Skip to main content
Log in

On the Scale Dependence of Cracking Resistance of Structured Solids (on the Example of Marine Ice Cover)

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The ice sheet is characterized by the development of fracture structures on a local and regional scale with the participation of fracture processes that occur at different scales, differing from each other by several orders of magnitude. The analysis shows that it is possible to distinguish a class of materials, which, in particular, include sea ice and other granular and structured materials (gypsum, concrete, paraffin, etc.), the effective fracture toughness of which during brittle fracture is affected by a large-scale factor, the role of which a gradient of external stresses appears. A model of this phenomenon is proposed for situations associated with variations in the local stress gradient with a change in the scale of the fracture region. Using the example of sea ice cover, we estimated the impact of the effect on the destruction scenarios of structured media.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. V. Lavrov, Ice Deformation and Strength (Gidrometeoizdat, Leningrad, 1969) [In Russian].

    Google Scholar 

  2. C. G. Hoover and Z. P. Bazant, “Cohesive Crack, Size Effect, Crack Band and Work–of Fracture Models Compared to Comprehensive Concrete Fracture Tests,” Int. J. Fract. 187 (1), 133–143 (2014).

    Article  Google Scholar 

  3. B. Frigo, A. P. Fantillia, and B. Chiaia, “Size Effect on Fracture Toughness of Snow,” in Proc. of XXIV Italian Group of Fracture Conference, 1–3 March 2017, Urbino, Italy (Procedia Structural Integrity, 2017), pp. 261–268.

    Google Scholar 

  4. K. P. Tyshko, N. V. Cherepanov, and V. I. Fedotov, Crystal Structure of Sea Ice Cover (Gidrometeoizdat, St. Petersburg, 2000) [In Russian].

    Google Scholar 

  5. R. V. Goldstein, V. M. Ladygin and N. M. Osipenko, “A Model of the Fracture of a Slightly Porous Material under Compression or Tension,” Fiz.-Tekh. Probl. Raz. Polez. Isk, No. 1, 3–13 (1974) [J. Mining Sci. (Engl. Transl.) 10 (1), 1–9 (1974)].

    Google Scholar 

  6. R. V. Goldstein, “Fracture in Compression,” Usp. Mekh. 2 (2), 3–20 (2003).

    Google Scholar 

  7. R. V. Goldstein and N. M. Osipenko, “Some Questions on Ice and Ice Cover Fracture in Compression,” In: Icestructure Interaction. IUTAM-IAHR Symp. St. John’s, New Foundland, Canada, (Springer-Verlag, Berlin, Heidelberg, 1991), pp. 251–266.

    Google Scholar 

  8. E. Z. Lajtai and V. N. Lajtai, “The Collapse of Cavities,” Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 12, 81–86 (1975).

    Article  Google Scholar 

  9. R. V. Goldstein and N. M. Osipenko, “Some Aspects of Strength in Sea Ice Mechanic,” Fiz. Mezomekh. 17 (6), 59–69 (2014) [Phys.Mesomech. (Engl. Transl.) 18 (2), 139–148 (2015)].

    Google Scholar 

  10. G. W. Timko and R. M. W. Trederking, “Compressive Strength of Ice Sheets,” Cold Reg. Sci. Tech. 17, 227–240 (1990).

    Article  Google Scholar 

  11. J. Schwarz and W. F. Weeks, “Engineering Properties of Sea Ice,” J. Glaciology 19 81, 499–531 (1977).

    Article  ADS  Google Scholar 

  12. R. V. Goldstein and N. M. Osipenko, “Fracture Mechanics and Several Problems of Ice Fracture,” in Mechanics and Physics of Ice (Nauka, Moscow, 1983), pp. 65–94 [in Russian].

    Google Scholar 

  13. J. P. Dempsey, R. M. Adamson, and S. V. Mulmule, “Scale Effects on the In-Situ Tensile Strength and Fracture of Ice. Part II: First-Year Sea Ice at Resolute, NWT,” Int. J. Fracture 95 (1), 347–366 (1999).

    Article  Google Scholar 

  14. J. P. Dempsey, S. J. DeFranco, R. M. Adamson, and S. V. Mulmule, “Scale Effects on the In-Situ Tensile Strength and Fracture of Ice. Part I: Large Grained Freshwater Ice at Spray Lakes Reservoir, Alberta,” Int. J. Fracture 95 (1), 325–345 (1999).

    Article  Google Scholar 

  15. J. Dempsey, D. M. Cole, and S. Wang, “Tensile Fracture of a Single Crack in First-Year Sea Ice,” Phil. Trans. Royal Soc. A: Math. Phys. Engng Sci. 376, (2129):20170346, September 2018. https://doi.org/10.1098/rsta.2017.0346.

    Article  Google Scholar 

  16. J. P. Dempsey, “Research Trends in IceMechanics,” Int. J. Sol. Struct. 37, 131–153 (2000).

    Article  MathSciNet  Google Scholar 

  17. C. A. Totman, O. E. Uzorka, J. P. Dempsey, and D. M. Cole, “Sub-Size Fracture Testing of FY Sea Ice,” in Proceedings of the 6th International Conference on Fracture Mechanics of Concrete and Concrete Structures, Catania, Italy, 17–22 June 2007, Vol. 3, pp. 1683–1690.

