Published in Physical Review Letters 73, 272 (1994).
(C) 1994 The American Physical Society

INSTABILITY DYNAMICS OF FRACTURE: A COMPUTER SIMULATION INVESTIGATION

Farid F. Abraham, D. Brodbeck, R. A. Rafey, W. E. Rudge
IBM Research Division
Almaden Research Center
650 Harry Road
San Jose, CA 95120-6099

Abstract:

Implementing molecular dynamics on the IBM SP1 and PVS parallel computers, we have studied the fracture of two-dimensional notched solids under tension using million atom systems. Many recent laboratory findings occur in our simulation experiments, one of the most intriguing being the dynamic instability of the crack tip as it approaches a fraction of the sound speed. A detailed comparison between laboratory and computer experiments is presented, and microscopic processes are identified. In particular, an explanation for the limiting velocity of the crack being significantly less than the theoretical limit is provided.


Continuum fracture theory typically assumes that cracks are smooth and predicts that they accelerate to a limiting velocity equal to the Rayleigh speed of the material (1,2). In contrast, experiment tells us that, in a common fracture sequence, an initially smooth and mirrorlike fracture surface begins to appear misty and then evolves into a rough, hackled region with a limiting velocity of about six-tenths the Rayleigh speed. In some brittle materials, the crack pattern can also exhibit a wiggle of a characteristic wavelength. Recent experiments have clearly shown that violent crack velocity oscillations occur beyond a speed of about one-third the Rayleigh speed and are correlated with the roughness of the crack surface (3-5). Two different amorphous brittle materials, PMMA (3,4) and soda-lime glass (5) were used. Unlike the PMMA, soda-lime glass has nearly crystalline order at small length scales. Since both materials showed similar fracture behavior, Gross et al. concluded that the fracture dynamics may be universal (5), or materials structure independent, and that a dynamical instability of the crack tip governs the crack velocity behavior and the morphology sequence of `mirror, mist and hackle (3-5).' All of these features are unexplained using continuum theory, though recent theoretical advances (e.g., by Langer (6) and Marder (7)), are providing very important insights into this difficult problem. This suggests that a fundamental understanding may require a microscopic picture of the fracturing process. Pioneering atomistic simulations of crack propagation by Ashurst and Hoover (8) and the brittle to ductile transition by Cheung and Yip (9) were too small in size to study the crack stability issue.


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