多主元合金中的化学短程有序

大量的研究表明多主元合金中广泛地存在对其性能提升有重要影响的化学短程序. 利用先进的透射电子显微成像技术可以在原子分辨率水平分析多主元合金中化学短程序的尺度、成分和构型.      

Acoustoelasticity model of inhomogeneously deformed bodies

We consider a mathematical model of dynamics of small elastic perturbations in an inhomogeneously deformed rigid body, where for the determining parameters of a local state we take the tensor characteristics of a given actual (strained) configuration (the Cauchy stress tensor and the Hencky or Almansi or Figner strain measure). An iteration algorithm is developed to solve the Cauchy problem stated in the framework of this model for a system of hyperbolic equations with variable coefficients that describes the propagation of elastic pulses in an inhomogeneous deformed continuum. In the case of two-dimensional stress fields, we obtain acoustoelasticity integral relations between the probing pulse parameters and the initial strain (stress) distribution in the direction of pulse propagation in the strained body. We also consider an example of application of the obtained integral relations in the inverse acoustic tomography problem for residual strains in a strip.     

Melnikov-Based Dynamical Analysis of Microcantilevers in Scanning Probe Microscopy

We study the dynamical behavior of a microcantilever-sample system that forms the basis for the operation of atomic force microscopes (AFM). We model the microcantilever by a single mode approximation. The interaction between the sample and the cantilever is modeled by a Lennard--Jones potential which consists of a short-range repulsive potential and a long-range van der Waals (vdW) attractive potential. We analyze the dynamics of the cantilever sample system when the cantilever is subjected to a sinusoidal forcing. Using the Melnikov method, the region in the space of physical parameters where chaotic motion is present is determined. In addition, using a proportional and derivative controller, we compute the Melnikov function in terms of the parameters of the controller. Using this relation, controllers can be designed to selectively change the regime of dynamical interaction.     

On the functional form of non-local elasticity kernels

The functional form of non-local elasticity kernels is studied within the context of the integral formalism. The study is limited to linear isotropic elasticity. The kernels are derived analytically based on the discrete structure of the material at the atomic scale. Atomistic simulations are used to validate the results. Materials in which the interatomic interactions are represented by pair, as well as embedded atom-type potentials are considered. The derived kernels have a range which extends up to the cut-off radius of the interatomic potential, are positive at the origin, and become negative approximately one atomic distance away, thus departing from the commonly assumed Gaussian functional form. The functional form of the potential and the radial distribution function of interacting neighbors about a representative atom fully define their shape. This new continuum model involves two material length scales that are both derived from atomistics for a Morse solid and for Al. Two applications are considered in closure. It is shown that in strained superlattices, the non-local model predicts maximum stresses that are much larger than those obtained within the local theory. This observation has implications for defect nucleation in these structures. Furthermore, the new non-local model improves upon the Gaussian one by predicting a more realistic wave dispersion relationship, with essentially zero group velocity at the boundary of the Brillouin zone.     

On strain and damage interactions during tearing: 3D in situ measurements and simulations for a ductile alloy (AA2139-T3)

Strain and damage interactions during tearing of a ductile Al-alloy with high work hardening are assessed in situ and in 3D combining two recently developed experimental techniques, namely, synchrotron laminography and digital volume correlation. Digital volume correlation consists of registering 3D laminography images. Via simultaneous assessments of 3D strain and damage at a distance of 1-mm ahead of a notch root of a thin Compact Tension-like specimen, it is found that parallel crossing slant strained bands are active from the beginning of loading in a region where the crack will be slanted. These bands have an intermittent activity but are stable in space. Even at late stages of deformation strained bands can stop their activity highlighting the importance of plasticity on the failure process rather than damage softening. One void is followed over the loading history and seen to grow and orient along the slant strained band at very late stages of deformation. Void growth and strain are quantified. Gurson–Tvergaard–Needleman-type simulations using damage nucleation for shear, which is based on the Lode parameter, are performed and capture slant fracture but not the initial strain fields and in particular the experimentally found slant bands. The band formation and strain distribution inside and outside the bands are discussed further using plane strain simulations accounting for plastic material heterogeneity in soft zones.     

