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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Polyurethane Microparticles for Stimuli Response and Reduced Oxidative Degradation in Highly Porous Shape Memory Polymers

Shape memory polymers (SMPs) have been found to be promising biomaterials for a variety of medical applications; however, the clinical translation of such technology is dependent on tailorable properties such as gravimetric changes in degradation environments. For SMPs synthesized from amino-alcohols, oxidation resulting in rapid mass loss may be problematic in terms of loss of material functionality as well as toxicity and cytocompatibility concerns. Control of gravimetric changes was achieved through the incorporation of small molecule antioxidants, either directly into the polymer matrix or included in microparticles to form a SMP composite material. Direct incorporation of small molecule antioxidants, such as phenolic alcohols, was found to alter shape memory attributes and increase elastic modulus at the expense of the strain to failure. Such changes could not ensure retention of the antioxidants and therefore did not increase oxidative stability. However, the inclusion of antioxidants in microparticles was found to produce materials with similar thermomechanical and shape memory properties while increasing oxidative resistance compared to controls. The microparticle composite SMPs also act as a platform for environmental sensing, such as pH-dependent fluorescence shifts and payload release, as demonstrated by fluorescent dyes and the release of antioxidants. The use of polyurethane-urea microparticles in porous SMPs is demonstrated to increase biostability of the materials, by approximately 25%, and ultimately extend their lifespan for use in aneurysm occlusion as determined through calculated in vivo degradation rates corresponding to a porcine aneurysm environment.

Weems, A. C.↗
NASA NTRS1984

Performance of thermal barrier coatings in high heat flux environments

Thermal barrier coatings were exposed to the high temperature and high heat flux produced by a 30 kW plasma torch. Analysis of the specimen heating rates indicates that the temperature drop across the thickness of the 0.038 cm ceramic layer was about 1100 C after 0.5 sec in the flame. An as-sprayed ZrO2-8%Y2O3 specimens survived 3000 of the 0.5 sec cycles with failing. Surface spalling was observed when 2.5 sec cycles were employed but this was attributed to uneven heating caused by surface roughness. This surface spalling was prevented by smoothing the surface with silicon carbide paper or by laser glazing. A coated specimen with no surface modification but which was heat treated in argon also did not surface spall. Heat treatment in air led to spalling in as early as 2 cycle from heating stresses. Failures at edges were investigated and shown to be a minor source of concern. Ceramic coatings formed from ZrO2-12%Y2O3 or ZrO2-20%Y2O3 were shown to be unsuited for use under the high heat flux conditions of this study.

Miller, R. A.↗
NASA NTRS1998

The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits

Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.

Carpenter, J. Russell↗
NASA NTRS2011

Use of Minute-by-Minute Cardiovascular Measurements During Tilt Tests to Strengthen Inference on the Effect of Long-Duration Space Flight on Orthostatic Hypotension

