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Estimation of Energy of Fracture Initiation in Brittle Materials with Cracks

  • Ruslan L. Lapin
  • Nikita D. Muschak
  • Vadim A. Tsaplin
  • Vitaly V. KuzkinEmail author
  • Anton M. Krivtsov
Chapter
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 100)

Abstract

We study deformation and fracture of a brittle material under mixed quasi-static loading. Numerical simulations of deformation of a cubic sample containing a single crack are carried out using the particle dynamics method. Effect of ratio of compressive and shear loads on energy of fracture initiation is investigated for two crack shapes and various crack orientations. The energy of fracture initiation in a material containing multiple cracks is estimated using the non-interaction approximation. It is shown that in the case of mixed loading (compression and shear) the energy is significantly lower than in the case of pure compression. Presented results may serve for minimization of energy consumption during disintegration of solid minerals.

Keywords

Brittle fracture Fracture initiation Cracks Particle dynamics method Desintegration of rocks Energy consumption 

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Notes

Acknowledgements

This work was supported by the Russian Science Foundation (Grant No. 17-79-30056). The authors are deeply grateful L.A Vaisberg for formulation of the problem and useful discussions. The work was initiated in the course of joint investigation of technological processes of vibration disintegration of materials, the main developer of which is REC “Mekhanobr-Tekhnika”. Numerical modeling was performed using the Polytechnic supercomputer center at Peter the Great St. Petersburg Polytechnic University.

