Ultrasonic attenuation in polycrystals using a self-consistent approach

The self-consistent method of averaging elastic moduli to define the effective medium of a polycrystal is used to investigate the dynamic problem of wave propagation. An alternative covariance tensor describing the elastic moduli fluctuations of the polycrystal containing self-consistent elastic properties is derived and found to be significantly smaller than the covariance tensor formed through traditional Voigt averaging. Attenuation curves are generated using the self-consistent elastic moduli and covariance tensors and these results are compared with previous Voigt-averaged estimates. The second-order polycrystalline dispersion relation for the self-consistent scheme is found for cases of low and high crystallite anisotropy. The attenuation coefficients and dispersion relations derived through the self-consistent scheme are considerably different than previous estimates. Experimentally measured longitudinal attenuation coefficients support the use of the self-consistent scheme for estimation of attenuation.     

Interaction Between a Time-Dependent Laminar Boundary Layer and an Inviscid Subsonic Flow Near a Region of Local Energy Supply

The results of numerical modeling of the time-dependent flows of a viscous heat-conducting gas occurring in the region of interaction between an external inviscid flow and a laminar boundary layer near a zone of local energy supply at high subcritical Reynolds numbers are presented. The solution of the Navier-Stokes equations is constructed on the basis of the method of matched asymptotic expansions. Numerical solutions of the nonlinear boundary-value problem describing the flow in the wall region of the boundary layer are given in similarity variables. It is shown that time- and space-localized energy supply results in the formation of a self-consistent flow disturbance, whose downstream propagation is accompanied by a disturbance amplitude growth during a short time interval, even after the energy supply has stopped. Calculations of the flows induced by two heat sources placed in tandem make it possible to conclude that the time lag for the second energy supply zone and the distance between the sources can be so chosen that superposition of the disturbances induced by the first and second sources leads, due to nonlinear effects, to a considerable increase in the amplitude of the total flow disturbance.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 64–75.Original Russian Text Copyright © 2005 by Kazakov.     

Wakes in a Dust Plasma. Comparison of Numerical Methods

A self-consistent model for plasma polarization around an isolated dust particle with a size of 10^?6 m under the action of an external electric field is presented. It is shown that there are self-consistent potential oscillations for various intensities of the external electric fields behind the dust particle. The calculation results are compared with data obtained by using the known numerical approaches.     

广义自洽Mori-Tanaka模型及涂层夹杂体复合材料的有效模量

经典广义自洽模型的最大不足是需要确定相材料的位移及应变场,这一过程十分繁杂,而且最后得到的有交剪切模量无法显式表达难以应用,该文摈弃这一经典做法,而从广义自洽模型的应变等价条件出发,在夹杂应变均匀的近似假定下,将Ｈｉｌｌ界面条件应用于整个二相体内,从而得到一种可以预报涂层夹杂体复合材料有效模量的广义自洽Ｍｏｒｉ－Ｔａｎａｋａ模型,与已有的实验及理论的比较表明,该模型准确可靠,而且有效体积和剪切模量     

界面对多相介质平均弹性性能和应力场的影响

在建立多相介质夹杂问题的自治模型基础上，应用自治有限元法研究了多相介质的平均弹性性能问题，通过数例讨论了在不同体分比下，界面对多相介质总体平均弹性性能的影响，结果表明，界面厚度对多相介质横向平均剪切模量和横向平均体积模量有明显的影响，而对纵向平均拉伸模量影响不大。为了进一步研究界面破坏特征，本文还分析了多相介质界面区域的应力场。     

基于自洽法的电化学沉积修复饱和混凝土细观描述

针对当前电化学沉积修复混凝土缺乏细观层次上的理论描述,首先,以饱和混凝土的细观结构和电化学沉积修复的主要机理为基础, 提出了含电化学沉积产物、水和混凝土基体在内的三相复合材料细观力学模型. 其次,为了从细观层次定量描述电化学沉积修复对混凝土宏观性能的影响,基于自洽法对上述细观力学模型进行多层次均匀化处理,获取电化学沉积修复饱和混凝土的有效性能,其中,第一层均匀化是采用广义自洽模型获取等效夹杂的有效性能,第二层均匀化是采用自洽方法和沃伊特(Voigt) 上限相结合的方式获取修复混凝土的有效性能. 最后,为了验证该文所提出模型和方法的有效性,对比了该文的预测结果、试验数据和已有模型,结果表明了该文模型和方法是合理的.      