Typical methodology for evaluating the effects of spaceflight on orthostatic hypotension (OH) has been survival analysis of tolerance times from 80 head-up tilt tests. However when scheduled test durations are short, there may not be enough failures to allow survival analysis to adequately estimate and compare the effects of flight phase (e.g. pre-flight, number of days post-flight), flight duration, and their interaction, as well as interactions with effects of interventions or countermeasures. The problem is exacerbated in the presence of a repeated measures design, in which subjects participate in tilt tests during various flight phases. Here we show how it is possible to dramatically improve the efficiency of statistical inference in this setting by making use of the additional information contained in minute-by-minute observations of cardiovascular parameters thought to be reflective of progression towards presyncope during tilt testing. Methods: We retrospectively examined operational tilt test (OTT; 10 -min 80 head-up tilt) data from 20 International Space Station (ISS) and 66 Shuttle astronauts 10 d before launch (L-10), on landing day (R+0) and during recovery (R+1, R+3, R+6-10) depending on the level of participation. Data from 5 ISS astronauts tested on R+0 or R+1 who used non-standard countermeasures were excluded. In addition to OTT survival time, 8 cardiovascular parameters (CP: heart rate, systolic, diastolic, and mean arterial blood pressure, pulse pressure, stroke volume, cardiac output, and total peripheral resistance) that might be predictive of progression towards presyncope were measured every minute of each OTT. Statistical analysis was predicated on a two ]stage model of causation. In the first stage, flight duration and time from landing affect the astronauts' degree of OH, which is manifested in the time trends and variation of the above CPs during OTTs. In the second stage, the behavior of these parameters directly affects OTT survival time. Actual analysis proceeded in the opposite direction. First we identified those CPs or linear combinations that best predicted OTT survival regardless of what spaceflight conditions led to OTT completion or presyncope. From these, we calculated a summary statistic (one per OTT) that best predicted survival. We then used mixed ]model regression analysis to relate changes in the summary statistic to flight phase and duration. Inference on the effects of phase, duration, and their interaction on OH follows directly from this second analysis. Results: A linear combination (W) of diastolic blood pressure (DBP) and stroke volume (SV) was found to be the best predictor of OTT survival using the complete data set of minute-by-minute observations of CPs for each OTT. Furthermore, the log-transformed standard deviation of W (Z = log SW) was found to be a strong predictor of survival in the reduced data set consisting of one observation per OTT. In other words, this measure of variability of W during an OTT was the best indicator of whether or not the subject could complete the 10-min test, with higher variability (i.e. higher values of Z) being associated with greater probability of failure. In the mixed-model regression analysis where Z was now treated as a outcome with flight phase and duration groups (ISS and STS) as predictors, we found that there was a significantly more variability in W (higher values of Z) for both groups at R+0, but with no evidence of an interaction until R+3, when the ISS group still had inflated variability, but not the STS group. Conclusions: Variability of the cardiovascular index W recovers more slowly after long-compared to short-duration spaceflight. Since high variability of W has also been shown to be predictive of OTT failure, a primary manifestation of OH, a logical conclusion is that recovery from OH also is slower after long-duration compared to short-duration spaceflights.

Feiveson, Alan H.↗
NASA NTRS1984

Performance of thermal barrier coatings in high heat flux environments

Thermal barrier coatings were exposed to the high temperature and high heat flux produced by a 30 kW plasma torch. Analysis of the specimen heating rates indicates that the temperature drop across the thickness of the 0.038 cm ceramic layer was about 1100 C after 0.5 sec in the flame. An as-sprayed ZrO2-8 percent Y2O3 specimens survived 3000 of the 0.5 sec cycles with falling. Surface spalling was observed when 2.5 sec cycles were employed but this was attributed to uneven heating caused by surface roughness. This surface spalling was prevented by smoothing the surface with silicon carbide paper or by laser glazing. A coated specimen with no surface modification but which was heat treated in argon also did not surface spall. Heat treatment in air led to spalling in as early as 1 cycle from heating stresses. Failures at edges were investigated and shown to be a minor source of concern. Ceramic coatings formed from ZrO2-12 percent Y2O3 or ZrO2-2O percent Y2O3 were shown to be unsuited for use under the high heat flux conditions of this study.

Miller, R. A.↗
NASA NTRS1985

Elevated temperature biaxial fatigue

A 3 year experimental program for studying elevated temperature biaxial fatigue of a nickel based alloy Hastelloy-X has been completed. A new high temperature fatigue test facility with unique capabilities has been developed. Effort was directed toward understanding multiaxial fatigue and correlating the experimental data to the existing theories of fatigue failure. The difficult task of predicting fatigue lives for nonproportional loading was used as an ultimate test for various life prediction methods being considered. The primary means of reaching improved understanding were through several critical nonproportional loading experiments. The direction of cracking observed on failed specimens was also recorded and used to guide the development of the theory. Cyclic deformation responses were permanently recorded digitally during each test. It was discovered that the cracking mode switched from primarily cracking on the maximum shear planes at room temperature to cracking on the maximum normal strain planes at 649 C. In contrast to some other metals, loading path in nonproportional loading had little effect on fatigue lives. Strain rate had a small effect on fatigue lives at 649 C. Of the various correlating parameters the modified plastic work and octahedral shear stress were the most successful.

