Abstract
Cracks, holes, and inclusions in an elastic solid can interact with a compressive stress field in a way which causes new cracks to grow from them. If these cracks extend to the sample surface, or if they interact with each other so that they grow in an unstable manner, then a macroscopic failure may follow. The initiation and growth of cracks from pores has been considered by Sammis & Ashby (1986): that from small angled cracks is analysed by Nemat-Nasser & Horii (1982), Cooksley (1984), and Ashby & Hallam (1986). In this chapter we consider the growth of cracks in compressive stress states and how they interact to cause a macroscopic failure.
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References
Akroyd, T. N. W. 1961. Concrete under triaxial stress. Concrete Res. 13, 111–18.
Ashby, M. F. & S. D. Hallam 1986. The failure of brittle solids containing small cracks under compressive stress states. Acta Metall. 34, 497–510.
Atkinson, B. K. & P. G. Meredith 1987. The theory of subcritical crack growth with application to minerals and rocks. In Fracture mechanics of rock, B. K. Atkinson (ed.) 111–66. London: Academic Press.
Coffin, L. F., Jr 1950. The flow and fracture of a brittle material. J. Appl. Mech. Sept., 17, 233–48.
Cooksley, S. D. 1984. Yield and fracture surfaces of brittle solids under multi-axial loading. PhD thesis. Engineering Department, University of Cambridge.
Costin, L. S. 1983. A microcrack model for the deformation and failure of brittle rock. J. Geophys. Res., 88, 9485–92.
Costin, L. S. 1985. Damage mechanics in the post-failure regime. Mech. Mat., 4, 149–60.
Coulomb, C. A. 1773. Sur une application des règles de maximis et minimis à quelques problèmes de statique relatifs à l’architecture. Acad. Roy. des Sciences Mémoires de Math, et de Physique par Divers Savants 7, 343–82.
Crossland, B. & W. H. Dearden 1958. Plastic flow and fracture of a “brittle” material (grey cast iron) with particular reference to the effect of fluid pressure. Proc. Instn Mech. Engrs 172, 805–20.
Edmund, J. M. & M. S. Paterson 1972. Volume changes during the deformation of rocks at high pressures. Int. J. Rock Mech. Min. Sci. 9, 161–82.
Franklin, J. A. 1971. Triaxial strength of rock materials. Rock Mech. 3, 86–98.
Griffiths, A. A. 1924. Theory of rupture. In Proc. 1st Int. Conf. Appl. Mech., Delft: Waltman, 55–63.
Gueguen, Y., T. Reuschlé and M. Darot 1989. Single-crack behaviour and crack statistics. This volume, 48–71.
Hallam, S. D. & J. P. Nadreau 1987. Failure maps for ice. In Proc. 9th Int. Conf. Port Ocean Engng under Arctic Conditions, Fairbanks, Vol III, 45–56.
Handin, H. 1953. An application of high pressure in geophysics; experimental rock deformation. Trans Am. Soc. Mech. Engrs 75, 315–24.
Hobbs, D. W. 1970. Strength and deformation properties of plain concrete subject to combined stress, part 1: strength results obtained on one concrete. Technical Report 42.451. Cement and Concrete Association.
Hobbs, D. W. 1974. Strength and deformation properties of plain concrete subject to combined stress, part 3: results obtained on a range of flint gravel aggregate concretes. Technical Report 42.497. Cement and Concrete Association.
Hoek, E. & L. T. Bieniawski 1965. Brittle fracture propagation in rock under compression. Int. J. Frac. Mech. 1, 135–55.
Jones, S. J. 1982. The confined compressive strength of polycrystalline ice.J. Glaciol. 28, 171–7.
Kobayashi, S. 1971. Initiation and propagation of brittle fracture in rock-like materials under compression. J. Soc. Mat. Sci. 20, 164–73.
Kobayashi, S. & W. Koyangi 1972. Fracture criteria of cement paste, mortar and concrete subjected to multi-axial compressive stresses. RILEM Int. Symp., Cannes, October, 131–48.
Marshall, G. P. & J. G. Williams 1973. The correlation of fracture data for PMMA. J. Mat. Sci. 8, 138–40.
McClintock, F. A. & J. B. Walsh 1962. Friction on Griffith’s cracks in rocks under pressure. In Proc. Fourth US Nat. Congr. Appl. Mech. II, New York, 1015–21.
Meredith, P. G. 1989. Fracture and failure of polycrystals: an overview. This volume, 5–47.
Mills, L. L. & R. M. Zimmerman 1970. Compressive strength of plain concrete under multi-axial loading conditions. J. Am. Concrete Inst. Title 67–47, 802–7.
Murrell, S. A. F. 1963. A criterion for brittle fracture of rocks and concrete under triaxial stress, and the effect of pore pressure on the criterion. In Proc. Fifth Symp. Rock Mech. 563–77. New York: Pergamon.
Murrell, S. A. F. 1965. The effect of triaxial stress systems on the strength of rocks at atmospheric temperatures. Geophys. J. R. Astron. Soc. 10, 231–81.
Murrell, S. A. F. and P. J. Digby 1970a. The theory of brittle fracture initiation under triaxial stress conditions - I. Geophys. J. R. Astron. Soc. 19, 309–34.
Murrell, S. A. F. & P. J. Digby 1970b. The theory of brittle fracture initiation under triaxial stress conditions - II. Geophys. J. R. Astron. Soc. 19, 499–512.
Nemat-Nasser, S. & H. Horii 1982. Compression induced non planar crack extension with application to splitting, exfoliation and rockburst. J. Geophys. Res. 87, 6805–21.
Newman, K. & J. B. Newman 1973. Design criteria for concrete under combined states of stress. In Criteria of concrete strength, Report 1, CIRIA contract, Imperial College, London.
Paterson, M. S. 1978. Experimental rock deformation - the brittle field. Berlin: Springer.
Pugh, H. L. L. D. & D. Green 1964. The effect of hydrostatic pressure on the plastic flow of metals. Proc. Inst. Mech. Engrs 179, 415–38.
Richart, F. E., A. Brandtzaeg & R. L. Brown 1928. A study of the failure of concrete under combined stress.Bull. Univ. III. Engng Expt Stat. 185, 104.
Sammis, C. G. & M. F. Ashby 1986. The failure of porous solids under compressive stress states. Acta Metall. 34, 511.
Steif, P. 1984. Crack extension under compressive loading. Engng Fract. Mech. 20, 463.
von Karman, Th. 1911. Festigkeitsversuche unter allScitgim druck Z. Ver. dt. Ing. 55, 1749—57.
Wallner, M., C. Caninenburg & H. Gonther 1979. Ermittlung zeit- und temperaturabhangiger mechanischer Kennwerte von Salzgesteinen. In Proc. 4th Int. Cong, on Rock Mechanics, Montreux, 1, 313–18.
Williams, M. L. 1957. On the stress distribution at the base of a stationary crack. J. Appl. Mech. Trans 24, 109–14.
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Hallam, S.D., Ashby, M.F. (1990). Compressive brittle fracture and the construction of multi-axial failure maps. In: Deformation Processes in Minerals, Ceramics and Rocks. The Mineralogical Society Series, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-6827-4_5
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DOI: https://doi.org/10.1007/978-94-011-6827-4_5
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