The normal contact of rough surfaces with fine discretization

Summary The numerical treatment of a 3-d frictionless normal contact of rough bodies made of a linear–elastic, isotropic material is considered. First, the governing equations and their discretized forms are presented. Due to the order of the problem, the computation time rapidly increases with the grid refinement. Therefore, common computer programs have to be limited to 50×50 contact points. Several numerical techniques (multigrid, iterative solver, distributive relaxation) are used. Cell-centered grid transformation is applied and grid operators have been established for this purpose. In order to handle upto 1000 × 1000 cells the program CON3D has been developed.     

45~#碳钢激光相变硬化层磨损特性的研究

本文在相同条件下对激光相变硬化处理、淬火-回火及未经处理的45~#碳钢的磨损特性进行了对比试验研究。结果表明,激光相变硬化处理明显地提高了材料表面的抗粘着和抗擦伤能力,因而可以使其在一定负荷和往复速度下的耐磨性能提高一个数量级。往复速度(频率)、负荷对激光相变硬化层和淬火-回火试样之磨损率的影响不同:淬火-回火试样的磨损率随着负荷的增大而迅速增大,但相变硬化层在负荷低于294N时的磨损率增加十分缓慢,只有当负荷超过294N之后才迅速增大;淬火-回火试样的磨损率是随往复频率的增大而迅速降低,而相变硬化层的磨损率随着往复频率的增大却是先上升而后下降,但其量值的变化较小,当往复频率高于每分钟500次时,二者的磨损率基本相同。     

Molecular-dynamics of a 2D Model of the Shape Memory Effect

This work investigates the thermodynamic properties of a qualitative atomistic model for austenite–martensite transitions. The model, still in 2D, employs Lennard-Jones potentials for the determination of the atomic interactions. By use of two atom species it is possible to identify three stable lattice structures in 2D, interpreted as austenite and two variants of martensite. The model is described in the first part of the work [6] in detail. The present work studies the thermodynamic properties of the model concerning a small, 2-dimensional test assembly consisting of 41 atoms. The phase stability is investigated by exploitation of the condition of minimal free energy. The free energy is calculated from the thermal equation of state, which is measured in numerical tensile tests. In the second part of this work a chain of eleven 41-atom assemblies is investigated. The chain is interpreted as an idealized larger body, where the individual crystallites represent crystallographic layers allowing for the creation of micro structure. By use of tensile tests at various temperature conditions we sketch how such chain may exhibit quasi-plasticity, pseudo-elasticity and the shape memory effect.     

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.     

形状记忆合金作动器的设计及优化

采用Ｂｒｉｓｉｏｎ［１］等提出的ＳＭＡ材料的本构关系，分析了形状记忆合金作动器在三种热交换方式（自然冷却、强制冷却和采用半导体热泵技术）下的动力特性，同时研究了ＳＭＡ丝在恒载和载荷变化时对完成正逆相变所用时间的影响，并简单讨论了影响作动器响应的几个因素和改进方法     

SYMPLECTIC STRUCTURE OF POISSON SYSTEM

When the Poisson matrix of Poisson system is non-constant, classical symplectic methods, such as symplectic Runge-Kutta method, generating function method, cannot preserve the Poisson structure. The non-constant Poisson structure was transformed into the symplectic structure by the nonlinear transform.Arbitrary order symplectic method was applied to the transformed Poisson system. The Euler equation of the free rigid body problem was transformed into the symplectic structure and computed by the midpoint scheme. Numerical results show the effectiveness of the nonlinear transform.     

任意多椭圆孔多裂纹无限大各向异性板应力强度因子求解的一种新方法

采用各向异性体平面弹性理论中的复势方法,应用保角变换技术,以F aber级数为工具,导出含任意多椭圆孔和裂纹群无限大各向异性板在远场载荷作用下其应力场和位移场的级数解,并在此基础上利用断裂力学方法确定裂纹尖端的应力强度因子,通过算例讨论了材料参数及裂纹、孔的尺寸等对应力强度因子的影响规律,得出了一些有益的结论。数值结果表明本文方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响。     

Fluid Flow-Induced Nonlinear Vibration of Suspended Cables

The nonlinear interaction of the first two in-plane modes of a suspended cable with a moving fluid along the plane of the cable is studied. The governing equations of motion for two-mode interaction are derived on the basis of a general continuum model. The interaction causes the modal differential equations of the cable to be non-self-adjoint. As the flow speed increases above a certain critical value, the cable experiences oscillatory motion similar to the flutter of aeroelastic structures. A co-ordinate transformation in terms of the transverse and stretching motions of the cable is introduced to reduce the two nonlinearly coupled differential equations into a linear ordinary differential equation governing the stretching motion, and a strongly nonlinear differential equation for the transverse motion. For small values of the gravity-to-stiffness ratio the dynamics of the cable is examined using a two-time-scale approach. Numerical integration of the modal equations shows that the cable experiences stretching oscillations only when the flow speed exceeds a certain level. Above this level both stretching and transverse motions take place. The influences of system parameters such as gravity-to-stiffness ratio and density ratio on the response characteristics are also reported.     

Internal loops in pseudoelastic behaviour of Ti-Ni shape memory alloys: Experiment and modelling

The stress-strain isothermal hysteresis loops due to the incomplete martensitic transformation are analysed for Ti-Ni shape memory alloys. Experiments show the existence of two distinct yield lines for phase transition; one for the forward transformation austenitemartensite (AM), the other for the reverse transformation MA. The tensile behaviour of single crystals with only one yield line (AM) [1] can be considered as an ideal case. An extension of a thermodynamic model for pseudoelasticity [2] allows these two yield lines to be taken into account.

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Sommario Per leghe Ti-Ni con memoria di forma vengono analizzati i cicli di isteresi isotermici tensione-deformazione prodotti da una incompleta trasformazione martensitica. Gli esperimenti mostrano l'esistenza di due distinte linee di snervamento per la transizione di fase, una verso la trasformazione austenitemartensite (AM), l'altra per la trasformazione inversa MA. Il comportamento a trazione di un singolo cristallo con una sola linea di snervamento (AM) [1], può essere considerato un caso ideale. L'estensione ad un modello termodinamico pseudo-elastico [2] consente di analizzare queste due linee di snervamento.

     

Ⅱ-Ⅲ混合型裂纹相变增韧分析

本文采用压力敏感准则和松函数法对相变增韧陶瓷Ⅱ-Ⅲ混合型裂纹的增韧效应进行了理论预测。分别给出了静止裂纹和定常扩展裂纹相变塑性屏蔽的理论表达式。结果表明：相变对静止裂纹有甚微的负屏蔽效应，并随KⅢ/KⅡ的比值而波动；相变对定常扩展裂纹的增韧结果除与材料弹性模量、相变尾区高度和相变体积分数有关外，还与KⅢ/KⅡ的比值有关。