Three fundamentally different failure theories for homogeneous and isotropic materials are examined in both the ductile and brittle ranges of behavior. All three theories are calibrated by just two independent failure properties. These three are the Coulomb-Mohr form, the Drucker-Prager form, and a recently derived theory involving a quadratic representation along with a fracture restriction. The three theories are given a detailed comparison and evaluation. The Coulomb-Mohr form and the Drucker-Prager form are found to predict physically unrealistic behavior in some important cases. The present form meets the consistency requirements.

Issue Section:
Technical Brief
Keywords:
fracture, ductility, brittleness
Topics:
Failure, Stress, Fracture (Materials), 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.
, 1914,
Abhandlungen aus dem Gebiete der Technischen
, 2nd ed.,
Ernst
, Berlin.
3.
Nadai
,
A.
, 1950,
Theory of Flow and Fracture of Solids, I and II
,
McGraw Hill
, New York.
4.
Drucker
,
D. C.
, and
Prager
,
W.
, 1952, “
Soil Mechanics and Plastic Analysis or Limit Design
,”
Q. Appl. Math.
0033-569X,
10
, pp.
157
–
165
.
Crossref
Search ADS
 
5.
Christensen
,
R. M.
, 2004, “
A Two Property Yield, Failure (Fracture) Criterion for Homogeneous, Isotropic Materials
,”
J. Eng. Mater. Technol.
0094-4289,
126
, pp.
45
–
52
.
Crossref
Search ADS
 
6.
von Karman
,
T.
, 1912, “
Festigkeits versuche unter allseitigem Druck
,”
Mitt. Forschungsarbeit Gebiete Ingeneeures
,
118
, pp.
37
–
68
.
7.
Böker
,
R.
, 1915, “
Die Mechanik der Bleibenden Formänderung in Kristallinish Aufgebauten Körpen
,”
Mitteilungen Forschungsarbeit auf dem Gebiete Ingeniurwesens
,
24
, pp.
1
–
51
.
8.
Schajer
,
G. S.
, 1998, “
Mohr-Coulomb Failure Criterion Expressed in Terms of Stress Invariants
,”
J. Appl. Mech.
0021-8936,
65
, pp.
1066
–
1068
.
Crossref
Search ADS
 
9.
Wilson
,
C. D.
, 2002, “
A Critical Reexamination of Classical Metal Plasticity
,”
J. Appl. Mech.
0021-8936,
69
, pp.
63
–
68
.
Crossref
Search ADS
 
10.
Christensen
,
R. M.
, 2003, “
The Brittle Versus the Ductile Nature of Fracture Modes I and II
,”
Int. J. Fract.
0376-9429,
123
, pp.
L157
–
L164
.
Crossref
Search ADS
 
11.
Schleicher
,
F.
, 1926, “
Der Spannongszustand an der Flieffgrenze Plastizitätsbedingung
,”
Z. Angew. Math. Mech.
0044-2267,
6
, pp.
199
–
216
.
Crossref
Search ADS
 
12.
von Mises
,
R.
, 1026, footnote to reference by Schleicher, Ref. (11).
13.
Stassi
,
F.
, 1967, “
Flow and Fracture of Materials According to a New Limiting Condition of Yielding
,”
Meccanica
0025-6455,
3
, pp.
178
–
195
.
14.
Paul
,
B.
, “
Macroscopic Criteria for Plastic Flow and Brittle Fracture
,”
Fracture
,
H.
Liebowitz
 ed.,
Academic Press
, New York, Vol.
II
, pp.
313
–
496
.
Copyright © 2006
 by American Society of Mechanical Engineers
You do not currently have access to this content.