the availability of reserves gives project team members an incentive to make decisions and behave in ways that increase costs. We theorize that the presence of reserves is a contributing factor to cost overruns because it causes organizations to use their funds less efficiently or to control spending less effectively. We draw a comparison to the insurance industry concept of moral hazard, the phenomenon that the presence of insurance causes insureds to have more frequent and higher insurance losses, and we attempt to apply actuarial techniques to quantifY the increase in the expected cost of a mission due to the availability of reserves. We create a theoretical model of reserve spending motivation by defining a variable ReserveSpending as a function of total reserves. This function has a positive slope; for every dollar of reserves available, there is a positive probability of spending it. Finally, the function should be concave down; the probability of spending each incremental dollar of reserves decreases progressively. We test the model against available NASA CADRe data by examining missions with reserve dollars initially available and testing whether they are more likely to spend those dollars, and whether larger levels of reserves lead to higher cost overruns. Finally, we address the question of how to prevent reserves from increasing mission spending without increasing cost risk to projects budgeted without any reserves. Is there a "sweet spot"? How can we derive the maximum benefit associated with risk reduction from reserves while minimizing the effects of reserve spending motivation?

Whitley, Sally↗
NASA NTRS2003

Gravitational Effects on Distortion in Sintering

During sintering a powder compact gains strength through low-temperature interparticle bonding, usually induced by solid-state surface diffusion, followed by further strength contributions from high-temperature densification. In cases where a liquid phase forms, sintering densification is accelerated and shape retention is sustained while open pores remain and contribute capillary forces. Unfortunately, sintering densification requires the compact become thermally softened to a point where creep strain rates reach levels near 10(exp -2)/s when the liquid forms. On the other hand, thermal softening of the powder compact substantially reduces the strength at high temperatures. Therefore, the in situ strength evolution during sintering is a primary focus to separate compact densification (as required for high performance) with minimized distortion (as required for net-shaping). With respect to gravitation effects on distortion during sintering there are two points of substantial weakness - prior to significant interparticle bonding and during final pore closure. This research is focused on understanding the competition among interparticle neck growth, densification, thermal softening, grain boundary wetting, capillary effects associated with liquid wetting and residual porosity, and gravity. Most surprising is the apparent role of gravity, where the deviatoric stress acting on the powder structure induces skeletal formation that reduces distortion. In contrast with theory, microgravity samples exhibit more distortion yet fail to fully densify. Results are presented on the experimental concepts supporting an emerging model of sintering strength evolution that enables understanding of both distortion and densification. The experiments have relied on tungsten heavy alloys, various combinations of dihedral angle, pore size, initial porosity, liquid:solid ratio, and heating rates. On Earth, the dominant factor with respect to distortion is the starting body heterogeneity. Current modeling efforts are seeking some means to uniformly predict the distortion based on a starting pore structure heterogeneity parameter. Densification is largely unaffected by the initial pore structure, but distortion is highly variable, suggesting that nonuniform pore closure might be a significant parameter during sintering. With respect to flight experiments, plans include removal of the solid body forces acting on the solid grains, allowing stabilization of the pore structure and examination of the buoyancy effects with regard to distortion. In microgravity there is the surprising result that compacts do not densify, yet distort a factor that is contrary to all current sintering models. Densification without distortion during liquid phase sintering was achieved by manipulating microstructure and its evolution during sintering. Microstructure parameters such as the solid volume fraction, dihedral angle, initial porosity, and pore size were varied to measure densification and distortion behavior during LPS using W-Ni-Cu alloys. Green compacts were formed using ethylene-bis-stearamide as a pore-forming agent with the amount of polymer controlling the initial porosity. Different initial pore sizes were generated by varying the polymer particle size. Dihedral angle was varied by changing the Ni:Cu ratio in the alloys. Finally, the solid volume fraction was adjusted via the tungsten content. Distortion was quantified using profiles determined with a coordinate measuring machine to calculate a distortion parameter. Sintering results showed that solid volume fraction and dihedral angle are the dominant factors on densification and distortion during liquid phase sintering. Distortion decreases with increasing solid volume fraction and dihedral angle, while initial porosity and pore size have no observable effect on distortion at nearly full densification. Various strategies emerge to improve distortion control in liquid phase sintering.

