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At least 55 records · Page 3

Method and models for R-curve instability calculations

This paper presents a simple method for performing elastic R-curve instability calculations. For a single material-structure combination, the calculations can be done on some pocket calculators. On microcomputers and larger, it permits the development of a comprehensive program having libraries of driving force equations for different configurations and R-curve model equations for different materials. The paper also presents several model equations for fitting to experimental R-curve data, both linear elastic and elastoplastic. The models are fit to data from the literature to demonstrate their viability.

Orange, Thomas W.↗

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗

Between Harmonic Crystal and Glass: Solids with Dimpled Potential-Energy Surfaces Having Multiple Local Energy Minima

Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.

36 MATERIALS SCIENCE↗

Fluid dynamics of heart assist device

Certain hemodynamic phenomena that arise in connection with the use of artificial blood pumping devices are reviewed. Among these are: (1) Flows produced by collapsing bulbs; (2) the impedance presented by the aorta; (3) limiting velocities and instability of flow in elastic vessels; (4) effectiveness of valveless arterio-arterial pumps, and (5) wave reflection phenomena and instabilities associated with the intra-aortic balloon pump.

Jones, R. T.↗

On the failure of hyperbolicity in elasticity

The failure of hyperbolicity leading to the instability as an ill-posedness of the Cauchy problem is investigated for elasticity. The criteria for that instability are derived in terms of the potential energy as a function of the strain invariants. The theory is illustrated by examples.

Zak, M.↗

The speed of wave-wave interactions in the atmosphere

Resonant wave-wave interactions are considered. Studies of the interaction coefficient show that rapid transfer of wave action can take place in the disjoined parts of the spectrum for three processes, namely: elastic scattering, parametric subharmonic instability and induced diffusion. Of the three processes, the vertical shear plays a role in two. The vertical shear of a moderate scale interacts through elastic scattering to make the spectrum vertically symmetric. On the other hand, the vertical shear of a large scale interacts through induced diffusion and is responsible for diffusion in k sub z space. When interacting with a vertical shear, it is known that the vertical shear acts as a catalyst and is not involved in energy transfer. Consequently, in both elastic scattering and induced diffusion, the vertical shear does not gain or lose energy. Through parametric subharmonic instability the more energetic large-scale waves are feeding energy into moderate and small scale waves of an elevation angle of 60 deg or larger.

Yeh, K. C.↗

ELASTIC STABILITY CONSIDERATIONS IN AIRCRAFT STRUCTURAL DESIGN

General instability in shell type structures is a relatively infrequent phenomenon. By general instability is meant that a complete section of a structure becomes elastically unstable, as compared with local crippling or buckling. The first step in design is to rough size the structure and determine its compatibility with air vehicle configuration and system instillations. After this step has been completed, it is possible to survey the layouts to determine whether general instability is likely to occur. The general parameters of length, diameter, frame spacing, element stiffness, etc., are than investigated to determine if a general failing stress exists which is less than any local column, beam column, or panel failing stress. In this way, a well-balanced design is determined and general stability failing modes eliminated.

ELASTIC STABILITY↗

Neutron starquake model for gamma-ray bursts

A neutron starquake model for gamma ray bursts is presented and critically analyzed. It is suggested that a slowly accreting neutron star may develop density inversions deep in its crust. These unstable layers, may be subject to elastic Rayleigh-Taylor instability which can liberate sufficient gravitational and perhaps also nuclear energy to account for individual bursts. Energy can be transported to the surface by shear waves and slowly transmitted into the magnetosphere as relativistic Alfven waves. Particle acceleration and gamma ray emission from the outer magnetosphere should ensue. Some observational implications are mentioned.

