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Nucleation fronts ignite the interface rupture that initiates frictional motion

Abstract

Rapid rupture fronts—akin to earthquakes—mediate the transition to frictional motion. Once formed, their singular form, dynamics and arrest are well described by fracture mechanics. Ruptures, however, first need to be created within initially rough frictional interfaces. Hence, static friction coefficients are not well defined, with frictional ruptures nucleating over a wide range of applied forces. A critical open question is, therefore, how the nucleation of rupture fronts actually takes place. Here we experimentally show that rupture fronts are preceded by slow nucleation fronts—self-similar entities not described by fracture mechanics. They emerge from initially rough frictional interfaces at a well-defined stress threshold, evolve at the characteristic velocity and timescales governed by stress levels, and propagate within a frictional interface to form the initial rupture from which fracture mechanics take over. These results are of fundamental importance to questions ranging from earthquake nucleation and prediction to processes governing material failure.

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Fig. 1: Experimental setup and rupture arrest by imposing barriers.
Fig. 2: Rupture arrest generates initial damage ahead.
Fig. 3: Nucleation is mediated by slowly propagating nucleation fronts.
Fig. 4: Shear stress level determines the nucleation time, τ.
Fig. 5: Nucleation dynamics scale with nucleation time τ.

Data availability

Source data for Figs. 2c,d,3a,c,d,4b and 5 are available with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon request. The data can also be directly accessed at https://doi.org/10.4121/14697138.v1.

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Acknowledgements

J.F. and S.G. acknowledge the support of the Israel Science Foundation (grant no. 840/19). We also thank M. Adda-Bedia for his invaluable input and advice.

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S.G. performed the experimental measurements. S.G. and J.F. contributed to the data analysis, experimental design and writing of the manuscript.

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Correspondence to Jay Fineberg.

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Peer review information Nature Physics thanks Anders Malthe-Sørenssen and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Fracture energy increase by the marker layer.

a, Schematic description of the experiment. Half of the interface was painted with a marker layer, and the strain signals were measured by a number of rosette type strain gages located about 3.5 mm above the interface. Blue (red) colors correspond to the bare (painted with marker) interface, respectively. b, Comparison of the \({\mathrm{{\Delta}}}{\it{\epsilon }}_{xx}\) (top) and \({\mathrm{{\Delta}}}{\it{\epsilon }}_{yy}\) (bottom) signals of the same rupture front in the bare (blue) and painted (red) regions, respectively. This rupture front propagated at a velocity of 1200 m/s=0.95cR. Superimposed are 3 successive measurements spaced 7mm apart in both the bare (blue) and painted (red) regions. The influence of the marker is evident on the amplitudes. Shown are (top) the \({\mathrm{{\Delta}}}{\it{\epsilon }}_{xx}\) and (bottom) \({\mathrm{{\Delta}}}{\it{\epsilon }}_{yy}\) components, whose respective amplitudes \(\delta {\it{\epsilon }}_{xx}\) and \(\delta {\it{\epsilon }}_{yy}\) are proportional to the instantaneous values of the stress intensity factor, K. c, \(\delta {\it{\epsilon }}_{xx}\) as a function of the rupture velocity in both regions. Each point is an average of 2–10 measurements; the error bars are their standard deviation. Colors denote the painted (red) and bare (blue) sections of the interface. (inset) The resulting fracture energy ratios of painted and bare surfaces. Use of the marker increases Γ on the interface by approximately a factor of 5. Representative green and orange error bars are presented in (a) and (b) for, respectively the painted and bare sections of the interface.

Extended Data Fig. 2 Calculation of theoretical stress intensity factors.

a, Two snapshots of the expanding rupture during the nucleation phase of the event presented in Fig. 3. We can approximate the general shape of the nucleating patch by a semi-elliptical edge crack47, as denoted by the white line. The ellipse’s axis ratio, a/l is approximately 0.85, and remains fairly constant throughout the entire nucleation phase. b, Schematic description of the calculation47 of the stress intensity factor K, of a semi-elliptical edge crack. The parameters w and b used in the calculation are noted. The nucleation patch was assumed to propagate in the x direction. The nucleation point at the center of the ellipse, is located at the center of the initial damage zone, a distance of ξ0/2 from the right edge of the marker. The propagation distance, l(t), used in the calculation is therefore l=ξ(t)-ξ0/2 in terms of the damage zone size, ξ0 and nucleation front location, ξ(t) which are both defined from the barrier edge (Fig. 3a). c, The theoretical stress intensity factor as a function of crack length for the 1D (dashed line) and the elliptical (full line) cases. The stress field used in this example is that denoted by the black line in Fig. 3c, where varr=1160 m/s Note that, experimentally, the onset of dynamic rupture (Fig. 3c) occurred at a length l=4 mm, which agrees well with the predicted value (l=3.9) for LG. The dotted line denotes the critical stress intensity factor, Kc, above which stationary cracks are unstable.

Extended Data Fig. 3 Comparison of theoretical and measured Griffith lengths.

Compared are the calculated Griffith lengths, LG with the measured distances of nucleation lengths, ξ(τ) from the nucleation locations, ξ0/2. The data shown correspond to the red data within Fig. 5a, in which nucleation fronts triggered rapid rupture fronts.

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Gvirtzman, S., Fineberg, J. Nucleation fronts ignite the interface rupture that initiates frictional motion. Nat. Phys. 17, 1037–1042 (2021). https://doi.org/10.1038/s41567-021-01299-9

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