固体相变过程中的宏细观力学问题及其研究进展

固体相变过程中的力学问题是近年来国际上固体力学与材料科学交叉领域中的一个研究热点,本文就作者在从事与相变有关的力学研究中所涉及到的问题以及国内外进展作一简述和展望,以引起国内学者的关注。      

螺旋波动力学及其控制

螺旋波是时空斑图结构演化的一个典型研究对象,无论从理论研究意义还是从应用价 值来看都是非常重要的,它可涉及到的领域包括:数学、物理、力学、天文、化学、生物、 医学等学科. 本文较为详细地讨论了螺旋波的动力学行为, 主要包含以下几方面: 螺旋波的 形成、螺旋波的几种常见的形式、螺旋波波头的运动、螺旋波失稳方式等. 由于螺旋波及其 破碎后的行为在许多具体的系统中的有害作用, 本文也介绍了螺旋波的几种控制方案: 反馈 控制方案、外力控制方案、调整参数控制方案等.     

超弹性形状记忆合金管单向拉伸试验的数值模拟

NiTi形状记忆合金具有很强的超弹性行为,这种超弹性行为是由于材料在应力作用下发生可逆的马氏体相变所引起。最近Sun和Lee^[4]在NiTi形状记忆合金管单向拉伸试验中观测到,应力诱导马氏体相变具有螺旋带状的形貌特征,本文对此作了数值模拟研究。采用包含应变软化效应的三线性本构关系,建立了NiTi形状记忆合金管的三维有限元模型。通过迭代计算,成功地再现了试验中所观察到的螺旋状相变带从形成到长大的全过程。数值计算结果表明,产生这一独特现象的力学机制,在于NiTi形状记忆合金管在拉伸状态下出现的局部变形失稳极其传播。     

热弹性马氏体相变连续介质热力学研究

介绍形状记忆合金热弹性马氏体相变连续介质热力学研究方法和最新进展, 着重分析了在推广的非线性弹性力学的框架下, 应用变分方法研究热弹性马氏体相变的理论和方法、存在的问题及发展趋势. 首先介绍如何计算马氏体相变24种变体的变形梯度, 然后拓展非线性弹性力学, 引入描述相变的多阱非凸弹性势能, 进而讨论了界面能和非局部能对相变微结构和相变过程的影响的相关研究理论方法和进展.      

铁电单晶Pb(Mg1/3Nb2/3)O3-0.32PbTiO3的实验及本构模型研究

对压力作用下沿[001]晶向极化的Pb(Mg弛豫型铁电单晶;极化旋转(相变);黏塑性模型;本构;细观力学国家自然科学基金,教育部全国优秀博士学位论文作者专项基金2006-11-06对压力作用下沿[001]晶向极化的Pb(Mg1/3Nb2/3)O3-0.32PbTiO3(PMN0.32PT)弛豫型铁电单晶的应力应变行为进行了实验研究,实验结果表明铁电单晶〈001〉晶向的应力应变行为和铁电多晶有本质的不同,是传统的电畴翻转机理所难以解释的,所提出的极化旋转(相变)模型合理地解释了实验中观察到的现象;基于提出的极化旋转(相变)模型,采用细观力学方法建立了铁电单晶的细观本构模型.在模型中采用黏塑性公式描述铁电单晶可能的8个相变系统的相变行为.为了验证模型的可靠性,用该模型模拟了铁电单晶〈001〉晶向的应力应变实验曲线.计算表明,该模型能较好地模拟铁电单晶〈001〉晶向的相变行为.     

TiNi合金冲击相变过程中温度变化规律的实验研究

针对初始SME(shape memory effect)和PE(pseudo-elastic)状态TiNi合金试样,采用带有红外测温系统的SHPB冲击压缩装置,实时测量了冲击相变过程中两种材料试样表面瞬态温度,并根据实验结果计算了相应的温度变化。实验结果表明,冲击加载相变过程中,温度随相变应变的增大而升高,当应变最大时,温度最高;卸载过程中,对初始PE状态试样,温度降低,对初始SME状态试样,温度保持最高温度不变或降低,这同加载最高温度有关;卸载完成后,两种试样温度均高于其初始温度。计算温度结果表明,相变耗散功对加、卸载相变过程中温度变化的作用不可忽略。     

