Anatoli M. Frishman

Distributed approximating functional fit of the H3 ab initio potential-energy data of Liu and Siegbahn

We report a distributed approximating functional (DAF) fit of the ab initio potential-energy data of Liu [J. Chem. Phys. 58, 1925 (1973)] and Siegbahn and Liu [ibid. 68, 2457 (1978)]. The DAF-fit procedure is based on a variational principle, and is systematic and general. Only two adjustable parameters occur in the DAF leading to a fit which is both accurate (to the level inherent in the input data; RMS error of 0.2765 kcal/mol) and smooth (“well-tempered,” in DAF terminology). In addition, the LSTH surface of Truhlar and Horowitz based on this same data [J. Chem. Phys. 68, 2466 (1978)] is itself approximated using only the values of the LSTH surface on the same grid coordinate points as the ab initio data, and the same DAF parameters. The purpose of this exercise is to demonstrate that the DAF delivers a well-tempered approximation to a known function that closely mimics the true potential-energy surface. As is to be expected, since there is only roundoff error present in the LSTH input data, even more ...

Distributed approximating functional approach to fitting multi-dimensional surfaces

Abstract A method for fitting multi-dimensional surfaces using known values of the function on a finite set of grid points is presented. The points in the set need not be regularly distributed in the domain of the variables and in fact can be random. The method is based on the theory of distributed approximating functionals. The method is illustrated by fitting model potential functions of one, two, and three variables.

Conductivity profile determination by eddy current for shot-peened superalloy surfaces toward residual stress assessment

This paper demonstrates a swept high frequency eddy current (SHFEC) methodology that can determine near-surface conductivity deviation profiles of shot-peened superalloy surfaces, from which residual stress state can be assessed nondestructively. Our methodology is built around a laboratory-grade SHFEC hardware and a model-based SHFEC data inversion software, both described in this article. For the demonstration, a series of shot-peened Inconel 718 block specimens is prepared and examined by the proposed SHFEC inversion technique. The conductivity depth profiles of the samples under various shot peening intensities have been obtained by the inversion. Several sensitivity and consistency test results are given to support the reliability of the inverted conductivity profiles. The extreme near-surface regions (10–20μm) of the shot-peened surfaces are also examined by various microstructural characterization methods such as scanning electron microscopy, energy dispersive x-ray spectroscopy, and x-ray diffract...

Distributed approximating functional approach to fitting and predicting potential surfaces. 1. Atom-atom potentials

Abstract A procedure is presented for obtaining an analytical representation of the potential energy for a diatomic system, knowing the potential only at finite number of internuclear separations. The approach is based on the distributed approximating functional (DAF), which has the property of delivering comparable accuracy for approximating a function and its derivatives, given such limited input data. The method is illustrated by applications to several atom-atom potentials, including those for the Li 2 and H 2 systems.

Quantification of precipitates and their effects on the response of nickel-base superalloy to shot peening

This paper reports on a microstructural study of a nickel-base superalloy, Inconel 718, with a focus on quantifying precipitate density and their effects on conductivity variations. The study is motivated by eddy current (EC) characterization of residual stresses, where observed EC signals are attempted to correlate with stress profiles of shot peened superalloy surfaces. It has been observed that the correlation is less universal than anticipated, and in fact strongly influenced by the material hardness, or the aging conditions. For example, the soft sample surface exhibits significantly stronger EC signals than the fully hardened sample when both are shot peened at the same Almen intensity. Thus, the objective of the present study is to examine this complex material response against aging and shot peening treatments at the microstructure scale, by the use of techniques such as transmission electron microscopy (TEM) and scanning electron microscopy (SEM). We will describe preparations of a series of Inco...

Effects of cold work on near-surface conductivity profiles in laser shock peened and shot peened nickel-base superalloy

This paper reports on a study of the effects of cold work induced by surface enhancement treatment on conductivity profiles in nickel-base superalloys, as part of the on-going efforts aimed at evaluating the feasibility of characterizing near-surface residual stress profiles in peened engine components using a swept frequency eddy current (SFEC) technique. The approach is based on the empirical piezoresistivity effect that correlates conductivity changes with residual stress, but recent studies have shown that conductivity changes induced by peening processes are also influenced by metallurgical factors such as cold work. In this study, conductivity deviation profiles were obtained by model-based inversion of SFEC signals from a set of aged Inconel 718 samples, which were either shot peened or laser shock peened to produce different residual stress and cold work profiles. The laser shock peened samples exhibit a larger increase in surface conductivity and deeper conductivity profiles, which are attributed...