Jordan, E. H.↗
NASA NTRS1984

Performance of thermal barrier coatings in high heat flux environments

Thermal barrier coatings were exposed to the high temperature and high heat flux produced by a 30 kW plasma torch. Analysis of the specimen heating rates indicates that the temperature drop across the thickness of the 0.038 cm ceramic layer was about 1100 C after 0.5 sec in the flame. An as-sprayed ZrO2-8 percent Y203 specimens survived 3000 of the 0.5 sec cycles with failing. Surface spalling was observed when 2.5 sec cycles were employed but this was attributed to uneven heating caused by surface roughness. This surface spalling was prevented by smoothing the surface with silicon carbide paper or by laser glazing. A coated specimen with no surface modification but which was heat treated in argon also did not surface spall. Heat treatment in air led to spalling in as early as 2 cycle from heating stresses. Failures at edges were investigated and shown to be a minor source of concern. Ceramic coatings formed from ZrO2-12 percent Y2O3 or ZrO2-20 percent Y2O3 were shown to be unsuited for use under the high heat flux conditions of this study.

Miller, R. A.↗
NASA NTRS2015

Insulation Resistance Degradation in Ni-BaTiO3 Multilayer Ceramic Capacitors

Insulation resistance (IR) degradation in NiBaTiO3 multilayer ceramic capacitors has been characterized by the measurement of both time to failure (TTF) and direct current leakage current as a function of stress time under highly accelerated life test conditions. The measured leakage current time dependence data fit well to an exponential form, and a characteristic growth time tau (sub SD) can be determined. A greater value of tau (sub SD) represents a slower IR degradation process. Oxygen vacancy migration and localization at the grain boundary region results in the reduction of the Schottky barrier height and has been found to be the main reason for IR degradation in NiBaTiO3 capacitors. The reduction of barrier height as a function oftime follows an exponential relation of phi (t ) = phi (0) e (exp -2Kt), where 13 the degradation rate constant K Koe (Ek/kT) is inversely proportional to the mean TTF (MTTF) and can be determined using an Arrhenius plot. For oxygen vacancy electromigration, a lower barrier height phi (0) will favor a slow IR degradation process, but a lower phi (0) will also promote electronic carrier conduction across the barrier and decrease the IR. As a result, a moderate barrier height phi (0) (and therefore a moderate IR value) with a longer MTTF (smaller degradation rate constant K) will result in a minimized IR degradation process and the most improved reliability in NiBaTiO3 multilayer ceramic capacitors.

reliability↗
NASA NTRS2015

Design of the Brine Evaporation Bag for Increased Water Recovery in Microgravity

The existing water recovery system on the International Space Station (ISS) is limited to 75% reclamation; consequently, long duration space missions are currently unfeasible due to the large quantity of water necessary to sustain the crew. The Brine Evaporation Bag (BEB) is a proposed system to supplement the existing water recovery system aboard the ISS that can to increase water recovery to 99%. The largest barrier to high water recovery is mineral scaling inside the water recovery equipment, which leads to equipment failure; therefore, some water must remain to keep the minerals dissolved. This waste stream is liquid brine containing salts, acids, organics, and water. The BEB is designed to recover this remaining water while protecting the equipment from scale. The BEB consists of a sealed bag containing a hydrophobic membrane that allows water vapor and gas to pass through. It is operated under vacuum, heated, and continuously filled with brine to boil away the water. The water vapor is recovered and the solids are contained inside the bag for disposal. The BEB can dry the brine to a solid block. Ongoing work includes improving the design of the BEB and the evaporator to prevent leaks, maximize the rate of water removal, and minimize energy use and weight. Additional testing will determine whether designs are heat- or mass-transfer limited and the optimal water recovery rate.