基于分子动力学模拟的单晶硅冲击压缩相变研究

晶体硅具有复杂的相变机制,在相图研究中受到广泛关注,其在动载荷下的变形机制是当前研究热点。为揭示晶体硅在强动加载下的变形和相变行为特征,基于分子动力学方法,采用平板冲击加载方式,模拟研究了单晶硅在初始环境温度为300 K时分别沿[001]、[110]和[111]晶向的不同强度下的冲击压缩行为,冲击粒子速度为0.3～3.2 km/s。研究发现,随着冲击粒子速度的增加,单晶硅剪切应力在逐渐增加后由于结构相变发生急剧下降,相变阈值和相变机制均呈现各向异性。其中,沿[001]晶向冲击压缩下观察到多种固-固相变以及固-液相变,并观察到与最新文献的实验高度一致的固-液共存现象。研究结果可为动加载下晶体硅的相变研究提供纳米尺度的结果支撑。     

纳米晶钽在单向拉伸载荷下的分子动力学模拟

利用分子动力学方法模拟了纳米晶钽在单轴拉伸载荷作用下的微观结构演化情况. 结果表明纳米晶钽在塑性变形过程中可以发生从BCC到FCC, HCP结构的应力诱导相变. FCC 结构原子百分比的最大值和试样的抗拉强度成线性关系,据此可推出一个相变发生的临界应 力值. 应变率越大,相变滞后于应力越严重. 当应变达到一定值时,试样会发生晶间断裂现 象,定量分析发现纳米晶钽晶间裂纹初始形成应变不受平均晶粒尺寸的影响,而与应变率和 模拟温度有着密切的关系.     

应力引起的镍钛单晶形状记忆合金相变的实验研究

在单晶形状记忆合金试样中,由于没有晶粒之间的约束,它的马氏体相界面移动比多晶容易,用实验方法研究其相变的特点,对建立新的理论模型有意义,因而对它的实验分析显得重要。本文利用高分辨率的CCD系统监测到NiTi单晶形状记忆合金在拉伸时的相变伪弹性的过程;利用X射线衍射法得到了NiTi单晶试样在拉伸方向的晶向;运用高分辨率的云纹干涉技术,获得了应力引起的NiTi单晶形状记忆合金相变时的变形场;利用高分辨率、高灵敏度的红外相机记录了NiTi单晶在拉伸状态下的温度变化规律;对低温下NiTi单晶的拉伸性能做了初步的研究,得到一些有意义的现象。     

伪弹性TiNi合金圆薄板的准静态力学行为实验研究

采用阴影云纹和应变片方法对伪弹性TiNi合金圆板在固支条件下的准静态力学行为进行了实验研究,得到了载荷位移曲线、全场离面位移和局部应变等数据.载荷位移曲线呈现非线性、滞回耗能和无残余变形的特性,表明试样已经发生马氏体相变.应变测量显示,相变局限于加载中心较小区域,相变区内,环向应变大于径向应变,且拉伸侧应变大于压缩侧的应变.有限元模拟揭示出相变区内两侧表层的相变范围、相变铰区和马氏体相含量的不对称分布规律.     

Mechanical analysis of phase transition experiments of the bacterial flagellar filament

Bacterial flagellar filaments can undergo a polymorphic phase transition in both vitro and vivo environments. Each bacterial flagellar filament has 12 different helical forms which are macroscopically represented by different pitch lengths and helix radii. For external mechanical force induced filament phase transitions, there is so far only one experiment performed by Hotani in 1982, who showed a very beautiful cyclic phase transition phenomenon in his experiment on isolated flagellar filaments. In the present paper, we give a detailed mechanical analysis on Hotani＇s experiments. Through theoretical computations, we obtained a phase transition rule based on the phase transition mechanism. The theoretical analysis provides a foundation facilitating the establishment of phase transition theory for bacterial flagellar filaments.     

MECHANICAL MODELING OF THE BISTABLE BACTERIAL FLAGELLAR FILAMENT

We extend the 2D Landau phase transition theory to the bacterial flagellar filament which displays the phase transition between the left handed normal form and the right handed semi-coiled form. The bacterial flagellar filament is treated as an elastic thin rod based on the Kirchhoff’s thin rod theory. Mechanical analysis is performed on the periodical phase transition of the filament between the two helical structures of the opposite charity. The curvature and twist are chosen as the order parameters in constructing the phase transition model of the filament. The established model is applied to study the instability properties of the filament and to investigate the loading and deformation conditions of the phase transition. In addition, the curvature and twist gradient energy are considered to describe the interface properties of the two phases.     