Stress dependence of the Hall coefficient of a nickel-base superalloy

This paper reports on the Hall Effect and their stress dependence, observed experimentally on the superalloy Inconel® 718. The work is motivated by the desire to develop a nondestructive method of characterizing the near-surface protective residual stress in metals. Our approach is based on Hall Effect measurements, because it is anticipated that these measurements are less contaminated by cold work and other effects than conductivity-based measurements such as eddy current. The challenge is that, in metals, the Hall coefficient is very small. To achieve the required sensitivity, the Hall coefficient was measured with an AC injected current and an AC magnetic field. The measurements were performed on a thin film sample. The Hall coefficient was found to be positive, and varies proportionally to the applied tension. The proportionality coefficient is significantly larger than estimated from the volumetric effect in a free carrier model.

SHOT‐PEENING INTENSITIES VS. EDDY CURRENT SIGNALS AS SEEN IN ITERATIVE TREATMENT‐MEASUREMENT EXPERIMENT

We report on progress in a swept high frequency eddy current (SHFEC) technique for characterization of surface residual stress on shot‐peened superalloy surfaces. Our aim here is to demonstrate the sensitivity of our measurement for practical shot peening intensities, i.e. at 4∼6 A. First, we present our improved probe and instrumentation being sufficiently sensitive to resolve the surface conditions at these low Almen intensities, where our earlier measurements encountered noise problems. The previous coil was also larger (18 mm in diameter) than desirable. Our new probe integrates smaller coils (12 mm in diameter, forming an AC bridge) and on‐board electronics on a common printed circuit board, mutually connected at the shortest possible distance. The operational‐amplifier‐based electronics acts as impedance buffers, and maintains the cabling impedance at the characteristic 50 Ω between the probe board and the instruments. We have thus reduced the instrumentation noises. Second, we present the result of...

SELF‐CONSISTENT SWEPT FREQUENCY EDDY CURRENT MEASUREMENTS FOR CHARACTERIZATION OF NEAR SURFACE MATERIAL CONDITIONS

This paper reports on a self‐consistent, swept frequency eddy current (SFEC) technique for characterizing surface and sub‐surface conditions of materials, with specific applications to detecting residual stresses in shot‐peened Ni‐base superalloys and surface oxidation in engineering components. The technique involves measuring lift‐off normalized vertical component signal to suppress lift off noise and instrumentation effect. Theoretical study shows that the vertical component signals are insensitive to coil dimensions, thus enabling EC measurements in separate frequency bands using multiple coils, while yielding continuous broad‐band data so that both the bulk conductivity and near‐surface conductivity profile can be determined by model‐based inversion. We demonstrate the technique on two surface‐modified materials, namely Inconel 718 samples shot peened at 4 A to 8 A, and an Ag‐1.5at%Al alloy which was used as a model material for a fundamental study of internal oxidation. For each sample set, the vert...

A SCALING LAW FOR NONDESTRUCTIVE EVALUATION OF SHOT PEENING INDUCED SURFACE MATERIAL PROPERTY DEVIATIONS

Shot peening is frequently used to improve mechanical characteristics of metallic components’ surfaces. The physical properties of shot peened surfaces exhibit deviations from their bulk values. This paper shows that there exists a scaling law (universality) among seemingly unrelated material property deviations and among different peening conditions. We present examples and support for scaling behaviors based on experimental data on Almen strip deflection, cold work and residual stress profiles of a shot peened nickel‐base superalloy (Waspaloy), and swept frequency eddy current signals used for NDE studies of another shot peened nickel‐base superalloy (Inconel 718). In addition, a fast impedance calculation formula for a coil placed on a metal with small, continuous conductivity deviation is presented and used for analytical and numerical study of eddy current signals.