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Deterministic Micromechanical Modelling of Failure or Flow in Discrete Planes of Densely Packed Particle Assemblies: Introductory Principles

  • Chapter
Granular Matter

Abstract

This introductory review of dense-phase powder flows consists of two parts. The first, concerned with the precedents in continuous or dense solids, discusses three topics: plastic flow, fracture, and solid-solid friction. The second part follows this scheme for particle systems, drawing on the descriptions provided for continua. The intention is to provide a general introduction to these topics for those readers who have only a limited familiarity with this subject, which is now attracting a growing interest as reflected, for example, at the winter school on the physics of granular media, held at Les Houches Physics Centre, France (Bideau and Dodds, 1991).

Little drops of water, little grains of sand, Make the mighty ocean and the pleasant land, So the little minutes, humble though they may be, Make the mighty ages of eternity.

(Julia A. Fletcher Carney [1823–1908], Little Things)

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References

  • Abdel-Ghani, M, Petrie, J.G., Seville, J.P.K., Clift, R., and Adams, M.J., Mechanical properties of cohesive particulate solids, Powder Technol., 65, 113–123, 1991.

    Article  Google Scholar 

  • Adams, M.J., Friction of granular non-metals, in Fundamentals of Friction, Singer, I.L. and Pollock, H.M., Eds., Kluwer Academic, Dordrecht, 1992, pp. 183–207.

    Google Scholar 

  • Adams, M.J. and Edmondson, B., Forces between particles in continuous and discrete liquid media, in Tribology in Particulate Technology, Briscoe B.J. and Adams, M.J., Eds., Adam Hilger, Bristol, 1987, pp. 154–172.

    Google Scholar 

  • Adams, M.J. and Seville, J.P.K., 1991, Unpublished data.

    Google Scholar 

  • Adams, M.J., Briscoe, B.J., and Kremnitzer, S.L., A survey of the adhesion, friction and lubrication of polyethyleneterephthalate monofilaments, in Physicochemical Aspects of Polymer Surfaces, Vol. I, Mittal, K.K., Ed., Plenum, New York, 1983, pp. 425–450.

    Google Scholar 

  • Adams, M.J., Briscoe, B.J., and Pope, L., A contact mechanics approach to the prediction of the wall friction of powders, in Tribology in Particulate Technology, Briscoe, B.J. and Adams, M.J., Eds., Adam Hilger, Bristol, 1987, pp. 8–22.

    Google Scholar 

  • Adams, M.J., Williams, D., and Williams, J.G., The use of linear elastic fracture mechanics for particulate solids, J. Materials Sci., 24, 1772–1776, 1989.

    Article  ADS  Google Scholar 

  • Adams, M.J., Briscoe, B.J., and Wee, T.K., The differential friction effect of keratin fibres, J. Phys. D: Appl. Phys., 23, 406–414, 1990.

    Article  ADS  Google Scholar 

  • Adams, M.J., Briscoe, B.J., Montamedi, F., and Streat, M., The frictional characteristics of coal particles, J. Phys. D: Appl. Phys., 26, 73–82, 1993a.

    Article  ADS  Google Scholar 

  • Adams, M.J., Briscoe, B.J., Kamjab, M., The deformation and flow of highly concentrated dispersions, Adv. Colloid Interface Sci., 1993b, in press.

    Google Scholar 

  • Adams, M.J., Mullier, M.A., and Seville, J.P.K., Agglomerate strength measurement using a uniaxial confined compression test, Powder Technol., 1993c, submitted.

    Google Scholar 

  • Bashir, Y.M. and Goddard, J.D., A novel simulation method for the quasi-static mechanics of granular assemblages, J. Rheol., 35, 849–885, 1991.

    Article  ADS  Google Scholar 

  • Bideau, D. and Dodds, D., Eds., Physics of Granular Media, Nova Science Publishers, New York, 1991.

    Google Scholar 

  • Bowden, F.P. and Tabor, D., Friction and Lubrication of Solids, Oxford University Press, London, 1954

    Google Scholar 

  • Bowden, P.B. and Jukes, J. A., The plastic yield behaviour of polymethylmethacrylate, J. Materials Sci., 3, 183–190, 1968.

    Article  ADS  Google Scholar 

  • Bridgman, P.W., The Physics of High Pressure, Dover, New York, 1970.