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.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.     

Implementation and validation of a slender vortex filament code: Its application to the study of a four‐vortex wake model

A computational code EZ‐vortex is developed for the motion of slender vortex filaments of closed or open shape. The integro‐differential equations governing the motion of the vortex centre lines are either the Callegari and Ting equations, which are the leading order solution of a matched asymptotic analysis, or equivalent forms of these equations. They include large axial velocity and nonsimilar profiles in the vortical cores. The fluid may be viscous or inviscid. This code is validated both against known solutions of these equations and results from linear stability analyses. The linear and non‐linear stages of a perturbed two‐vortex wake and of a four‐vortex wake model are then computed. Copyright © 2004 John Wiley & Sons, Ltd.     

IMPLEMENTATION OF VORTEX FILAMENT METHODS ON PARALLEL MACHINES WITH DISTRIBUTED ADAPTIVE DATA STRUCTURE

This paper addressed the implementation of vortex filament methods on parallel machines with distributed memory to simulate a three-dimensionally evolving jet. Vortical structure developments due to Kelvin–Helmholtz instability of the axially perturbed jet are also examined. The implementation is conducted in a single-programme multiple-data (SPMD) environment and the parallelism is focused on issues of data distribution, efficient support of parallel I/O and overlapping of communications with computations. In addition, since the number of segment markers in a filament is dynamically growing according to the requirement of numerical accuracy, a novel packet-oriented data structure is proposed not only to partition filament segment markers among distributed processors but also to support dynamical load balancing at run time. This work is the first to apply packet-oriented structures to implement a parallel vortex filament method. Experimental results indicate performance improvement from 1·5 to 2·6 times over static schemes on nCUBE2, DEC Alpha and IBM SP2 by incorporating the proposed scheme with packet-oriented structures. © 1997 by John Wiley & Sons, Ltd. Int. j. numer. methods fluids 24: 939–951, 1997.     

模态理论的进展

传统模态理论的基本思想,近年来得到进一步发展和完善,并被引伸到非线性结构振动分析、应力应变振动分析等领域中,发展迅速．本文在总结近年来国内外文献的基础上,根据笔者自己的研究,较系统地介绍了线性位移实模态、复模态分析,广义模态分析,非线性结构系统模态分析,应力应变场模态分析等方面的研究情况．      

A MODIFIED TORSION PENDULUM FOR MEASURING THE SHEAR MODULUS OF A SINGLE MICRO-SIZED FILAMENT

A modified torsion pendulum apparatus is developed for measuring the shear modu- lus of single filaments with uniform micro-sized diameter. A single filament fixed at both ends and with a ring-shaped mass attached at the middle is used as a clamped-clamped torsion pendulum. The shear modulus of single filaments can be expressed as a function of the oscillation frequency of the torsion pendulum. The oscillation motion is measured with a CCD laser displacement sensor, and its frequency is determined by the Fast Fourier Transform （FFT） method. The shear moduli of three types of filaments： copper wires, tungsten wires and carbon fibers are accurately measured with this technique. It is found that the size effect in shear moduli of both copper wires and tungsten wires is minor. Finally, the error analysis of our measurement technique is presented in detail.     

Averaging Theory of Arbitrary Order for Piecewise Smooth Differential Systems and Its Application

The averaging theory for studying periodic orbits of smooth differential systems has a long history. Whereas the averaging theory for piecewise smooth differential systems appeared only in recent years, where the unperturbed systems are smooth. When the unperturbed systems are only piecewise smooth, there is not an existing averaging theory to study existence of periodic orbits of their perturbed systems. Here we establish such a theory for one dimensional perturbed piecewise smooth periodic differential equations. Then we show how to transform planar perturbed piecewise smooth differential systems to one dimensional piecewise smooth periodic differential equations when the unperturbed planar piecewise smooth differential systems have a family of periodic orbits. Finally as application of our theory we study limit cycle bifurcation of planar piecewise differential systems which are perturbation of a \(\Sigma \)-center.     

非线性随机动力学与控制的哈密顿理论框架

 近几年来，笔者提出与发展了随机激励的耗散的哈密顿系统理 论，包括精确平稳解、等效非线性系统法、拟哈密顿系统随机平均法、 拟哈密顿系统的随机稳定性与随机分岔、首次穿越损坏分析方法及非 线性随机最优控制策略，从而构成了一个非线性随机动力学与控制的 哈密顿理论框架.本文简要介绍这一理论框架.