Brine Evaporation Bag↗
NASA NTRS1988

Computational simulation methods for composite fracture mechanics

Structural integrity, durability, and damage tolerance of advanced composites are assessed by studying damage initiation at various scales (micro, macro, and global) and accumulation and growth leading to global failure, quantitatively and qualitatively. In addition, various fracture toughness parameters associated with a typical damage and its growth must be determined. Computational structural analysis codes to aid the composite design engineer in performing these tasks were developed. CODSTRAN (COmposite Durability STRuctural ANalysis) is used to qualitatively and quantitatively assess the progressive damage occurring in composite structures due to mechanical and environmental loads. Next, methods are covered that are currently being developed and used at Lewis to predict interlaminar fracture toughness and related parameters of fiber composites given a prescribed damage. The general purpose finite element code MSC/NASTRAN was used to simulate the interlaminar fracture and the associated individual as well as mixed-mode strain energy release rates in fiber composites.

Murthy, Pappu L. N.↗
NASA NTRS1988

Novae as distance indicators

Nova shells are characteristically prolate with equatorial bands and polar caps. Failure to account for the geometry can lead to large errors in expansion parallaxes for individual novae. When simple prescriptions are used for deriving expansion parallaxes from an ensemble of randomly oriented prolate spheroids, the average distance will be too small by factors of 10 to 15 percent. The absolute magnitudes of the novae will be underestimated and the resulting distance scale will be too small by the same factors. If observations of partially resolved nova shells select for large inclinations, the systematic error in the resulting distance scale could easily be 20 to 30 percent. Extinction by dust in the bulge of M31 may broaden and shift the intrinsic distribution of maximum nova magnitudes versus decay rates. We investigated this possibility by projecting Arp's and Rosino's novae onto a composite B - 6200A color map of M31's bulge. Thirty two of the 86 novae projected onto a smooth background with no underlying structure due to the presence of a dust cloud along the line of sight. The distribution of maximum magnitudes versus fade rates for these unreddened novae is indistinguishable from the distribution for the entire set of novae. It is concluded that novae suffer very little extinction from the filamentary and patchy distribution of dust seen in the bulge of M31. Time average B and H alpha nova luminosity functions are potentially powerful new ways to use novae as standard candles. Modern CCD observations and the photographic light curves of M31 novae found during the last 60 years were analyzed to show that these functions are power laws. Consequently, unless the eruption times for novae are known, the data cannot be used to obtain distances.

Ford, Holland C.↗
NASA NTRS1997

Influence of High Cycle Thermal Loads on Thermal Fatigue Behavior of Thick Thermal Barrier Coatings

Thick thermal barrier coating systems in a diesel engine experience severe thermal Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF) during engine operation. In the present study, the mechanisms of fatigue crack initiation and propagation, as well as of coating failure, under thermal loads which simulate engine conditions, are investigated using a high power CO2 laser. In general, surface vertical cracks initiate early and grow continuously under LCF and HCF cyclic stresses. It is found that in the absence of interfacial oxidation, the failure associated with LCF is closely related to coating sintering and creep at high temperatures, which induce tensile stresses in the coating after cooling. Experiments show that the HCF cycles are very damaging to the coating systems. The combined LCF and HCF tests produced more severe coating surface cracking, microspallation and accelerated crack growth, as compared to the pure LCF test. It is suggested that the HCF component cannot only accelerate the surface crack initiation, but also interact with the LCF by contributing to the crack growth at high temperatures. The increased LCF stress intensity at the crack tip due to the HCF component enhances the subsequent LCF crack growth. Conversely, since a faster HCF crack growth rate will be expected with lower effective compressive stresses in the coating, the LCF cycles also facilitate the HCF crack growth at high temperatures by stress relaxation process. A surface wedging model has been proposed to account for the HCF crack growth in the coating system. This mechanism predicts that HCF damage effect increases with increasing temperature swing, the thermal expansion coefficient and the elastic modulus of the ceramic coating, as well as the HCF interacting depth. A good agreement has been found between the analysis and experimental evidence.

