压力相关的壁面滑移在滑动间隙流体动压力产生中的作用

近年来,壁面滑移在纳米流变学、微流体力学、薄模润滑和微机电系统(MEMS)等领域越来越引起关注。以前大部分研究集中于表面初始极限剪应力对薄模润滑的壁面滑移和流体动力学的影响。本文通过一个极限剪切应力比例系数主要研究了与压力相关的壁面滑移滑动间隙流体动压力产生中的作用,发现极限剪切应力比例系数以相反的两种方式影响着流体膜的流体动力学:在高初始剪应力区使流体动力增加,但在低初始剪应力区使流体动力减小,这意味着就极限剪切应力比例系数影响流体动压力而言,存在一个初始极限剪切应力的转换点。但是在界面滑移存在时,较小的极限剪切应力比例系数总是产生较小的摩擦阻力。     

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.     

Griffith crack moving in a piezoelectric strip

Summary  The dynamic problem of an impermeable crack of constant length 2a propagating along a piezoelectric ceramic strip is considered under the action of uniform anti-plane shear stress and uniform electric field. The integral transform technique is employed to reduce the mixed-boundary-value problem to a singular integral equation. For the case of a crack moving in the mid-plane, explicit analytic expressions for the electroelastic field and the field intensity factors are obtained, while for an eccentric crack moving along a piezoelectric strip, numerical results are determined via the Lobatto–Chebyshev collocation method for solving a resulting singular integral equation. The results reveal that the electric-displacement intensity factor is independent of the crack velocity, while other field intensity factors depend on the crack velocity when referred to the moving coordinate system. If the crack velocity vanishes, the present results reduce to those for a stationary crack in a piezoelectric strip. In contrast to the results for a stationary crack, applied stress gives rise to a singular electric field and applied electric field results in a singular stress for a moving crack in a piezoelectric strip. Received 14 August 2001; accepted for publication 24 September 2002 The author is indebted to the AAM Reviewers for their helpful suggestions for improving this paper. The work was supported by the National Natural Science Foundation of China under Grant 70272043.     

Drag increment of internal waves generated by horizontally moving spheroid in supercritical regime

A theory on the drag increment of internal waves with a spheroid moving horizontally at a high velocity （or for large internal Froude number） in uniformly vertically stratified fluid （or ocean） is presented in the present paper. A surface source distribution is employed to model a hydrodynamic interaction between the spheroid and the stratified fluid. From theoretical results, it is shown that there exists an asymptote of zero-drag increment in supercritical regimes, where internal Froude numbers are larger than the critical internal Froude numbers. When the spheroid reduces to a sphere, the results in this paper is in good agreement with the previous theoretical and experimental results of the sphere.     

DYNAMIC STRESS FIELD AROUND THE MODE Ⅲ CRACK TIP IN AN ORTHOTROPIC FUNCTIONALLY GRADED MATERIAL

The problem of a Griffith crack in an unbounded orthotropic functionally graded material subjected to antipole shear impact was studied. The shear moduli in two directions of the functionally graded material were assumed to vary proportionately as definite gradient. By using integral transforms and dual integral equations, the local dynamic stress field was obtained. The results of dynamic stress intensity factor show that increasing shear moduli’s gradient of FGM or increasing the shear modulus in direction perpendicular to crack surface can restrain the magnitude of dynamic stress intensity factor.     

滑滚表面间的流体膜壁面滑移和流体动力学

经典雷诺润滑理论建立在无壁面滑移的假设基础之上。近年来许多试验报告了发生在流体膜流动的壁面滑移证据。本文研究了两固体表面间的流体膜流动特性和流体动力学,发现壁面滑移显著影响膜的流体动力学问题,流体动压力不仅受黏度和几何间隙的影响,而且还由壁面滑移和表面运动强力控制,通过控制表面的吸附性质,甚至可以得到零摩擦表面。另一方面,如果两个表面具有相同的滑移特性,存在一个临界滑动速度使得流体动压效应完全消失;但是在纯滚动条件下,即使界面极限剪应力很小,仍然有相当可观的流体动压效应。     

Dynamic behavior of two parallel symmetric permeable cracks in a piezoelectric strip

The dynamic behavior of two parallel symmetric cracks in a piezoelectric strip under harmonic anti-plane shear waves is studied using the Schmidt method for permeable crack surface conditions. The cracks are parallel to the edge of the strip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the schmidt method. The results show that the stress and the electric displacement intensity factors depend on the geometry of the cracks, the frequency of incident waves, the distance between cracks and the thickness of the strip. It is also found that the electric displacement intensity factors for the permeable crack surface conditions are much smaller than those for the impermeable crack surface conditions. Project supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang Province, the National Science Foundation with the Excellent Young Investigator Award (No. 19725209) and the Scientific Research Foundation of Harbin Institute of Technology (HIT.2000.30).     