References

  1. Altenbach H, Öchsner A (eds) (2011) Cellular and Porous Materials in Structures and Processes, CISM International Centre for Mechanical Sciences, vol 521. Springer, ViennaGoogle Scholar
  2. Altenbach H, Sadowski T (eds) (2015) Failure and Damage Analysis of Advanced Materials, CISM International Centre for Mechanical Sciences, vol 560. Springer, ViennaGoogle Scholar
  3. Bîrsan M, Altenbach H (2011) On the theory of porous elastic rods. International Journal of Solids and Structures 48(6):910 – 924Google Scholar
  4. Bratov VA, Krivtsov AM (2016) Analysis of energy required for initiation of inclined crack underGoogle Scholar
  5. uniaxial compression and mixed loading. Engineering Fracture Mechanics 219:106,518Google Scholar
  6. Grechka V, Kachanov M (2006) Effective elasticity of rocks with closely spaced and intersecting cracks. GEOPHYSICS 71(3):D85–D91Google Scholar
  7. Jaworski D, Linkov A, Rybarska-Rusinek L (2016) On solving 3d elasticity problems for inhomoge- neous region with cracks, pores and inclusions. Computers and Geotechnics 71(6):295–309Google Scholar
  8. Kachanov M (1999) Solids with cracks and non-spherical pores: proper parameters of defect density and effective elastic properties. International Journal of Fracture 97(1-4):1 – 32Google Scholar
  9. Kachanov M, Sevostianov I (2005) On quantitative characterization of microstructures and effective properties. International Journal of Solids and Structures 42(2):309 – 336Google Scholar
  10. Kachanov M, Sevostianov I (2018) Micromechanics of Materials, with Applications, Solid Mechanics and Its Applications, vol 249. SpringerGoogle Scholar
  11. Krivtsov AM (2003) Molecular dynamics simulation of impact fracture in polycrystalline materials. Meccanica 38(01):61–70Google Scholar
  12. Krivtsov AM (2004) Molecular dynamics simulation of plastic effects upon spalling. Physics of the Solid State 46(6):1055–1060Google Scholar
  13. Krivtsov AM (2007) Deformation and Fracture of Solids with a Microstructure (in Russ.). Fizmatlit, MoscowGoogle Scholar
  14. Kumar M, Han D (2005) Pore shape effect on elastic properties of carbonate rocks, Society of Exploration Geophysicists, pp 1477–1480Google Scholar
  15. Kuna M (2013) Finite Elements in Fracture Mechanics, Solid Mechanics and Its Applications, vol 213. Springer NetherlandsGoogle Scholar
  16. Kushch VI, Sevostianov I, Mishnaevsky L (2009) Effect of crack orientation statistics on effective stiffness of mircocracked solid. International Journal of Solids and Structures 46(6):1574 – 1588Google Scholar
  17. Linkov AM (2002) Boundary Integral Equations in Elasticity Theory. Kluwer Academic Publishers, Dordrecht-Boston-LondonGoogle Scholar
  18. Min KB, Jing L (2003) Numerical determination of the equivalent elastic compliance tensor for fractured rock masses using the distinct element method. International Journal of Rock Mechanics and Mining Sciences 40(6):795 – 816Google Scholar
  19. Novozhilov VV (1969) On a necessary and sufficient criterion for brittle strength. Journal of Applied Mathematics and Mechanics 33(2):201 – 210Google Scholar
  20. Rejwer E, Rybarska-Rusinek L, Linkov A (2014) The complex variable fast multipole boundary element method for the analysis of strongly inhomogeneous media. Engineering Analysis with Boundary Elements 43:105–116Google Scholar
  21. Saenger EH (2008) Numerical methods to determine effective elastic properties. International Journal of Engineering Science 46(6):598 – 605Google Scholar
  22. Sayers CM, Kachanov M (1991) A simple technique for finding effective elastic constants of cracked solids for arbitrary crack orientation statistics. International Journal of Solids and Structures 27(6):671 – 680Google Scholar
  23. Shafiro B, Kachanov M (1997) Materials with fluid-filled pores of various shapes: Effective elastic properties and fluid pressure polarization. International Journal of Solids and Structures 34(27):3517 – 3540Google Scholar
  24. Shafiro B, Kachanov M (2000) Anisotropic effective conductivity of materials with nonrandomly oriented inclusions of diverse ellipsoidal shapes. Journal of Applied Physics 87(12):8561–8569Google Scholar
  25. Torquato S (1991) Random heterogeneous media: microstructure and improved bounds on effective properties. Applied Mechanics Reviews 44(2):37–76Google Scholar
  26. Tsaplin VA, Kuzkin VA (2017) On using quasi-random lattices for simulation of isotropic materials. Materials Physics and Mechanics 32(12):321–327Google Scholar
  27. Vaisberg LA, Kameneva EE (2014) X-ray computed tomography in the study of physico-mechanical properties of rocks. Gornyi Zhurnal 9:85–90Google Scholar
  28. Vaisberg LA, Baldaeva TM, Ivanov TM, Otroshchenko AA (2016) Screening efficiency with circular and rectilinear vibrations. Obogashchenie Rud 1:1–12Google Scholar
  29. Vaisberg LA, Kameneva EE, Nikiforova VS (2018a) Microtomographic studies of rock pore space as the basis for rock disintegration technology improvements. Obogashchenie Rud 3:51–55Google Scholar
  30. Vaisberg LA, Kruppa PI, Baranov VF (2018b) Microtomographic studies of rock pore space as theGoogle Scholar
  31. basis for rock disintegration technology improvements. Obogashchenie Rud 3:51–55Google Scholar
  32. Vesga LF, Vallejo LE, Lobo-Guerrero S (2008) DEM analysis of the crack propagation in brittle clays under uniaxial compression tests. International Journal for Numerical and Analytical Methods in Geomechanics 32(11):1405–1415Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ruslan L. Lapin
    • 1
  • Nikita D. Muschak
    • 1
  • Vadim A. Tsaplin
    • 1
    • 2
  • Vitaly V. Kuzkin
    • 1
    • 2
    Email author
  • Anton M. Krivtsov
    • 1
    • 2
  1. 1.Peter the Great St. Petersburg Polytechnic University, Department of Theoretical Mechanics, Institute of Applied Mathematics and MechanicsSt. PetersburgRussia
  2. 2.Laboratoty “Discrete models in mechanics”Institute for Problems in Mechanical Engineering of Russian Academy of SciencesSt. PetersburgRussia

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