Zhu, Dongming↗
NASA NTRS2001

Durability and Damage Development in Woven Ceramic Matrix Composites

Damage development in woven SiC/SiNC ceramic matrix composites (CMC's) under tensile and cyclic loading both at room and elevated temperatures have been investigated for the exhaust nozzle of high-efficient turbine engines. The ultimate strength, failure strain, proportional limit and modulus data at a temperature range of 23 to 1250 C are generated. The tensile strength of SiC/SiNC woven composites have been observed to increase with increased temperatures up to 1000 C. The stress/strain plot shows a pseudo-yield point at 25 percent of the failure strain (epsilon(sub r)) which indicates damage initiation in the form of matrix cracking. The evolution of damage beyond 0.25 epsilon(sub f), both at room and elevated temperature comprises multiple matrix cracking, interfacial debonding, and fiber pullout. Although the nature of the stress/strain plot shows damage-tolerant behavior under static loading both at room and elevated temperature, the life expectancy of SiC/SiNC composites degrades significantly under cyclic loading at elevated temperature. This is mostly due to the interactions of fatigue damage caused by the mechanically induced plastic strain and the damage developed by the creep strain. The in situ damage evolutions are monitored by acoustic event parameters, ultrasonic C-scan and stiffness degradation. Rate equations for modulus degradation and fatigue life prediction of ceramic matrix composites both at room and elevated temperatures are developed. These rate equations are observed to show reasonable agreement with experimental results.

Haque, A.↗
NASA NTRS2014

Decomposition Technique for Remaining Useful Life Prediction

The prognostic tool disclosed here decomposes the problem of estimating the remaining useful life (RUL) of a component or sub-system into two separate regression problems: the feature-to-damage mapping and the operational conditions-to-damage-rate mapping. These maps are initially generated in off-line mode. One or more regression algorithms are used to generate each of these maps from measurements (and features derived from these), operational conditions, and ground truth information. This decomposition technique allows for the explicit quantification and management of different sources of uncertainty present in the process. Next, the maps are used in an on-line mode where run-time data (sensor measurements and operational conditions) are used in conjunction with the maps generated in off-line mode to estimate both current damage state as well as future damage accumulation. Remaining life is computed by subtracting the instance when the extrapolated damage reaches the failure threshold from the instance when the prediction is made.

Saha, Bhaskar↗
NASA NTRS2009

International Space Station USOS Crew Quarters Ventilation and Acoustic Design Implementation

The International Space Station (ISS) United States Operational Segment (USOS) has four permanent rack sized ISS Crew Quarters (CQ) providing a private crewmember space. The CQ uses Node 2 cabin air for ventilation/thermal cooling, as opposed to conditioned ducted air from the ISS Temperature Humidity Control System or the ISS fluid cooling loop connections. Consequently, CQ can only increase the air flow rate to reduce the temperature delta between the cabin and the CQ interior. However, increasing airflow causes increased acoustic noise so efficient airflow distribution is an important design parameter. The CQ utilized a two fan push-pull configuration to ensure fresh air at the crewmember s head position and reduce acoustic exposure. The CQ interior needs to be below Noise Curve 40 (NC-40). The CQ ventilation ducts are open to the significantly louder Node 2 cabin aisle way which required significantly acoustic mitigation controls. The design implementation of the CQ ventilation system and acoustic mitigation are very inter-related and require consideration of crew comfort balanced with use of interior habitable volume, accommodation of fan failures, and possible crew uses that impact ventilation and acoustic performance. This paper illustrates the types of model analysis, assumptions, vehicle interactions, and trade-offs required for CQ ventilation and acoustics. Additionally, on-orbit ventilation system performance and initial crew feedback is presented. This approach is applicable to any private enclosed space that the crew will occupy.

