Finite-element analyses and fracture simulation in thin-sheet aluminum alloy

A two-dimensional, elastic-plastic finite-element analysis was used with a critical crack-tip-opening angle (CTOA) fracture criterion to model stable crack growth in thin-sheet 2024-T3 aluminum alloy under monotonic loading after precracking at different cyclic stress levels. Tests were conducted on three types of specimens: middle-crack, three-hole-crack and blunt-notch tensile specimens. An experiment technique was developed to measure CTOA during crack growth initiation and stable tearing using a high-resolution video camera and recorder. Crack front shapes were also measured during initiation and stable tearing using a fatigue marker-load technique. Three-dimensional elastic-plastic finite-element analyses of these crack shapes for stationary cracks were conducted to study the crack-front opening displacements. Predicted load against crack extension on middle-crack tension specimens agreed well with test results even for large-scale plastic deformations. The analyses were able to predict the effects of specimen size and precracking stress history on stable tearing. Predicted load against load-line displacements agreed well with test results up to maximum load bu the analyses tended to overpredict displacements as crack grew beyond the maximum load under displacement-controlled conditions. During the initiation phase, the measured CTOA values were high but decreased and remained nearly constant after a small amount of stable tearing. The constant value of CTOA agree well with the calculated value from the finite-element analysis. The larger CTOA values measured at the sheet surface during the initiation phase may be associated with the crack tunneling observed in the tests. Three-dimensional analyses for nonstraight crack fronts predicted much higher displacements near the free surface than in the interior

Three-dimensional CTOA and constraint effects during stable tearing in a thin-sheet material

A small strain theory, three-dimensional elastic-plastic finite element analysis was used to simulate fracture in thin sheet 2024-T3 aluminum alloy in the T-L orientation. Both straight and tunneled cracks were modeled. The tunneled crack front shapes as a function of applied stress were obtained from the fracture surface of tested specimens. The stable crack growth behavior was measured at the specimen surface as a function of applied stress. The fracture simulation modeled the crack tunneling and extension as a function of applied stress. The results indicated that the global constraint factor, alpha(sub g), initially dropped during stable crack growth. After peak applied stress was achieved, alpha(sub g) began to increase slightly. The effect of crack front shape on alpha(sub g) was small, but the crack front shape did greatly influence the local constraint and through-thickness crack-tip opening angle (CTOA) behavior. The surface values of CTOA for the tunneled crack front model agreed well with experimental measurements, showing the same initial decrease from high values during the initial 3mm of crack growth at the specimen's surface. At the same time, the interior CTOA values increased from low angles. After the initial stable tearing region, the CTOA was constant through the thickness. The three-dimensional analysis appears to confirm the potential of CTOA as a two-dimensional fracture criterion

The Invisible Thin Red Line

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world

Measurement and analysis of critical CTOA for an aluminum alloy sheet

The stable tearing behavior of thin sheets of 2024-T3 aluminum alloy was investigated for middle crack tension, M(T), and compact tension, C(T), specimens. The surface crack-tip opening angle (CTOA), applied loads, crack extension, and local displacements were measured. A critical CTOA fracture criterion was incorporated into a two-dimensional, elastic plastic finite element code and used to simulate the experimental fracture behavior. The CTOA measurements and observations of the fracture surfaces have shown that large values for surface CTOA were observed for small crack extensions (less than the sheet thickness); substantial tunneling of the crack was associated with small crack extensions; crack tunneling in the M(T) specimen was less than that observed in the C(T) configuration; for larger crack extensions, the measured CTOA values were determined to be approximately 6 degrees for both the M(T) and C(T) configuration; and for larger crack extensions, crack tunneling remained constant. The two-dimensional finite element predictions of fracture behavior assumed a constant critical CTOA value of 6 degrees and accounted for local crack tip constraint with a plane strain core of elements ahead of the crack tip. The plane strain core extended 5 mm above the crack plane. The simulations were within +/- 4 percent of the maximum applied load for the C(T) tests within 2 percent for the M(T) tests

Correlation between Mechanical Behavior and Actuator-type Performance of Ni-Ti-Pd High-temperature Shape Memory Alloys

High-temperature shape memory alloys in the NiTiPd system are being investigated as lower cost alternatives to NiTiPt alloys for use in compact solid-state actuators for the aerospace, automotive, and power generation industries. A range of ternary NiTiPd alloys containing 15 to 46 at.% Pd has been processed and actuator mimicking tests (thermal cycling under load) were used to measure transformation temperatures, work behavior, and dimensional stability. With increasing Pd content, the work output of the material decreased, while the amount of permanent strain resulting from each load-biased thermal cycle increased. Monotonic isothermal tension testing of the high-temperature austenite and low temperature martensite phases was used to partially explain these behaviors, where a mismatch in yield strength between the austenite and martensite phases was observed at high Pd levels. Moreover, to further understand the source of the permanent strain at lower Pd levels, strain recovery tests were conducted to determine the onset of plastic deformation in the martensite phase. Consequently, the work behavior and dimensional stability during thermal cycling under load of the various NiTiPd alloys is discussed in relation to the deformation behavior of the materials as revealed by the strain recovery and monotonic tension tests

