46 research outputs found
Critical examination of cohesive-zone models in the theory of dynamic fracture
We have examined a class of cohesive-zone models of dynamic mode-I fracture,
looking both at steady-state crack propagation and its stability against
out-of-plane perturbations. Our work is an extension of that of Ching, Langer,
and Nakanishi (CLN) (Phys. Rev. E, vol. 53, no. 3, p. 2864 (1996)), who studied
a non-dissipative version of this model and reported strong instability at all
non-zero crack speeds. We have reformulated the CLN theory and have discovered,
surprisingly, that their model is mathematically ill-posed. In an attempt to
correct this difficulty and to construct models that might exhibit realistic
behavior, we have extended the CLN analysis to include dissipative mechanisms
within the cohesive zone. We have succeeded to some extent in finding
mathematically well posed systems; and we even have found a class of models for
which a transition from stability to instability may occur at a nonzero crack
speed via a Hopf bifurcation at a finite wavelength of the applied
perturbation. However, our general conclusion is that these cohesive-zone
models are inherently unsatisfactory for use in dynamical studies. They are
extremely difficult mathematically, and they seem to be highly sensitive to
details that ought to be physically unimportant.Comment: 19 pages, REVTeX 3.1, epsf.sty, also available at
http://itp.ucsb.edu/~lobkovs