Reverse shear on inclined planes at the tip of a sharp crack

Plane strain plastic yielding at a crack tip has been represented by edge dislocations with Burgers vectors parallel to symmetrical planes inclined at 70° and 45° to the plane of the crack. The plastic displacement and the stresses near the crack tip were calculated by a numerical method and the effect of a reduction in applied stress was determined. Removal of the whole or a part of the initial load produces reverse shear in regions of the slip band nearest the crack tip. The amount of reverse shear depends only on the reduction in the load and not on its initial value. The reverse shear is associated with the presence of negative dislocations and the stresses near the crack tip may become compressive even though the applied (remote) stress is still tensile. The degree and extent of compression depends on the reduction in applied stress and on its original value. It is argued that the residual compressive stresses produced under fluctuating loads may produce crack closure and crack arrest. The effect of residual plasticity in a slip band left behind a growing crack has been estimated. It is shown that after an overload the excess residual plasticity opposing crack opening rises to a maximum value when the crack tip has advanced some distance from the point where the overload was applied.     

Anti-plane shear cracks in ideally plastic crystals

Cracks in ductile single crystals are analyzed here for geometries and orientations such that two-dimensional states of anti-plane shear constitute possible deformation fields. The crystals are modelled as ideally plastic and yield according to critical resolved shear stresses on their slip systems. Restrictions on the asymptotic forms of stress and deformation fields at crack tips are established for anti-plane loading of stationary and quasistatically growing cracks, and solutions are presented for several specific orientations in f.c.c. and b.c.c. crystals. The asymptotic solutions are complemented by complete elastic-plastic solutions for stationary and growing cracks under small scale yielding, based on previous work by Rice (1967, 1984) and Freund (1979). Remarkably, the plastic zone at a stationary crack tip collapses into discrete planes of displacement and stress discontinuity emanating from the tip; plastic flow consists of concentrated shear on the displacement discontinuities. For the growing crack these same planes, if not coincident with the crack plane, constitute collapsed plastic zones in which velocity and plastic strain discontinuities occur, but across which the stresses and anti-plane displacement are fully continuous. The planes of discontinuity are in several cases coincident with crystal slip planes but it is shown that this need not be the case, e.g., for orientations in which anti-plane yielding occurs by multi-slip, or for special orientations in which the crack tip and the discontinuity planes are perpendicular to the activated slip plane.     

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.     

ASYMPTOTIC ANALYSIS OF PLANE-STRAIN MODE I STEADY-STATE CRACK GROWTH IN TRANSFORMATION TOUGHENING CERAMICS(Ⅱ)

Based on a constitutive law which includes the shear components of transformation plasticity, the asymptotic solutions to near-tip fields of plane-strain mode I steadity propagating cracks in transformed ceramics are obtained for the case of linear isotropic hardening. The stress singularity, the distributions of stresses and velocities at the crack tip are determined for various material parameters. The factors influencing the near-tip fields are discussed in detail.Project supported by the National Natural Science Foundation of China     

Boundary slippage for generating hydrodynamic load-carrying capacity

Boundary slippage is used to generate the load-carrying capacity of the hydrodynamic contact between two parallel plane surfaces. In the fluid inlet zone, the fluidcontact interfacial shear strength on a stationary surface is set at low to generate boundary slippage there, while in the fluid outlet zone the fluid-contact interfacial shear strength on the stationary surface is set at high enough to prevent the occurrence of boundary slippage. The fluid-contact interfacial shear strength on the entire moving surface is set at high enough to prevent boundary slippage on the moving surface. These hydrodynamic contact configurations are analyzed to generate the pronounced load-carrying capacity. The optimum ratio of the outlet zone width to the inlet zone width for the maximum load-carrying capacity of the whole contact is found to be 0.5.     

