单晶硅的纳米力学响应及其相变机制

硅在大规模集成电路、MEMS/NEMS、半导体工业中具有不可替代作用,但是目前对硅的塑性变形及其相变机制的理解远未成熟.采用大规模分子动力学模拟研究(100)面的单晶硅在球形金刚石压头纳米压入过程中的纳米力学响应、相变过程和相分布规律.结果表明:在弹性变形阶段载荷-压深曲线与Hertz接触理论预测结果相吻合.两者的分离点准确地预示了塑性变形的发生.金刚石结构的Si-I相向体心结构的BCT5相转变导致了单晶硅初始的塑性变形.初始形成的BCT5相在次表面形成了一个倒置的金字塔形结构.Si-II相的形成则稍微滞后一些.在较大的载荷下BCT5在压入面上形成一个四重对称的图案分布.相对于小压头条件下大的BCT5相区,大压头更有利于SiII相的发展.卸载后生成的高压Si-II相和BCT5相全部转变为非晶硅.研究结果确认了单晶硅纳米压入中BCT5相的存在;揭示了单晶硅塑性变形的相变机理,即Si-I转变为BCT5和Si-II相;并强调了Si-I相向BCT5相转变对于单晶硅塑性变形的重要作用.     

RESEARCH ON METHOD TO CALCULATE VELOCITIES OF SOLID PHASE AND LIQUID PHASE IN DEBRIS FLOW

Velocities of solid phase and liquid phase in debris flow are one key problem to research on impact and abrasion mechanism of banks and control structures under action of debris flow. Debris flow was simplified as two-phase liquid composed of solid phase with the same diameter particles and liquid phase with the same mechanical features. Assume debris flow was one-dimension two-phase liquid moving to one direction, then general equations of velocities of solid phase and liquid phase were founded in two-phase theory. Methods to calculate average pressures, volume forces and surface forces of debris flow control volume were established. Specially, surface forces were ascertained using Bingham's rheology equation of liquid phase and Bagnold's testing results about interaction between particles of solid phase. Proportional coefficient of velocities between liquid phase and solid phase was put forward, meanwhile, divergent coefficient between theoretical velocity and real velocity of solid phase was provided too. To state succinctly before, method to calculate velocities of solid phase and liquid phase was obtained through solution to general equations. The method is suitable for both viscous debris flow and thin debris flow. Additionally, velocities every phase can be identified through analyzing deposits in-situ after occurring of debris flow. It is obvious from engineering case the result in the method is consistent to that in real-time field observation.     

冲击下宏观相边界的传播

研究了具有CdS型相变本构材料的宏观相边界传播规律。相边界包括纯新相和混合相两段。纯新相段可用逐步近似法,混合相段则必须用数值方法求解。给出了三种加卸载应力边界条件下的算例。在突加突卸的应力边界条件下,给出了相边界传播的解析解。在算例中,各种解法得到的结果彼此很好符合。     

Simulation of bacterial flagellar phase transition by non-convex and non-local continuum modeling

Bacterial flagellar filament can undergo a stress-induced polymorphic phase transition in both vitro and vivo environments. The filament has 12 different helical forms (phases) characterized by different pitch lengths and helix radii. When subjected to the frictional force of flowing fluid, the filament changes between a left-handed normal phase and a right-handed semi-coiled phase via phase nucleation and growth. This paper develops non-local finite element method (FEM) to simulate the phase transition under a displacement-controlled loading condition (controlled helix-twist). The FEM formulation is based on the Ginzburg-Landau theory using a one-dimensional non-convex and non-local continuum model. To describe the processes of the phase nucleation and growth, viscosity-type kinetics is also used. The non-local FEM simulation captures the main features of the phase transition: two-phase coexistence with an interface of finite thickness, phase nucleation and phase growth with interface propagation. The non-local FEM model provides a tool to study the effects of the interfacial energy/thickness and loading conditions on the phase transition.     

Kinetics of phase transformations in the peridynamic formulation of continuum mechanics

We study the kinetics of phase transformations in solids using the peridynamic formulation of continuum mechanics. The peridynamic theory is a nonlocal formulation that does not involve spatial derivatives, and is a powerful tool to study defects such as cracks and interfaces.We apply the peridynamic formulation to the motion of phase boundaries in one dimension. We show that unlike the classical continuum theory, the peridynamic formulation does not require any extraneous constitutive laws such as the kinetic relation (the relation between the velocity of the interface and the thermodynamic driving force acting across it) or the nucleation criterion (the criterion that determines whether a new phase arises from a single phase). Instead this information is obtained from inside the theory simply by specifying the inter-particle interaction. We derive a nucleation criterion by examining nucleation as a dynamic instability. We find the induced kinetic relation by analyzing the solutions of impact and release problems, and also directly by viewing phase boundaries as traveling waves.We also study the interaction of a phase boundary with an elastic non-transforming inclusion in two dimensions. We find that phase boundaries remain essentially planar with little bowing. Further, we find a new mechanism whereby acoustic waves ahead of the phase boundary nucleate new phase boundaries at the edges of the inclusion while the original phase boundary slows down or stops. Transformation proceeds as the freshly nucleated phase boundaries propagate leaving behind some untransformed martensite around the inclusion.     

