Brittle fracture in viscoelastic materials as a pattern-formation process

Fleck, M.; Pilipenko, D.; Spatschek, R.; Brener, E. A.

doi:10.1103/PhysRevE.83.046213

Journal Article

PreJuSER-19499

Brittle fracture in viscoelastic materials as a pattern-formation process

Fleck, M. ; Pilipenko, D. ; Spatschek, R. ; Brener, E. A.FZJ*

2011
APS College Park, Md.

Physical review / E 83(4), 046213 (2011) [10.1103/PhysRevE.83.046213]

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Please use a persistent id in citations: http://hdl.handle.net/2128/9272 doi:10.1103/PhysRevE.83.046213

Abstract: A continuum model of crack propagation in brittle viscoelastic materials is presented and discussed. Thereby, the phenomenon of fracture is understood as an elastically induced nonequilibrium interfacial pattern formation process. In this spirit, a full description of a propagating crack provides the determination of the entire time dependent shape of the crack surface, which is assumed to be extended over a finite and self-consistently selected length scale. The mechanism of crack propagation, that is, the motion of the crack surface, is then determined through linear nonequilibrium transport equations. Here we consider two different mechanisms, a first-order phase transformation and surface diffusion. We give scaling arguments showing that steady-state solutions with a self-consistently selected propagation velocity and crack shape can exist provided that elastodynamic or viscoelastic effects are taken into account, whereas static elasticity alone is not sufficient. In this respect, inertial effects as well as viscous damping are identified to be sufficient crack tip selection mechanisms. Exploring the arising description of brittle fracture numerically, we study steady-state crack propagation in the viscoelastic and inertia limit as well as in an intermediate regime, where both effects are important. The arising free boundary problems are solved by phase field methods and a sharp interface approach using a multipole expansion technique. Different types of loading, mode I, mode III fracture, as well as mixtures of them, are discussed.

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Note: M. F. and D. P. are thankful for support by DFG Grant No. SPP 1418 and R. S. for support by DFG Grant No. SPP 1296. E. B. gratefully acknowledges support by the Erna and Jacob Michael visiting professorship funds at the Weizmann Institute of Science, Rehovot.

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