A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials

A large strain elastic-viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tomé (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.     

The adhesive contact of viscoelastic spheres

We have formulated the restricted self-consistent model for the adhesive contact of linear viscoelastic spheres. This model is a generalization of both the Ting (J. Appl. Mech. 33 (1966) 845) approach to the viscoelastic contact of adhesionless spheres and the restricted self-consistent model for adhesive axisymmetric bodies. We also show how the model can be used in practice by giving a few examples of numerical solutions.     

Méthode d'homogénéisation auto-cohérente en calcul à la ruptureSelf-consistent homogeneization method in yield design

This work is aimed towards determining the macroscopic strength criterion of a heterogeneous material with a random microstructure. We use the self-consistent concept by considering a reference material, which is of same nature as the constituents of the heterogeneous material. We deduce that the estimates of the macroscopic strength domain are the solutions to self-consistent equations and we give their derivation procedure. To cite this article: S. Turgeman, B. Guessab, C. R. Mecanique 330 (2002) 623–626.     

A unified energy approach to a class of micromechanics models for composite materials

Several micromechanics models for the determination of composite moduli are investigated in this paper, including the dilute solution, self-consistent method, generalized self-consistent method, and Mori-Tanaka's method. These micromechanical models have been developed by following quite different approaches and physical interpretations. It is shown that all the micromechanics models share a common ground, the generalized Budiansky's energy-equivalence framework. The difference among the various models is shown to be the way in which the average strain of the inclusion phase is evaluated. As a bonus of this theoretical development, the asymmetry suffered in Mori-Tanaka's method can be circumvented and the applicability of the generalized self-consistent method can be extended to materials containing microcracks, multiphase inclusions, non-spherical inclusions, or non-cylindrical inclusions. The relevance to the differential method, double-inclusion model, and Hashin-Shtrikman bounds is also discussed. The application of these micromechanics models to particulate-reinforced composites and microcracked solids is reviewed and some new results are presented.     

Coupled effects of grain size distributions and crystallographic textures on the plastic behaviour of IF steels

Micro-macro scale transition theories were developed to model the inelastic behaviour of polycrystals starting from the local behaviour of the grains. The anisotropy of the plastic behaviour of polycrystalline metals was essentially explained by taking into account the crystallographic textures. Issues like plastic heterogeneities due to grain size dispersion, involving the Hall-Petch mechanism at the grain scale, were often not taken into account, and, only the role of a mean grain size was investigated in the literature. Here, both sources of plastic heterogeneities are studied using: (i) experimental data from EBSD measurements and tensile tests, and, (ii) a self-consistent model devoted to elastic-viscoplastic heterogeneous materials. The results of the model are applied to two different industrial IF steels with similar global orientation distributions functions but different mean grain sizes and grain size distributions. The coupled role of grain size distributions and crystallographic textures on the overall tensile behaviour, local stresses and strains, stored energy and overall plastic anisotropy (Lankford coefficients) is deeply analyzed by considering different other possible correlations between crystallographic orientations and grain sizes from the measured data.     

A generalized self-consistent Mori-Tanaka model for predicting the effective moduli of the coated inclusion based composite materials

The weak point of the generalized self-consistent method (GSCM) is that its solution for the effective shear moduli involves determining the complicated displacement and strain fields in constitutents. Furthermore, the effective moduli estimated by GSCM cannot be expressed in an explicit form. Instead of following the procedure of GSCM, in this paper a generalized self-consistent Mori-Tanaka method (GSCMTM) is developed by means of Hill's interface condition and the assumption that the strain in the inclusion is uniform. A comparison with the existing theoretical and experimental results shows that the present GSCMTM is sufficiently accurate to predict the effective moduli of the coated inclusion-based composite materials. Moreover, it is interesting to find that the application of Hill's interface condition in volumetric domain is equivalent to the Mori-Tanaka average field approximation. This project was supported by the National Natural Science Foundation of China and China Postdoctoral Science Foundation.     

