A Two-Property Yield, Failure (Fracture) Criterion for Homogeneous, Isotropic Materials

[+] Author and Article Information
Richard M. Christensen

Lawrence Livermore National Laboratory, Livermore, CA 94550Stanford University, Stanford, CA 94305

J. Eng. Mater. Technol 126(1), 45-52 (Jan 22, 2004) (8 pages) doi:10.1115/1.1631024 History: Received September 03, 2002; Revised April 11, 2003; Online January 22, 2004
Copyright © 2004 by ASME
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Coulomb, C. A., 1773, “In Memories de Mathematique et de Physique,” Academie Royal des Sciences par divers sans, 7 , pp. 343–382.
Mohr, O., 1900, “Welche Umstände Bedingen die Elastizitätsgrenze und den Bruch eines Materials,” Zeitschrift des Vereines Deutscher Ingenieure, 44 , pp. 1524–1530.
von Karman, T., 1912, “Festigkeitsversuche unter allseitigem Druck,” Mitt. Forschungsarbeit. Gebiete Ingeneeures, 118 , pp. 37–68.
Böker, R., 1915, “Die Mechanik der Bleibenden Formänderung in Kristallinish Aufgebauten Körpern,” Mitteilungen Forschungsarbeit auf dem Gebiete Ingenieurwesens, 24 , pp. 1–51.
Timoshenko, S. P., 1953, History of Strength of Materials, McGraw-Hill, New York.
Huber, M. T., 1904, Czapismo Technizne, 22 , p. 81.
von Mises, R., 1913, “Mechanik des festen Körper im Plastisch-Deformablen Zustand,” Nachr. Kgl. Ges. Wiss. Götingen, Math.-Physik Klasse.
Beltrami, E., 1889, “Considerazione Idrodinamiche,” Rend. 1st Lombardo Sci. Lettere, 22 , pp. 121–130.
Taylor,  G. I., and Quinney,  H., 1931, “The Plastic Distortion of Metals,” Proc. R. Soc. London, Ser. A, 230, pp. 323–362.
Todhunter, I., and Pearson, K., 1893, A History of the Theory of Elasticity and of the Strength of Materials, Cambridge University Press, London.
Thomson, W. (Lord Kelvin) and Tait, P. G., 1879, Treatise on Natural Philosophy, Cambridge University Press, London.
Love, A. E. H., 1927, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.
Paul, B., 1968, “Macroscopic Criteria For Plastic Flow and Brittle Fracture,” in Fracture H. Liebowitz, ed., II, Academic Press, New York, pp. 313–496.
Griffith,  A. A., 1921, “The Phenomena of Rupture and Flow in Solids,” Proc. R. Soc. London, Ser. A, pp. 163–198.
Griffith, A. A., 1924, “The Theory of Rupture,” Pro. 1st Int. Cong. Appl. Mech., pp. 55–63.
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,” Pro. Fifth Rock Mechanics Symposium, in Rock Mechanics C. Fairhurst, ed., Pergamon, pp. 563–577.
Christensen,  R. M., 1997, “Yield Functions/Failure Criteria for Isotropic Materials,” Proc. R. Soc. London, Ser. A, 453, pp. 1473–1491.
Christensen,  R. M., 2000, “Yield Functions, Damage States, and Intrinsic Strength,” Math. Mech. Solids, 5, pp. 285–300.
Popov, E. P., 1990, Engineering Mechanics of Solids, Prentice Hall, Englewood Cliffs, NJ.
Jaeger, J. C., and Cook, N. G. W., 1979, Fundamentals of Rock Mechanics, Chapman and Hall, London.
McClintock, F. A., and Walsh, J. B., 1962, “Friction on Griffith Cracks in Rocks Under Pressure,” Pro. Of the 4th U.S. National Congress of Applied Mechanics, pp. 1015–1021.
Christensen,  R. M., Freeman,  D. C., and DeTeresa,  S. J., 2002, “Failure Criteria for Isotropic Materials, Applications to Low Density Types,” Int. J. Solids Struct., 39, pp. 973–982.
Pae,  K. D., 1977, “The Macroscopic Yielding Behavior of Polymers in Multiaxial Stress Fields,” J. Mater. Sci., 12, pp. 1209–1214.
Cornet,  I., and Grassi,  R. C., 1955, “Fracture of Inoculated Iron Under Biaxial Stress,” ASME J. Appl. Mech., 22, pp. 172–174.
Ely,  R. E., 1965, “Strength of Graphite Tube Specimens Under Combined Stress,” J. Am. Ceram. Soc., 48, pp. 505–508.
Brace, W. F., 1964, “Brittle Fracture of Rocks,” in State of Stress in the Earth’s Crust, W. R. Judd, ed., American Elsevier, New York.


Grahic Jump Location
Coulomb-Mohr failure plane normal and shear stress envelope
Grahic Jump Location
Fracture cutoff effect, biaxial stress state
Grahic Jump Location
Torsion of a cast iron speciman showing 45 deg tensile fracture surface orientation, Popov 19
Grahic Jump Location
“Innoculated” iron yield/failure, Cornet and Grassi 24
Grahic Jump Location
Graphite yield/failure, Ely 25
Grahic Jump Location
Blair Dolomite yield/failure, Brace 26




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