Quadratic programming algorithm for wall slip and free boundary pressure condition

Wall slip is often observed in a highly sheared fluid film in a solid gap. This makes a difficulty in mathematical analysis for the hydrodynamic effect because fluid velocity at the liquid–solid interfaces is not known a priori. If the gap has a convergent–divergent wedge, a free boundary pressure condition, i.e. Reynolds pressure boundary condition, is usually used in the outlet zone in numerical solution. This paper, based on finite element method and parametric quadratic programming technique, gives a numerical solution technique for a coupled boundary non‐linearity of wall slip and free boundary pressure condition. It is found that the numerical error decreases with the number of elements in a negative power law having an index larger than 2. Our method does not need an iterative process and can simultaneously gives rise to fluid film pressure distribution, wall slip velocity and surface shear stress. Wall slip always decreases the hydrodynamic pressure. Large wall slip even causes a null hydrodynamic pressure in a pure sliding solid gap. Copyright © 2005 John Wiley & Sons, Ltd.     

Resistance of rough plates in a rotating fluid

Generalizing Navier’s partial slip condition, the flow due to a rough or striated plate moving in a rotating fluid is studied. It is found that the motion of the plate, the fluid surface velocity, and the shear stress are in general not in the same direction. The solution is extended to the case of finite depth, or Couette slip flow in a rotating system. In this case an optimum depth for minimum drag is found. The solutions are also closed form exact solutions of the Navier–Stokes equations. The results are fundamental to flows with Coriolis effects.     

Interface crack between a compressible elastomer and a rigid substrate with finite slippage

We study the deformation of a crack between a soft elastomer and a rigid substrate with finite interfacial slippage. It is assumed that slippage occurs when the interfacial shear traction exceeds a threshold. This leads to a slip zone ahead of the crack tip where the shear traction is assumed to be equal to the constant threshold. We perform asymptotic analysis and determine closed-form solutions describing the near-tip crack opening displacement and the corresponding stress distributions. These solutions are consistent with numerical results based on finite element analysis. Our results reveal that slippage can significantly affect the deformation and stress fields near the tip of the interface crack. Specifically, depending on the direction of slippage, the crack opening profile may appear more blunted or sharpened than the parabola arising from for the case of zero interfacial shear traction or free slippage. The detailed crack opening profile is determined by the constant shear traction in the slip zone. More importantly, we find that the normal stress perpendicular to the interface can increase or decrease when slippage occurs, depending on the direction of slippage and the shear traction in the slip zone.     

Influence of wall slip on the hydrodynamic behavior of a two-dimensional slider bearing

In the present paper, a multi-linearity method is used to address the nonlinear slip control equation for the hydrodynamic analysis of a two-dimensional (2-D) slip gap flow. Numerical analysis of a finite length slider bearing with wall slip shows that the surface limiting shear stress exerts complicated influences on the hydrodynamic behavior of the gap flow. If the slip occurs at either the stationary surface or the moving surface (especially at the stationary surface), there is a transition point in the initial limiting shear stress for the proportional coefficient to affect the hydrodynamic load support in two opposite ways: it increases the hydrodynamic load support at higher initial limiting shear stresses, but decreases the hydrodynamic load support at lower initial limiting shear stresses. If the slip occurs at the moving surface only, no fluid pressure is generated in the case of null initial limiting shear stress. If the slip occurs at both the surfaces with the same slip property, the hydrodynamic load support goes off after a critical sliding speed is reached. A small initial limiting shear stress and a small proportionality coefficient always give rise to a low friction drag. The project supported by the National Natural Science Foundation of China (10421002, 10332010), the National Basic Research Program of China (2006CB601205), and the Science Research Foundation of Liaoning Province (20052178). The English text was polished by Yunming Chen.     

Ultrasonic characterization of point defects induced by cross slip under pure shear

Longitudinal wave velocity is used to characterize the point defects in crystalline solids. High purity Al single crystal was selected for both the finite element analysis and experimental work. Since the jog motions of dislocations caused by intersected slides such as cross slips induce point defects, the total amount of cross slips was calculated instead of calculating directly from the point defects. The effect of crystal orientations on total amount of cross slips under pure shear was also investigated via the finite element method. The result suggest that if the initial shear stress direction is located at the inner side of stereographic triangle, only single slip activities occurred at the beginning of plastic deformation and no effects due to point defects were present. However, as the shear stress direction rotates along the slip direction, point defects are induced by cross slips between primary and secondary slip systems due to work-hardening. This phenomenon was then examined by measuring longitudinal wave velocity changes propagating in Al single crystal subjected to the combination loads of equi-biaxial tension and compression (a pure shear state). Good qualitative agreement between the finite element result and measured data suggest that the longitudinal wave velocity can be used as an index to characterize point defects in crystalline materials.     

