Partial slip condition

The so-called partial slip condition, where the contact area is divided into a central stuck zone and a surrounding annulus where some microslip is occurring during the course of the loading cycle. When the tangential load is plotted as a function of the relative displacement in a Iissajous representation, elliptical loops are obtained. 

Fig. 9 Changes in the crack initiation times and crack depths in an epoxy resin as a function of the amplitude of the imposed cyclic displacement, a Number of cycles to the initiation of the primary cracks at the edge of the contact zone, b Measured depths of the primary cracks at various number of cycles and displacement amplitudes. Circles 103 cycles, solid diamonds 5 x 103 cycles, squares 5 x 104 cycles, c Calculated values of the maximum tensile stress at the edge of the contact using Hamilton (gross slip condition) or Mindlin—Cattaneo (partial slip condition) theories. The two curves correspond to calculations using the initial (/x = 1.0) and the steady-state (/x = 1.5) values of the coefficient of friction. PSR Partial slip regime, MR mixed regime, GSR gross slip regime...

Under partial slip conditions, the estimate of the stress conditions at the edge of the contacts is complicated due to the unknown frictional behaviour within the partial slip annulus. If Coulomb s friction law is assumed to apply locally within this area, some contact mechanics calculation can, however, be... 

Fig.16 S-N fatigue diagram of a bulk diglycidyl ether of bisphenol (DGEBA)/isophoron diamine (IPD) epoxy polymer giving the maximum applied stress as a function of the number of cycles to failure (three-point bending, 25 Hz, stress ratio OminMnax = 0.1) (from [53]). The two dotted lines correspond to theoretical values of the amplitude of the effective tensile stress, Acr, calculated for (a) gross slip condition and (b) under partial slip condition for an imposed displacement ( 10 xm) which corresponds to the experimental contact endurance limit at 105 cycles...

This partial-slip condition, over a proportionately large surface area felt by the flow passing over the sharks skin, inhibits flow reversal which would otherwise lead to separation. Thus, the overall effect for the shark would be a reduction in pressure drag. 

Figure 4. Model under partial slip condition...

Figure 5.14 (a) The predicted velocity field corresponding to no-slip wall boundary conditions, (b) Tlie predicted velocity field corresponding to partial slip boundary conditions... 

A detailed derivation of Eq. (1.6a) using the no-slip boundary condition is provided in Section A.2 of the Appendix. If we were to generalize the analysis above with the partial-slip boundary condition, that is, Sv/Sz = pv (p = slip parameter) instead of the no-slip condition in Eq. (A.2) at the lubricant/solid boundary with q (z) = p, we would obtain... 

A gross slip condition, where sliding is induced within the whole contact interface after a preliminary partial slip stage. This condition is associated to trapezoidal tangential load/displacement loops. The plateau value of the tangential load provides a measurement of the coefficient of friction, //. = Q /P, where Q and P are the plateau value of the tangential load and the imposed normal load respectively. 

The occurrence of either partial slip or gross slip condition is dependent on the material mechanical properties, the magnitude of the coefficient of friction and the contact loading parameters (normal load, imposed displacement). When dealing with non-adhesive elastic materials, the effects of these... 

Fig. 5 Schematic description of the contact conditions encountered under small amplitude cyclic lateral micro-motions (fretting). S is the applied lateral displacement, Q is the lateral force and P is the applied constant normal load. The elliptic and trapezoidal Q(S) loops correspond to partial slip and gross slip condition respectively...

With polymers, complications may potentially arise due to the material viscoelastic response. For glassy amorphous polymers tested far below their glass transition temperature, such viscoelastic effects were not found, however, to induce a significant departure from this theoretical prediction of the boundary between partial slip and gross slip conditions [56]. 

This combined analysis of AoA and Ar, therefore establishes that the main cracks that nucleate close to the contact edge correspond to predominantly tensile fatigue cracks. This conclusion remains valid whatever the contact condition (partial slip or gross slip). In addition, the distribution of within the contact plane is of interest (Fig. 15). The maximum amplitude... 

In any fluid continuum possessing a viscosity, however small, the velocity of the fluid adjacent to the solid boundary is the same as the boundary, there is no relative motion between fluid particles and solid boundaries with which they are in contact. Despite its apparent simplicity, the no-slip boundary condition leads to some physical inconsistencies that are not yet resolved completely. For example, the no-slip condition cannot explain the motion of a liquid interface in contact with a solid boundary according to this condition, the liquid interface in a partially filled glass must remain... 

Boundary Slip of Liquids, Fig. 1 Schematic representation of the no-slip, partial slip, and perfect slip boundary conditions. Under no-slip boundary condition, the relative velocity. Vs, between the fluid and the solid wall is zero at... 

Barrat and Bocquet [6] carried out the molecular dynamics simulation of Couette and Poiseuille flows. In Couette flow, the upper wall is moved with a cmistant velocity, and in Poiseuille flow an external force drives the flow. Sample results from molecular dynamics simulation are reproduced in Fig. 7. The application of no-slip boundary condition leads to the expected linear and parabolic profiles, respectively, for Couette and Poiseuille flows. However, the velocity profile obtained from molecular dynamics simulation shows a sudden change of velocity in the near-waU region indicating the slip flow. The velocity profile for Couette flow away from the solid surface is linear with different slope than that of the no-slip case. The velocity for slip flow case is higher than that observed in the no-slip case for Poiseuille flow. For both Couette and Poiseuille flows, the partial slip boundary condition at the wall predict similar bulk flow as that observed by molecular dynamics simulation. Some discrepancy in the velocity profile is observed in the near-wall region. 

Boundary Slip of Liquids, Fig. 7 Velocity profile for (a) Couette and (b) Poiseuille flow comparison between molecular dynamics simulation, no-slip boimdary condition, and partial slip boundary condition... 

Bar sky and Robbins performed NEMD simulations of the interfacial structiue and rheology of binary blends of symmetric polymers which were made immiscible to various degrees by adjusting the cross-interaction parameters. A liquid film was sheared by sliding boundaries. They found that there was a difference in velocity of the two species at the interface, suggesting a partial slip boundary condition. They attributed this to a difference in the positions of the centres of mass of the species on opposite sides of the interface. The viscosity in the interfacial region was lower than the bulk viscosity. 

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