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Incubation time approach in rock fracture dynamics

  • V. Smirnov
  • Yuri V. Petrov
  • V. Bratov
Article

Abstract

The paper is summarizing latest results connected with application of the incubation time approach to problems of dynamic fracture of rock materials. Incubation time based fracture criteria for intact media and media with cracks are discussed. Available experimental data on high rate fracture of different rock materials and incubation time based fracture criteria are used in order to evaluate critical parameters of causing fracture in these materials. Previously discovered possibility to optimize (minimize) energy input for fracture is discussed in connection to industrial rock fracture processes. It is shown that optimal value of momentum associated with critical load in order to initialize fracture in rock media does strongly depend on the incubation time and the impact duration. Existence of optimal load shapes minimizing momentum for a single fracturing impact or a sequence of periodic fracturing impacts is demonstrated.

Keywords

incubation time dynamic fracture rocks dynamic strength fracture toughness crack resistance energy and momentum input fracture process optimization 

List of main symbols

x({x1,x2})

coordinate

t

time

x

local coordinate

t

local time

τ

incubation time of a fracture

d

characteristic size of a fracture process zone

σ

normal stress

σc

ultimate stress

KI

stress intensity factor for mode I loading

KIc

quasistatic limit for stress intensity factor for mode I loading (critical stress intensity factor)

ρ

mass density

λ

Lame constants

ui

displacement in direction x i .

σij

stress in direction ij

δij

Kronecker delta

p

pressure (stress)

P

load amplitude

t0

load duration

H(t)

Heaviside step function

c1

longitudinal wave speed

c2

transversal wave speed

t*

time to fracture

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References

  1. 1.
    Petrov Y V, Utkin A A. On the rate dependences of dynamic fracture toughness. Soviet Mater Sci, 1989, 25(2): 153–156CrossRefGoogle Scholar
  2. 2.
    Petrov Y V, Morozov N. On the modeling of fracture of brittle solids. J Appl Mech, 1994, 61: 710–712CrossRefGoogle Scholar
  3. 3.
    Morozov N, Petrov Y. Dynamics of Fracture. Berlin-Hidelberg-New York: Springer-Velrag, 2000zbMATHGoogle Scholar
  4. 4.
    Petrov Y V, Morozov N F, Smirnov V I. Structural macromechanics approach in dynamics of fracture. Fatigue Fract Eng Mater Struct, 2003, 26: 363–372CrossRefGoogle Scholar
  5. 5.
    Petrov Y V. On “quantum” nature of dynamic fracture of brittle solids. Dokl Akad Nauk USSR, 1991, 321(1): 66–68Google Scholar
  6. 6.
    Petrov Y V. Incubation time criterion and the pulsed strength of continua: Fracture, cavitation, and electrical breakdown. Dokl Phys, 2004, 49: 246–249CrossRefADSGoogle Scholar
  7. 7.
    Petrov Y, Sitnikova E. Temperature dependence of spall strength and the effect of anomalous melting temperatures in shock-wave loading. Tech Phys, 2005, 50: 1034–1037CrossRefGoogle Scholar
  8. 8.
    Irwin G. Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech, 1956, 24: 361–364Google Scholar
  9. 9.
    Ravi-Chandar K, Knauss W G. An experimental investigation into dynamic fracture. Int J Fract, 1984, 25: 247–262CrossRefGoogle Scholar
  10. 10.
    Kalthoff J F. Fracture behavior under high rates of loading. Eng Fract Mech, 1986, 23: 289–298CrossRefGoogle Scholar
  11. 11.
    Dally J W, Barker D B. Dynamic measurements of initiation toughness at high loading rates. Exp Mech, 1988, 28: 298–303CrossRefGoogle Scholar
  12. 12.
    Smith G C. An Experimental Investigation of the Fracture of a Brittle Material. Dissertation for the Doctoral Degree. Pasadena CA: California Institute of Technology, 1975Google Scholar
  13. 13.
    Bratov V, Gruzdkov A, Krivosheev S, et al. Energy balance in the crack growth initiation under pulsed-load conditions. Dokl Phys, 2004, 49(5): 338–341CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Volkov G A, Bratov V A, Gruzdkov A A, et al. Energy-based analysis of ultrasonically assisted turning. Shock Vib, 2011, 18(1–2): 333–341Google Scholar
  15. 15.
    Bratov V, Petrov Y. Optimizing energy input for fracture by analysis of the energy required to initiate dynamic mode I crack growth. Int J Solids Struct, 2007, 44: 2371–2380CrossRefzbMATHGoogle Scholar
  16. 16.
    Freund L B, Clifton R. On the uniqueness of plane elastodynamic solutions for running cracks. J Elast, 1974, 4: 293–299CrossRefzbMATHGoogle Scholar
  17. 17.
    Freund L B. Dynamic Fracture Mechanics. Cambridge: Cambridge Press, 1990CrossRefzbMATHGoogle Scholar
  18. 18.
    Owen D M, Zhuang S, Rosakis A J, et al. Experimental determination of dynamic crack initiation and propagation fracture toughness in aluminum sheets. Int J Fract, 1998, 90: 153–174CrossRefGoogle Scholar
  19. 19.
    Shockey D A, Erlich D C, Kalthoff J F, et al. Short-pulse fracture mechanics. Eng Frac Mech, 1986, 23(1): 311–319CrossRefGoogle Scholar
  20. 20.
    Zlatin N A, Pugachev G S. Temporal dependency of metal strength. Solid State Phys, 1975, 17: 2599–2602Google Scholar
  21. 21.
    Berezkin A N, Krivosheev S I, Petrov Y V, et al. Effect of delayed crack nucleation under threshold pulse loading. Dokl Phys, 2000, 45(11): 617–619CrossRefADSGoogle Scholar
  22. 22.
    Bratov V, Petrov Y V. Application of incubation time approach to simulate dynamic crack propagation. Int J Fract, 2007, 146: 53–60CrossRefGoogle Scholar
  23. 23.
    Bratov V. Incubation time fracture criterion for FEM simulations. Acta Mech Sin, 2011, 27: 541–549CrossRefADSGoogle Scholar
  24. 24.
    Krivosheev S I, Petrov Y V. Testing of dynamic property of materials under microsecond duration pressure created by the pulse current generator. In: Proc. of IX inter. Conf. On Megagauss Magnetic Field Generation and Related Topics. Moscow-St.-Petersburg, July 7–14, 2002. Selemir V D, Plyashkevich L N, ed. Sarov: VNIIEF, 2004. 112–115Google Scholar
  25. 25.
    Petrov Y V, Smirnov V I, Krivosheev S I, et al. Pulse loading of rocks. In: Extreme strength of materials and structures. Detonation. Shock waves. Proc. of the International conference VII Khariton’s topical scientific readings (March 14–18, 2005). Absracts. Sarov, 2005. 189–190Google Scholar
  26. 26.
    Royal Dutch Shell Petroleum Company Annual Report, 2003Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.St.-Petersburg State Transport UniversitySt.-PetersburgRussia
  2. 2.St.-Petersburg State UniversitySt.-PetersburgRussia
  3. 3.Institute of Problems of Mechanical EngineeringRussian Academy of SciencesSt.-PetersburgRussia

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