146 research outputs found
Stress correlations in glasses
We rigorously establish that, in disordered three-dimensional (3D) isotropic
solids, the stress autocorrelation function presents anisotropic terms that
decay as at long-range, with the distance, as soon as either
pressure or shear stress fluctuations are normal. By normal, we mean that the
fluctuations of stress, as averaged over spherical domains, decay as the
inverse domain volume. Since this property is required for macroscopic stress
to be self-averaging, it is expected to hold generically in all glasses and we
thus conclude that the presence of stress correlation tails is the rule
in these systems. Our proof follows from the observation that, in an infinite
medium, when both material isotropy and mechanical balance hold, (i) the stress
autocorrelation matrix is completely fixed by just two radial functions: the
pressure autocorrelation and the trace of the autocorrelation of stress
deviators; furthermore, these two functions (ii) fix the decay of the
fluctuations of sphere-averaged pressure and deviatoric stresses for windows of
increasing volume. Our conclusion is reached because, due to the precise
analytic relation (i) fixed by isotropy and mechanical balance, the constraints
arising via (ii) from the normality of stress fluctuations demand the spatially
anisotropic stress correlation terms to decay as at long-range. For the
sake of generality, we also examine situations when stress fluctuations are not
normal
An Acoustic Emission Evaluation of Environmentally Assisted Cracking of 7039-T6 Aluminum
Environmentally assisted cracking (EAC) is a significant problem in modern structures. The combination of a susceptible material, an adverse environment and mechanical stress can lead to unexpected failure of a structure by catastrophic crack growth. The mid-air failure of the aluminum alloy bulkhead and the subsequent loss of life on a Aloha Airlines flight on April 28, 1988 as shown in figure 1, illustrates this fact. Additionally, the operating environment of the US Army contributes to premature failure of structures such as aluminum alloy armor, high strength steel armor and high strength steel control components on Army helicopters [1]. These failures not only endanger life but they also seriously hamper the fighting readiness of U.S. forces because of equipment down time for inspection and repair of faulty components. Work has been performed to better characterize EAC resistance in high strength aluminum armor alloys [2]. These high strength alloys are particularly prone to failure in a chloride environment, an environment encountered in most of the world. If we plan to avoid such failures, we must better understand the EAC phenomena and more diligently detect growing cracks before they become critical in length. One characterization technique that promises to serve well both as a laboratory tool for understanding EAC and as a field device for detecting EAC is acoustic emission evaluation
Bulk Universality and Related Properties of Hermitian Matrix Models
We give a new proof of universality properties in the bulk of spectrum of the
hermitian matrix models, assuming that the potential that determines the model
is globally and locally function (see Theorem \ref{t:U.t1}).
The proof as our previous proof in \cite{Pa-Sh:97} is based on the orthogonal
polynomial techniques but does not use asymptotics of orthogonal polynomials.
Rather, we obtain the -kernel as a unique solution of a certain non-linear
integro-differential equation that follows from the determinant formulas for
the correlation functions of the model. We also give a simplified and
strengthened version of paper \cite{BPS:95} on the existence and properties of
the limiting Normalized Counting Measure of eigenvalues. We use these results
in the proof of universality and we believe that they are of independent
interest
\epsilon-regularity for systems involving non-local, antisymmetric operators
We prove an epsilon-regularity theorem for critical and super-critical
systems with a non-local antisymmetric operator on the right-hand side.
These systems contain as special cases, Euler-Lagrange equations of
conformally invariant variational functionals as Rivi\`ere treated them, and
also Euler-Lagrange equations of fractional harmonic maps introduced by Da
Lio-Rivi\`ere.
In particular, the arguments presented here give new and uniform proofs of
the regularity results by Rivi\`ere, Rivi\`ere-Struwe, Da-Lio-Rivi\`ere, and
also the integrability results by Sharp-Topping and Sharp, not discriminating
between the classical local, and the non-local situations
The discontinuous Galerkin method for fractional degenerate convection-diffusion equations
We propose and study discontinuous Galerkin methods for strongly degenerate
convection-diffusion equations perturbed by a fractional diffusion (L\'evy)
operator. We prove various stability estimates along with convergence results
toward properly defined (entropy) solutions of linear and nonlinear equations.
