Amplitude equations for systems with long-range interactions

We derive amplitude equations for interface dynamics in pattern forming systems with long-range interactions. The basic condition for the applicability of the method developed here is that the bulk equations are linear and solvable by integral transforms. We arrive at the interface equation via long-wave asymptotics. As an example, we treat the Grinfeld instability, and we also give a result for the Saffman-Taylor instability. It turns out that the long-range interaction survives the long-wave limit and shows up in the final equation as a nonlocal and nonlinear term, a feature that to our knowledge is not shared by any other known long-wave equation. The form of this particular equation will then allow us to draw conclusions regarding the universal dynamics of systems in which nonlocal effects persist at the level of the amplitude description.Comment: LaTeX source, 12 pages, 4 figures, accepted for Physical Review

Extending the scope of microscopic solvability: Combination of the Kruskal-Segur method with Zauderer decomposition

Successful applications of the Kruskal-Segur approach to interfacial pattern formation have remained limited due to the necessity of an integral formulation of the problem. This excludes nonlinear bulk equations, rendering convection intractable. Combining the method with Zauderer's asymptotic decomposition scheme, we are able to strongly extend its scope of applicability and solve selection problems based on free boundary formulations in terms of partial differential equations alone. To demonstrate the technique, we give the first analytic solution of the problem of velocity selection for dendritic growth in a forced potential flow.Comment: Submitted to Europhys. Letters, No figures, 5 page

Argonne National Laboratory Reports

The uniaxial stress-strain behavior of Zircaloy-2 and -4, Zircaloy-oxygen alloys with a uniform oxygen distribution, and composite specimens with a ZrO2/alpha/beta layer structure was investigated over the range of experimental conditions: temperature 25-1400 degrees C; strain rate ; oxygen content 0.11 - 4.4 wt %; grain size 5-50 micrometers; texture longitudinal, transverse, and diagonal orientations; and microstructural state, which consists of the equiaxed alpha phase and various transformed beta acicular structures. The work-hardening and strain-rate sensitivity parameters were determined from the experimental results, and the tensile properties were correlated with oxygen concentration, oxygen distribution in the material, and microstructure. Dynamic strain-aging phenomena were observed in Zircaloy at 200, 400, and 700 degrees C, and super-plastic deformation occurred at 850 and 1000 degrees C. An increase in the oxygen concentration in homogeneous Zircaloy-oxygen alloys increased the ultimate tensile strength and decreased the total strain, particularly below approximately 900/sup 0/C. In composite specimens with the ZrO2/alpha/beta structure, the total oxygen content had little effect on the ultimate tensile strength below approximately 1000 degrees C, but the strength increased with oxygen content at higher temperatures. Information on the effects of grain size, oxygen content, texture, and strain rate on the stress-strain behavior suggests that the dominant mechanism of super-plastic deformation in Zircaloy near approximately 850/sup 0/C is grain-boundary sliding at the alpha-beta interface with accommodation by diffusional creep, dislocation slip, and grain-boundary migration. Good correlation was obtained between ductility and values of the strain-rate sensitivity parameter

Test plan for high-burnup fuel cladding behavior under loss-of- coolant accident conditions

Excessive oxidation, hydriding, and extensive irradiation damage occur in high-burnup fuel cladding, and as result, mechanical properties of high-burnup fuels are degraded significantly. This may influence the current fuel cladding failure limits for loss-of- coolant-accident (LOCA) situations, which are based on fuel cladding behavior for zero burnup. To avoid cladding fragmentation and fuel dispersal during a LOCA, 10 CFR 50.46 requires that peak cladding temperature shall not exceed 1204 degrees C (2200 degrees F) and that total oxidation of the fuel cladding nowhere exceeds 0.17 times total cladding thickness before oxidation. Because of the concern, a new experimental program to investigate high-burnup fuel cladding behavior under LOCA situations has been initiated under the sponsorship of the U.S. Nuclear Regulatory Commission. A hot-cell test plan to investigate single-rod behavior under simulated LOCA conditions is described in this paper. In the meantime, industry fuel design and operating conditions are expected to undergo further changes as more advanced cladding materials are developed. Under these circumstances, mechanical properties of high-burnup fuel cladding require further investigation so that results from studies on LOCA, reactivity- initiated-accident (RIA), operational transient, and power-ramping situations, can be extrapolated to modified or advanced cladding materials and altered irradiation conditions without repeating major integral experiments in test reactors. To provide the applicable data base and mechanistic understanding, tests will be conducted to determine dynamic and static fracture toughness and tensile properties. Background and rationale for selecting the specific mechanical properties tests are also described

