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**An interacting micro-crack damage model for failure of brittle materials under compression.**
*(English)*
Zbl 1152.74037

Summary: A model is developed for brittle failure under compressive loading with an explicit accounting of micro-crack interactions. The model incorporates a pre-existing flaw distribution in the material. The macroscopic inelastic deformation is assumed to be due to the nucleation and growth of tensile “wing” micro-cracks associated with frictional sliding on these flaws. Interactions among the cracks are modeled by means of a crack-matrix-effective-medium approach in which each crack experiences a stress field different from that acting on isolated cracks. This yields an effective stress intensity factor at the crack tips which is utilized in the formulation of the crack growth dynamics. Load-induced damage in the material is defined in terms of a scalar crack density parameter, the evolution of which is a function of the existing flaw distribution and the crack growth dynamics. This methodology is applied for the case of uniaxial compression under constant strain rate loading. The model provides a natural prediction of a peak stress (defined as the compressive strength of the material) and also of a transition strain rate, beyond which the compressive strength increases dramatically with the imposed strain rate. The influences of the crack growth dynamics, the initial flaw distribution, and the imposed strain rate on the constitutive response and the damage evolution are studied. It is shown that different characteristics of the flaw distribution are dominant at different imposed strain rates: at low rates the spread of the distribution is critical, while at high strain rates the total flaw density is critical.

### MSC:

74R05 | Brittle damage |

74H35 | Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics |

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\textit{B. Paliwal} and \textit{K. T. Ramesh}, J. Mech. Phys. Solids 56, No. 3, 896--923 (2008; Zbl 1152.74037)

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### References:

[1] | Ashby, M.F.; Hallam, S.D., The failure of brittle solids containing small cracks under compressive stress states, Acta metall., 34, 497-510, (1986) |

[2] | Ashby, M.F.; Sammis, C.G., The damage mechanics of brittle solids in compression, Pageoph, 133, 489-521, (1990) |

[3] | Basista, M.; Gross, D., A note on crack interactions under compression, Int. J. fract., 102, L67-L72, (2000) |

[4] | Bhattacharya, K.; Ortiz, M.; Ravichandran, G., Energy-based model of compressive splitting in heterogeneous brittle solids, J. mech. phys. solids, 46, 2171-2181, (1998) · Zbl 0968.74056 |

[5] | Brace, W.F.; Bombolakis, E.G., A note on brittle crack growth in compression, J. geophys. res., 68, 3709-3713, (1963) |

[6] | Budiansky, B.; O’Connell, R.J., Elastic moduli of a cracked solid, Int. J. solids strcut., 12, 81-97, (1976) · Zbl 0318.73065 |

[7] | Chen, W.T., On an elliptic elastic inclusion in an anisotropic medium, Quart. J. mech. appl. math, 20, 307-313, (1967) · Zbl 0148.19201 |

[8] | Deng, H.; Nemat-Nasser, S., Dynamic damage evolution in brittle solids, Mech. mater., 14, 83-104, (1992) |

[9] | Eberhardt, E.; Stead, D.; Stimpson, B., Quantifying progressive pre-peak brittle fracture damage in rock during uniaxial compression, Int. J. rock mech. minor. sci., 36, 361-380, (1999) |

[10] | Eshelby, J., The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc. R. soc. London A A, 241, 376-396, (1957) · Zbl 0079.39606 |

[11] | Freund, L.B., Crack propagation in an elastic solid subjected to general loading II, Nonuniform rate of extension. J. mech. phys. solids, 20, 141-152, (1972) · Zbl 0237.73099 |

[12] | Freund, L.B., Dynamic fracture mechanics, (1990), Cambridge University Press New York · Zbl 0712.73072 |

[13] | Grady, D.E., Local inertial effects in dynamic fragmentation, J. appl. phys., 53, 322-325, (1982) |

[14] | Grady, D.E.; Kipp, M.E., Continuum modelling of explosive fracture in oil shale, Int. J. rock mech. miner. sci., 17, 147-157, (1980) |

[15] | Green, A.E.; Zerna, W., Theoretical elasticity, (1968), Clarendon Press Oxford · Zbl 0155.51801 |

[16] | Horii, H.; Nemat-Nasser, S., Elastic fields of interacting inhomogeneities, Int. J. solids strcut., 21, 731-745, (1985) · Zbl 0573.73015 |

[17] | Horii, H.; Nemat-Nasser, S., Brittle failure in compression: splitting, faulting and brittle-ductile transition, Philos. trans. R. soc. London A, 319, 337-374, (1986) · Zbl 0634.73109 |

