结合面静摩擦系数的统计模型

基于粗糙表面形貌的统计参数,综合考虑微凸体的完全弹性、弹-塑性和完全塑性三种变形机制,建立了结合面静摩擦系数的统计模型。该模型反映了静摩擦系数是由接触材料性能参数、表面形貌统计参数以及法向载荷共同决定的。通过仿真研究了微凸体高度的随机分布、塑性指数以及法向载荷等因素对静摩擦系数的影响规律。结果表明,修正的指数分布相比简单的指数分布对高斯分布有着较好的近似,且预测值近似等于高斯分布预测结果的均值;静摩擦系数随着塑性指数的增大而减小且变化趋缓;法向载荷增大时,静摩擦系数呈现减小的趋势,但在双对数坐标系下最大静摩擦力仍与法向载荷呈线性正比的关系。     

结合面静态接触参数的统计模型研究

基于对粗糙表面形貌统计分析的基础上,综合考虑微凸体的完全弹性、弹-塑性和完全塑性三种变形机制,建立了结合面的接触面积、接触载荷及接触刚度的统计模型。该模型揭示了结合面接触参数与材料性能参数及粗糙表面形貌参数之间复杂的非线性关系。在不同的微凸体高度随机分布及塑性指数条件下,对接触参数进行预估和对比研究。结果表明,修正的指数分布对高斯分布有着较好的近似,而简单的指数分布与高斯分布之间的误差较大,且相差1至3个数量级;接触表面间距减小时,接触参数值均呈现增大的趋势;塑性指数增大时,接触载荷和接触刚度都随之增大,而接触面积的变化较小。     

Constitutive equation of a non-simple elastic plastic material

Summary The mechanical response predicted by the constitutive equation of a non-simple elastic material is considered in relation to the total strain behaviour of an elastic-plastic solid extensively deformed in the range of plastic strain. Both loading and unloading are considered in relation to the range of total elastic-plastic strain. In the absence of appropriate experimental studies, comparison of the predictions of the proposed constitutive equation of a non-simple elastic material, when applied to the work-hardening behaviour of the material, has been restricted to a study of the characteristic stress-strain behaviour of a strain hardening material. This has centred on the correlation of stress-strain curves characteristic of the mechanical response of a material tested in simple compression, simple torsion and pure shear with the object of obtaining a universal stress-strain curve.With 1 Figure     

Elastic-plastic analysis of cracked plates in plane stress: An experimental study

Summary An experimental method is presented for the complete solution of the elastic-plastic plane stress problem of an edge-cracked plate obeying the Mises yield criterion and the Prandtl-Reuss incremental stress-strain flow rule. The material of the plate is assumed as a strain-hardened one with different degrees of hardening. The elastic and plastic components of strain were determined by using the method of birefringent coatings cemented on the surface of the metallic specimens made of the material under study. Normal incidence of circularly polarized light yielded the isolinics and isochromatics of the coating which provided the principal elastic strain differences and strain-directions at the interface. Evaluation of the stress intensity factor at the crack tip, by using the Griffith-Irwin definition, gave the sum of principal stresses at the crack tip. These data were sufficient to separate the components of strain at the coating-plate interface by using the classical shear-difference method.The stress components on the partially plastically deformed cracked plate were determined by using the Prandtl-Reuss stress-strain relationships in a step-by-step process following the whole history of loading of the plate. Thus, a radial distribution law for the equivalent stress and strain in all directions of the plate was established which gave the instantaneous position of the elastic-plastic boundary and its evolution during loading, as well as the distribution of elastic and plastic components of stresses allover the plate.Four cases were solved for various amounts of strain-hardening from a quasi perfectly plastic material to an almost brittle strain hardened one. The values of the characteristic parameters defining each type of material were established.The results derived compare excellently with existing ones based either on experimental or numerical solutions and since they are based on both the theory of elasticity and the incremental theory of plasticity they constitute a sound basis for comparison. Moreover, the algorithm based on this hybrid method is fast and stable requiring a minimum computer time, memory and data preparation.     