Spin Excitations in a Fermi Gas of Atoms

We have experimentally investigated a spin excitation in a quantum degenerate Fermi gas of atoms. In the hydrodynamic regime the damping time of the collective excitation is used to probe the quantum behavior of the gas. At temperatures below the Fermi temperature we measure up to a factor of 2 reduction in the excitation damping time. In addition we observe a strong excitation energy dependence for this quantum statistical effect.Comment: 4 pages, 3 figure

Observation of anomalous spin-state segregation in a trapped ultra-cold vapor

We observe counter-intuitive spin segregation in an inhomogeneous sample of ultra-cold, non-condensed Rubidium atoms in a magnetic trap. We use spatially selective microwave spectroscopy to verify a model that accounts for the differential forces on two internal spin states. In any simple understanding of the cloud dynamics, the forces are far too small to account for the dramatic transient spin polarizations observed. The underlying mechanism remains to be elucidated.Comment: 5 pages, 3 figure

Variations of a global constraint factor in cracked bodies under tension and bending loads

Elastic-plastic finite-element analyses were used to calculate stresses and displacements around a crack in finite-thickness plates for an elastic-perfectly plastic material. Middle- and edge-crack specimens were analyzed under tension and bending loads. Specimens were 1.25 to 20 mm thick with various widths and crack lengths. A global constraint factor alpha(sub g), an averaged normal-stress to flow-stress ratio over the plastic region, was defined to simulate three-dimensional (3D) effects in two-dimensional (2D) models. For crack lengths and uncracked ligament lengths greater than four times the thickness, the global constraint factor was found to be nearly a unique function of a normalized stress-intensity factor (related to plastic-zone size to thickness ratio) from small- to large-scale yielding conditions for various specimen types and thickness. For crack length-to-thickness ratios less than four, the global constraint factor was specimen type, crack length and thickness dependent. Using a 2D strip-yield model and the global constraint factors, plastic-zone sizes and crack-tip displacements agreed reasonably well with the 3D analyses. For a thin sheet aluminum alloy, the critical crack-tip-opening angle during stable tearing was found to be independent of specimen type and crack length for crack length-to-thickness ratios greater than 4

Estimating the Thermal Dose From Backscattered RF Echoes

Abstract. Over the years many different investigators have attempted to estimate the temperature rise resulting from ultrasound exposure in therapy applications. The developed methods typically rely on thermal expansion or temperature related sound speed variations both of which are dependent on tissue type and cannot be known a priori on a patient-specific basis. We have developed a method to estimate the thermal dose (temperature over time) from the backscattered RF echoes. RF echoes from within the same tissue type can be used to estimate the in vivo local attenuation (assumed to be the same as tissue absorption) as has been shown by other investigators. Similarly, the RF echoes can be compared to reference echoes while assuming a model for the scattering structures to estimate the total attenuation along the propagation path (i.e., the in vivo power spectrum). Hence, the temperature over time can be estimated from the measured in vivo power spectrum and the measured tissue absorption by solving the bioheat equation directly. The estimated thermal dose can then be used to monitor or plan ultrasound therapy on a patient-specific basis

A model for estimating ultrasound attenuation along the propagation path to the fetus from backscattered waveforms

Accurate estimates of the ultrasound pressure and/or intensity incident on the developing fetus on a patient-specific basis could improve the diagnostic potential of medical ultrasound by allowing the clinician to increase the transmit power while still avoiding the potential for harmful bioeffects. Neglecting nonlinear effects, the pressure/intensity can be estimated if an accurate estimate of the attenuation along the propagation path ͑i.e., total attenuation͒ can be obtained. Herein, a method for determining the total attenuation from the backscattered power spectrum from the developing fetus is proposed. The boundaries between amnion and either the fetus' skull or soft tissue are each modeled as planar impedance boundaries at an unknown orientation with respect to the sound beam. A mathematical analysis demonstrates that the normalized returned voltage spectrum from this model is independent of the planes orientation. Hence, the total attenuation can be estimated by comparing the location of the spectral peak in the reflection from the fetus to the location of the spectral peak in a reflection obtained from a rigid plane in a water bath. The independence of the attenuation estimate and plane orientation is then demonstrated experimentally using a Plexiglas plate, a rat's skull, and a tissue-mimicking phantom