Analogy between Turbulent-to-Vortex Shedding Flow Transition in Fluids and Ductile-to-Brittle Failure Transition in Solids

Abstract

By using complex potentials, some light is shed on the analogy between the singularity problems arising in fluid and fracture mechanics—in particular, those concerning plane irrotational flows around sharp obstacles and plane elasticity in cracked bodies. Applications to two equivalent geometries are shown: a thin plate transversally immersed in a uniform flow and a crack subjected to uniform out-of-plane shearing stress at infinity (Mode III). The matching between the fluid velocity field and the shearing stress field is consistent with the hydrodynamic analogy. Aside from the Reynolds criterion for the natural laminar-to-turbulent transition, a velocity-intensity factor criterion is defined to predict the forced turbulent-to-vortex-shedding fluid-flow transition (forced transitional flow) generated by a transversal plate obstacle. It is interesting to remark that the velocity-intensity factor presents physical dimensions intermediate between those of a velocity and a kinematic viscosity. In addition, it will be demonstrated that size affects the occurrence of natural-to-forced transitional phenomena in fluids, in a strict analogy to the scale-dependent ductile-to-brittle failure transitions in solids.

Keywords

• hydrodynamic analogy
• stress intensification
• velocity intensification
• ductile-to-brittle failure transition
• turbulent-to-vortex shedding flow transition
• scale effects