Nasr Ghoniem^*, Andrew Sheng, and Giacomo Po

University of California at Los Angeles, Los Angeles, California, USA

Computational modeling of complex fracture phenomena, where multiple  cracks propagate and interact in three-dimensional geometry is a very challenging task that has not been satisfactorily demonstrated.  Despite huge technological incentives, most of the exisiting methods are limited to simple geometry and a small number of interacting cracks.  The main reason appears to be the conceptual way that cracks are currently modeled as a disruption to an otherwise perfect continuum.

We have developed a fundamentally different approach to modeling discontinuities and defects in materials, namely the method of Parametric Dislocation Dynamics (PDD), where discrete crystal dislocations are represented by parametric space curves, and their collective interactions in 3-D is completely resolved [1-3].  It has been known for a while that cracks can be represented by a suitable distribution of discontinuities (Volterra or Somigliana type dislocations), where the Burgers vector can be either fixed (Volterra), or locally variable (Somigliana).  Thus, such objects can provide enormous flexibility in modeling complex shape cracks and their mutual interactions, if only a computational method can be developed.  We present here a new approach to modeling complex facture phenomena by extending the robust framework of our PDD method.  We show that suitable choices of the Volterra Burgers vector enables dislocation arrays to represent 2-D cracks in modes I, II, and III [4,5].  Moreover, it is shown that the Peach-Koehler force, which is the basis for motion and equilibrium in PDD simulations, is equivalent to the J-integral in fracture mechanics problems.  Crack propagation is shown to be a natural extension to dislocation motion in PDD simulations.  Several examples of crack problems in 3-D finite geometry will also be given to illustrate the utility of the proposed approach.

REFERNCES

[1] RJ Amodeo, NM Ghoniem “Dislocation dynamics. I. A proposed methodology for deformation micromechanics,” Physical Review B 41 (10), 6958, 1990.

[2] NM Ghoniem, SH Tong, LZ Sun “Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation,” Physical Review B 61 (2), 913, 2000.

[3] G Po, NM Ghoniem, “A variational formulation of constrained dislocation dynamics coupled with heat and vacancy diffusion,” JMPS, in Press, 2013.

[4] Nasr M. Ghoniem and Jianming Huang, "The Elastic Field of General-Shape 3-D Cracks," Phil. Mag., 86(27): 4195-4212 (2006).

[5] Akiyuki Takahashi and Nasr M. Ghoniem, " Fracture Mechanics of Propagating 3-D Fatigue Cracks with Parametric Dislocations," Phil. Mag., 93(20), 2662–2679 (2013).

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*Presenting Author