CRITICAL-EXAMINATION OF COHESIVE-ZONE MODELS IN THE THEORY OF DYNAMICFRACTURE

We have examined a class of cohesive-zone models of dynamic mode-I fra cture, looking both at steady-state crack propagation and its stabilit y against out-of-plane perturbations. Our work is an extension of that of Ching, Langer and Nakanishi (CLN), who studied a non-dissipative v ersion of this model and reported strong instability at all non-zero c rack speeds. We have reformulated the CLN theory and have discovered, surprisingly, that their model is mathematically ill-posed. In an atte mpt to correct this difficulty and to construct models that might exhi bit realistic behavior, we have extended the CLN analysis to include d issipative mechanisms within the cohesive zone. We have succeeded to s ome extent in finding mathematically well posed systems; and we even h ave found a class of models for which a transition from stability to i nstability may occur at a nonzero crack speed via a Hopf bifurcation a t a finite wavelength of the applied perturbation. However, our genera l conclusion is that these cohesive-zone models are inherently unsatis factory for use in dynamical studies. They are extremely difficult mat hematically, and they seem to be highly sensitive to details that ough t to be physically unimportant. (C) 1998 Elsevier Science Ltd. All rig hts reserved.