Torsional contact of an elastic flat-ended cylinder

Torsion of a flat-ended elastic bar pressed onto an elastically similar half-space and subject to torsion, in the presence of friction, is used as a vehicle to study complete contact subject to in-plane and anti-plane shearing forces. It is shown that, below a critical coefficient of friction, slip starts at the edge and progress inwards as the torsion is increased, whereas above this critical value slip starts a little way in from the edge and progress both inwards and outwards. Care is taken to preserve frictional orthogonality, with slip modelled as a piecewise-linear distribution of edge and screw dislocations. The solutions may be applied to any complete contact edge, as the problem is solved within the context of a Williams eigenexpansion.     

Mechanics of advancing pin-loaded contacts with friction

This paper considers finite friction contact problems involving an elastic pin and an infinite elastic plate with a circular hole. Using a suitable class of Green's functions, the singular integral equations governing a very general class of conforming contact problems are formulated. In particular, remote plate stresses, pin loads, moments and distributed loading of the pin by conservative body forces are considered. Numerical solutions are presented for different partial slip load cases. In monotonic loading, the dependence of the tractions on the coefficient of friction is strongest when the contact is highly conforming. For less conforming contacts, the tractions are insensitive to an increase in the value of the friction coefficient above a certain threshold. The contact size and peak pressure in monotonic loading are only weakly dependent on the pin load distribution, with center loads leading to slightly higher peak pressure and lower peak shear than distributed loads. In contrast to half-plane cylinder fretting contacts, fretting behavior is quite different depending on whether or not the pin is allowed to rotate freely. If pin rotation is disallowed, the fretting tractions resemble half-plane fretting tractions in the weakly conforming regime but the contact resists sliding in the strongly conforming regime. If pin rotation is allowed, the shear traction behavior resembles planar rolling contacts in that one slip zone is dominant and the peak shear occurs at its edge. In this case, the effects of material dissimilarity in the strongly conforming regime are only secondary and the contact never goes into sliding. Fretting tractions in the forward and reversed load states show shape asymmetry, which persists with continued load cycling. Finally, the governing integro-differential equation for full sliding is derived; in the limiting case of no friction, the same equation governs contacts with center loading and uniform body force loading, resulting in identical pressures when their resultants are equal.     

A Dynamic-induced Direct-shear Model for Dynamic Triggering of Frictional Slip on Simulated Granular Gouges

This study presents a dynamic-induced direct-shear model to investigate the dynamic triggering of frictional slip on simulated granular gouges. An incident P-wave is generated as a shear load and a normal stress is constantly applied on the gouge layer. The shear stress accumulates in the incident stage and the frictional slip occurs in the slip stage without the effect of the reflected wave. The experimental results show a non-uniform shear stress distribution along the gouge layer, which may be induced by a shear load induced torque and by normal stress vibration along the layer. The shear stress at the trailing edge strongly affects the frictional slip along the P-wave loading direction, while the rebound stress at the leading edge propagates along the opposite direction. The frictional slip is triggered when the maximum shear stress at the trailing edge reaches a critical value. The normal stress influences the maximum shear stress at the trailing edge, the maximum slip displacement and the slip velocity. The advantages and the limitations of this model are discussed at the end.     

Physics-based modeling for partial slip behavior of spherical contacts

A physics-based modeling approach for partial slip behavior of a spherical contact is proposed. In this approach, elastic and elastic–plastic normal preload and preload-dependent friction coefficient models are integrated into the Cattaneo–Mindlin partial slip solution. Partial slip responses to cyclic tangential loading (fretting loops) obtained by this approach are favorably compared with experiments and finite element results from the literature. In addition to load-deformation curves, tangential stiffness of the contact and energy dissipation per fretting cycle predictions of the models are also provided. Finally, the critical assumptions of elastically similar bodies, smooth contact surface and negligible adhesion, and limitations of this physics-based modeling approach are discussed.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

Sliding frictional contact between a square block and an elastically similar half-plane

The contact pressure distribution beneath a square block sliding along an elastically similar half-plane, in the presence of friction, is found. The considerable effect of the coefficient of friction on the trailing edge pressure distribution, and, in particular, the transition from power order behaviour to local separation and bounded behaviour when the coefficient of friction exceeds 0.392 is examined, and an appropriate asymptotic form developed.     