边界膜剪切弹性模量对于微接触性能的影响

建立接触模型,理论分析了微接触中边界膜剪切弹性模量对于接触性能的影响. 接触区由两平行平面形成,属一维接触. 上接触表面为粗糙表面,具有矩形微凸体. 下接触表面为光滑平面. 两接触表面均处理成刚性表面. 微接触区中充满流体. 它分成两个子区,在微接触的出口区由于极小的接触间隙充满边界膜,在微接触的入口区由于接触间隙较大充满流体膜. 边界膜和流体膜行为决定整个微接触性能. 当膜厚较大时,这里边界膜可看成纳米级薄膜. 由于上接触表面处有限的剪应力承受能力,边界膜可于上接触表面滑移. 设下接触表面处剪应力承受能力很大而边界膜在下接触表面不滑移. 由于边界膜-接触表面间相互作用,边界膜黏度、密度和剪切弹性模量均沿膜厚变化,在理论分析中使用它们的等效值,这些值与边界膜厚度有关. 流体膜在两个接触表面均不发生滑移,分析中不考虑流体膜剪切弹性模量. 流体膜采用传统分析法. 给出了理论分析和若干变工况参数下的计算结果.      

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.     

Re-examined principles of thrust generation by a track on soft ground

Dr. Bekker’s first book Theory of land locomotion offers in fact two different concepts of thrust generation on soft ground with respect to the slip: (a) as the push of grousers causing horizontal soil “distortion” and (b) as the shear force in the failure plane linked with the shear deformation. Bekker preferred the second concept and backed it up by the unique shear-ring measuring technique. To clear up the matter, the author decided to re-examine the thrust generation by a track plate experimentally in field conditions. The tests have shown that the initial stage of thrust generation in compressible ground is always horizontal soil compression by grousers, which divides the soil under a track into separate blocks initially at rest. This compression increases at least to the transition point, when a block is sheared off simultaneously at the bottom and in both lateral planes and starts sliding along the channel formed by the preceding grouser. The analysis of these measurements enabled to define the compressive displacement of the face of the soil block (travel of the grouser) appurtenant to the mentioned transition point, useful to define the thrust–slip curve. The case may also be described by the conventional shear stress–shear displacement relationship, imagined to take place in the bottom failure plane, however, namely the “shear displacement” is rather an unusual quantity.     

Soil stress state orientation beneath a tire at various loads and inflation pressures

Stress state transducers (SSTs) were used to determine the orientation of the major principal stress, σ₁, in soil beneath the centeline of an 18.4R38 radial-ply R-1 drive tire operated at 10% slip. Two soils, a sandy loam and a clay loam, were each prepared twice to obtain two density profiles. One profile of each soil had a hardpan and the soil above the hardpan was loose. The soil in the second profile was loosely tilled. The stress state was determined at a depth of 358 mm in the sandy loam and 241 mm in the clay loam soil. The tire was operated at two dynamic loads (13.2 and 25.3 kN), each at two levels of inflation pressure (41 and 124 kPa). When the orientation of σ₁ was determined directly beneath the axle, the mean angles of tilt in the direction of travel ranged from 6 to 23 degrees from vertical. Inflation pressure did not significantly affect the angle when the dynamic load was 13.2 kN in the sandy loam soil, and neither inflation pressure nor dynamic load significantly affected the angle in the clay loam soil. When the dynamic load was 25.3 kN in the sandy loam soil, the orientation of the major principal stress determined directly beneath the axle was tilted significantly more in the direction of travel when the tire was at 41 kPa inflation pressure than when at 124 kPa. These changes in stress orientation demonstrate the importance of measuring the complete stress state in soil, rather than stresses along only one line of action. The changing orientation of σ₁ as the tire passes over the soil indicates the soil undergoes kneading and supports future investigation of the contribution of changes in stress orientation to soil compaction.     

