Dynamic instabilities of fracture under biaxial strain using a phase field model.

We present a phase-field model of the propagation of fracture under plane strain. This model, based on simple physical considerations, is able to accurately reproduce the different behavior of cracks (the principle of local symmetry, the Griffith and Irwin criteria, and mode-I branching). In addition, we test our model against recent experimental findings showing the presence of oscillating cracks under biaxial load. Our model again reproduces well observed supercritical Hopf bifurcation and is therefore the first simulation which does so.

[1]  Pomeau.,et al.  Crack instabilities of a heated glass strip. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Michael P Marder,et al.  Origin of crack tip instabilities , 1994, chao-dyn/9410009.

[3]  H. Hentschel,et al.  Dynamical instabilities of quasistatic crack propagation under thermal stress. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Aranson,et al.  Continuum field description of crack propagation , 2000, Physical review letters.

[5]  J P Sethna,et al.  Fracture in mode I using a conserved phase-field model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  J. Sethna,et al.  Derivation of a general three-dimensional crack-propagation law: A generalization of the principle of local symmetry. , 1993, Physical review. B, Condensed matter.

[7]  Swinney,et al.  Instability in dynamic fracture. , 1991, Physical review letters.

[8]  K. Ravi-Chandar,et al.  An experimental investigation into dynamic fracture: I. Crack initiation and arrest , 1984 .

[9]  M. Sano,et al.  Transition between crack patterns in quenched glass plates , 1993, Nature.

[10]  Xiaopeng Xu,et al.  Numerical simulations of fast crack growth in brittle solids , 1994 .

[11]  M. Adda-Bedia.  Brittle fracture dynamics with arbitrary paths. III. The branching instability under general loading , 2005 .

[12]  H. Swinney,et al.  Oscillating fracture paths in rubber. , 2001, Physical review letters.

[13]  J. Fineberg,et al.  Propagating solitary waves along a rapidly moving crack front , 2001, Nature.

[14]  A. Karma,et al.  Phase-field model of mode III dynamic fracture. , 2001, Physical review letters.

[15]  Alain Karma,et al.  Unsteady crack motion and branching in a phase-field model of brittle fracture. , 2004, Physical Review Letters.

[16]  John R. Rice,et al.  A Critical Evaluation of Cohesive Zone Models of Dynamic Fracture , 2001 .

[17]  Jay Fineberg,et al.  Instability in dynamic fracture , 1999 .

[18]  John W. Hutchinson,et al.  Dynamic Fracture Mechanics , 1990 .

[19]  B. Lawn.  Fracture of Brittle Solids by Brian Lawn , 1993 .

[20]  Gregory J. Tallents,et al.  Temporal resolution of a transient pumping X-ray laser , 2001 .