German, Randall M.↗
NASA NTRS2006

Low-Density, Creep-Resistant Single-Crystal Superalloys

Several recently formulated nickel-base superalloys have been developed with excellent high-temperature creep resistance, at lower densities than those of currently used nickel-base superalloys. These alloys are the latest products of a continuing effort to develop alloys that have even greater strength-to-weight ratios, suitable for use in turbine blades of aircraft engines. Mass densities of turbine blades exert a significant effect on the overall weight of aircraft. For a given aircraft, a reduction in the density of turbine blades enables design reductions in the weight of other parts throughout the turbine rotor, including the disk, hub, and shaft, as well as supporting structures in the engine. The resulting total reduction in weight can be 8 to 10 times that of the reduction in weight of the turbine blades. The approach followed in formulating these alloys involved several strategies for identifying key alloying elements and the range of concentration of each element to study. To minimize the number of alloys needed to be cast, a design-of--experiments methodology was adopted. A statistics-based computer program that models the effects of varying compositions of four elements, including effects of two-way interactions between elements, was used to test all possible alloys within the design space. The starting points for the computational analysis were three alloy compositions mandated by engineering consensus. After likewise identification of key alloying elements to vary and the allowed ranges of concentrations, the computer program then selects a minimum number of alloys within the design space to allow determination of effects for all four elements and their interactions.

MacKay, Rebecca A.↗
NASA NTRSDate not supplied

Molecular dynamics simulation of effects of solutes on dislocation propagation in Ni-based superalloys

Ni-based superalloys are used in the hot sections of jet turbine engines because of their high strength, stability and resistance to oxidation. The properties of these alloys can be further optimized by adding alloying elements. Therefore, a fundamental knowledge on the effect of different elements on properties of Ni-based superalloys is required. Molecular dynamics simulation could shed light here but its application is hindered by the absence of reliable and computationally cheap semi-empirical potential of the interatomic interaction for 4 and more element alloys. We will present a new Ni-Al-Cr-Nb Finnis-Sinclair (FS) potential specially designed to simulate the dislocation propagation from to  phase. In order to construct this potential, we designed a special algorithm to incorporate the data on element partitioning in the potential development procedure. For example, it is known from experiment, that Cr is mostly present in the gamma phase. Figure 1 shows a snapshot obtained after equilibration of the model of the Ni68Al17Cr15 alloy at T=1000 K using the hybrid Monte-Carlo (MC)/molecular dynamics (MD) simulation with the developed semi-empirical potential. One can clearly see that the Cr partitioning is in agreement with the experimental data. We will discuss the developed algorithm to incorporate the solute partition data in details. Using the developed semi-empirical potential, we first investigated the effect of anti-site defects in the  phase on the single dislocation propagation. It was found that the dislocation velocity increases with the increasing of the anti-site defect concentration. This effect was attributed to smaller number of Al-Al pairs forming during the dislocation migration in the presence of the anti-site defects. Next, we investigated the effect of Nb on the dislocation pair propagation in the Kolbe mechanism. It was found that the addition of Nb leads to considerable decrease in the dislocation propagation rate. This is in agreement with the experimental data on the effect of Nb on the creep resistance of the Ni-based superalloys. We will discuss the origin of this effect.

