一种考虑静水压力和偏应力共同作用的相变临界准则

同时考虑静水压力和偏应力的影响,分别建立了“应力诱发”和“形变诱发”相变的临界准则．准则在主应力空间中给出的相变临界曲面呈现明显的拉压不对称性．在弹性阶段,偏应力对相变总是起促进作用．塑性屈服后,偏应力通过塑性功产生的温升影响相变临界面,从而对高温相到低温相转变起阻碍作用,反之起促进作用．静水压力对相变可能起促进作用,也可能起阻碍作用,取决于相变时材料的体积是膨胀还是收缩．建立的相变临界准则对准静态加载条件下的Fe-20％Ni-0．5％合金和Fe-30％Ni合金和一维应变冲击条件下的Fe-32％Ni-0．035％。C合金中的γ-α相变进行了拟合和预测,预测与实验结果有较好的吻合。在主应力空间中柱形屈服面可能与锥形相变临界面相交,从而在一定条件下将发生“形变诱发”相变和“应力诱发”相变间的转变,这一推论有待实验的验证。     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

纳米单晶NiTi合金单程形状记忆效应的分子动力学模拟

采用基于第二近邻修正型嵌入原子势的分子动力学方法研究了纳米单晶NiTi合金的单程形状记忆效应,详细阐明了温度诱发马氏体相变和应力诱发马氏体重定向过程中纳米单晶的变形行为和微结构演化,进一步分析了加/卸载速率对NiTi合金单程形状记忆效应的影响。结果表明,NiTi纳米单晶在应力加载过程中发生马氏体重定向,卸载后存在残余应变;当加热到奥氏体转变结束温度以上时,马氏体逆相变为奥氏体相,残余应变逐渐减小,但未完全回复;随着应力加载速率的增加,重定向临界应力和模量逐渐增加;再次降温过程中不同加载速率下的原子结构演化各不相同。     

NiTi形状记忆合金动态压缩力学行为的实验研究

采用材料试验机和SHPB实验技术,对在不同初始温度(298～873K)和应变率(5×10-4、～2.3×103s-1)下的NiTi形状记忆合金的压缩力学行为进行了实验研究。结果表明:马氏体状态下的NiTi合金的力学行为对应变率的变化敏感,位错屈服段的硬化模量、相屈服段的硬化模量及马氏体重取向前的弹性模量对应变率的变化不敏感,而位错塑性变形前的弹性模量随应变率的提高迅速增大;奥氏体状态下的NiTi合金随着实验温度升高,无论是应力诱发马氏体相变应力还是奥氏体相屈服应力都逐渐下降,材料表现出温度软化效应。从超弹性温度范围内的卸载曲线中观察到了应力诱发马氏体到奥氏体的逆转变。     

相变复合波在伪弹性TiNi合金薄壁管中的传播

相变可以改变材料的性质,从而严重影响波在介质中传播的结构。采用考虑静水压力和偏应力联合作用的增量型相变本构模型,研究了在拉(压)-扭联合作用下半无限长TiNi合金薄壁管内相变复合波的传播规律。基于广义特征理论分析了相变复合波的特征波速及简单波解的基本性质。利用数值方法研究了两种典型情况下管内相变耦合波传播的规律,管内传播的应力路径和波的结构与初始状态及加载幅值有关,展现出和普通弹塑性材料截然不同的性质。     

NiTi形状记忆合金裂纹尖端热力耦合行为研究

本文对NiTi形状记忆合金I型裂纹尖端热力耦合行为进行了数值仿真分析和实验验证。建立了包含相变和热力耦合的本构模型,通过有限元计算得到了裂纹尖端附近的纵向应变、马氏体体积分数和温度场分布,依据马氏体相变情况对裂纹尖端有效应力强度因子进行了修正,揭示了加载速率对形状记忆合金裂纹尖端有效应力强度影子的影响规律。参数研究表明,随着加载频率的增加,裂纹尖端附近温度逐渐升高,马氏体相变区域逐渐缩小,有效应力强度因子呈下降趋势,形状记忆合金表现出增韧效应,有助于减缓裂纹扩展。本研究结果对于揭示热力耦合作用下超弹性形状记忆合金疲劳裂纹扩展规律具有重要参考意义。     