适用于自洽强度方法的冲击加载-再加载实验技术

针对自洽强度方法存在的冲击加载-再加载的难题,提出了一种采用较高硬度材料为支撑制作组合飞片的简便方法。利用该方法获得了铝、锡和锆基金属玻璃较理想的冲击加载-再加载粒子速度剖面,验证了该方法的有效性。由本文获得的冲击加载-再加载粒子速度剖面,并根据自洽方法,计算得到了铝、锡和锆基金属玻璃再加载过程剪应力变化数据。进一步分析表明,在本文涉及的压力范围内,仅由冲击加载-卸载实验得到的铝、锡和锆基金属玻璃屈服强度将比实际结果降低20%~50%。因此,在采用自洽方法计算高压强度时,冲击加载-再加载数据不可或缺。     

反平面剪切作用下双材料滑动界面的细观力学模型

非理想粘结界面对多相材料力学性能具有重要影响。对于双材料间含众多随机分布微裂纹的界面，宏观上可以等效为连续损伤的弱界面，其两侧的面力连续而位移有间断。只有切线方向的位移间断，而法线方向位移连续的弱界面称之为滑动界面。在反平面剪切的作用下，我们证明了对于含有随机分布微裂纹的弹性双材料界面在宏观上等效为线弹簧型滑动界面，并获得了滑动界面柔度的一般表达式。利用Mori—Tanaka方法和广义自洽方法，我们研究了滑动界面柔度系数和微裂纹密度的关系。对这两种方法所得的结果进行比较发现，Mori—Tanaka方法得到的界面柔度比广义自洽方法得到的界面柔度大。当裂纹密度比较小时，这两种方法求得的界面柔度很接近。两种方法的结果都表明，界面柔度随裂纹密度的增加而增加。Mori—Tanaka方法比广义自治方法求解更为简便。     

Prediction of the effective elastic properties of spheroplastics by the generalized self-consistent method

The problem of predicting the effective elastic properties of composites with prescribed random location and radius variation in spherical inclusions is solved using the generalized self-consistent method. The problem is reduced to the solution of the averaged boundary-value problem of the theory of elasticity for a single inclusion with an inhomogeneous transition layer in a medium with desired effective elastic properties. A numerical analysis of the effective properties of a composite with rigid spherical inclusions and a composite with spherical pores is carried out. The results are compared with the known solution for the periodic structure and with the solutions obtained by the standard self-consistent methods. Perm’ State Technical University, Perm’ 614600. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 186–190, May–June, 1999.     

层次分析法在工程岩体分类中的应用

层次分析法是一种考虑定性与定量相结合的多目标决策分析方法。岩体工程分类受多种因素影响,本文选用多种因素进行全面的综合分析,建立了由4个层次组成的岩体工程分类层次分析体系,详细介绍了不同层次的判断矩阵的构造及分类过程。实测数据计算结果表明:岩体工程分类层次分析体系简单、适用、系统性强,评价结果真实、有效。     

On the elastic–viscoplastic behavior of nanocrystalline materials

A new constitutive law is introduced to quantify the macroscopic effect of grain boundary dislocation emission on the behavior of pure face center cubic nanocrystalline materials. It is postulated that an emitted dislocation ends its trajectory in the grain boundary opposite to the source causing mass transfer. Dislocation emission by grain boundary ledges, considered here as the primary grain-boundary sources, is modeled as a thermally activated mechanism and the penetration of an emitted dislocation is assimilated as a soft collision. The macroscopic behavior of the material is retrieved via the use of a secant self-consistent scheme. The material is seen as a two-phase composite where the inclusion phase represents grain cores, their behavior is driven by dislocation glide, and where the matrix phase, governed by the newly introduced dislocation emission and penetration mechanism, represents both grain boundaries and triple junctions. The long range stress field arising from the presence of grain boundaries is taken into account in the critical glide resistance stress at 0 K in the inclusion phase. The model is applied to polycrystal copper and results in pure tension and creep are compared to experiments. Good agreements between the experimental measurements and the model predictions are observed.