Partial slip

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... 

The fretting wear rate is directly proportional to the normal load for a given slip amplitude. However, in the total-slip situation, the frequency has little effect. (Water-house)88 In a partial-slip situation, the frequency of oscillation has little effect on wear rate per unit distance in the low-frequency range, whereas the increase in the strain rate at high frequencies leads to increased fatigue damage and increased corrosion due to a rise in temperature.75... 

Fig. 6.14 Experimental (coarse lines) and predicted hysteresis loops (fine lines) for unidirectional SiQ/CAS. Tlie predictions, which assume partial slip along the fiber-matrix interfaces, were based upon a residual compressive stress in the fibers of 50 MPa and values of r of 8, 2 and 1 MPa. The loop width and the permanent offset strain increase as t decreases. After Pryce and Smith.54...

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. 

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]. 

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... 

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... 

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...

The force-displacement relations in contact mechanics are often nonlinear. A prominent example is the transition from stick to slip. Even for nonlinear interactions, there is a strictly quantitative relationship between the shifts of frequency and bandwidth. A/ and AT, on the one hand, and the force acting on the crystal, T(t), on the other. A/ and Ar are proportional to the in-phase and the out-of-phase component of F(t), respectively. Evidently, F(t) cannot be explicitly derived from A/ and Ar. Still, any contact-mechanical model (like the Mindlin model of partial slip) can be tested by comparing the predicted... 

If roughness plays a role, the Mindlin model does not apply. Still, the Mindlin model is a good example of a broader class of models of partial slip. Bureau et al. have proposed a quantitative extension of the microslip model accounting for multi-contact interfaces [34]. Partial slip also occurs in multiasperity contacts because the microcontacts located at the rim are expected to rupture first. These contacts experience the largest lateral stress and the low-... 

Fig. 5 Shift of frequency a and bandwidth b as a function of amplitude for a quartz plate covered with a monolayer of glass spheres (d = 200 p.m) at a various humidities. The data were acquired via ring-down [32]. From the slopes, one infers the partial slip length, Xs and the coefficient of static friction, /Xs...

Dislocation - An extended displacement of a crystal from a regular lattice. An edge dislocation results when one portion of the crystal has partially slipped with respect to the other, resulting in an extra plane of atoms extending through part of the crystal. A screw dislocation transforms successive atomic planes into the surface of a helix. 

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