Edge dislocations generated from a microcrack under initial residual stress of non-uniform distribution

Crystal nucleation gives rise to inhomogeneity in the crystal lattice. The prevailing stresses and strains caused by non-uniform cooling can create microcracks with residual stresses locked-in at the end segments. These stresses can have a non-uniform distribution where the amplitude can increase or decrease from the microcrack tip which is highly strained to generate edge dislocations under in-plane shear. A dual scale microdislocation crack model is considered by focusing attention near the microcrack tip singularity such that more than 10 orders of magnitude in lineal dimension can be covered from the atomic to the microscopic scale. The concept of a scale multiplier is employed to connect the microscopic and atomic scale results. Discontinuity at the cross-scaling location is necessitated by dividing the full range of the non-equilibrium process into two regions within which equilibrium mechanics can be used. When needed, additional mesoregions can be added to reduce the transient discontinuities.Solved in closed form is the solution for the generation of edge dislocations due to non-uniform residual stress distributions at the end segment of the microcrack tip which will henceforth be referred to simply as the “tip”. Three different Cases I, II and III will be considered where the residual stress will possess a peak at the different locations. Case I for the furthest away from the tip, Case II for the peak nearest to the tip and Case III for the peak in the middle of the residual stress segment. Compared are the scale multiplier α whose maximum value being one corresponding to no discontinuity at cross-scaling. Hence, small α corresponds to large discontinuity. For Cases I, II and III, αs are found, respectively as 0.17, 0.43 and 0.28. The largest discontinuity occurred at α = 0.17 when the peak of the residual stress is farthest away from the microcrack tip. The largest number of edge dislocations or imperfections are also generated for Case I. The precise location of the residual stress peak is related to the magnitude and the segment length of the residual stress. These findings are manifestation of the variety of non-homogeneities that can arise in a metal alloy during crystal formation, not to mention the prevailing conditions at the grain boundaries. The idea is not to account for the details per se but to test the sensitivities of the microscopic and atomic parameters involved. To this end, the energy density function for the dual scale model will be determined and discussed in connection with what has been emphasized.     

The stability of elastically strained nanorings and the formation of quantum dot molecules

Self-assembled nanorings have recently been identified in a number of heteroepitaxially strained material systems. Under some circumstances these rings have been observed to break up into ring-shaped quantum dot molecules. A general non-linear model for the elastic strain energy of non-axisymmetric epitaxially strained nanostructures beyond the small slope assumption is developed. This model is then used to investigate the stability of strained nanorings evolving via surface diffusion subject to perturbations around their circumference. An expression for the fastest growing mode is determined and related to experimental observations. The model predicts a region of stability for rings below a critical radius, and also a region for larger rings which have a proportionally small thickness. The predictions of the model are shown to be consistent with the available results. For the heteroepitaxial InP on In_0.5Ga_0.5P system investigated by Jevasuwan et al. (2013), the nanorings are found to be stable below a certain critical size. This is in good quantitative agreement with the model predictions. At larger sizes, the rings are unstable. The number of dots in the resulting quantum dot molecule is similar to the mode number for the fastest growing mode. Second order terms show that the number of dots is expected to reduce as the height of the ring increases in proportion to its thickness. The strained In_0.4Ga_0.6As on GaAs nanorings of Hanke et al. (2007) are always stable and this is in accordance with the findings of the analysis. The Au nanorings of Ruffino et al. (2011) are stable as well, even as they expand during annealing. This observation is also shown to be consistent with the proposed model, which is expected to be useful in the design and tailoring of heteroepitaxial systems for the self-organisation of quantum dot molecules.     

Nanoscale strain engineering of graphene and graphene-based devices

Structural distortions in nano-materials can induce dramatic changes in their electronic properties. This situation is well manifested in graphene, a two-dimensional honeycomb structure of carbon atoms with only one atomic layer thickness. In particular, strained graphene can result in both charging effects and pseudo-magnetic fields, so that controlled strain on a perfect graphene lattice can be tailored to yield desirable electronic properties. Here, we describe the theoretical foundation for strain-engineering of the electronic properties of graphene, and then provide experimental evidence for strain-induced pseudo-magnetic fields and charging effects in monolayer graphene. We further demonstrate the feasibility of nano-scale strain engineering for graphene-based devices by means of theoretical simula-tions and nano-fabrication technology.     