Molecular dynamics simulation of liquid argon flow at platinum surfaces

The micro Poiseuille flow for liquid argon flowing in a nanoscale channel formed by two solid walls was studied in the present paper. The solid wall material was selected as platinum, which has well established interaction potential. We consider the intermolecular force not only among the liquid argon molecules, but also between the liquid argon atoms and the solid wall particles, therefore three regions, i.e. the liquid argon computation domain, the top and bottom solid wall regions are included for the force interaction. The present MD (Molecular Dynamics) simulation was performed without any assumptions at the wall surface. The objective of the study is to find how the flow and the slip boundaries at the wall surface are affected by the applied gravity force, or the shear rate. The MD simulations are performed in a nondimensional unit system, with the periodic boundary conditions applied except in the channel height direction. Once the steady state is reached, the macroscopic parameters are evaluated using the statistical mechanics approach. For all the cases tested numerically in the present paper, slip boundaries occur, and such slip velocity at the stationary wall surface increases with increasing the applied gravity force, or the shear rate. The slip length, which is defined as the distance that the liquid particles shall travel beyond the wall surfaces to reach the same velocity as the wall surface, sharply decreases at small shear rate, then slightly decreases with increasing the applied shear rate. We observe that the liquid viscosity remains nearly constant at small shear rates, and the Newtonian flow occurs. However, with increasing the shear rate, the viscosity increases and the non-Newtonian flow appears.     

压头不同晶向下纳米压痕的多尺度研究

为了研究压头晶体各向异性对纳米压痕的影响,采用多尺度准连续介质(QC)法模拟了不同晶向Ni压头与Ag薄膜的纳米压痕过程。通过对比不同晶向下压头在薄膜上触发的原子滑移,发现压头的晶向引起的界面失配位错在很大程度上决定薄膜开启初始原子滑移系的难易。然后对比了压头在不同晶向下测得的薄膜纳米硬度,发现其计算值是一样的。最后研究压头表面和压痕表面的正应力和切应力的分布,分析了应力分布与原子滑移系的关系。     

Boundary conditions for stokes flows near a porous membrane

A theoretical development is carried out to model the boundary conditions for Stokes flows near a porous membrane, which, in general, allows non-zero slip as well as normal flow at the surface. Two types of models are treated: an infinitesimally thin plate with a periodic array of circular apertures and a series of parallel slits. For Stokes flows, the mean normal flux and slip velocity are proportional to the pressure difference across the membrane and the average shear stress at the membrane, respectively. The appropriate proportionality constants which depend on the membrane geometry are calculated as functions of the porosity. An interesting feature of the results is that the slip at the membrane has, in general, a direction different from that of the applied shear for these models.     

Characterization of yield stress fluids with concentric cylinder viscometers

The methods normally employed for shear rate calculations from concentric cylinder viscometer data generally are not applicable for fluids with a yield stress. In cylindrical systems with large radius ratios, as usually is the case with suspensions, the yield stress induces two possible flow regimes in the annulus. Unless the yield value is exceeded everywhere in the gap only part of the fluid can be sheared while the remaining region behaves like a solid plug. A correct calculation of the shear rate must take into account the presence of a variable effective gap width determined by the extent of the sheared layer. For time-independent yield stress fluids, a two-step procedure, which does not require any specific flow model, is proposed for analysing the experimental torque-speed data. Under the partially sheared condition, the shear rate can be computed exactly, whereas for the fully sheared flow the Krieger and Elrod approximation is satisfactory. The method is assessed by examining both semi-ideal data generated with a Casson fluid with known properties, and experimental data with an industrial suspension. A more complicated problem associated with characterization of time-dependent yield stress fluids is also identified and discussed. An approximate procedure is used to illustrate the dependence of the shear rate on time of shear in constant-speed experiments.     

Thrust and slip of a low-pressure tire on compressible ground by the compression-sliding approach

Driving wheels with low-pressure lugged tires are standard propulsion components of wheeled off-road vehicles. Such wheels have been mostly treated in theory as shorter tracks or even as “black boxes”. These procedures, however, appear not to be necessary since an updated theory of thrust generation, based on experiments with double-plate meter, was presented at the 2008 ISTVS Turin conference. This theory is based on the compaction-sliding (CS) concept, which claims that the rearward displacement of soil, a reason for slip, starts as horizontal soil compression by lugs (C-stage at lower thrust), followed by the slide of sheared off soil blocks (S-stage at higher thrust). The thrust in terms of ISTVS Standards equals gross tractive effort minus internal rolling resistance of a tire. The resultant thrust of a tire equals the sum of component thrusts of individual soil segments. The respective technique provides thrust-slip curves, which reflect tire size, loading, inflation pressure and tread pattern design, e.g. tread density, lug angle, pitch, height and tire casing lay-out and thus can be useful notably in assessing the traction properties of new tire designs. Concerning the evaluation of tire traction tests or similar applications, the CS approach offers a simplified version of thrust-slip formula (G-function), which complies with the CS concept and is easy to use.     

