A critical review is given of the various historical attempts to formulate a general, three-dimensional theory of failure for broad classes of homogeneous, isotropic elastic materials. Following that, a recently developed two-parameter yield/failure criterion is compared with the historical efforts and it is further interpreted and extended. Specifically, the yield/failure criterion is combined with a fracture restriction that places limits on certain tensile stress states, without involving any additional parameters. An evaluation is conducted using available experimental data obtained from a variety of materials types. The two materials parameters are given a primary designation as yield type properties over a specified range of ductile behavior, and as failure or fracture type properties over the complementary brittle range.

Issue Section:
Technical Papers
Keywords:
fracture mechanics, reviews, failure (mechanical), ductile fracture, brittle fracture
Topics:
Failure, Fracture (Materials), Stress, Fracture (Process), Brittleness
1.
Coulomb, C. A., 1773, “In Memories de Mathematique et de Physique,” Academie Royal des Sciences par divers sans, 7, pp. 343–382.
2.
Mohr, O., 1900, “Welche Umsta¨nde Bedingen die Elastizita¨tsgrenze und den Bruch eines Materials,” Zeitschrift des Vereines Deutscher Ingenieure, 44, pp. 1524–1530.
3.
von Karman, T., 1912, “Festigkeitsversuche unter allseitigem Druck,” Mitt. Forschungsarbeit. Gebiete Ingeneeures, 118, pp. 37–68.
4.
Bo¨ker, R., 1915, “Die Mechanik der Bleibenden Forma¨nderung in Kristallinish Aufgebauten Ko¨rpern,” Mitteilungen Forschungsarbeit auf dem Gebiete Ingenieurwesens, 24, pp. 1–51.
5.
Timoshenko, S. P., 1953, History of Strength of Materials, McGraw-Hill, New York.
6.
Huber, M. T., 1904, Czapismo Technizne, 22, p. 81.
7.
von Mises, R., 1913, “Mechanik des festen Ko¨rper im Plastisch-Deformablen Zustand,” Nachr. Kgl. Ges. Wiss. Go¨tingen, Math.-Physik Klasse.
8.
Beltrami, E., 1889, “Considerazione Idrodinamiche,” Rend. 1st Lombardo Sci. Lettere, 22, pp. 121–130.
9.
Taylor
,
G. I.
, and
Quinney
,
H.
,
1931
, “
The Plastic Distortion of Metals
,”
Proc. R. Soc. London, Ser. A
,
230
, pp.
323
–
362
.
10.
Todhunter, I., and Pearson, K., 1893, A History of the Theory of Elasticity and of the Strength of Materials, Cambridge University Press, London.
11.
Thomson, W. (Lord Kelvin) and Tait, P. G., 1879, Treatise on Natural Philosophy, Cambridge University Press, London.
12.
Love, A. E. H., 1927, A Treatise on the Mathematical Theory of Elasticity, Cambridge University Press.
13.
Paul, B., 1968, “Macroscopic Criteria For Plastic Flow and Brittle Fracture,” in Fracture H. Liebowitz, ed., II, Academic Press, New York, pp. 313–496.
14.
Griffith
,
A. A.
,
1921
, “
The Phenomena of Rupture and Flow in Solids
,”
Proc. R. Soc. London, Ser. A
,
pp.
163
–
198
.
15.
Griffith, A. A., 1924, “The Theory of Rupture,” Pro. 1st Int. Cong. Appl. Mech., pp. 55–63.
16.
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.
17.
Christensen
,
R. M.
,
1997
, “
Yield Functions/Failure Criteria for Isotropic Materials
,”
Proc. R. Soc. London, Ser. A
,
453
, pp.
1473
–
1491
.
18.
Christensen
,
R. M.
,
2000
, “
Yield Functions, Damage States, and Intrinsic Strength
,”
Math. Mech. Solids
,
5
, pp.
285
–
300
.
19.
Popov, E. P., 1990, Engineering Mechanics of Solids, Prentice Hall, Englewood Cliffs, NJ.
20.
Jaeger, J. C., and Cook, N. G. W., 1979, Fundamentals of Rock Mechanics, Chapman and Hall, London.
21.
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.
22.
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
.
23.
Pae
,
K. D.
,
1977
, “
The Macroscopic Yielding Behavior of Polymers in Multiaxial Stress Fields
,”
J. Mater. Sci.
,
12
, pp.
1209
–
1214
.
24.
Cornet
,
I.
, and
Grassi
,
R. C.
,
1955
, “
Fracture of Inoculated Iron Under Biaxial Stress
,”
ASME J. Appl. Mech.
,
22
, pp.
172
–
174
.
25.
Ely
,
R. E.
,
1965
, “
Strength of Graphite Tube Specimens Under Combined Stress
,”
J. Am. Ceram. Soc.
,
48
, pp.
505
–
508
.
26.
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.
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