##
**Numerical simulations of fast crack growth in brittle solids.**
*(English)*
Zbl 0825.73579

Summary: Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that, for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about \(29^\circ\) from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.

PDF
BibTeX
XML
Cite

\textit{X. P. Xu} and \textit{A. Needleman}, J. Mech. Phys. Solids 42, No. 9, 1397--1434 (1994; Zbl 0825.73579)

Full Text:
DOI

### References:

[1] | Belytschko, T.; Chiapetta, R. L.; Bartel, H. D., Efficient large scale non-linear transient analysis by finite elements, Int. J. Numer. Meth. Engng, 10, 579-596 (1976) |

[2] | Belytschko, T.; Lu, Y. Y.; Gu, L., Element free Galerkin methods, Int. J. Numer. Meth. Engng, 37, 229-256 (1994) · Zbl 0796.73077 |

[3] | Broberg, K. B., On the behaviour of the process region at a fast running crack tip, (Kawata, K.; Shioiri, J., High Velocity Deformation of Solids (1979), Springer: Springer Berlin, Heidelberg), 182-194 |

[4] | Eshelby, J. D., Energy relations and the energy-momentum tensor in continuum mechanics, (Kanninen, M. F.; Adler, W. F.; Rosenfield, A. R.; Jaffe, R. I., Inelastic Behavior of Solids (1970), McGraw-Hill: McGraw-Hill New York, NY), 77-115 |

[5] | Field, J. E., Brittle fracture: its study and application, Contemp. Phys., 12, 1-31 (1971) |

[6] | Fineberg, J.; Gross, S. P.; Marder, M.; Swinney, H. L., Instability in the propagation of fast cracks, Phys. Rev., B45, 5146-5154 (1992) |

[7] | Finot, M.; Shen, Y.-L.; Needleman, A.; Suresh, S., Micromechanical modelling of reinforcement fracture in particle-reinforced metal-matrix composites, Metall. Trans. (1994), (to be published) |

[8] | Freund, L. B., Crack propagation in an elastic solid subject to general loadingâ€”I. Constant rate of extension, J. Mech. Phys. Solids, 20, 129-140 (1972) · Zbl 0237.73099 |

[9] | Freund, L. B., Dynamic Fracture Mechanics (1990), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0712.73072 |

[10] | Gao, H., Surface roughening and branching instabilities in dynamic fracture, J. Mech. Phys. Solids, 41, 457-486 (1993) |

[11] | Johnson, E., Process region changes for rapidly propagating cracks, Int. J. Fract., 55, 47-63 (1992) |

[12] | Johnson, E., Process region influence on energy release rate and crack tip velocity during rapid crack propagation, Int. J. Fract., 61, 183-187 (1993) |

[13] | Krieg, R. D.; Key, S. W., Transient shell response by numerical time integration, Int. J. Numer. Meths. Engng, 7, 273-286 (1973) |

[14] | Kulakhmetova, Sh. A.; Saraikin, V. A.; Slepyan, L. I., Plane problem of a crack in a lattice, Mech. Solids, 19, 102-108 (1984) |

[15] | Lee, O. S.; Knauss, W. G., Dynamic crack propagation along a weakly bonded plane in a polymer, Exp. Mech., 29, 342-345 (1989) |

[16] | Levy, A. J., Separation at a circular interface under biaxial load, J. Mech. Phys. Solids, 42, 1087-1104 (1994) · Zbl 0800.73346 |

[17] | Marder, M.; Liu, X., Instability in lattice fracture, Phys. Rev. Lett., 71, 2417-2420 (1993) |

[18] | McClintock, F. A.; Argon, A. S., Mechanical Behavior of Materials (1966), Addison-Wesley: Addison-Wesley Reading, MA |

[19] | Nakamura, T.; Shih, C. F.; Freund, L. B., Computational methods based on an energy integral in dynamic fracture, Int. J. Fract., 27, 229-243 (1985) |

