Void formation and roughening in slow fracture

Itai Afek*, Eran Bouchbinder, Eytan Katzav, Joachim Mathiesen, Itamar Procaccia

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

Slow crack propagation in ductile, and in certain brittle materials, appears to take place via the nucleation of voids ahead of the crack tip due to plastic yields, followed by the coalescence of these voids. Postmortem analysis of the resulting fracture surfaces of ductile and brittle materials on the Îm-mm and the nm scales, respectively, reveals self-affine cracks with anomalous scaling exponent ζâ‰0.8 in 3 dimensions and ζ≠0.65 in 2 dimensions. In this paper we present an analytic theory based on the method of iterated conformal maps aimed at modelling the void formation and the fracture growth, culminating in estimates of the roughening exponents in 2 dimensions. In the simplest realization of the model we allow one void ahead of the crack, and address the robustness of the roughening exponent. Next we develop the theory further, to include two voids ahead of the crack. This development necessitates generalizing the method of iterated conformal maps to include doubly connected regions (maps from the annulus rather than the unit circle). While mathematically and numerically feasible, we find that the employment of the stress field as computed from elasticity theory becomes questionable when more than one void is explicitly inserted into the material. Thus further progress in this line of research calls for improved treatment of the plastic dynamics.

Original languageAmerican English
Article number066127
JournalPhysical Review E
Volume71
Issue number6
DOIs
StatePublished - Jun 2005
Externally publishedYes

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