Mikhail I. Mendelev↗
NASA NTRS2016

Separating the Influence of Environment from Stress Relaxation Effects on Dwell Fatigue Crack Growth in a Nickel-Base Disk Alloy

Both environmental embrittlement and crack tip visco-plastic stress relaxation play a significant role in determining the dwell fatigue crack growth (DFCG) resistance of nickel-based disk superalloys. In the current study performed on the Low Solvus High Refractory (LSHR) disk alloy, the influence of these two mechanisms were separated so that the effects of each could be quantified and modeled. Seven different microstructural variations of LSHR were produced by controlling the cooling rate and the subsequent aging and thermal exposure heat treatments. Through cyclic fatigue crack growth testing performed both in air and vacuum, it was established that four out of the seven LSHR heat treatments evaluated, possessed similar intrinsic environmental resistance to cyclic crack growth. For these four heat treatments, it was further shown that the large differences in dwell crack growth behavior which still persisted, were related to their measured stress relaxation behavior. The apparent differences in their dwell crack growth resistance were attributed to the inability of the standard linear elastic fracture mechanics (LEFM) stress intensity parameter to account for visco-plastic behavior. Crack tip stress relaxation controls the magnitude of the remaining local tensile stresses which are directly related to the measured dwell crack growth rates. It was hypothesized that the environmentally weakened grain boundary crack tip regions fail during the dwells when their strength is exceeded by the remaining local crack tip tensile stresses. It was shown that the classical creep crack growth mechanisms such as grain boundary sliding did not contribute to crack growth, but the local visco-plastic behavior still plays a very significant role by determining the crack tip tensile stress field which controls the dwell crack growth behavior. To account for the influence of the visco-plastic behavior on the crack tip stress field, an empirical modification to the LEFM stress intensity parameter, Kmax, was developed by incorporating into the formulation the remaining stress level concept as measured by simple stress relaxation tests. The newly proposed parameter, Ksrf, did an excellent job in correlating the dwell crack growth rates for the four heat treatments which were shown to have similar intrinsic environmental cyclic fatigue crack growth resistance.

Dwell crack growth↗
NASA NTRSDate not supplied

Structural Analysis Findings of Open Spelter Socket Cable Terminations

A three-dimensional nonlinear finite element model of a representative open spelter socket termination was developed to examine the underlying mechanics of load transfer from a structural cable through the termination, the sensitivity of the joint design to wire brooming, zinc material nonlinearity, contact friction between the zinc and socket, voids within the zinc, and, finally, the effects of repeated loading on the joint. Primary factors affecting open spelter socket design are cast zinc plastic flow, depth of zinc slug seating, and quality of wire brooming. Zinc plasticity and proper brooming allows for efficient load transfer by developing confining pressure on the broomed wires in the narrow part of the socket, which keep the wires from pulling out of the zinc and shift failure to occur outside the socket. Highest wire stresses in the cable occur in the outer ring adjacent to the termination. While industry use of stay cables are typically designed to carry less than half the rated breaking force in aggregate, the constituent stresses within the zinc and the wires have the potential to exceed their respective allowable in operation and should be evaluated for fatigue- and creep-critical applications.

Pavel Babuska↗
NASA NTRS2000

Fretting Stresses in Single Crystal Superalloy Turbine Blade Attachments

Single crystal nickel base superalloy turbine blades are being utilized in rocket engine turbopumps and turbine engines because of their superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal nickel base turbine blade superalloys are PWA 1480/1493 and PWA 1484. These alloys play an important role in commercial, military and space propulsion systems. High Cycle Fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Blade attachment regions are prone to fretting fatigue failures. Single crystal nickel base superalloy turbine blades are especially prone to fretting damage because the subsurface shear stresses induced by fretting action at the attachment regions can result in crystallographic initiation and crack growth along octahedral planes. Furthermore, crystallographic crack growth on octahedral planes under fretting induced mixed mode loading can be an order of magnitude faster than under pure mode I loading. This paper presents contact stress evaluation in the attachment region for single crystal turbine blades used in the NASA alternate Advanced High Pressure Fuel Turbo Pump (HPFTP/AT) for the Space Shuttle Main Engine (SSME). Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. Blades and the attachment region are modeled using a large-scale 3D finite element (FE) model capable of accounting for contact friction, material orthotrophy, and variation in primary and secondary crystal orientation. Contact stress analysis in the blade attachment regions is presented as a function of coefficient of friction and primary and secondary crystal orientation, Stress results are used to discuss fretting fatigue failure analysis of SSME blades. Attachment stresses are seen to reach peak values at locations where fretting cracks have been observed. Fretting stresses at the attachment region are seen to vary significantly as a function of crystal orientation. Attempts to adapt techniques used for estimating fatigue life in the airfoil region, for life calculations in the attachment region, are presented. An effective model for predicting crystallographic crack initiation under mixed mode loading is required for life prediction under fretting action.