[20] | Needleman, A., A continuum model for void nucleation by inclusion debonding, J. Appl. Mech., 54, 525-531 (1987) · Zbl 0626.73010 |

[21] | Needleman, A., An analysis of decohesion along an imperfect interface, Int. J. Fract., 42, 21-40 (1990) |

[22] | Needleman, A., An analysis of tensile decohesion along an interface, J. Mech. Phys. Solids, 38, 289-324 (1990) |

[23] | Needleman, A.; Tvergaard, V., An analysis of ductile rupture modes at a crack tip, J. Mech. Phys. Solids, 35, 151-183 (1987) · Zbl 0601.73106 |

[24] | Povirk, G. L.; Needleman, A.; Nutt, S. R., An analysis of the effect of residual stresses on deformation and damage mechanisms in Al-SiC composites, Mater. Sci. Engng, A132, 31-38 (1991) |

[25] | Ravi-Chandar, K.; Knauss, W. G., An experimental investigation into dynamic fracture: I. Crack initiation and arrest, Int. J. Fract., 25, 247-262 (1984) |

[26] | Ravi-Chandar, K.; Knauss, W. G., An experimental investigation into dynamic fracture: II. Microstructural aspects, Int. J. Fract., 26, 65-80 (1984) |

[27] | Ravi-Chandar, K.; Knauss, W. G., An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching, Int. J. Fract., 26, 141-154 (1984) |

[28] | Rice, J. R., A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35, 379-386 (1968) |

[29] | Rice, J. R.; Ben-Zion, Y.; Kim, K.-S., Three-dimensional perturbation solution for a dynamic planar crack moving unsteadily in a model elastic solid, J. Mech. Phys. Solids, 42, 813-843 (1994) · Zbl 0806.73056 |

[30] | Rose, J. H.; Ferrante, J.; Smith, J. R., Universal binding energy curves for metals and bimetallic interfaces, Phys. Rev. Lett., 47, 675-678 (1981) |

[31] | Slepyan, L. I., Principle of maximum energy dissipation rate in crack dynamics, J. Mech. Phys. Solids, 41, 1019-1033 (1993) · Zbl 0775.73214 |

[32] | Suo, Z.; Ortiz, M.; Needleman, A., Stability of solids with interfaces, J. Mech. Phys. Solids, 40, 613-640 (1992) · Zbl 0760.73030 |

[33] | Tvergaard, V., Influence of void nucleation on ductile shear fracture at a free surface, J. Mech. Phys. Solids, 30, 399-425 (1982) · Zbl 0496.73087 |

[34] | Tvergaard, V., Effect of fibre debonding in a whisker-reinforced metal, Mater. Sci. Engng, A125, 203-213 (1990) |

[35] | Tvergaard, V.; Hutchinson, J. W., The relation between crack growth resistance and fracture process parameters in elastic plastic solids, J. Mech. Phys. Solids, 40, 1377-1392 (1992) · Zbl 0775.73218 |

[36] | Tvergaard, V.; Hutchinson, J. W., The influence of plasticity on mixed mode interface toughness, J. Mech. Phys. Solids, 41, 1119-1135 (1993) · Zbl 0775.73219 |

[37] | Tvergaard, V.; Needleman, A., An analysis of the brittle ductile transition in dynamic crack growth, Int. J. Fract., 59, 53-67 (1993) |

[38] | Xu, X.-P.; Needleman, A., Void nucleation by inclusion debonding in a crystal matrix, Modell. Simul. Mater. Sci. Engng, 1, 111-132 (1993) |

[39] | Xu, X.-P.; Needleman, A., Continuum modelling of interfacial decohesion, (Rabier, J.; George, A.; Brechct, Y.; Kubin, L., Dislocations |

[40] | Yoffe, E. H., The moving Griffith crack, Phil. Mag., 42, 739-750 (1951) · Zbl 0043.23504 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.