[18] | Huang, C.; Subhash, G., Influence of lateral confinement on dynamic damage evolution during uniaxial compressive response of brittle solids, J. mech. phys. solids, 51, 1089-1106, (2003) · Zbl 1049.74040 |

[19] | Huang, C.; Subhash, G.; Vitton, S.J., A dynamic damage growth model for uniaxial compressive response of rock aggregates, Mech. mater., 34, 267-277, (2002) |

[20] | Huang, Y.; Hu, K.X.; Chandra, A., A generalized self-consistent mechnaics method for microcracked solids, J. mech. phys. solids, 42, 1273-1291, (1994) · Zbl 0807.73038 |

[21] | Kachanov, M., Elastic solids with many cracks: a simple method of analysis, Int. J. solids strcutures, 23, 23-43, (1987) · Zbl 0601.73096 |

[22] | Kobayashi, A.S., Dynamic fracture of ceramics and CMC, (), 185-196 |

[23] | Lankford, J., Mechanisms responsible for strain rate dependent compressive strength in ceramic materials, J. am. ceram. soc., 64, C33-C35, (1981) |

[24] | Lankford, J., High strain rate compression and plastic flow of ceramics, J. mater. sci. lett., 15, 745-750, (1996) |

[25] | Nemat-Nasser, S.; Deng, H., Strain-rate effect on brittle failure in compression, Acta metall. mater., 42, 1013-1024, (1994) |

[26] | Nemat-Nasser, S.; Horii, H., Compression induced nonplanar crack extension with application to splitting, exfoliation and rockburst, J. geophys. res., 87, 6805-6821, (1982) |

[27] | Nemat-Nasser, S.; Obata, M., A microcrack model of dilatancy in brittle materials, Trans. ASME J. appl. mech., 55, 24-35, (1988) |

[28] | Paliwal, B.; Ramesh, K.T.; McCauley, J.W., Direct observation of the dynamic compressive failure of a transparent polycrystalline ceramic (Alon), J. am. ceram. soc., 89, 2128-2133, (2006) |

[29] | Ravichandran, G.; Subhash, G., A micromechanical model for high strain rate behavior of ceramics, Int. J. solids struct., 32, 2627-2646, (1995) · Zbl 0881.73112 |

[30] | Rosakis, A.J.; Ravichandran, G., Dynamic failure mechanics, Int. J. solids strcut., 37, 331-348, (2000) · Zbl 1075.74070 |

[31] | Sarva, S.; Nemat-Nasser, S., Dynamic compressive strength of silicon carbide under unaxial compression, Mater. sci. eng. A, 317, 140-144, (2001) |

[32] | Schulson, E.M.; Kuehn, G.A.; Jones, D.A.; Fifolt, D.A., The growth of wing cracks and the brittle compressive failure of ice, Acta metall. mater., 39, 2651-2655, (1991) |

[33] | Shao, J.F.; Rudnicki, J.W., A microcrack-based continuous damage model for brittle geomaterials, Mech. mater., 32, 607-619, (2000) |

[34] | Suresh, S.; Nakamura, T.; Yeshurun, Y.; Yang, K.-H.; Duffy, J., Tensile fracture toughness of ceramic materials: effects of dynamic loading and elevated temperatures, J. am. ceram. soc., 73, 2457-2466, (1990) |

[35] | Tapponnier, P.; Brace, W.F., Development of stress-induced microcracks in westerly granite, Int. J. rock mech. miner. sci., 13, 103-112, (1976) |

[36] | Vekinis, G.; Ashby, M.F.; Beaumont, P.W.R., The compressive failure of alumina containing controlled distributions of flaws, Acta metall. mater., 39, 2583-2588, (1991) |

[37] | Wang, H.; Ramesh, K.T., Dynamic strength and fragmentation of hot-pressed silicon carbide under uniaxial compression, Acta mater., 52, 355-367, (2003) |

[38] | Weerasooriya, T.; Moy, P.; Casem, D., A four-point bend technique to determine dynamic fracture toughness of ceramics, J. am. ceram. soc., 89, 990-995, (2006) |

[39] | Xu, X.H.; Ma, S.P.; Xia, M.F.; Ke, F.J.; Bai, Y.L., Damage evaluation and damage localization of rock, Theor. appl. fract. mech., 42, 131-138, (2004) |

[40] | Zhou, F.; Molinari, J.-F.; Ramesh, K.T., Effects of material properties on the fragmentation of brittle materials, Int. J. fract., 139, 169-196, (2006) · Zbl 1197.74150 |

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