A method for calculating phase-locked loop performance near threshold.
Near-threshold behavior of phase-locked devices, noting phase error processes
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Near-threshold behavior of phase-locked devices, noting phase error processes
Near-threshold behavior of phase-locked devices, noting phase error processes
The experimental methods to determine near-threshold fatigue crack growth rate data are prescribed in ASTM standard E647. To produce near-threshold data at a constant stress ratio (R), the applied stress-intensity factor (K) is decreased as the crack grows based on a specified K-gradient. Consequently, as the fatigue crack growth rate threshold is approached and the crack tip opening displacement decreases, remote crack wake contact may occur due to the plastically deformed crack wake surfaces and shield the growing crack tip resulting in a reduced crack tip driving force and non-representative crack growth rate data. If such data are used to life a component, the evaluation could yield highly non-conservative predictions. Although this anomalous behavior has been shown to be affected by K-gradient, starting K level, residual stresses, environmental assisted cracking, specimen geometry, and material type, the specifications within the standard to avoid this effect are limited to a maximum fatigue crack growth rate and a suggestion for the K-gradient value. This paper provides parallel experimental and computational simulations for the K-decreasing method for two materials (an aluminum alloy, AA 2024-T3 and a titanium alloy, Ti 6-2-2-2-2) to aid in establishing clear understanding of appropriate testing requirements. These simulations investigate the effect of K-gradient, the maximum value of stress-intensity factor applied, and material type. A material independent term is developed to guide in the selection of appropriate test conditions for most engineering alloys. With the use of such a term, near-threshold fatigue crack growth rate tests can be performed at accelerated rates, near-threshold data can be acquired in days instead of weeks without having to establish testing criteria through trial and error, and these data can be acquired for most engineering materials, even those that are produced in relatively small product forms.
Cyclic near-threshold FCG behavior of two disk superalloys was evaluated, and was shown to exhibit an unexpected sudden failure mode transition from a mostly transgranular failure mode at higher stress intensities to an almost completely intergranular failure mode in the threshold regime. The change in failure modes was associated with a crossover effect in which the conditions that produced higher FCG rates in the Paris regime resulted in lower FCG rates and increased ΔKth values in the threshold region. High resolution scanning and transmission electron microscopy was used to carefully characterize the crack tips at these near-threshold conditions. Formation of stable Al-oxide followed by Cr and Ti oxides was found to occur at the crack tip prior to formation of unstable oxides. To contrast with the threshold failure mode regime, a quantitative assessment of the role that the intergranular failure mode has on cyclic FCG behavior in the Paris regime was also performed. It was demonstrated that the even a very limited intergranular failure content dominates the FCG response under mixed mode failure conditions.
Fatigue crack growth (FCG) research conducted in the near threshold regime has identified a room temperature creep crack growth damage mechanism for a fine grain powder metallurgy (PM) aluminum alloy (8009). At very low DK, an abrupt acceleration in room temperature FCG rate occurs at high stress ratio (R = Kmin/Kmax). The near threshold accelerated FCG rates are exacerbated by increased levels of Kmax (Kmax less than 0.4 KIC). Detailed fractographic analysis correlates accelerated FCG with the formation of crack-tip process zone micro-void damage. Experimental results show that the near threshold and Kmax influenced accelerated crack growth is time and temperature dependent.
Cyclic near-threshold fatigue crack growth (FCG) behavior of two disk superalloys was evaluated and was shown to exhibit an unexpected sudden failure mode transition from a mostly transgranular failure mode at higher stress intensity factor ranges to an almost completely intergranular failure mode in the threshold regime. The change in failure modes was associated with a crossover of FCG resistance curves in which the conditions that produced higher FCG rates in the Paris regime resulted in lower FCG rates and increased Kth values in the threshold region. High-resolution scanning and transmission electron microscopy were used to carefully characterize the crack tips at these near-threshold conditions. Formation of stable Al-oxide followed by Cr-oxide and Ti-oxides was found to occur at the crack tip prior to formation of unstable oxides. To contrast with the threshold failure mode regime, a quantitative assessment of the role that the intergranular failure mode has on cyclic FCG behavior in the Paris regime was also performed. It was demonstrated that even a very limited intergranular failure content dominates the FCG response under mixed mode failure conditions.