Quantum phase transition of Ising-coupled Kondo impurities

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization group arguments, we show that at this transition the conductance G through the system either displays a zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G = e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization group calculations. In the singlet phase close to the quantum phase transtion, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic mini-domain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.Comment: 24 pages, 12 figs; (v2) minor changes, flow equation section extende

Irradiation-assisted stress corrosion cracking of austenitic stainless steels: Recent progress and new approaches

Irradiation-assisted stress corrosion cracking (IASCC) of several types of BWR field components fabricated from solution-annealed austenitic stainless steels (SSs), including a core internal weld, were investigated by means of slow-strain-rate test (SSRT), scanning electron microscopy (SEM), Auger electron spectroscopy (AES), and field-emission-gun advanced analytical electron microscopy (FEG-AAEM). Based on the results of the tests and analyses, separate effects of neutron fluence, tensile properties, alloying elements and major impurities identified in the American Society for Testing and Materials (ASTM) specifications, minor impurities, water chemistry, and fabrication-related variables were determined. The results indicate strongly that minor impurities not specified by the ASTM-specifications play important roles, probably through a complex synergism with grain-boundary Cr depletion. These impurities, typically associated with steelmaking and component fabrication processes, are very low or negligible in solubility in steels and are the same impurities that have been known to promote intergranular SCC significantly when they are present in water as ions or soluble compounds. It seems obvious that IASCC is a complex integral problem which involves many variables that are influenced strongly by not only irradiation conditions, water chemistry, and stress but also iron and steelmaking processes, fabrication of the component, and joining and welding. Therefore, for high-stress components in particular, it would be difficult to mitigate IASCC problems at high fluence based on the consideration of water chemistry alone, and other considerations based on material composition and fabrication procedure would be necessary as well

Environmentally assisted cracking in light water reactors. Semiannual report, July 1998-December 1998.

This report summarizes work performed by Argonne National Laboratory on fatigue and environmentally assisted cracking (EAC) in light water reactors from July 1998 to December 1998. Topics that have been investigated include (a) environmental effects on fatigue S-N behavior of primary pressure boundary materials, (b) irradiation-assisted stress corrosion cracking of austenitic stainless steels (SSs), and (c) EAC of Alloys 600 and 690. Fatigue tests have been conducted to determine the crack initiation and crack growth characteristics of austenitic SSs in LWR environments. Procedures are presented for incorporating the effects of reactor coolant environments on the fatigue life of pressure vessel and piping steels. Slow-strain-rate tensile tests and posttest fractographic analyses were conducted on several model SS alloys irradiated to {approx}0.3 and 0.9 x 10{sup 21} n {center_dot} cm{sup -2} (E > 1 MeV) in helium at 289 C in the Halden reactor. The results have been used to determine the influence of alloying and impurity elements on the susceptibility of these steels to irradiation-assisted stress corrosion cracking. Fracture toughness J-R curve tests were also conducted on two heats of Type 304 SS that were irradiated to {approx}0.3 x 10{sup 21} n {center_dot} cm{sup -2} in the Halden reactor. Crack-growth-rate tests have been conducted on compact-tension specimens of Alloys 600 and 690 under constant load to evaluate the resistance of these alloys to stress corrosion cracking in LWR environments

Environmentally assisted cracking in light water reactors. Semiannual report, October 1993--March 1994. Volume 18

