Abstract
The brittle fragmentation of spheres is studied numerically by a 3D Discrete Element Model. Large scale computer simulations are performed with models that consist of agglomerates of many spherical particles, interconnected by beam-truss elements. We focus on a detailed description of the fragmentation process and study several fragmentation mechanisms involved. The evolution of meridional cracks is studied in detail. These cracks are found to initiate in the inside of the specimen with quasi-periodic angular distribution and give a broad peak in the fragment mass distribution for large fragments that can be fitted by a two-parameter Weibull distribution. The results prove to be independent of the degree of disorder in the model, but mean fragment sizes scale with velocity. Our results reproduce many experimental observations of fragment shapes, impact energy dependence or mass distribution, and significantly improve the understanding of the fragmentation process for impact fracture since we have full access to the failure conditions and evolution.
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References
Andrews EW, Kim KS (1998) Threshold conditions for dynamic fragmentation of ceramic particles. Mech Mater 29: 161–180. doi:10.1016/S0167-6636(98)00014-3
Andrews EW, Kim KS (1999) Threshold conditions for dynamic fragmentation of glass particles. Mech Mater 31: 689–703. doi:10.1016/S0167-6636(99)00024-1
Antonyuk S, Khanal M, Tomas J, Heinrich S, Morl L (2006) Impact breakage of spherical granules: experimental study and DEM simulation. Chem Eng Process 45: 838–856. doi:10.1016/j.cep.2005.12.005
Arbiter N, Harris CC, Stamboltzis GA (1969) Single fracture of brittle spheres. T Soc Min Eng 244: 118–133
Åström JA (2006) Statistical models of brittle fragmentation. Adv Phys 55: 247–278. doi:10.1080/00018730600731907
Åström JA, Holian BL, Timonen J (2000) Universality in fragmentation. Phys Rev Lett 84: 3061–3064. doi:10.1103/PhysRevLett.84.3061
Åström JA, Linna RP, Timonen J, Moller PF, Oddershede L (2004) Exponential and power-law mass distributions in brittle fragmentation. Phys Rev E Stat Nonlin Soft Matter Phys 70: 026104. doi:10.1103/PhysRevE.70.026104
Behera B, Kun F, McNamara S, Herrmann HJ (2005) Fragmen- tation of a circular disc by impact on a frictionless plate. J Phys-Condens Mater 17: S2439–S2456
Bićanić N (2004) Discrete element methods. In: Stein E, de Borst R Hughes T (eds) Encyclopedia of computational mechanics: fundamentals. Wiley pp 311–337
Bolander JE, Sukumar N (2005) Irregular lattice model for quasistatic crack propagation. Phys Rev B 71: 094106. doi:10.1103/PhysRevB.71.094106
Chau KT, Wei XX, Wong RHC, Yu TX (2000) Fragmentation of brittle spheres under static and dynamic compressions: experiments and analyses. Mech Mater 32: 543–554. doi:10.1016/S0167-6636(00)00026-0
Cheong YS, Reynolds GK, Salman AD, Hounslow MJ (2004) Modelling fragment size distribution using two-parameter Weibull equation. Int J Miner Process 74: S227–S237. doi:10.1016/j.minpro.2004.07.012
Cundall PA, Strack ODL (1979) Discrete numerical-model for granular assemblies. Geotechnique 29: 47–65
Diehl A, Carmona HA, Araripe HA, Andrade JS, Farias GA (2000) Scaling behavior in explosive fragmentation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 62: 4742–4746. doi:10.1103/PhysRevE.62.4742
Gilvarry JJ, Bergstrom BH (1961) Fracture of brittle solids: 1. Distribution function for fragment size in single fracture. J Appl Phys 32: 400–410
Gilvarry JJ, Bergstrom BH (1962) Fracture of brittle solids. III. Expermental results on the distribution of fragment size in single fracture. J Appl Phys 33: 3211–3213
Herrmann, HJ, Roux, S (eds) (1990) Statistical models for the fracture of disordered media. North-Holland, Amsterdam
Herrmann HJ, Hansen A, Roux S (1989) Fracture of Disordered, elastic Lattices in 2 dimensions. Phys Rev B 39: 637–648. doi:10.1103/PhysRevB.39.637
Khanal M, Schubert W, Tomas J (2004) Ball impact and crack propagation—simulations of particle compound material. Granul Matter 5: 177–184. doi:10.1007/s10035-003-0149-3
