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Granular Matter

, 19:41 | Cite as

DEM simulation of polyhedral particle cracking using a combined Mohr–Coulomb–Weibull failure criterion

  • Anton Gladkyy
  • Meinhard KunaEmail author
Original Paper

Abstract

In this work, at first a new failure criterion for breakage of brittle particle systems is proposed, which combines the classical Mohr–Coulomb strength criterion with the probabilistic Weibull concept. This failure criterion is especially applicable to particle systems under compression load and accounts for the size-dependence of the material’s strength. Second, the Discrete Element Method (DEM) is implemented for sharp edged particles of convex polyhedral shape. The Mohr–Coulomb–Weibull criterion is integrated into the running DEM procedure to simulate progressive particle cracking and comminution of particle systems. The feasibility of the model was tested with simple uniaxial and triaxial compressive loading states, and the influence of relevant material parameters was studied. As a first application example of the method, an oedometric experiment was simulated, whereby coarse quartzite particles are compressed in a piston-die press. The results show good qualitative agreement with the experimentally observed particle size distribution. Thus, the ability of the suggested approach has been proved to reproduce important features as the size effect and the influence of stress state.

Keywords

DEM Polyhedral particle Failure criterion Mohr–Coulomb–Weibull Particle breakage 

Notes

Acknowledgements

The authors express their sincere appreciations to Prof. H. Lieberwirth and M. Klichowicz (Institute of Mineral Processing Machines) for the provided experimental data. This work was funded by the German Research Foundation, Project DFG KU 929/19-2.

Compliance with ethical standards

Conflict of interest

The author declares that they have no conflict of interest.

