Energy-based model of compressive splitting in heterogeneous brittle solids

Journal of the Mechanics and Physics of Solids

Volumn 46, Issue 10, 1998, Pages 2171-2181

  Bhattacharya, K ^a   Ortiz, M ^a   Ravichandran, G ^a  

^a California Institute of Technology   (United States)

Author keywords

A. fracture; B. ceramic material; C. energy methods; Polycrystalline material; Rock

Indexed keywords

BRITTLENESS; CERAMIC MATERIALS; COMPRESSIVE STRESS; FRACTURE; POLYCRYSTALLINE MATERIALS;

BRITTLE SOLID; ENERGY BASED MODEL;

MATHEMATICAL MODELS;

EID: 0032178875     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(98)00026-X     Document Type: Article

References (33)

1. Ashby, M. F. and Hallam, S. D. (1986) The failure of brittle solids containing small cracks under compressive stress states. Acta Metallurgica 34, 497-510.
2. Ashby, M. F. and Sammis, C. G. (1990) The damage mechanics of brittle solids in compression. J. Geoph. 133, 489-521.
3. Azuhata, T., Soha, T. and Suzuki, K. (1996) Elastic constants of III-V compound semiconductors: modification of Keyes' relation. J. Phys.: Condens. Matter 8, 3111-3119.
4. Ball, J. M. (1982) Discontinuous equilibrium solutions and cavitation in non-linear elasticity. Phil. Trans. Royal Soc. London A 306, 557-611.
5. Bass, J. (1995) Elasticity of minerals, glasses and melts. In Handbook of Physical Constants, ed. T. J. Ahrens, 2, 45-63.
6. Brace, W. F. and Bombolakis, E. G. (1963) A note on brittle crack growth in compression. J. Geophys. Res. 68, 3709-3713.
7. Cannon, N. P., Schulson, E. M., Smith, T. R. and Frost, H. J. (1990) Wing cracks and brittle compressive fracture. Acta Metallurgica Materiala 38, 1995-1962.
8. Chen, W. and Ravichandran, G. (1966) Static and dynamic compressive behavior of aluminum nitride under moderate confinement. Journal of the American Ceramic Society 79, 579-584.
9. Dandekar, D. P. (1994) Shear strengths of aluminum nitride and titanium diboride under plane shock wave compression. Journal de Physique III 4, 379-384.
10. Espinosa, H. D. and Brar, N. S. (1995) Dynamic failure mechanism of ceramic bars-experiments and numerical simulations. Journal of the Mechanics and Physics of Solids 43, 1615.
11. Grady, D. E. (1995) Dynamic properties of ceramic materials. Sandia Report SAND94-3266, Sandia National Laboratories, Albuquerque, NM.
12. Griffith, A. A. (1920) The phenomena of rupture and flow in solids. Phil. Trans. Royal Soc. London A 221, 163-198.
13. Handin, H. (1953) An application of high pressure in geophysics : experimental rock deformation. Trans. Am. Soc. Mech. Engrs 75, 315-324.
14. Hashin, Z. (1996) Finite thermoelastic fracture criterion with application to laminate cracking analysis. Journal of the Mechanics and Physics of Solids 44, 1129-1145.
15. Heard, H. C. (1960) Transition from brittle to ductile flow in Solenhofen limestone as a function of temperature, confining pressure and interstitial fluid pressure. Geol. Soc. Am. Memoir, ed. D. Grigg and J. Handin, 79, 193-226.
16. Heard, H. C. and Cline, C. F. (1990) Mechanical behavior of polycrystalline BeO, Al2O3 and AlN at high pressures. J. Mat. Sci. 15, 1889-1897.
17. Horii, H. and Nemat-Nasser, S. (1986) Brittle failure in compression: splitting, faulting and brittle-ductile transition. Phil. Trans. Royal Soc. Lond. A 319, 337-374.
18. Hoek, E. and Bieniawski, Z. T. (1965) Brittle fracture propagation in rock under compression. International Journal of Fracture Mechanics 1, 137-155.
19. Hou, H. S. and Abeyaratne, R. (1992) Cavitation in elastic and elastic-plastic solids. Journal of the Mechanics and Physics of Solids 40, 571-592.
20. James, R. D. and Spector, S. J. (1991) The formation of filamentary voids in solids. Journal of the Mechanics and Physics of Solids 39, 783-813.
21. Lehner, F. and Kachanov, M. (1996) On modelling of winged cracks forming under compression. International Journal of Fracture 7, R69-R75.
22. McClintock, F. A. and Walsh, J. B. (1963) Friction on Griffith cracks under pressure. Proceedings of the U.S. National Congress on Applied Mechanics - 1962, 2, 1015-1021. ASME Press, New York.
23. Nemat-Nasser, S. and Horii, H. (1982) Compression induced non-planar crack extension with application to splitting, exfoliation and rockburst. J. Geophys. Res. 87, 6805-6821.
24. Ortiz, M. and Popov, E. P. (1982) Plain concrete as a composite material. Mech. Mater. 1, 139.
25. Ortiz, M. (1985) A constitutive theory for the inelastic behavior of concrete. Mech. Mater. 4, 67-93.
26. Ravichandran, G. and Subhash, G. (1995) A micromechanical model for high strain rate behavior of ceramics. International Journal of Solids and Structures 32, 2627-2646.
27. Rosenberg, Z., Brar, N. S. and Bless, S. J. (1991) Dynamic high-pressure properties of AlN ceramic as determined by flyer plate impact. Journal of Applied Physics 70, 167-171.
28. Rosenberg, Z., Brar, N. S. and Bless, S. J. (1992) Shear strength of titanium diboride under shock loading measured by transverse Manganin gauges. In Shock Compression of Condensed Matter - 1991, ed. S. C. Schmidt, R. D. Dick, J. W. Forbes and D. G. Tasker, pp. 471-473. Elsevier, Amsterdam.
29. Simmons, G. and Wang, H. (1971) Single Crystal Elastic Constants and Calculated Aggregated Properties. The MIT Press, Cambridge.
30. Smith, T. R. and Schulson, E. M. (1994) Brittle compressive failure of salt-water columnar ice under biaxial loading. Journal of Glaciology 40, 265-276.
31. Vekinis, G., Ashby, M. F. and Beaumont, P. W. R. (1991) The compressive failure of alumina containing controlled distribution of flaws. Acta Metallurgica Materiala 39, 2583-2588.
32. Wang, E. Z. and Shrive, N. G. (1995) Brittle fracture in compression - mechanisms, models and criteria. Engr. Fract. Mech. 52, 1107-1126.
33. Wastiels, J. (1979) Behavior of concrete under multiaxial stresses - a review. Cement and Concrete Research 9, 35.