Kun F, Herrmann HJ (1996a) Fragmentation of colliding discs. Int J Mod Phys C 7: 837–855. doi:10.1142/S0129183196000697
Kun F, Herrmann HJ (1996b) A study of fragmentation processes using a discrete element method. Comput Methods Appl M 138: 3–18. doi:10.1016/S0045-7825(96)01012-2
Kun F, Herrmann HJ (1999) Transition from damage to fragmentation in collision of solids. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 59: 2623–2632. doi:10.1103/PhysRevE.59.2623
Lilliu G, Van Mier JGM (2003) 3D lattice type fracture model for concrete. Eng Fract Mech 71: 927–941. doi:10.1016/S0013-7944(02)00158-3
Linna RP, Åström JA, Timonen J (2005) Dimensional effects in dynamic fragmentation of brittle materials. Phys Rev E Stat Nonlin Soft Matter Phys 72: 015601. doi:10.1103/PhysRevE.72.015601
Lu CS, Danzer R, Fischer FD (2002) Fracture statistics of brittle materials: weibull or normal distribution. Phys Rev E Stat Nonlin Soft Matter Phys 65: 067102. doi:10.1103/PhysRevE.65.067102
Majzoub R, Chaudhri MM (2000) High-speed photography of low-velocity impact cracking of solid spheres. Philos Mag Lett 80: 387–393. doi:10.1080/095008300403521
Meibom A, Balslev I (1996) Composite power laws in shock fragmentation. Phys Rev Lett 76: 2492–2494. doi:10.1103/PhysRevLett.76.2492
Mott NF (1946) Fragmentation of spherical cases. Proc R Soc Lond A Math Phys Sci 189: 300–308. doi:10.1098/rspa.1947.0042
Oddershede L, Dimon P, Bohr J (1993) Self-organized criticality in fragmenting. Phys Rev Lett 71: 3107–3110. doi:10.1103/PhysRevLett.71.3107
Potapov AV, Campbell CS (1996) A three-dimensional simulation of brittle solid fracture. Int J Mod Phys C 7: 717–729. doi:10.1142/S0129183196000594
Potapov AV, Campbell CS (1997) The two mechanisms of particle impact breakage and the velocity effect. Powder Technol 93: 13–21. doi:10.1016/S0032-5910(97)03242-7
Potapov AV, Hopkins MA, Campbell CS (1995) A 2-dimensional dynamic simulation of solid fracture. I. Description of the model. Int J Mod Phys C 6: 371–398. doi:10.1142/S0129183195000277
Pöschel T, Schwager T (2005) Computational granular dynamics: models and algorithms. Springer-Verlag, Berlin
Rapaport DC (2004) The art of molecular dynamics simulation. Cambridge University Press, Cambridge
Salman AD, Biggs CA, Fu J, Angyal I, Szabo M, Hounslow MJ (2002) An experimental investigation of particle fragmentation using single particle impact studies. Powder Technol 128: 36–46. doi:10.1016/S0032-5910(02)00151-1
Schönert K (2004) Breakage of spheres and circular discs. Powder Technol 143–144: 2–18
Schubert W, Khanal M, Tomas J (2005) Impact crushing of particle-particle compounds—experiment and simulation. Int J Miner Process 75: 41–52. doi:10.1016/j.minpro.2004.01.006
Thornton C, Yin KK, Adams MJ (1996) Numerical simulation of the impact fracture and fragmentation of agglomerates. J Phys D Appl Phys 29: 424–435. doi:10.1088/0022-3727/29/2/021
Thornton C, Ciomocos MT, Adams MJ (1999) Numerical simulations of agglomerate impact breakage. Powder Technol 105: 74–82. doi:10.1016/S0032-5910(99)00120-5
Tomas J, Schreier M, Groger T, Ehlers S (1999) Impact crushing of concrete for liberation and recycling. Powder Technol 105: 39–51. doi:10.1016/S0032-5910(99)00116-3
Turcotte DL (1986) Fractals and fragmentation. J Geophys Res-solid 91: 1921
Wittel FW, Kun F, Herrmann HJ, Kröplin BH (2004) Fragmen- tation shells. Phys Rev Lett 93: 035504
Wittel FW, Kun F, Herrmann HJ, Kröplin BH (2005) Breakup of shells under explosion and impact. Phys Rev E Stat Nonlin Soft Matter Phys 71: 016108. doi:10.1103/PhysRevE.71.016108
Wu SZ, Chau KT, Yu TX (2004) Crushing and fragmentation of brittle spheres under double impact test. Powder Technol 14–34: 41–55
Yip M, Li Z, Liao BS, Bolander JE (2006) Irregular lattice models of fracture of multiphase particulate materials. Int J Fract 140: 113–124. doi:10.1007/s10704-006-7636-6
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Wittel, F.K., Carmona, H.A., Kun, F. et al. Mechanisms in impact fragmentation. Int J Fract 154, 105–117 (2008). https://doi.org/10.1007/s10704-008-9267-6
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DOI: https://doi.org/10.1007/s10704-008-9267-6