The evolution of the process zone when a complete contact is subject to cyclically varying loads

A rigid punch pressed against an incompressible half-plane by a constant normal load is subject to both a cyclically varying shearing force, and a synchronously varying underlying bulk tension. The evolution of the slip/stick distribution along the contact interface is found during a loading cycle. An asymptotic approach is subsequently used to determine the order of singularity, and hence spatial distribution of the local stress state. A generalised stress intensity factor is then defined to scale the corresponding asymptotic solution, and hence map out the evolution of the process zone. The analysis shows that there is a smooth transition in the form of the asymptotic solution in moving from an ‘adhered’ contact edge to a ‘slipping’ contact edge, and vice versa. The implications of the results to fretting fatigue are discussed.     

Frictional energy dissipation in contact of nominally flat rough surfaces under harmonically varying loads

If the nominal contact tractions at an interface are everywhere below the Coulomb friction limit throughout a cycle of oscillatory loading, the introduction of surface roughness will generally cause local microslip between the contacting asperities and hence some frictional dissipation. This dissipation is important both as a source of structural damping and as an indicator of potential fretting damage. Here we use a strategy based on the Ciavarella-Jäger superposition and a recent solution of the general problem of the contact of two half spaces under oscillatory loading to derive expressions for the dissipation per cycle which depend only on the normal incremental stiffness of the contact, the external forces and the local coefficient of friction. The results show that the dissipation depends significantly on the relative phase between the oscillations in normal and tangential load—a factor which has been largely ignored in previous investigations. In particular, for given load amplitudes, the dissipation is significantly larger when the loads are out of phase. We also establish that for small amplitudes the dissipation varies with the cube of the load amplitude and is linearly proportional to the second derivative of the elastic compliance function for all contact geometries, including those involving surface roughness. It follows that experimental observations of less than cubic dependence on load amplitude cannot be explained by reference to roughness alone, or by any other geometric effect in the contact of half spaces.     

基于LuGre摩擦模型的接触约束法旋转柔性梁斜碰撞研究

基于接触约束法和LuGre摩擦模型对在重力场作用下作大范围旋转运动的柔性梁系统和斜坡发生含摩擦斜碰撞的动力学问题进行研究. 首先运用刚柔耦合的多体系统动力学理论对大范围运动的柔性梁进行离散化和动力学建模, 在碰撞时采用冲量动量法求出跳跃速度, 其次在法向上引入接触约束求解出碰撞力, 在切向上采用LuGre摩擦模型分两种方式求解摩擦力, 第一种是在滑动时摩擦力由摩擦系数和碰撞力计算得出, 黏滞状态下引入切向约束计算拉格朗日乘子反应实际摩擦力, 根据黏滞/滑动切换判断计算出碰撞过程摩擦力(与Coulomb摩擦模型计算摩擦力一致); 第二种根据LuGre摩擦模型摩擦系数和法向碰撞力计算其摩擦力, 从而在碰撞时无需黏滞/滑动切换, 采用相同的摩擦力计算公式. 通过与Coulomb摩擦模型对比发现, LuGre摩擦模型描述碰撞切向摩擦过程更精确, LuGre摩擦模型黏滞时建立约束方程和碰撞采用统一的摩擦力公式这两种建模方式描述的斜碰撞动力学特性没有区别, 进而说明采用法向接触约束和LuGre摩擦模型具有满足碰撞非嵌入情况、避免黏滞/滑动切换、描述摩擦力相对准确的优势.      

Elastic beam on a rigid frictional foundation under monotonic and cyclic loading

An elastic beam resting on a frictional foundation and loaded by the concentrated force or moment applied at its tip is considered. The evolution of slip zones along the beam is discussed for both monotonie and cyclic loading. It is shown that an infinite number of slip zones develop and their propagation satisfies in some cases a self-similarity property. Transient hysteretic effects under cyclic loading are discussed. The closed form analytical solution is presented for the elastic friction model in the case of monotonie loading.     

Frictional complete contacts between elastically similar bodies subject to normal and shear load

The problem of trapezium shaped punches pressed into a frictional, elastically similar half-plane and subject to sequential normal and shear loading is studied. The initial mix of stick, slip and separation regions is described, together with the steady state response when the shearing force is cycled. Conditions for full stick are established.     

The structure of shock layers in elastic-plastic media: Micro-plastic regime

The Granato-Lücke theory of internal friction is used as the basis of a model of shock-wave formation and propagation in elasto-plastic solids below the general yield point. The structure of shock layers in such a model is shown to be in general asymmetric and, at sufficiently large jumps in strain, to exhibit oscillations in the strain at its trailing edge.     

