pure and applied geophysics

, Volume 133, Issue 3, pp 489–521 | Cite as

The damage mechanics of brittle solids in compression

  • M. F. Ashby
  • C. G. Sammis
Article

Abstract

The development of microcrack damage in brittle solids in compression is analyzed, using a simple model. The model is developed from recent detailed analysis of the initiation, propagation and linkage of microfractures from pre-existing cracks, voids, or other inhomogeneities. It describes the evolution of damage with strain and from it a criteria for failure can be established. The results are used to construct failure surfaces in stress space which combine information about brittle failure with data describing the onset of plastic yielding. Such failure surfaces are constructed for a number of rocks and are compared with previously published experimental data.

Key words

Damage mechanics brittle fracture microcracks fracture mechanics rock mechanics fracture nucleation crack growth 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, O. L., andGrew, P. (1976),Stress Corrosion Theory of Crack Propagation with Applications to Geophysics, Rev. Geophys. Space Phys.15, 77–104.Google Scholar
  2. Ashby, M. F., andHallam S. D. (1986),The Failure of Brittle Solids Containing Small Cracks under Compressive Stress States, Acta Metall.34, 497–510.Google Scholar
  3. Atkinson, B. K., andMeredith, P. G.,Experimental fracture mechanics data for rocks and minerals, In:Fracture Mechanics of Rock (ed. Atkinson, B. K.) (Academic Press, New York 1987a) pp. 477–525.Google Scholar
  4. Atkinson, B. K., andMeredith, P. G.,The theory of subcritical crack growth with applications to minerals and rocks, InFracture Mechanics of Rock (ed. Atkinson, B. K.) (Academic Press, New York (1987b) pp. 111–166.Google Scholar
  5. Birch, F. (1960),The Velocity of Compressional Waves in Rocks to 10 Kilobars, Part 1, J. Geophys. Res.65, 1083–1102.Google Scholar
  6. Brace, W. F., Paulding, B. W., andScholz, C. (1966),Dilatancy in the Fracture of Crystalline Rocks, J. Geophys. Res.71, 3939–3953.Google Scholar
  7. Costin, L. S. (1983).A Microcrack Model for the Deformation and Failure of Brittle Rock, J. Geophys. Res.88, 9485–9492.Google Scholar
  8. Costin, L. S. (1985),Damage Mechanics in the Post-failure Regime, Mechanics of Materials4, 149–160.Google Scholar
  9. Costin L. S., andHolcomb, D. J. (1981),Time-dependent Failure of Rock under Cyclic Loading, Tectonophysics,79, 279–296.Google Scholar
  10. Edmond, J. M., andPaterson, M. S. (1972)Volume Changes During the Deformation of Rocks at High Pressures, Int. J. Rock Mech. Min. Sci.9, 161–182.Google Scholar
  11. Gowd, T. N., andRummel, F. (1980),Effect of Confining Pressure on the Fracture Behavior of a Porous Rock, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr17, 225–229.Google Scholar
  12. Griffith, A. A.,Theory of rupture, InProc. First International Congress Applied Mechanics (Delft 1924) pp. 55–63.Google Scholar
  13. Griggs, D. T., andHandin J.,Observations on fracture and a hypothesis of earthquakes, InRock Mechanics (eds. Griggs, D. T., and Handin, J.) (Geol. Soc. Am. Memoir79 1960), pp. 347–364.Google Scholar
  14. Hallbauer, D. K., Wagner, H., andCook, N. G. W. (1973),Some Observations Concerning the Microscopic and Mechanical Behaviour of Quartzite Specimens in Stiff, Triaxial Compression Tests, Int. J. Rock Mech. Min. Sci.10, 713–726.Google Scholar
  15. Handin, H. (1953),An Application of High Pressure in Geophysics: Experimental Rock Deformation, Trans. Am. Soc. Mech. Engrs.75, 315–324.Google Scholar
  16. Heard, H. C.,Transition from brittle fracture to ductile flow in Solenhofen limestone as a function of temperature, confining pressure, and interstitial fluid pressure, InRock Deformation (eds. Griggs, D., and Handin, J.) (Geol. Soc. Am. Memoir79 1960) pp. 193–226.Google Scholar
  17. Holcomb, D. J., andCostin, L. S. (1986),Damage in brittle materials: Experimental methods, InProceedings of the Tenth U.S. National Congress of Applied Mechanics (ed. Lamb, J. P.) pp. 107–113.Google Scholar
  18. Horii, H., andNemat-Nasser, S. (1985),Compression-induced Microcrack Growth in Brittle Solids: Axial Splitting and Shear Failure, J. Geophys. Res.90, 3105–3125.Google Scholar
  19. Horii, H., andNemat-Nasser, S. (1986),Brittle Failure in Compression: Splitting, Faulting and brittle-ductile Transition, Phil. Trans. Roy. Soc.A319, 337–374.Google Scholar
