Slippery but Tough: The Rapid Fracture of Lubricated Frictional Interfaces

We study the onset of friction for rough contacting blocks whose interface is coated with a thin lubrication layer. High speed measurements of the real contact area and stress fields near the interface reveal that propagating shear cracks mediate lubricated frictional motion. While lubricants reduce interface resistances, surprisingly they significantly increase the energy dissipated $\mathrm{\Gamma }$ during rupture. Moreover, lubricant viscosity affects the onset of friction but has no effect on $\mathrm{\Gamma }$. Fracture mechanics provide a new way to view the otherwise hidden complex dynamics of the lubrication layer.

Figure 1

Experimental setup and stick-slip behavior. (a) Normal $F_N$ and shear $F_S$ forces are applied to contacting PMMA blocks. Shear is applied uniformly via translation of a rigid stage. Strain gage rosettes measure the three components of the 2D-strain tensor at 14 locations along and 3.5 mm above the interface, while the real contact area is measured optically. (b) Loading curves, $F_S/F_N$ versus time, are plotted for typical experiments, with $F_N=4000\mathrm{N}$: dry (solid blue line), boundary lubricated (dashed green line), and, for comparison, in the mixed lubricated regime (dotted red line). The lubricant used is a hydrocarbon oil (TKO-77).

Figure 2

Singular interfacial shear cracks govern friction initiation. (a) The spatiotemporal evolution of the contact area $A(x,t)$ of a typical lubricated interface (hydrocarbon oil, TKO-77). Each line is a snapshot in time of $A(x,t)$, normalized by $A_0=A(x,0)$ immediately prior to the event. Here, a rupture accelerates to a propagation velocity $c_f=0.92c_R$. The rupture tips $x_{\text{tip}}(t)$ are the locations where $A(x,t)$ drops sharply. (b) Variation of the strain field $\mathrm{\Delta }{ϵ}_{ij}(x-x_{\text{tip}})$ with the distance from the rupture tips $x_{\text{tip}}$, for ruptures propagating along dry (blue line) and lubricated [green line, rupture presented in (a)] interfaces. In both, the applied normal stress was $⟨{\sigma }_{yy}⟩=7\pm 0.5\mathrm{MPa}$ and strains were measured at $x=77\mathrm{mm}$, where $c_f\sim 0.3c_R$. Black solid lines are fits to the LEFM solution for $y=3.5\mathrm{mm}$ [Eq. (1)]. The only fitting parameter is the fracture energy; ${\mathrm{\Gamma }}_{\text{dry}}=2.6\pm 0.3\mathrm{J}{\mathrm{m}}^{-2}$ for the dry and ${\mathrm{\Gamma }}_{\text{lub}}=23\pm 3\mathrm{J}{\mathrm{m}}^{-2}$ for the lubricated interfaces.

Figure 3

Dependence of the fracture energy with normal stress. (a) Comparison of $\mathrm{\Delta }{ϵ}_{ij}(x-x_{\text{tip}})$ for dry and lubricated experiments, when normalized by $\sqrt{\mathrm{\Gamma }}$, for different normal loads. Units are $(\mathrm{Pa}\mathrm{m}{)}^{-1/2}$. Superimposed are the dry experiment in Fig. 2 and five lubricated (TKO-77) experiments where $c_f\sim 0.3c_R$ with $⟨{\sigma }_{yy}⟩$ as in the legend, yielding ${\mathrm{\Gamma }}_{\text{dry}}=2.6\mathrm{J}{\mathrm{m}}^{-2}$ and ${\mathrm{\Gamma }}_{\mathrm{TKO}}=12.3$, 18.2, 23, 25, and $29.5\mathrm{J}{\mathrm{m}}^{-2}$. (b) $\mathrm{\Gamma }$ is measured by fitting the strain field with the LEFM solution [as in Fig. 2] for both the dry and lubricated interfaces versus $F_N$. All $\mathrm{\Gamma }$ vary linearly with $F_N$; $\mathrm{\Gamma }$ is independent of the lubricant viscosity while being highly dependent on lubricant composition.

Figure 4

Measurements of ${\sigma }_{xy}^{\text{res}}$, $X_c$, ${\sigma }_{xy}^{\text{peak}}$, and $d_c$. (a) Shear stress as a function of the distance from $x_{\text{tip}}$ for ruptures propagating ($c_f\sim 0.3c_R$) along a dry (blue crosses) and lubricated interfaces with hydrocarbon oil (green diamonds) and silicone oil with $\nu ={10}^4{\mathrm{mm}}^2{\mathrm{s}}^{-1}$ (red circles). $\mathrm{\Gamma }=2.6$, 9, and $23\mathrm{J}{\mathrm{m}}^{-2}$ for, respectively, dry, silicone, and hydrocarbon oils for $⟨{\sigma }_{yy}⟩=7\mathrm{MPa}$. The blue and green plots are measurements presented in Fig. 2, where strain variations are, instead, presented in terms of the absolute stress values. (b) Reduction of the contact area $A-A_0$, normalized by the total drop in $A$, $\mathrm{\Delta }A=A_0-A_{\text{res}}$, as a function of the distance from $x_{\text{tip}}$ for the three experiments in (a). The dissipative zone size $X_c$ is defined as the length scale where a 60% drop of $\mathrm{\Delta }A$ occurs. (c) Shear stress versus slip distance where ${\sigma }_{xy}^{\text{peak}}$ and $d_c$ are estimated within the linear slip-weakening model [32]. Respectively, for the dry and lubricated with silicone and hydrocarbon oil interfaces, the residual stresses, defined in (a), are 2.4, 1, and 1.7 MPa, the peak stresses ${\sigma }_{xy}^{\text{peak}}$, using Eq. (2), are 4.6, 5.1, and 8.2 MPa, and $d_c$ are 2.4, 4.4, and $7\mu \mathrm{m}$. Integration over the blue (green, red) hatched areas provides the dry (lubricated) fracture energy.

Figure 5

Dependence of the macroscopic frictional resistance with $\nu$. Profiles of the (a) initial ${\sigma }_{xy}^{\text{pre}}$ and (b) residual ${\sigma }_{xy}^{\text{res}}$ stresses for interfaces lubricated with silicone oils having $\nu =5$ (diamonds), 100 (circles), and ${10}^4$ (squares) ${\mathrm{mm}}^2{\mathrm{s}}^{-1}$. Normal stress distributions are identical for the three experiments and $\mathrm{\Gamma }=6.7\pm 0.3\mathrm{J}{\mathrm{m}}^{-2}$. ${\sigma }_{xy}^{\text{res}}$ does not depend on the viscosity of the silicone oil. (c) Histograms of the static friction coefficient ${\mu }_S$ of sliding events for lubricated interfaces with silicone oils of different viscosity. Around 50 events are considered for each $\nu$. Higher $\nu$ yield lower frictional resistance. (d) Three examples of $c_f(x)$ for the lubricants in (a) and (b). The larger $\nu$ is, the slower the front is. Dashed line denotes $c_R$. Same symbols and colors in (a)–(d) as in (b).