切向荷载下弹塑性材料的微观位移特性

Fujimoto(2000)研究了受切向荷载作用的微凸体在完全弹性接触或完全塑性接触条件下的微观位移特性。而实际大多数微凸体在法向荷载作用下,因材料的弹塑性性质导致其接触是很难达到完全弹性接触或完全塑性状态的。因此,如何解决切向荷载作用下处于弹塑性接触状态的微凸体的微观位移特性就显得非常重要。作者以Fujimoto模型为基础,结合Cattaneo和Mindlin理论,研究了切向荷载作用下处于弹塑性接触状态微凸体的摩擦力-微观位移关系,并给出了一个计算实例,显示该文理论模型的合理性。     

Elastic-Plastic Analysis Under Proportional and Non-Proportional Loading Paths Using Deformation Plasticity Theory

Abstract

An estimation of elastic-plastic stresses and strains is presented for mechanical components, using pseudo elastic analysis based on the deformation theory of plasticity. Analysis of two applications, one under proportional loading and other under non-proportional loading paths using pseudo elastic finite element method, is presented. A rectangular plate with a hole under tension loading and a rectangular plate fixed at one end under bending-tension non-proportional loading are considered for analysis. Pseudo Elastic finite element analysis for proportional loading uses elastic solutions and varies material properties for elements in plastic zone to estimate elastic-plastic solution. A finite element code is developed based on pseudo elastic analysis method. An attempt is made to extend pseudo elastic analysis to analyze bending-tension non-proportional loading problem. Both applications in consideration are assumed to be of Von Mises material and follow isotropic hardening rule with elastic-linear hardening material model. Non-linear analysis of the plate with a hole under proportional tensile loading and that of rectangular plate under bending-tension non-proportional loading are performed in ANSYS and results are compared for validation and are observed to be in good agreement with present analysis.     

Investigation into cylinder-on-flat adhesion elastic–plastic micro-contact under repeated loading and unloading condition

The evolution of microcontact induced deformation and stress states under repeated loading and unloading condition is of great interest for the scientific understanding as well as from the engineering design considerations of microelectromechanical systems (MEMS) based switches and similar other devices since they operate under cyclic condition. This study, therefore, investigated the microcontact interaction between deformable smooth cylindrical segment and deformable smooth flat using the finite element analysis. Elastic and elastic–plastic material behaviors and adhesion interaction are considered. The detailed information about contact area, displacement and stress state in the contact region under cycling condition are presented. Contact area varies nonlinearly even when the applied load is varying linearly in a cycle. Additionally, contact areas during loading and unloading portions of a cycle are not equal at the same load level. The deformation and contact area increases in the presence of adhesion force and also with elastic–plastic material behavior. However, the adhesion force is reduced while the contact area is increased during the microcontact between elastic–plastic bodies in comparison to those between elastic bodies. The maximum increase in stress and deformation states occurs during the first cycle, and then slowly with increasing number of cycles. Further, the maximum stress state is not at the contact surface and also not at instant of the maximum applied external force. Finally, adhesion force during microcontact interaction can be of the same order as the applied external force. Therefore, design and analysis of microcontacts in micromechanical switches and similar other devices should include the effects of adhesion force and cyclic effects. The views expressed in this article are those of the authors and do not reflect the official policy or position of the United State Air Force, Department of Defense, or the U.S. Government.     

Analysis of the apparent friction of polymeric surfaces

The apparent friction coefficient is the ratio between the tangential force and the normal load applied to moving body in contact with the surface of a material. This coefficient includes a so-called “true local friction” at the interface and a “geometrical friction” which is the ploughing effect. The material underneath a moving tip may display various types of behaviour: elastic, elastic–plastic where elastic and plastic strain are present in the contact area, or fully plastic. As is usual in polymers, the material behaviour is time and temperature dependent and may exhibit strain hardening. A surface flow line model of a scratching tip which links the apparent friction to the local friction and contact geometry was recently proposed. An inverse analysis is used in the present work to estimate the local friction from the measured apparent friction and a knowledge of the contact area and tip shape. The polymer true friction coefficient displays temperature and sliding speed dependency, which may be attributed to the surface thermodynamics. It is shown that the local friction depends on the level of strain in the polymer at the contact interface.     