Arakere, Nagaraj K.↗
NASA NTRSDate not supplied

Py MILab: Capturing, Analyzing and Storing Test Data

Integrated Computational Materials Engineering (ICME) has recently received widespread attention due to its promises in reducing dependence on physical testing for engineering design by relying on simulation, reducing both time and cost to market for various applications. ICME however requires validated multiscale material models, which is heavily dependent on available test data with full material and test pedigree, including material processing, test and measurement equipment, raw data collection, and analysis methodology and results. Populating searchable information management systems with such rich data sets is often burdensome for data producers, resulting in a lack of findable data for modelers to validate and verify their models. To overcome these cultural barriers to ICME, NASA has developed of various database-integration toolsets that perform both data management activities within the organization’s best practices with additional functionality that relieves the effort of the data producer and promotes adoption of information management system. One such tool currently under development is Py MILab, an automatic framework for automatic capturing, analysis, maintenance, and storage of material test data. Py MILab uses a modular approach for capturing raw data, analyzing the data, and storing the data in a database, interfaced by neutral file structures, to promote plug-and-play capabilities for various analysis types. TMAnalysis is a Python-based tool that performs automatic data reduction and analysis of uniaxial thermomechanical test data. The TMAnalysis toolset can be implemented within the Analysis module of Py MILab, and thus requires a populated neutral file form the Raw Data Module of Py MILab and outputs a Analysis neutral file compatible with the Database Module of Py MILab. TMAnalysis is able to perform automatic segmentation of multistage tests and perform data analysis and reduction, including determination of point-wise properties in tension, compression, and shear, analysis of stress relaxation tests, creep analysis and zone identification, and combination of these stage types for tests with complex loading histories. The TMAnalysis code is accompanied with a graphical user interface (GUI) that allows users to easily analyze test data in bulk, verify the automatic, consistent analysis performed by the backend code, and edit stage segmentation if necessary before producing the output neutral files, ensuring data is properly analyzed and maintained with full traceability.

Data management↗
NASA NTRS2002

Effect of Crystal Orientation on Fatigue Failure of Single Crystal Nickel Base Turbine Blade Superalloys

High cycle fatigue (HCF) induced failures in aircraft gas turbine and rocket engine turbopump blades is a pervasive problem. Single crystal nickel turbine blades are being utilized in rocket engine turbopumps and jet engines throughout industry because of their superior creep, stress rupture, melt resistance, and thermomechanical fatigue capabilities over polycrystalline alloys. Currently the most widely used single crystal turbine blade superalloys are PWA 1480/1493, PWA 1484, RENE' N-5 and CMSX-4. These alloys play an important role in commercial, military and space propulsion systems. Single crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the part geometry a significant factor in the overall analysis. The failure modes of single crystal turbine blades are complicated to predict due to the material orthotropy and variations in crystal orientations. Fatigue life estimation of single crystal turbine blades represents an important aspect of durability assessment. It is therefore of practical interest to develop effective fatigue failure criteria for single crystal nickel alloys and to investigate the effects of variation of primary and secondary crystal orientation on fatigue life. A fatigue failure criterion based on the maximum shear stress amplitude /Delta(sub tau)(sub max))] on the 24 octahedral and 6 cube slip systems, is presented for single crystal nickel superalloys (FCC crystal). This criterion reduces the scatter in uniaxial LCF test data considerably for PWA 1493 at 1200 F in air. Additionally, single crystal turbine blades used in the alternate advanced high-pressure fuel turbopump (AHPFTP/AT) are modeled using a large-scale three-dimensional finite element model. This finite element model is capable of accounting for material orthotrophy and variation in primary and secondary crystal orientation. Effects of variation in crystal orientation on blade stress response are studied based on 297 finite element model runs. Fatigue lives at critical points in the blade are computed using finite element stress results and the failure criterion developed. Stress analysis results in the blade attachment region are also presented. Results presented demonstrates that control of secondary and primary crystallographic orientation has the potential to significantly increase a component S resistance to fatigue crack growth with- out adding additional weight or cost. [DOI: 10.1115/1.1413767]