The OPCM strain gauges for strain and stress measurement of orthotropic material structures

The orthotropic mechanical sensor of piezoelectric composite material made from piezoelectric ceramic and resin materials and their sensing mechanism are presented. The sensing equations of the adhered-and embedded-type sensing units are deduced, which are used to detect the stresses in orthotropic material structures. The surface strain of the orthogonal plate is measured under the action of the planar stress field, and the error is analyzed. Supported by the National Natural Science Foundation (No. 59635640), the Science Foundation of Jiangsu Education Committe (99KJD130001) and the Science Foundation of Jiangsu Province (BK99116).     

The probability stability of viscoelastic plates

The almost sure stability of homogeneous viscoelastic plates subjected to a random wide-band stationary in-plane load is investigated. The viscoelastic behavior of the plate is described in terms of the Boltzmann superposition principle, the relaxation kemels of which are represented by the sums of exponents. On the assumption that the in-plane load is random wide-band stationary process, sufficient conditions for almost sure stability of viscoelastic plates are obtained by the applications of Lyapunov's direct method. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation.     

Effects of irregularity and initial stresses on the dynamic response of viscoelastic half-space due to a moving load

The present article deals with the stresses developed in an initially stressed irregular viscoelastic half-space due to a load moving with a constant velocity at a rough free surface.Expressions for normal and shear stresses are obtained in closed form. The substantial effects of influence parameters, viz., depth(from the free surface), irregularity factor, maximum depth of irregularity, viscoelastic parameter, horizontal and vertical initial stresses,and frictional coefficient, on normal and shear stresses are investigated. Moreover, comparative study is carried out for three different cases of irregularity, viz., rectangular irregularity,parabolic irregularity and no irregularity, which is manifested through graphs.     

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.     

Stokes＇ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions. The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai. The English text was polished by Keren Wang.     

SQUEEZE FILM FLOW WITH NONLINEAR BOUNDARY SLIP

A nonlinear boundary slip model consisting of an initial slip length and a critical shear rate was used to study the nonlinear boundary slip of squeeze fluid film confined between two approaching spheres. It is found that the initial slip length controls the slip behavior at small shear rate, but the critical shear rate controls the boundary slip at high shear rate. The boundary slip at the squeeze fluid film of spherical surfaces is a strongly nonlinear function of the radius coordinate. At the center or far from the center of the squeeze film, the slip length equals the initial slip length due to the small shear rate. However, in the high shear rate regime the slip length increases very much. The hydrodynamic force of the spherical squeeze film decreases with increasing the initial slip length and decreasing the critical shear rate. The effect of initial slip length on the hydrodynamic force seems less than that of the critical shear rate. When the critical shear rate is very small the hydrodynamic force increases very slowly with a decrease in minimum film thickness. The theoretical predictions agree well with the experiment measurements.     

Reevaluation of the adhesive relationship between the tire and the soil

The author proved in an earlier article that the shear diagram is not in accord with its mechanical definition. The shear stress cannot be zero at the beginning of the initial rising portion of the curve. Shearing is not an increasing loading process, rather it is a limiting case to which a finite shear stress belongs. On the other hand the sheared surface varies under the tire. There are kinematic reasons for this. Points on the tire surface describe a looped cycloid and they slip in a backward direction (opposite to the direction of travel) while contacting the soil. Thus the driving force, which points in the direction of travel, is the product of the shear stress of finite magnitude and the sheared area. The latter increases proportionally with slip. The author describes his equation which is based on the principles discussed above. He supports his theory with a numerical example.     

Effect of irregularity and heterogeneity on the stresses produced due to a normal moving load on a rough monoclinic half-space

The present study aims to study the normal and shear stresses produced in a rough irregular heterogeneous monoclinic half-space due to a normal moving load. Closed form expressions of normal and shear stresses have been obtained. It is observed that both normal stress and shear stress are affected not only by depth, the frictional coefficient on a rough surface, and the maximum depth of irregularity but also by the heterogeneity and types of irregularity in the medium. The comparative study has been made to analyze the effect of different types of irregularity on both the stresses. There is a significant effect of depth, frictional coefficient, heterogeneity, maximum depth of irregularity and irregularity factor on the normal and shear stresses in both heterogeneous monoclinic and heterogeneous isotropic medium. A comparison is made to study the effects of the said parameters on the normal and shear stress produced in both heterogeneous medium. These effects are highlighted and depicted by means of graphs. As a special case of the problem, the stress produced due to normal moving load in an isotropic half-space with and without heterogeneity, irregularity has been discussed.