POWER LAW DISTRIBUTION AND SELF-ORGANIZED CRITICALITY OF DISPERSED PARTICLES

Research on particulate characteristics has been an important frontier in physics and chemistry during the past decades. It has however been mostly focused on granular materials with short-range interactions. In this work, it was found that the power law of particle size distribution applied to the long-range interacting system of floating dust in air, from which we deduced that self-organized criticality might hold for floating dust just as granular materials with short-range interactions. This feature may reveal underlying kinetic mechanisms, important in dispersed particle systems. In industry, power law of size distribution of dispersed particles can be used to investigate the change of dust size, and the power law parameter could be taken as an important index for dust separation.     

梁的动力稳定性分析的有限元方法

提出了对梁进行动力学稳定性分析的有限元方法──给出了单元质量矩阵，抗弯刚度矩阵，几何刚度矩阵及相应的Ｍａｔｈｉｅｕ方程，通过坐标变换消除了方程的动力与静力耦合，然后说明了由这种具有参数激励耦合的多自由度系统的Ｍａｔｈｉｅｕ方程求得系统一般参数共振及组合参数共振的过渡曲线的约束参数方法与多尺度方法。最后作为算例求出了均匀简支梁受简谐轴向力作用时的过渡曲线。     

Perturbation methods based upon varying action integrals

Direct perturbation solution procedures to non-linear systems are developed from variational statements derived from the principle of invariance of the action integral under infinitesimal transformations. Solution procedures that are the variational equivalent of the classical perturbation methods of strained parameters, the KBM method of averaging and the method of multiple time scales are presented.     

Using a Smoothing Averaging Operator to Evaluate Macroscopic Parameters in Structurally Inhomogeneous Materials

A smoothing averaging operator is used in passing from structural to macroscopic modeling of the stress–strained state of an article from a composite material taking into account finite strains. A model is constructed using an integral operator, in which the macroscopic laws of conservation of energy and mass and the equation of motion have the ordinary form used to describe processes in homogeneous materials. As an example, macroscopic parameters are evaluated in a system consisting of an ensemble of inclusions in an infinite matrix.     

金属互连结构的电迁移失效分析新算法

综合考虑了电子风、温度梯度、应力梯度和原子密度梯度四种电迁移驱动机制,基于ANSYS软件平台和FORTRAN程序提出一种新的电迁移失效分析算法.通过ANSYS电-热-结构耦合分析获得模型的电流密度分布、温度分布和应力分布,基于FORTRAN编写的原子密度重分布算法获得不同时刻的原子密度,依据空洞生成和扩展失效准则进行电迁移动态空洞演化模拟并得到失效寿命.最后,SWEAT结构与CSP结构的应用算例验证r算法的精度.     

Strain hardening in 2D discrete dislocation dynamics simulations: A new ‘2.5D’ algorithm

The two-dimensional discrete dislocation dynamics (2D DD) method, consisting of parallel straight edge dislocations gliding on independent slip systems in a plane strain model of a crystal, is often used to study complicated boundary value problems in crystal plasticity. However, the absence of truly three dimensional mechanisms such as junction formation means that forest hardening cannot be modeled, unless additional so-called ‘2.5D’ constitutive rules are prescribed for short-range dislocation interactions. Here, results from three dimensional dislocation dynamics (3D DD) simulations in an FCC material are used to define new constitutive rules for short-range interactions and junction formation between dislocations on intersecting slip systems in 2D. The mutual strengthening effect of junctions on preexisting obstacles, such as precipitates or grain boundaries, is also accounted for in the model. The new ‘2.5D’ DD model, with no arbitrary adjustable parameters beyond those obtained from lower scale simulation methods, is shown to predict athermal hardening rates, differences in flow behavior for single and multiple slip, and latent hardening ratios. All these phenomena are well-established in the plasticity of crystals and quantitative results predicted by the model are in good agreement with experimental observations.     