Theoretical latent hardening in crystals—II. BCC crystals in tension and compression

The general latent hardening law of single slip derived in the first paper of this series (Havner, Baker and Vause, 1979) is applied to an analysis of “overshooting” phenomena in bcc crystals in tension and compression. This new law, which predicts anisotropic hardening of latent slip systems, is based upon the simple theory of finite distortional crystal hardening introduced by Havner and Shalaby (1977).Because of historical ambiguities regarding identification of the slip plane in bcc metals, parallel analyses are presented corresponding to two separate criteria: (i) slip on {110}, {112} and {123} crystallographic planes only; and (ii) slip on the plane of maximum resolved shear stress containing a 〈111〉 direction. It is established that the new hardening law is a theory of “overshooting” in bcc crystals according to either identification of the slip plane.A qualitative comparison between theoretical results and two experimental papers on Fe crystals is included. The general difficulties in making comparisons with the experimental literature on finite distortional latent hardening are briefly discussed.     

Finite element modeling of interfacial forces and contact stresses of pneumatic tire on fresh snow for combined longitudinal and lateral slips

Significant challenges exist in the prediction of interaction forces generated from the interface between pneumatic tires and snow-covered terrains due to the highly non-linear nature of the properties of flexible tires, deformable snow cover and the contact mechanics at the interface of tire and snow. Operational conditions of tire-snow interaction are affected by many factors, especially interfacial slips, including longitudinal slip during braking or driving, lateral slip (slip angle) due to turning, and combined slip (longitudinal and lateral slips) due to brake-and-turn and drive-and-turn maneuvers, normal load applied on the wheel, friction coefficient at the interface and snow depth. This paper presents comprehensive three-dimensional finite element simulations of tire-snow interaction for low-strength snow under the full-range of controlled longitudinal and lateral slips for three vertical loads to gain significant mechanistic insight. The pneumatic tire was modeled using elastic, viscoelastic and hyperelastic material models; the snow was modeled using the modified Drucker-Prager Cap material model (MDPC). The traction, motion resistance, drawbar pull, tire sinkage, tire deflection, snow density, contact pressure and contact shear stresses were obtained as a function of longitudinal slip and lateral slip. Wheel states - braked, towed, driven, self-propelled, and driving - have been identified and serve as key classifiers of discernable patterns in tire-snow interaction such as zones of contact shear stresses. The predicted results can be applied to analytical deterministic and stochastic modeling of tire-snow interaction.     

Macro slip theory of plasticity for polycrystalline solids

A macro slip theory is presented in this paper. Four independent slip systems are proposed for polycrystalline solids. Each slip system consists of a slip plane which lies on a face of the octahedron in stress space and a slip direction which is coincident with shear stress acting on the same face of the octahedron. It is proved that for proportional loading, present results are identical with the classical flow theory of plasticity. For nonproportional loading, the macro slip theory shows good predicting ability. The calculated results are in good agreement with the experimental data. The project supported by Chinese Academy of Science     

剪切水-气界面下湍流猝发特征的实验研究

利用氢气泡时间线-脉线组合示踪技术定量地考察剪切水-气界面下的湍流猝发现象,分析 猝发事件的信号特征,重点探讨猝发与湍能产生之间的联系. 在猝发过程中,水面近区的瞬 时流速和Reynolds切应力出现较大幅度的脉动,它们在时间和空间垂直方向上表现出高度 的相干性,这是猝发事件的一个显著特征. 在猝发期,猝发事件涉及的空间区域内Reynolds 切应力和湍流脉动强度明显比平均值和非猝发期的情况大. 其结果表明：在所考察的实验 条件下,猝发是剪切水-气界面附近湍流产生的主要过程.     

Emission of dislocations from nanovoids under combined loading

Among all directions available for dislocation emission from the surface of a cylindrical circular void, the direction of the most likely emission is determined. It is shown that this direction is different from the direction of the maximum shear stress at the surface of the void due to the applied loading. The critical stress and the direction of the dislocation emission are determined for circular nanovoids under remote uniaxial, pure shear, and arbitrary biaxial loading. The analysis includes effects of the loading orientation relative to the discrete slip plane orientation. It is shown that dislocations are emitted more readily from larger nanovoids and that wider dislocations are emitted under lower applied stress than narrow dislocations. Different mechanisms, under much lower stress, operate for growth of the micron-size voids.