Dynamic forcing of crack fronts: From non-local elasticity to shock wave behavior

Abstract

The motion of deformed interfaces underlies a myriad of phenomena such as phase transformation, ferromagnetism, wetting, superconductivity, etc. It also impacts the materials’ resistance to failure, that takes place through the propagation of a crack that can deform under the effect of microstructural heterogeneities. These mechanisms are generally described in the quasi-static limit for which long-range crack front elasticity prevails. Here, we design an experiment where crack fronts are tracked as they are forced to deform at a prescribed speed $v$. As $v$ approaches $v_{\circ }$, a limit speed for crack deformation imposed by the microscopic failure processes, we observe that deformations are progressively damped. In the limit $v\gg v_{\circ }$, at large forcing speed, the long-range elastic interactions seemingly fade away, giving way to a shock wave behavior that manifests as triangular fronts reminiscent of Mach cones. Combining experimental observations and fracture mechanics-based modeling, we evidence a dynamic length scale that decreases as the crack front dynamics evolve from the quasi-static regime to the newly evidenced shock-wave regime. In essence, this length scale delimits the apparent range of the long-range elasticity that vanishes at very large forcing speed. Our original protocol for dynamic forcing unfolds how deformations settle down at finite speed along long-range elastic interfaces. Applied to failure phenomena, it illustrates how the microscopic dissipative processes localized at the crack tip govern the large-scale dynamics of crack fronts. It also shows that the extent of the long-range interactions underlying the behavior of interfaces in elastic solids can be truncated, and therefore potentially be engineered, paving the way for the design of interfaces with programmable dynamic.