基于相位差谱的空间相关非平稳地震动场的模拟

地震动的非平稳特性主要是由其相位差谱决定的,相位差谱与相位导数之间存在线性倍数关系。根据相位导数的显式计算公式,从能量的角度解释了相位导数的均值大致决定了时程峰值的发生时刻,相位导数的方差决定了强震段的持续时间。在相关地震动场模拟方法中,首次将相位差谱的统计模型引入空间相关非平稳地震动场的模拟方法之中,利用快速傅立叶变换技术生成地震动场。表示地震动随机特性的随机相位谱利用相位差谱的统计模型生成,生成的地震动场不仅具有空间相关性,而且在时域、频域内均具有非平稳特性。     

温度对冲击相变波传播的影响

冲击加载下,相界面的传播是一热力耦合过程.相变波阵面不仅是力学和物质间断面,也是温度界面.为考虑温度对相变波传播的影响,论文首先建立了相界面上的热传导方程和热力耦合的相变本构方程,然后采用一维特征线理论和有限差分数值计算相结合的方法,分析了温度界面和相变波的基本相互作用规律,进而给出了连续温度梯度下和绝热冲击下相变波传播规律.结果表明,温度对相变波传播的作用主要体现在两个方面,一方面是作为温度界面将与各类间断面相互作用,另一方面冲击相变波阵面后区域热力学状态变化影响卸载波结构.其原因在于相变方式(可逆、不可逆)和相变阈值应力具有强烈的温度相关性.     

On a Model of Heterogenous Deformation of Elastic Bodies by the Mechanism of Multiple Appearance of New Phase Layers

A model describing a possible scenario of martensite type phase transformations is examined. A new phase is supposed to nucleate in the form of plane parallel layers. As the boundary condition, average strains are imposed. Then, the governing parameters of the two-phase structure are the concentration of new phase layers, their orientation and also the orientation of anisotropy axes. The parameters depend on the average strains and are determined by the requirement to minimize the average Helmholtz free-energy function. Once a general procedure has been discussed, average strain–stress diagrams are constructed for two cases. In the first case, for the simplicity sake, both phases are assumed to be isotropic. In the second case anisotropy is produced by a non-spherical phase transformation strain tensor. For both cases phase transition zones (PTZs) are constructed. The PTZ is formed in the space of strains by those which can exist on equilibrium interfaces. Loading and unloading paths, corresponding to uniaxial stretching and plane stretching/compression, are examined and related with the PTZ. Effects of internal stresses induced by the nucleation of new phase areas and the anisotropy of new phase are discussed.     

Mathematical modeling of transport-growth processes in multiphase biological continua

The model of a growing medium consisting of two phases, liquid and solid, is developed. Growth is treated as a combination of the irreversible deformation of the solid phase and its mass increment due to mass exchange with the liquid phase. The inelastic strain rate of the solid phase depends on the stresses in it, which are determined by the forces both external with respect to the medium and exerted by the liquid phase. In the liquid phase the pressure develops due to the presence of a chemical component whose displacement is hampered by its interaction with the solid phase. The approach developed makes it possible to waive many problems discussed in the theory of growing continua. Possible generalizations are considered.     

A combined Lagrangian method for simulation of axisymmetric gas-particle vortex flows

A combined fully Lagrangian approach for meshless modeling of unsteady axisymmetric vortex flows of a gas-particle mixture with an incompressible carrier phase is developed. The approach proposed is based on the combination of a meshless vortex method for calculating axisymmetric flows of the carrier phase described by the Navier–Stokes (or Euler) equations and the full Lagrangian method for calculating the parameters of the dispersed phase. The combination of these methods reduces the problem of modeling the two phase flows to the solution of a high-order system of ordinary differential equations for the coordinates of toroidal vortex elements in the carrier phase and the particle trajectories, the velocity components, and the components of the Jacobian of transformation from the Eulerian to the Lagrangian variables in the dispersed phase. The application of the method is illustrated by modeling the behavior of an admixture of inertial Stokes particles with a small mass concentration in unsteady flows like solitary vortex rings in a viscous carrier phase and groups of vortex rings in an effectively inviscid carrier phase.     

Electromechanical phase transition of a dielectric elastomer tube under internal pressure of constant mass

The electromechanical phase transition for a dielectric elastomer(DE) tube has been demonstrated in recent experiments, where it is found that the unbulged phase gradually changed into bulged phase.Previous theoretical works only studied the transition process under pressure control condition, which is not consistent with the real experimental condition. This paper focuses on more complex features of the electromechanical phase transition under internal pressure of constant mass. We derive the equilibrium equations and the condition for coexistent states for a DE tube under an internal pressure, a voltage through the thickness and an axial force. We find that under mass control condition the voltage needed to maintain the phase transition increases as the process proceeds. We analyze the entire process of electromechanical phase transition and find that the evolution of configurations is also different from that for pressure control condition.     

