Recently, Associate Prof. Songlin Shi from the department of engineering mechanics, starting from the issues of fracture mechanics and interfacial frictional instability, proposed a rupture nucleation mechanism dominated by the cohesive zone scale of material interfaces. The work was published in Physical Review Letters under the title "Interplay of Cohesive, Griffith, and Geometric Scales in the Nucleation of Friction." The corresponding author is Prof. Jay Fineberg from the Hebrew University.

The nucleation process of frictional rupture plays a key role in phenomena such as solid frictional instability, composite interface failure, and earthquake fault slip. However, a unified understanding of its physical mechanism remains lacking. On the one hand, classical linear elastic fracture mechanics (LEFM) dictates that fast rupture occurs when a crack grows to a critical length where the elastic energy release balances the interfacial dissipation energy. Yet, whether this energy criterion applies during the early stages of nucleation is still debated. On the other hand, research from the perspective of friction constitutive laws has developed various nucleation models and numerical frameworks based on slip-weakening or rate-and-state friction laws, aiming to describe how local instabilities evolve spontaneously along an interface. Recent experiments have shown that shear nucleation often undergoes a dynamic transition from two-dimensional to quasi-one-dimensional growth and accelerates rapidly as the rupture zone approaches the interface width. However, the nucleation scales observed in many interfaces are significantly larger than the system's geometric width, exceeding existing theoretical predictions. This suggests that rupture nucleation may be jointly regulated by the competition between intrinsic material scales and geometric scales, and the dominant mechanism remains to be clarified.

The researchers conducted controlled frictional shear rupture experiments on the interface between two polycarbonate (PC) blocks (Fig. 1(a)). By incrementally applying shear loading to trigger interfacial instability, they obtained a stable and repeatable shear rupture process. Using high-resolution optical measurement techniques, they simultaneously recorded the evolution of the real contact area and the local slip fields at the interface, achieving sub-micrometer precision in analyzing the spatiotemporal evolution of the nucleation zone (Fig. 1(b)). The experiments revealed that rupture does not occur instantaneously but instead undergoes a prolonged nucleation stage characterized by extremely slow propagation. Only when the rupture length grows to a critical value, lc, does the front velocity suddenly jump to nearly the Rayleigh wave speed, entering the fast dynamic rupture phase (Fig. 1(c)). Further experiments showed that as the interfacial fracture energy Γ increases, both the nucleation duration and the critical length decrease significantly. However, under all experimental conditions, the measured critical length lc was significantly larger than the geometric width W of the interface (Fig. 1 (d, e)), indicating that the nucleation dynamics of this interface are not dominated by geometric constraints.

Further analysis revealed that during the nucleation stage, the real contact area at the interface decayed only slowly, indicating that the interface did not undergo complete failure but rather experienced a progressive damage evolution. This slow and sustained process of contact degradation implies that a cohesive zone with a finite spatial extent is gradually forming and expanding outward. By jointly analyzing the decay of the contact area and the local slip, the cohesive constitutive relation of this interface was directly constructed (Figure 1(f)). It was found that this relation can be accurately described by an exponential slip-weakening law, from which an intrinsic material length scale, the cohesive length ξ, can be defined. The results show that ξ is significantly larger than the interface width W, indicating that in this material system, the nucleation dynamics are primarily controlled by the progressive establishment of the cohesive zone, rather than being triggered by geometric scales. Only when the rupture length exceeds the cohesive scale and reaches the characteristic length lG predicted by the Griffith energy balance (Figure 1(e)) does the stress singularity form, subsequently triggering rapid instability (dynamic fracture). This study reveals that when ξ > W, the nucleation dynamics of frictional rupture are mainly governed by the cohesive scale, rather than by geometric topology. The cohesive length ξ is an intrinsic material property of the interface, whereas lG is determined by loading conditions and system dimensions. The hierarchical relationship between these different scales dictates the essence of the nucleation mechanism. This finding holds significant implications for understanding the failure of engineering materials and the preparatory processes of earthquakes in natural faults.

Figure 1 (a) Schematic diagram of the experimental setup. (b) Two-dimensional evolution of a typical rupture process: nucleation rapidly transitions to high-speed dynamic rupture. (c) Evolution of the two-dimensional rupture front during the nucleation stage. (d) Temporal evolution of the nucleation zone height, one-dimensional rupture length, and average contact area. (e) Comparison between the characteristic length lG predicted by Griffith fracture theory and the critical length lc measured experimentally. (f) Schematic of the cohesive law and the experimental stress-slip relationship.

Paper link: https://journals.aps.org/prl/abstract/10.1103/9fkf-g172