Fracture, a ubiquitous phenomenon leading to catastrophic material failure, is well-understood in two dimensions (2D) where the fracture front is a point. However, real-world fractures are three-dimensional (3D) surfaces terminating at a crack front line. While a 2D approximation suffices when the crack front is straight and the fracture surface planar, any distortion introduces complexities. These distortions, arising from material heterogeneities or inertial effects during rapid propagation, alter stress singularities and lead to intricate fracture surface structures. Previous research has hinted at localized bond rupture followed by lateral atomic kink motion in crystalline materials, but detailed experimental observations of 3D fracture dynamics and the impact of distortions remain scarce. This study addresses this gap by investigating the initiation, propagation, and arrest of extended fractures, visualizing their dynamics and demonstrating the importance of crack-front distortions. The research uses a controlled experimental setup to achieve an uninterrupted, extended fracture front, allowing for precise measurement and analysis of the propagation mechanisms. The findings are expected to be fundamental to understanding fracture behavior across various length scales and materials.

Existing literature extensively covers 2D fracture mechanics, where the stress at the crack tip is characterized by a universal singularity, and the energy balance between dissipation and stored elastic energy governs the fracture propagation. However, the 3D scenario presents numerous complex behaviors. Studies have noted the influence of crack-front distortions on stress singularities, leading to complex fracture surface structures observed post-mortem. In-plane distortions from a straight line also complicate propagation dynamics. Slow, quasi-static propagation can be impacted by material heterogeneities causing crack front impedance. Rapid propagation introduces wave-mediated interactions along the fracture front, potentially resulting in fast transverse propagation of distortions. Theoretical and simulation work suggests that localized bond rupture followed by lateral kink motion might be an energetically favorable propagation mechanism in crystalline materials. Despite these insights, direct experimental observation of 3D fracture dynamics and distortion effects remains limited, hindering comprehensive understanding of fracture initiation and propagation.

The study employed a novel experimental system to investigate extended fracture propagation. A penny-shaped crack in a 10-cm-diameter cylindrical geometry of 3D-printed optically clear polymethylmethacrylate (PMMA) provided an uninterrupted extended fracture front. Fluid injection, with viscosity controlled by water-glycerol mixtures, allowed precise manipulation of loading conditions. High-speed imaging (100,000 frames per second) visualized the fracture front's movement. Different fluid viscosities (1 cP to 400 cP) created varying lags between the fluid front and the fracture front. Kymographs, plotting image intensity along radial directions versus time, revealed a stick-break instability: long pauses (stick) interspersed with rapid forward motion (break). The length of the break (δl) correlated with the lag (Δ) between fluid and fracture fronts. The stress intensity factor (K) for a fluid-driven penny-shaped fracture was calculated. A model incorporating a nucleation process (K increased by δK above the critical toughness Kc), along with fluid flow considerations (Poiseuille equation), successfully predicted the μ dependence of the lag and the correlation between δl and λ. Further analysis of high-speed images revealed localized nucleation of break events followed by rapid transverse expansion of the crack front, with velocities comparable to the Rayleigh-wave speed (determined via acoustic methods). Numerical simulations using a spectral boundary integral method modeled the crack propagation in a 3D linear elastic medium, reproducing the observed behavior, particularly for larger jump sizes (δl).

The key findings demonstrate that extended fracture propagation occurs through a two-step process: 1) localized nucleation at a specific point on the crack front and 2) a subsequent rapid transverse expansion of the crack front. This transverse expansion occurs at velocities approaching the Rayleigh-wave speed of the material, especially when the lag between the applied stress and the fracture front is significant. The experiments show a strong correlation between the length of the break events (δl) and the lag (Δ) between the fluid and fracture fronts. A model based on linear elastic fracture mechanics and incorporating a nucleation process and fluid flow successfully predicts this correlation and the viscosity dependence of the lag. The simulations, which employed a spectral boundary integral method, mirrored the experimental results, particularly for larger jump sizes, confirming the crucial role of high-speed transverse propagation. For smaller jump sizes, however, the simulations diverged from experimental observations, highlighting potential limitations of the brittle fracture framework at these scales. The study also examined how the frequency of nucleation events depends on the lag between the applied stress and the fracture front, with closer nucleation events occurring at smaller lags, leading to the simultaneous propagation of multiple transverse fractures.

These findings significantly advance our understanding of 3D fracture propagation. The observed two-step process – localized nucleation followed by rapid transverse expansion – challenges previous assumptions of uniform crack front advancement. The high transverse velocities observed underscore the importance of considering transverse dynamics in fracture mechanics, especially for extended fractures. The close agreement between experimental observations and simulations, particularly for larger jump sizes, validates the model's accuracy and strengthens the conclusions. The discrepancies observed at smaller jump sizes suggest that refinements to the model, potentially incorporating fluid flow effects more explicitly, are necessary for a complete description of fracture behavior across all length scales. The stick-break instability highlights a previously unobserved dynamic in fluid-driven fractures, potentially relevant to other fracture types.

This research provides compelling evidence for a new mechanism of extended fracture propagation: localized nucleation followed by rapid transverse expansion at velocities approaching the Rayleigh-wave speed. The experimental setup, incorporating fluid-driven fractures in a circular geometry, allows for precise control and observation of the process. The quantitative agreement between experimental results and numerical simulations solidifies the findings' significance. Future research should focus on refining the model to address the discrepancies observed at smaller jump sizes and extending the model to encompass more complex geometries and material properties. This improved understanding of fracture propagation could have significant implications for various fields, including earthquake prediction, materials science, and resource extraction.

The study utilized a specific experimental setup with a circular geometry and fluid-driven fractures. Extending these findings to other geometries and fracture mechanisms requires further research. The simulations employed a brittle fracture framework, which may not perfectly capture material behavior at all scales, particularly at very small jump sizes. While the model successfully predicts the behavior for larger lags, further refinement is needed to completely account for small-scale dynamics. The acoustic measurements to determine the high-frequency elastic moduli were indirect and could potentially introduce some uncertainties.