This report summarizes work performed by Argonne National Laboratory (ANL) on fatigue and environmentally assisted cracking (EAC) in light water reactors (LWRs) during the six months from October 1993 to March 1994. EAC and fatigue of piping, pressure vessels, and core components in LWRs are important concerns in operating plants and as extended reactor lifetimes are envisaged. Topics that have been investigated include (a) fatigue of low-alloy steel used in piping, steam generators, and reactor pressure vessels, (b) EAC of wrought and cast austenitic stainless steels (SSs), and (c) radiation-induced segregation and irradiation-assisted stress corrosion cracking (IASCC) of Type 304 SS after accumulation of relatively high fluence. Fatigue tests have been conducted on A302-Gr B low-alloy steel to verify whether the current predictions of modest decreases of fatigue life in simulated pressurized water reactor water are valid for high-sulfur heats that show environmentally enhanced fatigue crack growth rates. Additional crack growth data were obtained on fracture-mechanics specimens of austenitic SSs to investigate threshold stress intensity factors for EAC in high-purity oxygenated water at 289{degrees}C. The data were compared with predictions based on crack growth correlations for wrought austenitic SS in oxygenated water developed at ANL and rates in air from Section XI of the ASME Code. Microchemical and microstructural changes in high- and commercial-purity Type 304 SS specimens from control-blade absorber tubes and a control-blade sheath from operating boiling water reactors were studied by Auger electron spectroscopy and scanning electron microscopy to determine whether trace impurity elements, which are not specified in the ASTM specifications, may contribute to IASCC of solution-annealed materials

Dislocation Creep of Olivine: Backstress Evolution Controls Transient Creep at High Temperatures

Transient creep occurs during geodynamic processes that impose stress changes on rocks at high temperatures. The transient is manifested as evolution in the viscosity of the rocks until steady-state flow is achieved. Although several phenomenological models of transient creep in rocks have been proposed, the dominant microphysical processes that control such behavior remain poorly constrained. To identify the intragranular processes that contribute to transient creep of olivine, we performed stress-reduction tests on single crystals of olivine at temperatures of 1250–1300°C. In these experiments, samples undergo time‐dependent reverse strain after the stress reduction. The magnitude of reverse strain is ~10-3 and increases with increasing magnitude of the stress reduction. High-angular resolution electron backscatter diffraction analyses of deformed material reveal lattice curvature and heterogeneous stresses associated with the dominant slip system. The mechanical and microstructural data are consistent with transient creep of the single crystals arising from accumulation and release of backstresses among dislocations. These results allow the dislocation‐glide component of creep at high temperatures to be isolated, and we use these data to calibrate a flow law for olivine to describe the glide component of creep over a wide temperature range. We argue that this flow law can be used to estimate both transient creep and steady‐state viscosities of olivine, with the transient evolution controlled by the evolution of the backstress. This model is able to predict variability in the style of transient (normal versus inverse) and the load-relaxation response observed in previous work.LH and DW acknowledge support from the Natural Environment Research Council, grant NE/M000966/1, LH and CT acknowledge support from the Natural Environment Research Council, grant 1710DG008/JC4, and DW acknowledges support from the Netherlands Organisation for Scientific Research, User Support Programme Space Research, grant ALWGO.2018.038, and startup funds from Utrecht University. LH recognizes funds used to develop the uniaxial apparatus from the John Fell Fund at the University of Oxford

The influence of thermal cycles on the microstructure of grade 92 steel

The microstructure in the heat-affected zone (HAZ) of welds made from the 9 wt pct chromium martensitic Grade 92 steel is complex and has not yet been completely understood. There is a lack of systematic microstructural investigations to define the different regions of the microstructure across the HAZ of Grade 92 steel welds as a function of the welding process. In this study, the microstructure in the HAZ of an as-fabricated single-pass bead-on-plate weld on a parent metal of Grade 92 steel was systematically investigated by using an extensive range of electron and ion-microscopy-based techniques. A dilatometer was used to apply controlled thermal cycles to simulate the microstructures in the different regions of the HAZ. A wide range of microstructural properties in the simulated materials were then characterized and compared with the experimental observations from the weld HAZ. It was found that the microstructure in the HAZ of a single-pass Grade 92 steel weld can be categorized as a function of a decreasing peak temperature reached as (1) the completely transformed (CT) region, in which the original matrix is completely reaustenitized with complete dissolution of the pre-existing secondary precipitate particles; (2) the partially transformed (PT) region, where the original matrix is partially reaustenitized along with a partial dissolution of the secondary precipitate particles from the original matrix; and (3) the overtempered (OT) region, where the pre-xisting precipitate particles coarsen. The PT region is considered to be the susceptible area for damage in the commonly reported HAZ failures in weldments constructed from these types of steels