Broyan, James Lee, Jr.↗
NASA NTRS2010

International Space Station Crew Quarters Ventilation and Acoustic Design Implementation

The International Space Station (ISS) United States Operational Segment has four permanent rack sized ISS Crew Quarters (CQs) providing a private crew member space. The CQs use Node 2 cabin air for ventilation/thermal cooling, as opposed to conditioned ducted air-from the ISS Common Cabin Air Assembly (CCAA) or the ISS fluid cooling loop. Consequently, CQ can only increase the air flow rate to reduce the temperature delta between the cabin and the CQ interior. However, increasing airflow causes increased acoustic noise so efficient airflow distribution is an important design parameter. The CQ utilized a two fan push-pull configuration to ensure fresh air at the crew member's head position and reduce acoustic exposure. The CQ ventilation ducts are conduits to the louder Node 2 cabin aisle way which required significant acoustic mitigation controls. The CQ interior needs to be below noise criteria curve 40 (NC-40). The design implementation of the CQ ventilation system and acoustic mitigation are very inter-related and require consideration of crew comfort balanced with use of interior habitable volume, accommodation of fan failures, and possible crew uses that impact ventilation and acoustic performance. Each CQ required 13% of its total volume and approximately 6% of its total mass to reduce acoustic noise. This paper illustrates the types of model analysis, assumptions, vehicle interactions, and trade-offs required for CQ ventilation and acoustics. Additionally, on-orbit ventilation system performance and initial crew feedback is presented. This approach is applicable to any private enclosed space that the crew will occupy.

Broyan, James L., Jr.↗
NASA NTRS2019

Quasi-Static and Dynamic Analysis of Composite Panels: Characterization and Validation

The predictive capability of a progressive damage model to simulate the quasi-static and dynamic crushing of composite specimens is evaluated in this article. The material model is commercially available within the ABAQUS finite element software package, i.e., “Damage for Fiber reinforced Composites”, and is often utilized to simulate damage progression and failure in static and dynamic failure scenarios such as crushing of a composite plate. The composite specimens used in this study consist of quasi-isotropic C-shaped and corrugated composite panels comprised of carbon fiber/epoxy braided fabric. The C-shaped panel specimen is used to calibrate the model and optimize material/model properties through comparison with experimental results. Then, using the same model parameters, the quasi-static crush response of the corrugated panel is predicted. The predictive capability of the model is further demonstrated by simulating the dynamic crushing response of both C-shaped and corrugated panels using the same material properties as in the quasi-static crush case with only minor adjustments for the dynamic elastic properties (i.e., rate dependent modulus). Results show that the in-built material model available in ABAQUS can successfully reproduce experimental results for both panels (C-shaped and corrugated) subjected to both quasi-static and dynamic loading scenarios. A small-scale parametric study on physical (experimentally measurable) and nonphysical (purely mathematical) model parameters was also conducted. It can be concluded that, achieving successful simulation results requires a more in-depth understanding of the influence of model parameter variation on the mechanical response of the composite together with the strategies and challenges of the utilized modeling methodology (e.g., FEA mesh density, etc.).

Naghipour Ghezeljeh, Paria↗
NASA NTRS1990

Behavior of surface and corner cracks subjected to tensile and bending loads in Ti-6Al-4V alloy

The behavior of part-through flaws with regard to failure under monotonic loading and their growth under fatigue loading was studied experimentally and analytically. Comparisons are made of experimental values of toughness obtained using surface and corner cracked specimens with those obtained using standard test specimens, and also experimental growth cycles were compared with numerical predictions using the NASA/FLAGRO computer program. Tests were conducted on various types of surface and corner cracks under tensile and bending loads. Room temperature lab air provided the test environment. The material used in this study was the Ti-6Al-4V alloy in the solution treated and aged (STA) and stress relieved condition. Detailed tabulation of the fracture toughness data and results of life prediction using the NASA/FLAGRO program are presented. Fatigue crack growth rates for the part-through cracked specimens are compared with a base curve fitted from the data obtained using standard specimens. The fatigue loading used in the crack growth testing was constant-amplitude sinusoidal type.

Forman, Royce G.↗