  20. Hunsche, U.,Fracture experiments on cubic rock salt samples, InMechanical Behaviour of Salt (eds. Hardy, H. R., Jr., and Langer, M.) (Trans. Tech. Publication, Clausthal, Germany 1984) pp. 169–179.Google Scholar
  21. Irwin, G. R.,Fracture, Handbuch der Physik, Vol. 6, (Springer, Berlin 1958), pp. 551–590.Google Scholar
  22. Jaeger, J. C., andCook, N. G. W.,Fundamentals of Rocks Mechanics, 2nd Ed. (Chapman and Hall, London 1976).Google Scholar
  23. Janach, W., andGuex, L. H. (1980),In-plane Propagation of Shear Microcracks in Brittle Rocks under Triaxial Compression, J. Geophys. Res.85, 2543–2553.Google Scholar
  24. Kemeny, J., andCook N. G. W.,Crack models for the failure of rocks in compression, InConstitutive Laws for Engineering Materials: Theory and Applications (ed. Desai, C. S.) (Elsevier 1987) pp. 879–887.Google Scholar
  25. Knott, J. F.,Fundamentals of Fracutre Mechanics (Butterworths, London 1973).Google Scholar
  26. Martin, R. J. (1972),Time-dependent Crack Growth in Quartz and its Application to the Creep of Rocks, J. Geophys. Res.77, 1406–1419.Google Scholar
  27. Mogi, K. (1966),Some Precise Measurements of Fracture Strength of Rocks under Uniform Compressive Stress, Rock Mech. Eng. Geol.4, 41–55.Google Scholar
  28. Nemat-Nasser, S., andHorii, H. (1982),Compression Induced Nonplanar Crack Extension with Application to Splitting, Exfoliation, and Rockburst, J. Geophys. Res.87, 6805.Google Scholar
  29. Newman, J. B. (1978),A failure model for concrete, InDevelopments in Concrete Technology—1 (ed. Lydon, F. D.) Applied Science5, 151–160.Google Scholar
  30. Olsson, W. A., andPeng, S. S. (1976),Microcrack Nucleation in Marble, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.13, 53–59.Google Scholar
  31. Paterson, M. S.,Experimental Rock Deformation—The Brittle Field (Springer-Verlag, New York 1978).Google Scholar
  32. Rutter, E. H. (1972),The Effects of Strain-rate Changes on the Strength and Ductility of Solenhofen Limestone at Low Temperature and Confining Pressures, Int. J. Rock Mech. Min. Sci. and Geomech. Abstr.9, 183–189.Google Scholar
  33. Sammis, C. G., andAshby, M. F. (1986),The Failure of Brittle Porous Solids under Compressive Stress States, Acta Metall,34, 511–526.Google Scholar
  34. Sano, O., Ito, I., andTerada, M. (1981),Influences of Strain Rate on Dilatancy and Strength of Oshima Granite under Uniaxial Compression, J. Geophys. Res.86, 9299–9311.Google Scholar
  35. Schock, R. N., andHeard, H. C. (1974),Static Mechanical Properties and Shock Loading Response of Granite, J. Geophys. Res.79, 1662–1666.Google Scholar
  36. Scholz, C. H.,A. short geophysical history of Westerly granite, Preface toEarthquake Source Mechanics (eds. Das, S., Boatwright, J., and Scholz, C. H.) (Am. Geophys. Union Monograph37 1986) p. ix.Google Scholar
  37. Shimada, M. (1981),The Method of Compression Test under High Pressures in a Cubic Press and the Strength of Granite, Tectonophysics72, 343–357.Google Scholar
  38. Shimada, M., Cho, A., andYukutake, H. (1983).Fracture Strength of Dry Silicate Rocks at High Confining Pressures and Activity of Acoustic Emission, Tectonophysics96, 159–172.Google Scholar
  39. Tada, H., Paris, P. C., andIrwin, G. R.,The Stress Analysis of Cracks Handbook (Del Res., St. Louis, Mo. 1985).Google Scholar
  40. Topponnier, P., andBrace, W. F. (1976).Development of Stress-induced Microcracks in Westerly Granite, Int. J. Rock Mech. Min. Sci.13, 103–112.Google Scholar
  41. Von Karman, T. (1911),Festigkeitsversuche unter allseitigem Druck Z. Ver. Dt. Ing.55, 1749–1757.Google Scholar
  42. Wawersik, W. R., andFairhurst, C. (1970),A Study of Brittle Rock Failure in Laboratory Compression Experiments, Int. J. Rock Mech. Min. Sci.7, 561–575.Google Scholar
  43. Wawersik, W. R., andBrace, W. F. (1971),Post-failure Behavior of a Granite and a Diabase, Rock Mech.3, 61–85.Google Scholar
  44. Waza, T., Kurita, K., andMizutani, H. (1980),The Effect of Water on the Subcritical Crack Growth in Silicate Rocks, Tectonophysics67, 25–34.Google Scholar

Copyright information

© Birkhäuser Verlag 1990

Authors and Affiliations

  • M. F. Ashby
    • 1
  • C. G. Sammis
    • 2
  1. 1.Engineering DepartmentCambridge UniversityCambridgeEngland
  2. 2.Department of Geological SciencesUniversity of Southern CaliforniaUniversity ParkUSA

Personalised recommendations