Blandford, R. D.↗

An elastic-plastic finite element analysis of crack initiation, stable crack growth, and instability

Studies have been conducted to develop efficient techniques to simulate crack extension and to examine various local and global fracture criteria. Of the considered criteria, the crack-tip-opening angle (CTOA) or displacement (CTOD) at a specified distance from the crack tip was shown to be most suited for modeling stable crack growth and instability during the fracture process. The results obtained in a number of studies show the necessity for studying different crack configurations when assessing the validity of any fracture criteria. One of the objectives of the present investigation is related to a critical evaluation of the CTOD growth criterion using an elastic-plastic finite element analysis under monotonic loading to failure. The analysis was found to predict three stages of crack growth behavior under monotonic loading to failure. Calculated CTOD values agreed well with experimental values for crack growth initiation.

Newman, J. C., Jr.↗

Significant issues in proof testing: A critical appraisal

Issues which impact on the interpretation and quantification of proof test benefits are reviewed. The importance of each issue in contributing to the extra quality assurance conferred by proof testing components is discussed, particularly with respect to the application of advanced fracture mechanics concepts to enhance the flaw screening capability of a proof test analysis. Items covered include the role in proof testing of elastic-plastic fracture mechanics, ductile instability analysis, deterministic versus probabilistic analysis, single versus multiple cycle proof testing, and non-destructive examination (NDE). The effects of proof testing on subsequent service life are reviewed, particularly with regard to stress redistribution and changes in fracture behavior resulting from the overload. The importance of proof test conditions are also addressed, covering aspects related to test temperature, simulation of service environments, test media and the application of real-time NDE. The role of each issue in a proof test methodology is assessed with respect to its ability to: promote proof test practice to a state-of-the-art; aid optimization of proof test design; and increase awareness and understanding of outstanding issues.

Chell, G. G.↗

Methods and apparatus for improving sensor performance

Methods and apparatus for improving performance of a sensor having a sensor proof mass elastically suspended at an initial equilibrium position by a suspension force, provide a tunable force opposing that suspension force and preset the proof mass with that tunable force to a second equilibrium position less stable than the initial equilibrium position. The sensor is then operated from that preset second equilibrium position of the proof mass short of instability. The spring constant of the elastic suspension may be continually monitored, and such continually monitored spring constant may be continually adjusted to maintain the sensor at a substantially constant sensitivity during its operation.

Kaiser, William J.↗

Finite-element analysis of initiation, stable crack growth and instability using a crack-tip-opening displacement criterion

An elastic-plastic (incremental and small strain) finite element analysis was used with a crack growth criterion to study crack initiation, stable crack growth, and instability under monotonic loading to failure of metallic materials. The crack growth criterion was a critical crack-tip-opening displacement (CTOD) at a specified distance from the crack tip, or equivalently, a critical crack-tip-opening angle (CTOA). Whenever the CTOD (or CTOA) equaled or exceeded a critical value, the crack was assumed to grow. Single values of critical CTOD were used in the analysis to model crack initiation, stable crack growth, and instability for 7075-T651 and 2024-T351 aluminum alloy compact specimens. Calculated and experimentally measured CTOD values at initiation agreed well for both aluminum alloys. These critical CTOD values were also used to predict failure loads on center-crack tension specimens and a specially-designed three-hole-crack tension specimen made of the two aluminum alloys and of 304 stainless steel. All specimens were 12.7 mm thick. Predicted failure loads for 7075-T651 aluminum alloy and 304 stainless steel specimens were generally within + or - 15 percent of experimental failure loads, whereas the predicted failure loads for 2024-T351 aluminum alloy specimens were generally within + or - 5 percent of the experimental loads.

Newman, J. C., Jr.↗

Post-instability behavior of solids

The necessity of model reformulation in elasticity results from the failure of hyperbolicity of the governing equations of motion for classical models. The reformulation is based upon the introduction of additional kinematical microstructures in the form of multivalued displacement and velocity field (or fractal functions) which are generated by the mechanism of the instability. The small scale motions describing this microstructure interact with the original large scale motion and restore the hyperbolicity of new governing equations of motion. The applications of the reformulated models to the problem of vibrational control and impact energy absorption are discussed.

Zak, M.↗