Crack branching at low tip speeds: spilling the T
Résumé
Using the criterion that a crack will extend along the direction of maximum circumferential stress, this paper demonstrates the influence of the coupling between the crack-parallel T-stress and the tip speed vc on the directional (in)stability of dynamics cracks in brittle materials, i.e., branching, turning and limiting velocities. The proposed (in)stability criterion evolves within the theory of dynamic fracture: we build on the work of Ramulu and Kobayashi (1983) by introducing a reference distance rc ahead of the crack-tip to incorporate the contribution of the higher-order terms in the asymptotic solution of the elastic crack-tip fields. The theoretical aspect is first explored, a methodology to numerically (and experimentally) advocate the instability—as a co-action of T-stress and a fast running crack—is then proposed and validated on Borden et al. (2012)’s branching benchmark. An experimental setup combining Ultra-High-Speed High-Resolution imaging with advanced Digital Image Correlation algorithms and a novel crack-branching inertial impact test enables for never-seen-before quantification of the rich dynamical behaviour of the fracture. Thus experimentally validating the developed crack (in)stability criterion.
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