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。     

形状记忆合金伪弹性行为模拟

基于对伪弹性形状记忆合金(SMA)典型应力-应变曲线的特征分析,在原Graesser本构模型中增加简洁多项式来描述SMA应力诱发马氏体相变完成后在变形马氏体相下继续加载阶段的变形特征;并引入应变幅值与混相下SMA弹性模量的关系来改进不同应变幅值下卸载时SMA的应力-应变关系,从而提出了一种新的SMA一维本构关系模拟其伪弹性力学行为。该模型对直径为0.5mm的NiTi合金丝的拉伸加载、卸载试验曲线的模拟结果表明:改进本构模型与原Graesser模型相比,其能够准确地模拟SMA在不同应变幅值下加载和卸载应力-应变关系。此外,通过研究SMA本构模型的物理关系,推导出了控制SMA滞回曲线特征的关键参数fT与相变临界应力、弹性常数之间的明确关系,可利用该关系直接确定参数fT,摆脱了只靠试算获取该参数的传统做法,其准确性得到了试验验证。     

具有层状微观结构的NiTi单晶本构模型

建立了应力诱发的具有层状微观结构的NiTi单晶本构模型. 模型考虑母相和马氏体相弹性各向异性性质的差异, 以NiTi单晶相变过程中可能出现的24个马氏体变体为基础, 利用相变驱动力和理想界面的连续条件推导了马氏体相变的发生及发展过程, 以及单晶相变过程中宏微观应力应变的演化, 数值模拟了在不同加载方向材料的应力应变响应.结果表明, 对于不同的加载方向, NiTi单晶既存在强化也存在软化现象.      

NiTi合金力学和阻尼性质研究及伪弹性退化分析

试验考察了NiTi合金在不同应变幅值循环载荷作用下的力学特性和阻尼性能,并引入了残余内应力分析伪弹性退化机理。用马氏体相变开始应力、残余应变等参数表征NiTi合金伪弹性特征,用等效阻尼比表征NiTi合金的阻尼性能。试验结果分析表明:应变幅值增加会加快NiTi合金伪弹性随循环次数的退化;当应变幅值处于马氏体相变开始和结束应变之间时,不同应变幅值下NiTi合金的马氏体相变平台随循环次数增加同步降低,且当NiTi合金在相变中段卸载时其阻尼性能最好;结合残余内应力与残余应变正相关线性关系可分析NiTi合金伪弹性退化内在机理。该研究可为循环载荷下NiTi合金伪弹性行为的准确描述提供依据,并可为NiTi合金阻尼器的设计提供参考。     

铈γ→α相变的室温动态特性

通过试样组件尺寸匹配设计的被动围压SHPB实验,获得了99.8%纯铈在1.7GPa静水压内的、包含γ?α相变和逆相变过渡区的室温动态静水压-体应变连续曲线。研究显示:室温铈γ→α相变是具有明显滞后现象的一级相变,而非以往研究认为的体积跃变的一级相变;相变过渡区的静水压范围是0.8~1.3GPa。逆相变过渡区的静水压范围是0.6~1.1GPa;逆相变过渡区的静水压-体应变曲线滞后于相变过渡区的静水压-体应变曲线0.15GPa静水压;在相变和逆相变过渡区内,静水压-体应变曲线按照约4.2GPa体积模量的线性关系演化;演化机制为γ和α两相均匀混合、静水压驱动两相组份转化。基于该演化机制,构建了描述相变前后和相变过程的静水压-体应变响应的三段线性模型。     

Equations of heterophase equilibrium of a biomembrane

Summary Phase transitions in a shell are considered within the frame example work of a biomembrane of a general shape divided into parts containing different phases. The configuration of a boundary separating these phases is determined by the condition of minimum of the total membrane free energy with respect to its position. Equations of equilibrium for both the membrane phases and the phase boundary are deduced. They allow to describe the heterophase state of the biomembrane. Received 11 December 1997; accepted for publication 31 July 1998     

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.     

