The recently developed theory for isotropic material failure is briefly outlined. Many steps and stages of the verification process for the theory are fully documented so that it can be used with assurance in a wide variety of directions. Then, the failure theory is used to develop a new measure or index for the degree of ductility of material failure in any state of stress. This new failure property is named the ductility number, Nd. It is rigorously derived, intuitively compatible, and very easy to use. Applications and interpretations of Nd are given.

References

1.
Coulomb
,
C. A.
,
1773
, “
Memoires de Mathematiques et de Physique
,”
l'Academie Royal des Sciences par divers Savants
, Vol.
7
, pp.
343
382
.
2.
Mohr
,
O.
,
1900
, “
Welche Umstande bedingen die Elastizitatsgrenze und den Bruch eines Materials
,”
Z. Ver. Dtsch. Ing.
,
44
, pp.
1524
1530
.
3.
von Karman
,
T. V.
,
1912
, “
Fesigkeitsversuche unter allseitigem Druck
,”
Mitt. Forshungsarbeit Geb. Ing.
,
118
, pp.
27
68
.
4.
Christensen
,
R. M.
,
2013
,
The Theory of Materials Failure
,
Oxford University Press
,
Oxford, UK
.
5.
Christensen
,
R. M.
,
2018
, “
The Ductile/Brittle Transition Provides the Critical Test for Materials Failure Theory
,”
Proc. R. Soc. A
,
474
(
2210
), p.
20170817
.
6.
Christensen
,
R. M.
,
2016
, “
Perspective on Materials Failure Theory and Applications
,”
ASME J. Appl. Mech.
,
83
(
11
), p.
111001
.
7.
Taylor
,
G. I.
, and
Quinney
,
H.
,
1931
, “
The Plastic Distortion of Metals
,”
Philos. Trans. R. Soc. London
,
A230
, pp.
323
362
.
8.
Cornet
,
I.
, and
Grassi
,
R. C.
,
1955
, “
Fracture of Innoculated Iron
,”
ASME J. Appl. Mech.
,
22
, pp.
172
174
.
9.
Brace
,
W. F.
,
1964
, “
Brittle Fracture of Rocks
,”
State of Stress in the Earth's Crust
,
W. R.
Judd
, ed.,
Elsevier
,
New York
.
10.
Christensen
,
R. M.
,
Li
,
Z.
, and
Gao
,
H.
,
2018
, “
An Evaluation of the Failure Modes Transition and the Christensen Ductile/Brittle Failure Theory Using Molecular Dynamics
,”
Proc. R. Soc. A
,
474
(
2219
), p.
20180361
.
You do not currently have access to this content.