Direct simulation for concentrated fibre suspensions in transient and steady state shear flows

A numerical method to simulate fibre suspensions in transient and steady state shear flows for concentrated solutions is reported, which takes into account short-range hydrodynamic interaction via lubrication forces, contact forces and hydrodynamic forces. Fibres are assumed to have varying lengths as observed in industrial composites and this can be described with a fibre distribution length function. Stresses in the composite have been calculated from a constitutive equation or from an approximate expression for the effective stress of fibre suspensions. This simulation will assist in modelling of short fibre filled industrial composites. Our first results shown here qualitatively agree with experiments.     

The structure of multidimensional strained flames under transcritical conditions

Strained flames are commonly used to study the structure of reactive layers and describe the local properties of turbulent combustion. This model is attractive because constant strain rate flames only depend on a transverse coordinate and can be treated as a one-dimensional problem. This configuration is considered in a multidimensional context in which the strained flow is obtained by two counterflowing streams of reactants. It is used to examine the structure of transcritical strained flames in which one or two reactants are injected at a high pressure exceeding the critical value while their temperature is below the critical value. Calculations are carried out in a two-dimensional domain to test numerical models developed for multidimensional simulations and test thermodynamic and transport models devised to deal with high pressure real gas effects. Multidimensional strained flame calculations carried out in this study serve to check the validity of a new version of a Navier–Stokes flow solver (AVBP) conceived to deal with transcritical combustion of interest to liquid propellant rocket applications. This article describes the basic elements of such simulations and discusses results of calculations. It is shown that the calculated multidimensional strained flames have the expected features in terms of structure and response to the imposed strain rate. To cite this article: L. Pons et al., C. R. Mecanique 337 (2009).     

AN SEPARATION OF THE ALEATORY AND EPISTEMIC UNCERTAINTIES WITH CORRELATED NORMAL VARIABLES AND ANALYSIS OF THE INFLUENCE OF PARAMETERS

针对主观和客观不确定性同时存在且输入变量相关的结构系统,研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离,通过引入独立标准正态空间辅助变量,使得分布参数的主观不确定性能够从输入变量客观不确定性中分离,进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.     

正态相关变量主客观不确定性分离和参数影响分析

针对主观和客观不确定性同时存在且输入变量相关的结构系统,研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离,通过引入独立标准正态空间辅助变量,使得分布参数的主观不确定性能够从输入变量客观不确定性中分离,进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.      

弯曲衬底上应变异质外延薄膜形态失稳的相场模拟

论文旨在研究弯曲衬底上应变异质外延薄膜的表面非线性演化行为,研究采用了基于Eshelby等效方法的相场微弹性模型来模拟二维应变Si1-xGex/Si薄膜/衬底系统的形态失稳.建立了关于等效特征应变和长程序参量的自由能泛函,数值求解了时间相关的Ginzburg-Landau动力学方程.系统自由能包括化学能,弹性应变能以及薄膜、衬底与真空相两两之界面能.跟踪了全时的形态演化过程,给出了指定时刻的量子点形态轮廓图.结果表明,量子点倾向于沉积在弯曲衬底的波谷处,波谷处是能量有利位置,量子点在此处比在波峰处更加稳定.论文所做的相场模拟可以用来预测量子点形成的轮廓、尺寸和位置,可以为控制和生成周期性自组装表面纳米结构提供理论指导.     

水力劈裂问题的态型近场动力学建模

将态型近场动力学理论引入水力劈裂问题的模拟。构建了能反映岩土类材料准脆性断裂特征的态型近场动力学本构模型,并在物质点间相互作用力模型中加入等效水压力项,以实现在新生裂纹面上跟踪施加水压力。同时,考虑裂纹面间的接触,引入物质点间的短程排斥力作用,并设计了相应的接触算法。通过自编程序将模型和算法应用于含初始裂纹、不含初始裂纹以及含坝基软弱结构面的混凝土重力坝在高水头作用下的水力劈裂过程模拟,并与扩展有限元等模拟结果对比,验证了本文模型和算法的可行性和准确性。