SURFACE ROUGHENING AND BRANCHING INSTABILITIES IN DYNAMIC FRACTURE

WHY ARE MOST experimentally observed terminal fracture speeds only around half of the theoretically predicted value, i,e. the Rayleigh wave speed c(R)? A wavy-crack model to be discussed in this paper gives a short answer to the above question: at high speeds, cracks tend to propagate along a wavy fracture path so that the apparent crack velocity can be maintained at 0.5c(R)in order to maximize the time-rate of energy being absorbed into the fracture process. The wavy-crack model is motivated by experimental observations that rapidly moving cracks develop roughened fracture surfaces. The essence of that model is to separate the microscopic crack-tip motion with local velocity v(c) from the macroscopically observable crack motion with apparent velocity v(a). From the macroscopic point of view, the energy going into the fracture process per unit time per unit length of the crack front is approximately GAMMA(a) = (1-v(a)/c(R)v(a)G(a)*, where G(a)* denotes the quasi-static energy release rate. By propagating along a wavy path, a crack is able to maintain its apparent velocity v(a) at 0.5c(R) to maximize GAMMA(a), while it may locally propagate at a significantly higher velocity in accordance with the local energy balance between the crack driving force and the material resistance to fracture. Much theoretical investigation on the wavy-crack problem and applications remains to be done in future work. For present purposes, a perturbation analysis is used to gain some preliminary insights, particularly on issues regarding the stability of a mode I fracture path during dynamic crack propagation. The perturbation results are supportive of the notion that wavy fracture paths become favorable at high crack speeds, that the apparent crack which moves only at around 0.5c(R) favors a mode I path and tends to suppress a branching tendency, and that the local crack tip motion with significantly higher velocity promotes crack branching. Discussions on various aspects of dynamic fracture indicate that the wavy-crack model is capable of explaining important discrepancies currently existing between theory and experiments. In particular, analyses indicate that the basic mechanism of dynamic crack branching is somewhat like a thermally activated kinetic process. The fracture energy supplied from the applied loads acts as the driving force, the high inertia, branch-promoting local crack tip field acts as a nucleation source of microbranches and the relatively low inertia, branch-suppressing apparent crack sets an energetic barrier for macroscopic branching. This energy barrier is controlled by the macroscopic non-singular T(a) stress, in that it may be increased by a more compressive T(a) and decreased by a less compressive T(a).