FLUTTER OF CRACK TIPS

Flutter of a crack tip occurs when the relatively flexible tip collide s with density fluctuations in a solid. The crack velocity must exceed a critical value. The crack tip behaves like a self-excited oscillato r. Its fundamental frequency can be estimated using Friedel's dislocat ion model of a crack. Surface energy, gamma, provides the restoring fo rce for displacements, x of the leading dislocation line. The force co nstant is, -4 gamma x/b, where b is the Burgers displacement. The osci llator frequency is then about: (v(L)b)/pi where v(L) is the velocity of longitudinal acoustic waves. Thus it is proposed that self-excited oscillations of crack tips cause the hackle markings on fracture surfa ces after high speed crack propagation.