Arakere, N. K.↗
NASA NTRS1996

Effect of Full-Chord Porosity on Aerodynamic Characteristics of the NACA 0012 Airfoil

A test was conducted on a model of the NACA 0012 airfoil section with a solid upper surface or a porous upper surface with a cavity beneath for passive venting. The purposes of the test were to investigate the aerodynamic characteristics of an airfoil with full-chord porosity and to assess the ability of porosity to provide a multipoint or self-adaptive design. The tests were conducted in the Langley 8-Foot Transonic Pressure Tunnel over a Mach number range from 0.50 to 0.82 at chord Reynolds numbers of 2 x 10(exp 6), 4 x 10(exp 6), and 6 x 10(exp 6). The angle of attack was varied from -1 deg to 6 deg. At the lower Mach numbers, porosity leads to a dependence of the drag on the normal force. At subcritical conditions, porosity tends to flatten the pressure distribution, which reduces the suction peak near the leading edge and increases the suction over the middle of the chord. At supercritical conditions, the compression region on the porous upper surface is spread over a longer portion of the chord. In all cases, the pressure coefficient in the cavity beneath the porous surface is fairly constant with a very small increase over the rear portion. For the porous upper surface, the trailing edge pressure coefficients exhibit a creep at the lower section normal force coefficients, which suggests that the boundary layer on the rear portion of the airfoil is significantly thickening with increasing normal force coefficient.

Mineck, Raymond E.↗
NASA NTRS2010

Probabilistic Multi-Factor Interaction Model for Complex Material Behavior

Complex material behavior is represented by a single equation of product form to account for interaction among the various factors. The factors are selected by the physics of the problem and the environment that the model is to represent. For example, different factors will be required for each to represent temperature, moisture, erosion, corrosion, etc. It is important that the equation represent the physics of the behavior in its entirety accurately. The Multi-Factor Interaction Model (MFIM) is used to evaluate the divot weight (foam weight ejected) from the external launch tanks. The multi-factor has sufficient degrees of freedom to evaluate a large number of factors that may contribute to the divot ejection. It also accommodates all interactions by its product form. Each factor has an exponent that satisfies only two points - the initial and final points. The exponent describes a monotonic path from the initial condition to the final. The exponent values are selected so that the described path makes sense in the absence of experimental data. In the present investigation, the data used were obtained by testing simulated specimens in launching conditions. Results show that the MFIM is an effective method of describing the divot weight ejected under the conditions investigated. The problem lies in how to represent the divot weight with a single equation. A unique solution to this problem is a multi-factor equation of product form. Each factor is of the following form (1 xi/xf)ei, where xi is the initial value, usually at ambient conditions, xf the final value, and ei the exponent that makes the curve represented unimodal that meets the initial and final values. The exponents are either evaluated by test data or by technical judgment. A minor disadvantage may be the selection of exponents in the absence of any empirical data. This form has been used successfully in describing the foam ejected in simulated space environmental conditions. Seven factors were required to represent the ejected foam. The exponents were evaluated by least squares method from experimental data. The equation is used and it can represent multiple factors in other problems as well; for example, evaluation of fatigue life, creep life, fracture toughness, and structural fracture, as well as optimization functions. The software is rather simplistic. Required inputs are initial value, final value, and an exponent for each factor. The number of factors is open-ended. The value is updated as each factor is evaluated. If a factor goes to zero, the previous value is used in the evaluation.

Abumeri, Galib H.↗