    Google Scholar 

  • Briscoe, B.J., The shear properties of thin organic films, in Reviews on the Deformation Behaviour of Materials, Vol. III, No. 3, Feltham, P., Ed., Scientific Publications, Israel, 1980, pp. 151–191.

    Google Scholar 

  • Briscoe, B.J., Friction, fact and fiction, Chem. Ind., pp. 467–474, July 17, 1982.

    Google Scholar 

  • Briscoe, B.J. and Smith, A.C., Polymer friction and polymer yield: a comparison, Polymer, 22, 1587–1590, 1981.

    Article  Google Scholar 

  • Briscoe, B.J., Pope, L., and Adams, M.J., The influence of particle surface topography on the interfacial friction of powders, in I. Chem. E. Symp. Ser., No. 91, I. Chem. E., Rugby, pp. 197–211, 1985a.

    Google Scholar 

  • Briscoe, B.J., Winkler, A., and Adams, M.J., A statistical analysis of the frictional forces generated between monofilaments during intermittent sliding, J. Phys. D: Appl. Phys., 18, 2143–2167, 1985b.

    Article  ADS  Google Scholar 

  • Burns, S.J. and Lawn, B.R., A simulated crack experiment illustrating the energy balance criterion, Int. J. Fract. Mech., 4, 339–345, 1968.

    Google Scholar 

  • Chakrabarty, J., Theory of Plasticity, McGraw-Hill, New York, 1987.

    Google Scholar 

  • Charalambides, M., Kinlock, A.J., Wang, Y., and Williams, J.G., On the analysis of mixed-mode failure, 1992, to be published.

    Google Scholar 

  • Chudnovsky, A., Saada, A., and Lesser, A.J., Micromechanisms of deformation in fracture in overconsolidated clays, Can. Geotech. J., 25, 213–221, 1988.

    Article  Google Scholar 

  • Coulomb, C.A., in Memoires de mathematique et de physique (Academie des Sciences par divers savans), 7, 343–382, 1776.

    Google Scholar 

  • Desrues, J., Lauier, J., and Stutz, P., Localisation of the deformation in tests on sand samples, Eng. Fract. Mech., 21, 909–921, 1985.

    Article  Google Scholar 

  • Dowson, D., History of Tribology, Longman, London, 1979.

    Google Scholar 

  • Drescher, A., Analytical Methods in Bin-Load Analysis, Elsevier, Amsterdam, 1991.

    Google Scholar 

  • Fisher, L.R. and Israelachvili, J.N., Direct measurement of the effect of meniscus forces on adhesion: a study of the applicability of macroscopic thermodynamics to microscopic liquid interfaces, Colloids Surf., 3, 303–319, 1981.

    Article  Google Scholar 

  • Greenwood, J.A. and Johnson, K.L., The mechanics of adhesion of viscoelastic solids, Philos. Mag., 43, 697–711, 1981.

    Article  ADS  Google Scholar 

  • Greenwood, J.A. and Williamson, J.B.P., Contact of nominally flat surfaces, Proc. R. Soc. Lond. A, 295, 300–319, 1966.

    Article  ADS  Google Scholar 

  • Griffith, A.A. The phenomenon of rupture and flow in solids, Phil. Trans. R. Soc. Lond. A, 221, 163–198, 1921.

    Article  ADS  Google Scholar 

  • Hardy, W., Boundary lubrication — plane surfaces and the limitations of Amonton’s law, Proc. R. Soc. Lond. A, 108, 1–27, 1925.

    Article  ADS  MathSciNet  Google Scholar 

  • Holeman, L.E., The compaction behaviour of particulate materials. An elucidation based on percolation theory, Powder Technol., 66, 265–280, 1991.

    Article  Google Scholar 

  • Horne, M.R., The behaviour of rotund, rigid, cohesionless particles, Proc. R. Soc. Lond. A, 286, 62–97, 1965.

    Article  ADS  Google Scholar 

  • Hubner, H. and Jillek, W., Sub-critical crack extension and crack resistance in polycrystalline alumina, J. Materials Sci., 12, 117–125, 1977.

    Article  ADS  Google Scholar 

  • Hull, D., and Bacon, D.J., Introduction to Dislocations, Pergamon Press, Oxford, 1984.