    Google Scholar 

  18. J. P. Dempsey, Y. Xie, R. M. Adamson, and D. M. Farmer, “Fracture of a Ridged Multi-Year Arctic Sea Ice Floe,” Cold Reg. Sci. Techn. 76–77, 63–68 (2012).

    Article  Google Scholar 

  19. G. P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974; McGraw-Hill, New York, 1979).

    Google Scholar 

  20. V. M. Vainshelbaum and R. V. Goldstein, “On the Material Scale Length as a Measure of Plastic Material Fracture Toughness and its Meaning in the Fracture Mechanics,” Preprint No. 77, Institute for Problems in Mechanics, The USSR Academy of Sciences, Moscow (1976).

    Google Scholar 

  21. Z.P. Bazant and J. Planas, Fracture and Size Effect in Concrete and Other QuasibrittleMaterials (CRC Press, Boca Raton, 1998).

    Google Scholar 

  22. Z.P. Bazant, “Size Effect in Blunt Fracture: Concrete, Rock, Metal,” ASC. J. Engng Mech. 110, 518–535 (1984).

    Article  Google Scholar 

  23. K. Duan, X.-Z. Hu, and F. H. Wittmann, “Size Effect on Fracture Resistance and Fracture Energy of Concrete,” Mat. Struct. 36 (3), 74–80 (2003).

    Article  Google Scholar 

  24. S. V. Suknev, “Nonlocal and Gradient Ffracture Criteria for Quasi-Brittle Materials under Compression,” Phiz. Mezomekh. 21 (4), 22–32 (2018)

    Google Scholar 

  25. E. Z. Lajtai, “Effect of Tensile Stress Gradient on Brittle Fracture Initiation,” Int. J. Rock Mech. Min. 9 (5), 569–578 (1972).

    Article  Google Scholar 

  26. M. A. Legan, “On the Relationship Between the Gradient Criteria for Local Strength in the Region of Stress Concentration and the Linear FractureMechanics,” Prikl. Mekh. Tekhn. Fiz. 34 (4), 146–154 (1993).

    MATH  Google Scholar 

  27. M. D. Novopashin and S. V. Suknev, “Gradient Criteria of Limit State,” Vestn. SamGU Est. Ser., No. 4 (54), 316–334 (2007).

    Google Scholar 

  28. Z. P. Bazant, “Size Effect in Blunt Fracture: Concrete, Rock, Metal,” ASC. J. Engng Mech. 110, 518–535 (1984).

    Article  Google Scholar 

  29. Stress Intensity Factors Handbook Ed. by Y. Murakami, (Pergamon Press, Oxford, 1987; Mir, Moscow, 1990).

    Google Scholar 

  30. Z. P. Bazant, M. T. Kazemi, T. Hasegawa, and J. Mazars, “Size Effect in Brazilian Split-Cylinder Tests: Measurments and Fracture Analysis,” ACI Materials J. 88, 325–332 (1991).

    Google Scholar 

  31. V. V. Bogorodskii and V. P. Gavrilo, Ice (Gidrometeoizdat, Leningrad, 1980) [in Russian].

    Google Scholar 

  32. S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (McGraw, New York, 1970; Nauka, Moscow, 1975).

    MATH  Google Scholar 

  33. R. V. Goldstein and N. M. Osipenko, “On a Model of Structured Medium Fracture under Compression Conditions,” Izv. Ros. Akad. Nauk. Mekh. Tv. Tela, No. 6, 86–97 (2010) [Mech. Sol. (Engl. Transl.) 45 (6), 835–843 (2010)].

    Google Scholar 

  34. G. W. Timco and S. O’Brien, “Flexural Strength Equation for Sea Ice,” Cold Reg. Sci. Tech. 22, 285–298 (1994).

    Article  Google Scholar 

  35. Ch. Pen, “Experimental Studies and Analysis of the Characteristics of Sea Ice Flexural Strength along the Coast of the Gulf of Bohai,” Mol. Uch. 27, 39–46 (2017).

    Google Scholar 

  36. I. Dykins, “Tensile and Flexural Properties of Saline Ice,” in Proc. Int. Symp. on Physics of Ice (Munich, 1968), pp. 9–14.

    Google Scholar 

Download references

Acknowledgement

This work was financially supported by the program of the Presidium of the RAS No. I.2.55P: “The Arctic—scientific foundations of new technologies for conservation and development”.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. M. Osipenko.

Additional information

Russian Text © Author(s), 2019, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2019, No. 5, pp. 70–85.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Osipenko, N.M. On the Scale Dependence of Cracking Resistance of Structured Solids (on the Example of Marine Ice Cover). Mech. Solids 54, 1051–1062 (2019). https://doi.org/10.3103/S0025654419070069

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654419070069

Keywords

Navigation