受冲板壳结构的弹塑性力学特性分析

采用基于随动坐标系的 4节点假设应变场壳单元及显式有限元方法分析受冲板壳结构的弹塑性力学特性。材料模型采用弹塑性等向强化模型 ,接触搜寻采用一体化接触搜寻方法 ,接触力由罚参数法计算 ,算例表明 :该方法简明、直观、快捷、方便     

A perturbation method used for static contact and low velocity impact

An approximate method for the solution of static and dynamic contact problems between bodies with non-linear material behaviour is described. The method is a perturbation technique based on the linear elastic quasi-static solution. Here the method is applied to the problem of a sphere in contact with a half-space which means that the Hertz solution is used. The governing equations are rewritten so that the problem for the perturbed variables is one with surface forces in the contact region and volume forces inside the bodies. The latter are due to accelerations and strain gradients calculated from the quasi-static solution and the equation of motion. The contact condition results in an integral equation for the surface forces. Results are compared with FEM calculations, which show very good agreement for the dynamic case, both with linear elastic and non-linear (plastic) material behaviour. For the static case with non-linear material behaviour the results are good approximately up to the point where the inelastic zone reaches the surface of the bodies.     

Criteria for cavitation of rubber particles: Influence of plastic yielding in the matrix

The principles of the cavitation criteria for rubber particles in polymeric matrices are briefly reviewed. Although these criteria are based on a linear elastic analysis, it is shown that it is possible to extend them to take into account the elastic-plastic behaviour of the matrix. In this objective, the representative volume element of a periodic material was meshed and computations were performed using a finite element method. The results reported in this paper focus mainly on cavitation under uniaxial tension and examine the influence on the hydrostatic stress in the rubber particles of different parameters such as the volume fraction of rubber, the plastic behaviour of the matrix or the ratio of the elastic moduli. In all cases, plastic yielding in the matrix leads to saturation of the hydrostatic stress in the rubber phase. It is also shown that the history of cavitation barely influences the progression of plasticity in the matrix.     

Consideration of the mechanical behaviour of small fatigue cracks

The mechanical behaviour of small fatigue cracks is investigated for a low, medium and high strength material. At first an elastic consideration is performed which give a good impression how the stress fields change with crack size. In part 2 a full elastic-plastic analysis of short cracks is performed using a new numerical scheme to simulate the growth of shear bands emanating from the crack tip. The influence of material and loading paramters as well as of the crack size on the plastic crack tip opening displacement is discussed. It is also investigated how it is possible to get a conservative estimate of the crack tip deformation at small cracks.     

Elastic–plastic behaviour in materials loaded with a spherical indenter

Certain ceramic materials display an indentation response similar to that observed for ductile metals when loaded with a spherical indenter. This unusual behaviour, for what are nominally brittle materials, influences the mode of contact damage in applications such as machining, wear, impact damage and hardness testing. The shape of the plastic zone beneath the indenter is typically fully contained within the circle of contact on the specimen surface and thus conventional hardness theories, such as the popular expanding cavity model, provide an inadequate account of indentation response of the material. The present work demonstrates, by experiment, finite element modelling and theoretical considerations, that the indentation response is determined by the interaction between the evolving plastic zone and the mechanical properties of the specimen material, in particular, the ratio of the elastic modulus to the yield stress. This revised version was published online in November 2006 with corrections to the Cover Date.     

轮轨接触表面有液态介质时的接触问题研究

采用接触单元方法,结合初应力法,对于具有表面微观粗糙度和有液态介质存在于轮轨接触表面的弹塑性接触问题进行了研究,获得了轮轨表面接触压力分布、应力分布等结果。结果表明,它们都存在不同程度的峰值,且这些峰值比Hertzian 接触压力大许多,这是由于有表面微观粗糙度的存在,接触过程中凸出的部分进入了接触,而凹下的部分还未进入接触所致。对于法向接触压力,总的来说弹性计算结果的峰值比弹塑性计算结果的峰值要大。而且轮轨接触表面无液态介质存在时的弹塑性计算结果的接触压力峰值比有液态介质存在下的弹塑性计算结果的峰值要大,这是由于接触表面有液态介质存在时,在凹下的部位液态介质不易自由流动和不可压缩特性,引起了液态介质承受了压力所致。     