    Google Scholar 

  • Irwin, G.R., Analysis of stresses and strains near the end of a crack traversing a plate, Trans. ASME: J. Appl. Mech., 24, 361–400, 1957.

    Google Scholar 

  • Isherwood, D.P., Die wall friction effects in the compaction of polymer granules, in Tribology in Particulate Technology, Briscoe, B.J. and Adams, M.J., Eds., Adam Hilger, Bristol, 1987, pp. 234–248.

    Google Scholar 

  • Johnson, K.L., Kendall, K., and Roberts, A.D., Surface free energy and the contact of elastic solids, Proc. R. Soc. Lond. A, 324, 301–313, 1971.

    Article  ADS  Google Scholar 

  • Kendall, K., Alford, N. McN., and Birchall, J.D., The strength of green bodies, in Ceram. Proc. Spec. Ceramics, No. 8, Inst. Ceramics, Stoke-on-Trent, pp. 255–265, 1986.

    Google Scholar 

  • Mandl, G. and Fernandez Luque, R., Fully developed plastic shear flow of granular materials, Geotechnique, 20, 277–307, 1970.

    Article  Google Scholar 

  • Matsuoka, H., A microscopic study on shear mechanism of granular materials, Soils Found., 14, 29–43, 1974.

    Article  Google Scholar 

  • Mehta, A. and Barker, G.C., Vibrated powders—a microscopic approach, Phys. Rev. Lett., 67, 394–397, 1991.

    Article  ADS  Google Scholar 

  • Mohr, O., Zeitschrift des Vereines Deutscher Ingenieure, 44, 1524–1530, 1900.

    Google Scholar 

  • Morgenstern, N.R. and Tchalenko, J.S., Microscopic structures in kaolin subjected to direct shear, Geotechnique, 17, 309–328, 1967.

    Article  Google Scholar 

  • Nedderman, R.M. and Laohakul, C., The thickness of the shear zone of flowing granular materials, Powder Technol., 25, 91–100, 1980.

    Article  Google Scholar 

  • Nemat-Nasser, S., On the behaviour of materials in simple shear, Soils Found., 20, 59–73, 1980.

    Article  Google Scholar 

  • Newland, P.L. and Allely, B.H., Volume changes in drained triaxial tests on granular materials, Geotechnique, 7, 17–34, 1957.

    Article  Google Scholar 

  • Oda, M., Significance of fabric in granular mechanics, in Proc. U.S./Japan Seminar on Continuum Mechanical and Statistical Approaches in the Mechanics of Granular Materials, Cowin, S.T. and Satake, M., Eds., National Science Foundation and Japan Society for the Promotion of Science, pp. 7–26, 1978.

    Google Scholar 

  • Palmer, A.C. and Rice, J.R., The growth of slip surfaces in the progressive failure of over-consolidated clay, Proc. R. Soc. Lond. A, 332, 527–548, 1973.

    Article  ADS  MATH  Google Scholar 

  • Parker, A.P., The Mechanics of Fracture and Fatigue, E. & F.N. Spon., London, 1981.

    MATH  Google Scholar 

  • Paul, B., Macroscopic criteria for plastic flow and brittle fracture, in Fracture, An Advanced Treatise, Vol. II, Mathematical Fundamentals, Liebowitz, H., Ed., Academic Press, New York, 1968, pp. 315–496.

    Google Scholar 

  • Rankine, W.J.M., A Manual of Applied Mechanics, 1st ed., Griffin, London, 1858.

    Google Scholar 

  • Reynolds, O., On the dilatancy of media composed of rigid particles in contact, Philos. Mag., 8, 22–53, 1885.

    Google Scholar 

  • Rice, J.R., A path independent integral and approximate analysis of strain concentration by notches and cracks, J. Appl. Mech., 35, 379–386, 1968.

    Google Scholar 

  • Roscoe, K.H., The influence of strains in soil mechanics. 10th Rankine lecture, Geotechnique, 20, 327–346, 1978.

    Google Scholar 

  • Roscoe, K.H. and Schofield, A.N., Discussion of Rowe, J. Soil Mech. Fdns. Am. Soc. Civ. Eng., 90, 136–150, 1964.

    Google Scholar 

  • Rowe, P.W., The stress-dilatancy relation for static equilibrium of an assembly of particles in contact, Proc. R. Soc. Lond. A, 269, 500–527, 1962.