Micromechanical analysis of friction anisotropy in rough elastic contacts

Computational contact homogenization approach is applied to study friction anisotropy resulting from asperity interaction in elastic contacts. Contact of rough surfaces with anisotropic roughness is considered with asperity contact at the micro scale being governed by the isotropic Coulomb friction model. Application of a micro-to-macro scale transition scheme yields a macroscopic friction model with orientation- and pressure-dependent macroscopic friction coefficient. The macroscopic slip rule is found to exhibit a weak non-associativity in the tangential plane, although the slip rule at the microscale is associated in the tangential plane. Counterintuitive effects are observed for compressible materials, in particular, for auxetic materials.     

Dynamic shearing resistance of molten metal films under high pressures and extremely high shearing rates

In the present study plate-impact pressureshear experiments have been conducted to study the dynamic shearing resistance of molten metal films at shearing rates of approximately 10⁷ s⁻¹. These molten films are generated by pressure-shear impact of relatively low melt-point metals such as 7075-T6 Al alloy with high hardness and high flow-strength tool-steel plates. By employing high impact speeds and relatively smooth impacting surfaces, normal interfacial pressures ranging from 1–3 GPa and slip speeds of over 100 m/s are generated during the pressure-shear loading. The resulting friction stress (∼100 to 400 MPa) combined with the high slip speeds generate conditions conductive to interfacial temperatures approaching the fully melt temperature regime of the lower melt-point metal (7075-T6 aluminum alloy) comprising the tribo-pair. During pressure-shear loading, laser interferometry is employed to measure normal and transverse motion at the rear surface of the target plate. The normal component of the particle velocity provides the interfacial normal traction while the transverse component provides the shearing resistance of the interface as it passes through melt. In order to extract the critical interfacial parameters, such as the interfacial slip-speed and interfacial temperatures, a Lagrangian finiteelement code is developed. The computational procedure accounts for dynamic effects, heat conduction, contact with friction, and full thermo-mechanical coupling. At temperatures below melt the flyer and target materials are described as an isotropic thermally softening elastic-viscoplastic solid. For material elements with temperatures in excess of the melt point, a purely Newtonian fluid constitutive model is employed. The results of this hybrid experimental-computational study provide insights into the dynamic shearing resistance of molten metal films at high pressures and extremely high shearing rates.     

Transition from stick to slip in Hertzian contact with “Griffith” friction: The Cattaneo–Mindlin problem revisited

Classically, the transition from stick to slip is modelled with Amonton–Coulomb law, leading to the Cattaneo–Mindlin problem, which is amenable to quite general solutions using the idea of superposing normal contact pressure distributions – in particular superposing the full sliding component of shear with a corrective distribution in the stick region. However, faults model in geophysics and recent high-speed measurements of the real contact area and the strain fields in dry (nominally flat) rough interfaces at macroscopic but laboratory scale, all suggest that the transition from ‘static’ to ‘dynamic’ friction can be described, rather than by Coulomb law, by classical fracture mechanics singular solutions of shear cracks. Here, we introduce an ‘adhesive’ model for friction in a Hertzian spherical contact, maintaining the Hertzian solution for the normal pressures, but where the inception of slip is given by a Griffith condition. In the slip region, the standard Coulomb law continues to hold. This leads to a very simple solution for the Cattaneo–Mindlin problem, in which the “corrective” solution in the stick area is in fact similar to the mode II equivalent of a JKR singular solution for adhesive contact. The model departs from the standard Cattaneo–Mindlin solution, showing an increased size of the stick zone relative to the contact area, and a sudden transition to slip when the stick region reaches a critical size (the equivalent of the pull-off contact size of the JKR solution). The apparent static friction coefficient before sliding can be much higher than the sliding friction coefficient and, for a given friction fracture “energy”, the process results in size and normal load dependence of the apparent static friction coefficient. Some qualitative agreement with Fineberg's group experiments for friction exists, namely the stick–slip boundary quasi-static prediction may correspond to the arrest of their slip “precursors”, and the rapid collapse to global sliding when the precursors arrest front has reached about half the interface may correspond to the reach of the “critical” size for the stick zone.     

