An energy-based microstructure model to account for fatigue scatter in polycrystals

Scatter observed in the fatigue response of a nickel-based superalloy, U720, is linked to the variability in the microstructure. Our approach is to model the energy of a persistent slip band (PSB) structure and use its stability with respect to dislocation motion as our failure criterion for fatigue crack initiation. The components that contribute to the energy of the PSB are identified, namely, the stress field resulting from the applied external forces, dislocation pile-ups, and work-hardening of the material is calculated at the continuum scale. Further, energies for dislocations creating slip in the matrix/precipitates, interacting with the GBs, and nucleating/agglomerating within the PSB are computed via molecular dynamics simulations. Through this methodology, fatigue life is predicted based on the energy of the PSB, which inherently accounts for the microstructure of the material. The present approach circumvents the introduction of uncertainty principles in material properties. It builds a framework based on mechanics of microstructure, and from this framework, we construct simulated microstructures based on the measured distributions of grain size, orientation, neighbor information, and grain boundary character, which allows us to calculate fatigue scatter using a deterministic approach. The uniqueness of the approach is that it avoids the large number of parameters prevalent in previous fatigue models. The predicted lives are in excellent agreement with the experimental data validating the model capabilities.     

On isoperimetric problems for domains with partly known boundaries

In the present paper, we discuss the isoperimetric problems for domains with partly known boundaries, i.e., the problem of determining a domain that minimizes the capacity functional in the class of plain double-connected domains having the same fixed area and outer boundary. The formulas for capacity variations obtained in this paper allows us to formulate necessary conditions.It is proved that the convexity of the fixed outer boundary implies the convexity of the inner boundary corresponding to an optimal domain. Then, we discuss the case where the fixed part of the boundary is a square.Further, we consider similar problems with more complicated functionals. We introduce the concept of a minimal function in the class of equimeasurable functions. This concept allows us to unify the approach to all of these problems. At the end, we produce a hypothesis that, if proved, would enable us to characterize the shape of the optimal domains in the isoperimetric problems mentioned above.The author wishes to express his appreciation to Dr. K. A. Lurie for his help and unceasing attention.     

Grain Boundary Grooving as an Indicator of Grain Boundary Phase Transformations

The atomic force microscopy (AFM) was used to study the grain boundary (GB) groove profiles far away from the melting temperature T _m. It is shown that AFM allows one to measure the temperature dependence of the GB energy in a rather broad temperature interval (from 0.85 T _m to T _m). The GB energy and GB segregation of Bi were measured at 1123 K in the interval of the Bi bulk concentration x ^v _Bi from 5 to 140 ppm Bi. The transition from monolayer to multilayer adsorption is observed for the 19a GB at 1123 K and x ^v _Bi = 60 at. ppm Bi. At the same point (1123 K and x ^v _Bi = 60 at. ppm Bi) a discontinuity of the first derivative of the GB energy is observed. These features were explained using the model of GB prewetting phase transformation developed previously.     

Atomic Structure and Properties of the (310) Symmetrical Tilt Grain Boundary (STGB) in SrTiO3 Part II: Comparison with Experimental Studies

The atomistic simulation results presented in Part I for SrTiO₃ (310) symmetrical tilt grain boundary (STGB, the so-called = 5 GB with 36.8° symmetrical misorientation about [001]) are analyzed in the context of available experimental studies. In particular, atomic imaging studies of SrTiO₃ GBs via high resolution TEM and incoherent Z-contrast STEM imaging; and determination of oxygen positions by combining electron energy loss spectroscopy (EELS) and bond-valence-sum rules, are compared with simulation results. The atomistic simulation data on the GB energies are compared with relative experimental estimates obtained via a novel approach of faceting of focused ion beam (FIB) induced microvoids.While there are considerable differences in details of simulation and experimental results, some basic trends seem to emerge about the core structural framework of GBs in SrTiO₃. The paper highlights the limitations of both, experimental and simulation techniques, and argues in favor of synergistic use of diverse experimental and simulation approach to determine the atomic structure and properties of GBs.     

中国优秀物理学家的杰出代表——葛庭燧

回顾介绍了葛庭燧院士的生平和他在科学研究、人才培养方面所作出的贡献,展示了他的高尚情操,分析了他取得卓著成就的原因.     

Transparent boundary conditions for the Helmholtz equation in some ramified domains with a fractal boundary

The paper addresses a class of boundary value problems in some self-similar ramified domains, with the Laplace or Helmholtz equations. Much stress is placed on transparent boundary conditions which allow the solutions to be computed in subdomains. A self similar finite element method is proposed and tested. It can be used for numerically computing the spectrum of the Laplace operator with Neumann boundary conditions, as well as the eigenmodes. The eigenmodes are normalized by means of a perturbation method and the spectral decomposition of a compactly supported function is carried out. Finally, a numerical method for the wave equation is addressed.     

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

This paper presents a local domain‐free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier–Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of ‘freshly cleared nodes/cells’ encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite‐element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual‐time‐stepping scheme based on artificial compressibility. In order to validate the present method for moving‐boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in‐line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving–pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.     

Modification of Electrical Activity of Grain Boundaries in EFG Silicon Under Influence of Hydrogen Plasma

We investigated an influence of hydrogen plasma treatment on electrical properties of shaped silicon polycrystals. Hydrogen penetration into polycrystalline silicon is demonstrated to depend on the state of the crystal (as-grown or annealed) and type of grain boundary (general or weakly deviated from special orientations). It is found that interaction of atomic hydrogen with grain boundaries can result not only in decrease of their electrical activity, but also in increase of potential barrier height at relatively high (more than 2 × 10¹⁸ cm^–2) doses of incorporated hydrogen. This phenomenon is explained by a phenomenological model which takes into account passivation of grain boundary dangling bonds and boron atoms in the bulk as two main mechanisms controlling hydrogenation effect.     

Efficient construction of high‐resolution TVD conservative schemes for equations with source terms: application to shallow water flows

High‐resolution total variation diminishing (TVD) schemes are widely used for the numerical approximation of hyperbolic conservation laws. Their extension to equations with source terms involving spatial derivatives is not obvious. In this work, efficient ways of constructing conservative schemes from the conservative, non‐conservative or characteristic form of the equations are described in detail. An upwind, as opposed to a pointwise, treatment of the source terms is adopted here, and a new technique is proposed in which source terms are included in the flux limiter functions to get a complete second‐order compact scheme. A new correction to fix the entropy problem is also presented and a robust treatment of the boundary conditions according to the discretization used is stated. Copyright © 2001 John Wiley & Sons, Ltd.