Cyclic plasticity near a cracklike elliptical flaw

An elastic-plastic analysis of a cracklike elliptical flaw under cyclic tensile loading is discussed. A highly efficient numerical approach combining aspects of the finite element and boundary collocation methods was developed to allow accurate solution detail in the root region of the flaw. Conditions of localized yielding at the flaw root is the focus of the work with applied stress levels small relative to yield stress and plastic zone dimensions comparable to the root radius of curvature. The flaw is considered isolated in an infinite sheet under plane strain constraint. Numerical results are given for the stress and strain distributions and the plastic zone changes during a constant amplitude cyclic loading. These elastic-plastic results are compared with the predictions of elastic and fully plastic analysis and also with sharp crack solutions.     

Shakedown limit of rail surfaces including material hardening and thermal stresses

Sliding friction between railway wheels and rails results in elevated contact temperatures and gives rise to severe thermal stresses at the wheel and rail surfaces. The thermal stresses have to be superimposed on the mechanical contact stresses. Due to the distribution of stresses, the rail surface is generally subjected to higher stresses than the wheel surface. The elastic limit is reduced and yield begins at lower mechanical loads. During the first cycles of plastic deformation, the material hardens and residual stresses build up. The residual stresses provide the structure to shake down to pure elastic behaviour in subsequent load cycles up to a shakedown limit. The kind of hardening observed for rail steel has a considerable influence on the shakedown limit. The shakedown limit is dropped to lower mechanical loads due to the thermal stresses in the rail surface as well. This might cause structural changes in the rail material and rail damage.     

A note on the inertia and strain-rate effects in the tam and calladine model

The dynamic behaviour of a simple plate structure subjected to an axial impact is studied using an elastic-plastic model which takes into account inertia effects and the influence of material strain-rate sensitivity. The entire time-dependent deformation process, including elastic unloading and plastic reloading is obtained. The predictions for the absorbed energy are in reasonable agreement with the corresponding experimental results reported by Tam and Calladine and the detailed behaviour provides some further insight into the dynamic plastic buckling of structural elements.     

基于分形的三维粗糙表面弹塑性接触力学模型与试验验证

基于分形几何理论,利用双变量的Weierstrass-Mandelbrot函数模拟三维分形粗糙表面,建立了三维分形粗糙表面弹塑性接触模型。推导出各等级微凸体发生弹性、弹塑性以及完全塑性变形的存在条件。确定了粗糙表面上各等级微凸体的面积分布密度函数,获得了总接触载荷和真实接触面积之间的关系式。计算结果表明:单个微凸体的临界接触面积与其尺寸相关,随着微凸体等级的增大,微凸体的高度和峰顶曲率半径减小。微凸体的变形顺序为弹性变形、弹塑性变形和完全塑性变形,与经典的赫兹模型保持一致。粗糙表面的力学性能仅与最小等级及后续的6个等级微凸体相关,其余微凸体基本上对整个粗糙表面的力学性能影响很小。最后对粗糙表面的接触力学性能进行了试验测试,验证了该模型的合理性与正确性。     

多孔氧化铝模板的纳米力学性能测试与分析

为了掌握多孔氧化铝模板的纳米力学性能,采用二次氧化法制备孔径在30～40nm之间且高度有序的纳米阵列氧化铝模板,并使用扫描电子显微镜(SEM)对其形貌进行表征;在原位纳米力学测试系统上进行微压痕实验,对样品表面力学性能(纳米硬度、模量)进行测试;利用原子力成像功能对实验区域扫描成像,在纳米尺度下观察和分析样品形貌.结果表明,AAO模板在同一深度处对应的硬度、模量值明显高于相应的基体材料铝,膜基体系的抗载能力明显提高;在压入深度为70～240nm时,AAO膜板的硬度和模量值分别为5.8GPa和106GPa,但从深度250nm时开始出现减小趋势;单晶铝与压针的接触为理想刚塑性接触,AAO模板与压针的接触为弹塑性接触.