    Article  ADS  Google Scholar 

  • Savage, S.B., Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech., 53–96, 1979.

    Google Scholar 

  • Singer, I.L. and Pollock, H.M., Fundamentals of Friction, Kluwer Academic, Dordrecht, 1992.

    Google Scholar 

  • Smid, J. and Novosad, J., Pressure distribution under heaped bulk solids, I, Chem. E. Symp. Ser., No. 63, P3D/V/1–12, 1981.

    Google Scholar 

  • Sokolovski, V.V., Statics of Granular Media, Pergamon Press, New York, 1965.

    Google Scholar 

  • Spencer, R.S., Gilmore, G.D., and Wiley, R.M., Behaviour of granulated powders under pressure, J. Appl. Phys., 21, 527–531, 1953.

    Article  ADS  Google Scholar 

  • Stephens, D.J. and Bridgwater, J., The mixing and segregation of cohesionless particulate materials. 1. Failure zone formation, Powder Technol., 21, 17–28, 1978.

    Article  Google Scholar 

  • Swain, M.V., Microfracture about scratches in brittle solids, Proc. R. Soc. Lond. A, 366, 575–597, 1979.

    Article  ADS  Google Scholar 

  • Taylor, G.I., The mechanism of plastic deformation of crystals, Proc. R. Soc. Lond., 145, 362–404, 1934.

    Article  ADS  MATH  Google Scholar 

  • Terzaghi, K. and Peck, R.B., Soil Mechanics in Engineering Practice, 2nd ed., John Wiley & Sons, New York, 1967.

    Google Scholar 

  • Thornton, C., Computer-simulated experiments on particulate materials, in Particulate Technology, Briscoe, B.J. and Adams, M.J., Eds., Adam Hilger, Bristol, 1987, pp. 292–302.

    Google Scholar 

  • Thornton, C., 1991, Private communication.

    Google Scholar 

  • Timoshenko, S., Theory of Elasticity, McGraw-Hill, New York, 1934.

    MATH  Google Scholar 

  • Tokue, T., A stress-dilatancy model of granular material under general stress conditions, Soils Found., 19, 63–80, 1979.

    Google Scholar 

  • Travers, T., Bideau, D., Gervois, A., Troadec, J.P., and Messager, J.C., Uniaxial compression effects on 2D mixtures of hard and soft cylinders, J. Phys. A: Math. Gen., 19, L1033–L1038, 1986.

    Article  ADS  Google Scholar 

  • Tüzün, U., Adams, M.J., and Briscoe, B.J., An interface dilation model for the prediction of wall friction in a particulate bed, Chem. Eng. Sci., 43, 1083–1098, 1988.

    Article  Google Scholar 

  • Ueng, T.S. and Lee, C.J., Deformation of sand under shear—particulate approach, J. Geotech. Eng., 116, 1625–1640, 1990.

    Article  Google Scholar 

  • Ward, I.M., Mechanical Properties of Solid Polymers, John Wiley & Sons, London, 1971.

    Google Scholar 

  • Walton, O.R., Braun, R.L., Mallon, R.G., and Cervellie, D.K., Particle-dynamics calculations of gravity flow inelastic frictional spheres, in Micromechanics of Granular Materials, Sutake, M. and Jenkins, J.T., Eds., Elsevier, Amsterdam, 1988, pp. 153–162.

    Google Scholar 

  • Williams, J.G., Fracture Mechanics of Polymers, Ellis Horwood, Chichester, 1984.

    Google Scholar 

  • Wu, S., Polymer Interface and Adhesion, Marcel Dekker, New York, 1982.

    Google Scholar 

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Authors
  1. M. J. Adams
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  2. B. J. Briscoe
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Editors and Affiliations

  1. Interdisciplinary Research Center in Advanced Materials, University of Birmingham, Edgbaston, Birmingham, B15 2TT, UK

    Anita Mehta

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Adams, M.J., Briscoe, B.J. (1994). Deterministic Micromechanical Modelling of Failure or Flow in Discrete Planes of Densely Packed Particle Assemblies: Introductory Principles. In: Mehta, A. (eds) Granular Matter. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4290-1_8

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  • DOI: https://doi.org/10.1007/978-1-4612-4290-1_8

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8725-4

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