Modeling of macroscopic response of phase transforming materials under quasi-static loading

Based on a continuum model of solid-solid phase transformations, the macroscopic response of a bar of a thermoelastic phase transforming material loaded quasistatically is investigated. A critical loading rate is identified for the evolution of a single phase boundary in the bar during an isothermal process. It is shown that, when the loading rate is larger than this critical loading rate, nucleation occurs either continuously or at multiple sites; when the loading rate is lower than this critical loading rate, the size of the hysteresis loop increases with increasing loading rate, and decreases with an increase in the mobility of the phase boundary. The heat conduction due to the heat generated by the latent heat of the phase transformation is considered for a special case.     

Estimation of Phase and Its Higher Order Derivatives from a Single Complex Interferogram

This paper reports a method for the simultaneous estimation of unwrapped phase and higher order phase derivatives from a single phase fringe pattern recorded in an optical interferometric setup, thereby overcoming substantial barriers to achieving such measurements. The proposed method considers the interference phase as a weighted linear combination of Gaussian radial basis functions defined along a given row or column at a time. The Gaussian radial basis functions are defined with a constant standard deviation and equally spaced centers. Unscented Kalman filter is employed for the accurate estimation of the weights of the basis functions using the state space representation of the spatial evolution of the interferogram. The estimated weights along with the numerically computed gradients of the basis functions also provide the estimations of phase derivatives of arbitrary order. The proposed representation of interference phase along with the unscented Kalman filter provides high robustness against the speckle noise. Simulation study is preformed to evaluate the dependence of the phase and phase derivative estimation accuracy on the selection of basis dimension and the noise level. Experimental results demonstrate the practical applicability of the proposed method.     

低相变阈值金属高压加载下的相变层裂特性

采用激光速度干涉仪（VISAR）和X光联合测试技术,在冲击压力远高于相变应力加载下,实验研究低相变阈值金属FeMnNi合金的相变层裂特性,结果发现等厚对称碰撞加载下FeMnNi合金出现反常的层裂行为。针对该反常的层裂行为,利用塑性波、相变波、稀疏波和逆相变引发的稀疏冲击波的相互作用过程进行分析,结果表明,该实验状态下FeMnNi合金样品存在相变和逆相变行为,逆相变引发的稀疏冲击波是导致反常层裂行为的主要因素。     

The transition from phase locking to drift in a system of two weakly coupled van der pol oscillators

We investigate the slow flow resulting from the application of the two variable expansion perturbation method to a system of two linearly coupled van der Pol oscillators. The slow flow consists of three non-linear coupled odes on the amplitudes and phase difference of the oscillators. We obtain regions in parameter space which correspond to phase locking, phase entrainment and phase drift of the coupled oscillators. In the slow flow, these states correspond respectively to a stable equilibrium, a stable limit cycle and a stable libration orbit. Phase entrainment, in which the phase difference between the oscillators varies periodically, is seen as an intermediate state between phase locking and phase drift. In the slow flow, the transitions between these states are shown to be associated with Hopf and saddle-connection bifurcations.     

Dynamics of propagating phase boundaries in NiTi

Propagating boundaries of phase transformation have been generated in polycrystalline NiTi specimens under a tensile impact loading condition. Multiple strain gages were used to monitor the time evolution of the strain at different spatial locations in the specimen. Nucleation and propagation of multiple phase fronts were detected in these experiments; the phase front speed was found to be in the range between 37 and 370 m/s. The strain measurements were interpreted through the one-dimensional analysis of Abeyaratne and Knowles [1997. On the kinetics of an austenite→martensite phase transformation induced by impact in Cu-Al-Ni shape-memory alloy. Acta Mater. 45, 1671-1683] and a model of partial phase transformation in the polycrystalline specimen. The driving force for the motion of the phase front was evaluated from the measurements in order to establish the kinetic relation.     

WAG Displacements of Oil-Condensates Accounting for Hydrocarbon Ganglia

During two-phase flow in porous media, non-wetting phase is present simultaneously in states of mobile connected continuum and of trapped isolated ganglia. Mass exchange between these two parts of non-wetting phase is going on by dissolution and diffusion of component in the wetting phase, so, compositions of non-wetting phase in both parts are different. Nevertheless, the traditional mathematical model for two-phase multicomponent transport in porous media assumes the homogeneous distribution of each component in the overall non-wetting phase. New governing equations honouring ganglia of non-wetting phase are derived. They are successfully verified by a number of laboratory tests. Analytical model is developed for miscible water-alternate-gas (WAG) displacement of oil-condensates. The modelling shows that the significant amount of oil-condensate is left in porous media after miscible WAG, while the traditional model predicts that the miscible displacement results in the total sweep.