Effects of grain sizes, shapes, and distribution on minimum sizes of representative volume elements of cubic polycrystals

In the literature the concept of representative volume element (RVE) was introduced to correlate the effective or macroscopic properties of materials with the properties of the microscopic constituents and microscopic structures of the materials. However, to date little quantitative knowledge is available about minimum RVE sizes of various engineering materials. In our recent paper [J. Mech. Phys. Solids 50 (2002) 881], a new definition of minimum RVE size was introduced based on the concept of nominal modulus. Numerical experiments using the finite element method (FEM) were then carried out for determining the minimum RVE sizes of more than 500 cubic polycrystals in the plane stress problem, under the assumption that all grains in a polycrystal have the same square shape––called the simple polycrystal model. The major finding is that the minimum RVE sizes for effective elastic moduli have a roughly linear dependence on crystal anisotropy degrees. The present paper takes into account the effect of grain sizes, shapes, and distribution on the minimum RVE sizes for real cubic polycrystals that are formed by crystallization processes. Similar roughly linear dependence is found again, with the slope about 19% lower than that in the simple polycrystal model. This finding is interesting and useful because numerical experiments on minimum RVE sizes for a large number of crystals are quite time-consuming and the simple polycrystal model reduces significantly the FEM pre- and post-processing works. This should be particularly true in numerically testing minimum RVE sizes for three-dimensional polycrystals and for nonelastic properties in future works. With a maximum relative error 5%, all the polycrystals tested have a minimum RVE size of 16 or less times the grain size.     

A comparative study of numerical solutions to non-linear discrete crack modelling of concrete beams involving sharp snap-back

Numerical problems are often encountered in modelling crack propagation in concrete beams using non-linear finite element (FE) analysis, especially when sharp snap-back behaviour in load-displacement relations occurs. This paper firstly identifies 16 arc-length control based numerical strategies based on extensive literature review. They are then used to carefully model the structural behaviour of a four-point single notched shear beam using discrete crack modelling approach in which cracks are represented by interface elements with bilinear softening constitutive laws. Based on extensive FE analyses, detailed comparisons of the merits and demerits of these numerical algorithms are then made. The results indicate that the effectiveness and efficiency of different algorithms may vary considerably from one to another, with the local arc-length based procedures in conjunction with tangential stiffness strategy and reversible unloading model being the most robust.     

High-strain-rate superplasticity of nanocrystalline aluminum alloy 1570

The structure and mechanical properties of nanocrystalline aluminum alloy 1570 obtained by means of severe plastic deformation have been studied. Being tested in a temperature range from 300 to 400°C, the alloy exhibits high-strain-rate superplasticity. At 400°C, the superplasticity is manifested in a very broad range of strain rates, extending from 5 × 10^?3 to 1 s^?1.     

A Recursive Frequency Estimator Using Linear Prediction and a Kalman-Filter-Based Iterative Algorithm

This paper proposes a new Kalman-filter-based recursive frequency estimator for discrete-time multicomponent sinusoidal signals whose frequencies may be time-varying. The frequency estimator is based on the linear prediction approach and it employs the Kalman filter to track the linear prediction coefficients (LPCs) recursively. Frequencies of the sinusoids can then be computed using the estimated LPCs. Due to the coloredness of the linear prediction error, an iterative algorithm is employed to estimate the covariance matrix of the prediction error and the LPCs alternately in the Kalman filter in order to improve the tracking performance. Simulation results show that the proposed Kalman-filter-based iterative frequency estimator can achieve better tracking results than the conventional recursive least-squares-based estimators.     

Effects of compressive and tensile stress on the growth mode of epitaxial oxide films

Oxide films were deposited on different substrates by laser molecular beam epitaxy. Reflection high-energy electron diffraction was performed to in situ investigate the change of growth mode and the lattice relaxation during the growth. An asymmetrical phenomenon was found in the two kinds of strain states, compressive stress and tensile stress of heterostructures with different lattice mismatch. In the case of BaTiO₃/SrTiO₃ (2.2%), 2D layer-by-layer growth mode without lattice relaxation can be maintained for a longer period for BTO films on STO with compressive stress, comparing to STO films on BTO with tensile stress. When MgO films were deposited on SrTiO₃ with a large mismatch of 7.8%, compressive stress leads to rapid lattice relaxation with a very thin wet layer, and 3D strained island were observed. As a comparison, SrTiO₃ films on MgO with tensile stress were configured. No RHEED patterns can be observed duo to a large tensile stress.