Hydrogen autoionization rates for molecular vibrational transitions near threshold, using internal conversion model
Be photoionization cross section calculated noting autoionization dominance near threshold, 1P phase shift and resonances location
Electron impact ionization of H atom in 1s state near threshold, noting cross section and power law
Direct and autoionization of H molecule by electron impact near threshold noting cross section, photoionization and vibrational and rotational energy changes
Near threshold fatigue crack propagation in pipeline steels in high pressure environments was studied. The objective was to determine the level of threshold stress intensity for fatigue crack growth rate behavior in a high strength low alloy X60 pipeline-type steel. Complete results have been generated for gaseous hydrogen at ambient pressure, laboratory air at ambient pressure and approximately 60% relative humidity as well as vacuum of 0.000067 Pa ( 0.0000005 torr) at R-ratios = K(min)/K(max) of 0.1, 0.5, and 0.8. Fatigue crack growth rate behavior in gaseous hydrogen, methane, and methane plus 10 percent hydrogen at 6.89 MPa (100 psi) was determined.
Fatigue crack propagation in the near-threshold region has been studied in coarse grain Al 7029 alloy. Over eighty percent of the crack surfaces are planar areas parallel to either 100-oriented or 111-oriented planes. The 100-plane crack surfaces show 'pine tree' morphological features formed by slip on two sets of intersecting planes. The 111-plane crack surfaces were planar and shiny. They were formed primarily by slip on a single dominant 111-oriented slip plane with sparse and very light secondary slip markings. Crack growth rates were measured and correlated with Delta-K.
The polarization of Lyman-a radiation, produced by electron-impact excitation of atomic hydrogen, has been measured over the extended energy range from near threshold to 1800 eV. Measurements were obtained in a crossed-beam experiment using a silica-reflection linear polarization analyzer in tandem with a vacuum-ultraviolet monochromator to isolate the emitted line radiation. Comparison with various theoretical calculations shows that the present experimental results are in good agreement with theory over the entire range of electron-impact energies and, in particular, are in excellent agreement with theoretical convergent-close-coupling (CCC) calculations performed in the present work. Our polarization data are significantly different from the previous experimental measurements of Ott, Kauppila, and Fite.
The polarization of Lyman-(alpha) radiation, produced by electron impact excitation of atomic hydrogen, has been measured for the first time over the extended energy range from near-threshold to 1800eV. Measurements were obtained in a crossed-beams experiment using a silica-reflection linear polarization analyzer in tandem with a vacuum ultraviolet (VUV) monochromator to isolate the emitted line radiation.
The threshold region of the double-photoionization cross section is of particular interest because both ejected electrons move slowly in the Coulomb field of the residual ion. Near threshold both electrons have time to interact with each other and with the residual ion. Also, different theoretical models compete to describe the double-photoionization cross section in the threshold region. We have investigated that cross section for lithium and beryllium and have analyzed our data with respect to the latest results in the Coulomb-dipole theory. We find that our data support the idea of a Coulomb-dipole interaction.
Constant-Kmax fatigue crack growth tests were performed on two finegrain nickel-base alloys Inconel 718 (DA) and Ren 95 to determine if these alloys exhibit near-threshold time-dependent crack growth behavior observed for fine-grain aluminum alloys in room-temperature laboratory air. Test results showed that increases in K(sub max) values resulted in increased crack growth rates, but no evidence of time-dependent crack growth was observed for either nickel-base alloy at room temperature.
A plasticity-induced crack-closure model was used to study fatigue crack growth and closure in thin 2024-T3 aluminum alloy under constant-R and constant-K(sub max) threshold testing procedures. Two methods of calculating crack-opening stresses were compared. One method was based on a contact-K analyses and the other on crack-opening-displacement (COD) analyses. These methods gave nearly identical results under constant-amplitude loading, but under threshold simulations the contact-K analyses gave lower opening stresses than the contact COD method. Crack-growth predictions tend to support the use of contact-K analyses. Crack-growth simulations showed that remote closure can cause a rapid rise in opening stresses in the near threshold regime for low-constraint and high applied stress levels. Under low applied stress levels and high constraint, a rise in opening stresses was not observed near threshold conditions. But crack-tip-opening displacement (CTOD) were of the order of measured oxide thicknesses in the 2024 alloy under constant-R simulations. In contrast, under constant-K(sub max) testing the CTOD near threshold conditions were an order-of-magnitude larger than measured oxide thicknesses. Residual-plastic deformations under both constant-R and constant-K(sub max) threshold simulations were several times larger than the expected oxide thicknesses. Thus, residual-plastic deformations, in addition to oxide and roughness, play an integral part in threshold development.