Finally, the qualitative behavior of solutions of such equations are
illustrated through numerical experiments
Stress corrosion cracking in Al-Zn-Mg-Cu aluminum alloys in saline environments
Copyright 2013 ASM International. This paper was published in Metallurgical and Materials Transactions A, 44A(3), 1230 - 1253, and is made
available as an electronic reprint with the permission of ASM International. One print or electronic copy may
be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via
electronic or other means, duplications of any material in this paper for a fee or for commercial purposes, or
modification of the content of this paper are prohibited.Stress corrosion cracking of Al-Zn-Mg-Cu (AA7xxx) aluminum alloys exposed to saline environments at temperatures ranging from 293 K to 353 K (20 °C to 80 °C) has been reviewed with particular attention to the influences of alloy composition and temper, and bulk and local environmental conditions. Stress corrosion crack (SCC) growth rates at room temperature for peak- and over-aged tempers in saline environments are minimized for Al-Zn-Mg-Cu alloys containing less than ~8 wt pct Zn when Zn/Mg ratios are ranging from 2 to 3, excess magnesium levels are less than 1 wt pct, and copper content is either less than ~0.2 wt pct or ranging from 1.3 to 2 wt pct. A minimum chloride ion concentration of ~0.01 M is required for crack growth rates to exceed those in distilled water, which insures that the local solution pH in crack-tip regions can be maintained at less than 4. Crack growth rates in saline solution without other additions gradually increase with bulk chloride ion concentrations up to around 0.6 M NaCl, whereas in solutions with sufficiently low dichromate (or chromate), inhibitor additions are insensitive to the bulk chloride concentration and are typically at least double those observed without the additions. DCB specimens, fatigue pre-cracked in air before immersion in a saline environment, show an initial period with no detectible crack growth, followed by crack growth at the distilled water rate, and then transition to a higher crack growth rate typical of region 2 crack growth in the saline environment. Time spent in each stage depends on the type of pre-crack (“pop-in” vs fatigue), applied stress intensity factor, alloy chemistry, bulk environment, and, if applied, the external polarization. Apparent activation energies (E a) for SCC growth in Al-Zn-Mg-Cu alloys exposed to 0.6 M NaCl over the temperatures ranging from 293 K to 353 K (20 °C to 80 °C) for under-, peak-, and over-aged low-copper-containing alloys (~0.8 wt pct), they are typically ranging from 20 to 40 kJ/mol for under- and peak-aged alloys, and based on limited data, around 85 kJ/mol for over-aged tempers. This means that crack propagation in saline environments is most likely to occur by a hydrogen-related process for low-copper-containing Al-Zn-Mg-Cu alloys in under-, peak- and over-aged tempers, and for high-copper alloys in under- and peak-aged tempers. For over-aged high-copper-containing alloys, cracking is most probably under anodic dissolution control. Future stress corrosion studies should focus on understanding the factors that control crack initiation, and insuring that the next generation of higher performance Al-Zn-Mg-Cu alloys has similar longer crack initiation times and crack propagation rates to those of the incumbent alloys in an over-aged condition where crack rates are less than 1 mm/month at a high stress intensity factor
Surface modifications of AISI 420 stainless steel by low energy Yttrium ions
In this work, we study surface modifications of AISI 420 stainless steel specimens in order to improve their surface properties. Oxidation resistance and surface micro-hardness were analyzed. Using an ion beam delivered by a Laser Ion Source (LIS) coupled to an electrostatic accelerator, we performed implantation of low energy yttrium ions on the samples. The ions experienced an acceleration passing through a gap whose ends had a potential difference of 60 kV. The gap was placed immediately before the samples surface. The LIS produced high ions fluxes per laser pulse, up to 3x1011 ions/cm2, resulting in a total implanted flux of 7x1015 ions/cm2. The samples were characterized before and after ion implantation using two analytical techniques. They were also thermally treated to investigate the oxide scale. The crystal phases were identified by an X-ray diffractometer, while the micro-hardness was assayed using the scratch test and a profilometer. The first analysis was applied to blank, implanted and thermally treated sample surface, while the latter was applied only to blank and implanted sample surfaces. We found a slight increase in the hardness values and an increase to oxygen resistance. The implantation technique we used has the advantages, with respect to conventional methods, to modify the samples at low temperature avoiding stray diffusion of ions inside the substrate bulk
Regularity of Infinity for Elliptic Equations with Measurable Coefficients and Its Consequences
This paper introduces a notion of regularity (or irregularity) of the point
at infinity for the unbounded open subset of \rr^{N} concerning second order
uniformly elliptic equations with bounded and measurable coefficients,
according as whether the A-harmonic measure of the point at infinity is zero
(or positive). A necessary and sufficient condition for the existence of a
unique bounded solution to the Dirichlet problem in an arbitrary open set of
\rr^{N}, N\ge 3 is established in terms of the Wiener test for the regularity
of the point at infinity. It coincides with the Wiener test for the regularity
of the point at infinity in the case of Laplace equation. From the topological
point of view, the Wiener test at infinity presents thinness criteria of sets
near infinity in fine topology. Precisely, the open set is a deleted
neigborhood of the point at infinity in fine topology if and only if infinity
is irregular.Comment: 20 page
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