Equilibrium Configurations of an Inflated Cylindrical Membrane

We study the inflation of a cylindrical elastic membrane under conditions where more than one equilibrium radius is possible at the same pressure. In particular, we investigate the existence of solutions connecting two sections of different radii. The existence of such solutions is found to be linked to a Maxwell equal area rule.     

Numerical study of dynamic phase transitions in shock tube

Shock tube problem of a van der Waals fluid with a relaxation model was investigated.In the limit of relaxation parameter tending towards zero,this model yields a specific Riemann solver.Relaxing and relaxed schemes were derived.For an inci- dent shock in a fixed tube,numerical simulations show convergence toward the Riemann solution in one space dimension.Impact of parameters was studied theoretically and nu- merically.For certain initial shock profiles,nonclassical reflecting wave was observed.In two space dimensions,the effect of curved wave fronts was studied,and some interesting wave patterns were exposed.     

Evolution of a long-wave train in loss of stability of a phase interface in geothermal systems

The transition to instability of phase interfaces in geothermal systems when a water stratum overlies a steam stratum and the most unstable mode corresponds to zero wavenumber is considered. The nonlinear Kolmogorov-Petrovskii-Piskunov equation describing the evolution of a narrow strip of weakly unstable modes is obtained. This equation is an analog of the well-known Ginzburg-Landau equation corresponding to the case of destabilization of modes with finite wavenumbers. It is shown that in the neighborhood of the critical points there exist two locations of the plane phase interface which coincide at the instant at which the instability threshold is reached and then disappear.     

Constitutive Relations for a Viscoelastic Body under Crystallization Conditions

The problem of describing the thermomechanical behavior of viscoelastic polymer materials under conditions of their post-production cooling accompanied by crystallization is considered. A variant for constructing phenomenological constitutive relations, which continuously reflect the relation between the stress and strain tensors in a wide range of temperature variation, is suggested. The relations are based on representation of the medium in the form of a composition of a melted material and a completely crystallized material with allowance for the history of permanent incipience and deformation of the new phase in the interval of phase-transformation temperatures. To determine the material functions and constants, experiments are planned on specimens at temperatures corresponding to particular phase states. Results of experiments and numerical analysis of the fields of displacements generated by solidification of a circular polyethylene plate are given.__________Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 4, pp. 78–87, July–August, 2005.     

马氏体相变过程中形核、失稳及多界面微结构的动力学模拟

材料发生相变的过程中会出现失稳、滞后回线及多界面的微结构等复杂现象，而稳定性的丧失使其动力学方程的求解十分困难。对于形状记忆合金中的马氏体相变，相变过程中材料的等效杨氏模量变为负值，使得传统的动力学方程成为病态的，无法直接求解，必须要进行正则化。而相变的滞后回线与微结构的出现也说明经典的弹性理论不再适用，必须要引入新的能量项以能刻画这些现象。本文在非线性弹性理论的框架下，引入应变梯度界面能和位移非均匀能，利用变分原理建立了材料相变的一维动力学模型。高阶项的引入极大地改善了方程的性质，使数值求解成为可能。计算结果表明，该模型确能较有效地描述相变时的失稳与微结构。     

复正交矩阵区对角化条件及其对相变问题的应用

本文给出(2n×2n)复正交矩阵正交相似于(2×2)正交矩阵直接和的充分必要条件,作为实际例子,并讨论它对二维Ising模型相变问题的应用。     

Moving inelastic discontinuities and applications to martensitic phase transition

Summary In this work, equations of the kinetics and kinematics are developed for heterogeneous materials containing inelastic discontinuities with moving boundaries. From the derived free energy and the power of external forces one obtains the driving force acting on the moving boundary. Introducing the interface operators and some hypothesis on inelastic fields, one gets the driving force for the formation of an ellipsoidal domain. The theoretical model is illustrated by the derivation of nucleation and growth conditions of a martensitic plate inside an inhomogeneous plastic strain field. The obtained results are combined with a study of the kinetics and kinematics to derive the constitutive equation of an austenitic single crystal, from which the overall behavior of polycrystalline TRIP steels is deduced using the self-consistent scale-transition method. Comparison with experimental data shows a good agreement. Received 7 May 1999; accepted for publication 14 June 1999