Analytical solutions for inherently incremental,similar elastic contact problems with bulk stress

Analytical solutions are obtained for a class of inherently incremental, similar elastic half-plane frictional contact problems which involve simultaneous application of a changing, remote bulk-stress during oblique loading. The method is based on Abel Integral Equations. The spatial gradient of the slip function is obtained uniquely by the conditions determining the existence of a bounded solution to the shear traction Cauchy SIE and global shear equilibrium, provided there is stick at all points in the contact throughout the loading. Solutions are obtained for both the cylindrical indenter and the flat punch with rounded edges. The method also lends itself easily to generalization to non-linear load paths and a number of such problems are considered. Problems involving the development of slip zones within the contact may be solved in some special cases.     

Hertzian fracture at unloading

Hertzian fracture through indentation of flat float glass specimens by steel balls has been examined experimentally. Initiation of cone cracks has been observed and failure loads together with contact and fracture radii determined at monotonically increasing load but also during unloading phases. Contact of dissimilar elastic solids under decreasing load may cause crack inception triggered by finite interface friction and accordingly the coefficient of friction was determined by two different methods. In order to make relevant predictions of experimental findings, a robust computational procedure has been developed to determine global and local field values in particular at unloading at finite friction. It was found that at continued loading it is possible to specify in advance how the contact domain divides into invariant regions of stick and slip. The maximum tensile stress was found to occur at the free surface just outside the contact contour, the relative distance depending on the different elastic compliance properties and the coefficient of friction. In contrast, at unloading invariance properties are lost and stick/slip regions proved to be severely history dependant and in particular with an opposed frictional shear stress at the contact boundary region. This causes an increase of the maximum tensile stress at the contour under progressive unloading. Predictions of loads to cause crack initiation during full cycles were made based on a critical stress fracture criterion and proved to be favourable as compared to the experimental results.     

有限长滚子黏滑接触分析

有限长线接触在齿轮传动与滚子轴承中广泛存在,滚子端部的应力集中严重影响机械零件的疲劳寿命. 本文中基于矩阵法和重叠半空间模型方法建立了有限长滚子黏滑接触的数值计算模型,利用共轭梯度法和快速傅里叶变换方法对模型进行了求解;并且分析了滚子自由端面和不同切向力对滚子黏滑接触的影响. 结果表明:当两有限长滚子的自由端面完全重合时,切应力在端面不会出现应力集中现象,端面的黏着区域相比于中间截面的黏着区会缩小. 此外,随着切向力的增大,端面黏滑区域的切应力增大.      

与冲蚀有关的粘着与犁沟摩擦系数

提出一种与冲击磨损有关的有效摩擦系数，它被定义为冲击过程中，每一瞬间的切向有效摩擦力与法向载荷之比．有效摩擦力被表示为剪切项与犁沟项之组合．剪切项依赖于剪切金屑接合点的状态——滑移或滚动．犁沟项依赖于冲击物在冲击途中使靶材料发生移动的状态．此有效摩擦系数被应用于研究刚性球自由斜冲击延性靶问题．在忽略剪切项仅计及犁沟项的情况下，研究表明，Hutchings实验中的有效冲击摩擦系数是冲击过程与初始冲击角的函数，就时间平均而言，大于Hutchins为拟合计算与实验结果所取的摩擦系数常值0.05．有迹象表明，对于与固粒延性冲蚀有关的刚性球自由斜冲击延性靶问题，在一定条件下，有效摩擦系数主要由犁沟效应确定．     

位移幅值对铜镁合金微动磨损行为的影响

在研制的多功能微动磨损试验机上,开展了不同位移幅值下铜镁合金微动磨损试验,以研究位移幅值对铜镁合金微动磨损行为的影响. 微动过程中记录摩擦系数曲线与F_t-D-N曲线,利用光学显微镜(OM)、扫描电镜(SEM)、能量色散X射线光谱仪(EDS)及三维形貌仪对损伤区域进行了微观分析. 结果显示:随着位移幅值的增加,铜镁合金微动运行状态由部分滑移进入完全滑移,未发现混合滑移状态;部分滑移区中呈现由弹性变形协调逐渐向塑性变形协调转变的趋势. 磨损体积随位移幅值的增加而增加,在完全滑移区中体积损失非常严重. 在弹性变形协调的部分滑移状态下,接触表面损伤轻微,而由塑性变形协调的部分滑移状态下,接触中心出现较大切应力,疲劳裂纹扩展至接触表面导致材料剥落,接触边缘有磨粒磨损和氧化磨损的痕迹. 在完全滑移状态下,接触表面损伤主要为疲劳剥层,磨粒磨损和氧化磨损.