References

  1. 1.
    Cundall, P., Strack, O.: A discrete numerical model for granular assemblies. Geotechnique 29(1), 47–65 (1979)CrossRefGoogle Scholar
  2. 2.
    Weerasekara, N., Powell, M., Cleary, P., Tavares, L., Evertsson, M., Morrison, R., Quist, J., Carvalho, R.: The contribution of DEM to the science of comminution. Powder Technol. 248, 3–24 (2003). (Discrete element modelling) CrossRefGoogle Scholar
  3. 3.
    Matuttis, H.-G., Chen, J.: Understanding the Discrete Element Method: Simulation of Non-spherical Particles for Granular and Multi-body Systems. Wiley, Hoboken (2014)CrossRefzbMATHGoogle Scholar
  4. 4.
    Lu, G., Third, J., Müller, C.: Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem. Eng. Sci. 127, 425–465 (2015)CrossRefGoogle Scholar
  5. 5.
    Wang, J., Yu, H.S., Langston, P., Fraige, F.: Particle shape effects in discrete element modelling of cohesive angular particles. Granul. Matter 13(1), 1–12 (2011)CrossRefGoogle Scholar
  6. 6.
    Nassauer, B., Liedke, T., Kuna, M.: Polyhedral particles for the discrete element method. Granul. Matter 15(1), 85–93 (2013)CrossRefGoogle Scholar
  7. 7.
    Eliáš, J.: Simulation of railway ballast using crushable polyhedral particles. Powder Technol. 264, 458–465 (2014)CrossRefGoogle Scholar
  8. 8.
    Nassauer, B., Liedke, T., Kuna, M.: Development of a coupled discrete element (DEM)–smoothed particle hydrodynamics (SPH) simulation method for polyhedral particles. Comput. Part. Mech. 3(1), 95–106 (2016)CrossRefGoogle Scholar
  9. 9.
    Nassauer, B., Kuna, M.: Impact of micromechanical parameters on wire sawing: a 3D discrete element analysis. Comput. Part. Mech. 2, 63–71 (2015)CrossRefGoogle Scholar
  10. 10.
    Potyondy, D., Cundall, P.: A bonded-particle model for rock. Int. J. Rock Mech. Min. Sci. 41(8), 1329–1364 (2004)CrossRefGoogle Scholar
  11. 11.
    D’Addetta, A.G., Kun, F., Ramm, E.: On the application of a discrete model to the fracture process of cohesive granular materials. Granul. Matter 4(2), 77–90 (2002)CrossRefzbMATHGoogle Scholar
  12. 12.
    Gutierrez, A., Guichou, J.: Computational simulation of fracture of materials in comminution devices. Miner. Eng. 61, 73–81 (2014)CrossRefGoogle Scholar
  13. 13.
    Laufer, I.: Grain crushing and high-pressure oedometer tests simulated with the discrete element method. Granul. Matter 17(3), 389–412 (2015)CrossRefGoogle Scholar
  14. 14.
    Cleary, P., Sinnott, M.: Simulation of particle flows and breakage in crushers using DEM: Part 1—Compression crushers. Miner. Eng. 74, 178–197 (2015)CrossRefGoogle Scholar
  15. 15.
    Delaney, G., Morrison, R., Sinnott, M., Cummins, S., Cleary, P.: Dem modelling of non-spherical particle breakage and flow in an industrial scale cone crusher. Miner. Eng. 74, 112–122 (2015)CrossRefGoogle Scholar
  16. 16.
    Potapov, A., Campbell, C.: A three-dimensional simulation of brittle solid fracture. Int. J. Mod. Phys. C 7(5), 717–729 (1996)ADSCrossRefGoogle Scholar
  17. 17.
    Ma, G., Zhou, W., Regueiro, R., Wang, Q., Chang, X.: Modeling the fragmentation of rock grains using computed tomography and combined FDEM. Powder Technol. 308, 388–397 (2017)CrossRefGoogle Scholar
  18. 18.
    De Bono, J., McDowell, G.: Particle breakage criteria in discrete-element modelling. Geotechnique 66(12), 1014–1027 (2016)CrossRefGoogle Scholar
  19. 19.
    Lobo-Guerrero, S., Vallejo, L.E.: Crushing a weak granular material: experimental numerical analyses. Gotechnique 55(3), 245–249 (2005)CrossRefGoogle Scholar
  20. 20.
    Kloss, C., Goniva, C., Hager, A., Amberger, S., Pirker, S.: Models, algorithms and validation for opensource DEM and CFD-DEM. Prog. Comput. Fluid Dyn. Int. J. 12(2/3), 140–152 (2012)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Šmilauer, V., et al.: Yade Documentation 2nd edn. The Yade Project (2015). http://yade-dem.org/doc/. doi: 10.5281/zenodo.34073
  22. 22.
    Cundall, P.: Formulation of a three-dimensional distinct element model—Part I. A scheme to detect and represent contacts in a system composed of many polyhedral blocks. Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 25(3), 107–116 (1988)CrossRefGoogle Scholar
  23. 23.
    Eliáš, J.: Yade, polyhedra implementation. https://git.io/v6PD8 (2013)
  24. 24.
    Kettner, L.: 3D polyhedral surface. In: CGAL User and Reference Manual, 4.8.1 edn. CGAL Editorial Board (2016)Google Scholar
  25. 25.
    Guennebaud, G., Jacob, B., et al.: Eigen v3. http://eigen.tuxfamily.org (2010)
  26. 26.
    Labuz, J.F., Zang, A.: Mohr–Coulomb failure criterion. Rock Mech. Rock Eng. 45(6), 975–979 (2012)ADSCrossRefGoogle Scholar
  27. 27.
    Luding, S.: The effect of friction on wide shear bands. Part. Sci. Technol. 26(1), 33–42 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    Weibull, W.: A statistical theory of the strength of materials. Ingeniörsvetenskapsakademiens handlingar, Generalstabens litografiska anstalts förlag (1939)Google Scholar
  29. 29.
    Weibull, W.: A statistical distribution function of wide applicability. J. Appl. Mech. 18, 293–297 (1951)zbMATHGoogle Scholar
  30. 30.
    Rasche, S., Strobl, S., Kuna, M., Bermejo, R., Lube, T.: Determination of strength and fracture toughness of small ceramic discs using the small punch test and the ball-on-three-balls test. In: Procedia Materials Science, 20th European Conference on Fracture, vol. 3, pp. 961–966 (2014)Google Scholar
  31. 31.
    Tsoungui, O., Vallet, D., Charmet, J.-C., Roux, S.: Size effects in single grain fragmentation. Granul. Matter 2(1), 19–27 (1999)CrossRefGoogle Scholar
  32. 32.
    Šmilauer, V., et al.: Dem formulation. In: Yade Documentation 2nd edn. The Yade Project (2015). http://yade-dem.org/doc/. doi: 10.5281/zenodo.34044
  33. 33.
    Luding, S.: Introduction to discrete element methods. In: Darve, F., Ollivier, J.-P. (eds.) European Journal of Environmental and Civil Engineering, pp. 785–826. Lavoisier, Paris (2008)Google Scholar
  34. 34.
    Klichowicz, M., Reichert, M., Lieberwirth, H., Muetze, T.: Self-similarity and energy-size relationship of coarse particles comminuted in single particle mode. In: Proceedings of the XXVII International Mineral Processing Congress (2014)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Institute of Mechanics and Fluid DynamicsTU Bergakademie FreibergFreibergGermany

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