Skip to Main Content
Skip Nav Destination
ASTM Selected Technical Papers
Fatigue and Fracture Mechanics: 29th Volume
By
TL Panontin
TL Panontin
1
NASA Ames Research Center
?
Moffett Field, CA Symposium Chair and Editor
Search for other works by this author on:
SD Sheppard
SD Sheppard
2
Stanford University
?
Stanford, CA Symposium Chair and Editor
Search for other works by this author on:
ISBN-10:
0-8031-2486-4
ISBN:
978-0-8031-2486-8
No. of Pages:
917
Publisher:
ASTM International
Publication date:
1999

The Exclusion Region theory is a new theoretical construct that attempts to address both the difficulty of solving the boundary-value problem in the presence of a crack, and the subsequent difficulty of extracting from the solution a physically relevant fracture criterion. The theory starts with the presumption that, within a small radius of the separation front, the stress field as determined from the local constitutive model does not provide a meaningful representation of the internal force distribution for purposes of imposing equilibrium. Equilibrium (or momentum conservation) therefore cannot be applied pointwise within this exclusion region to solve for the displacement field. Instead, the material displacement field within the exclusion region is given by an assumed form that accommodates the separation of a material surface into a pair of new free surfaces. The enriched kinematics of the exclusion region may therefore be regarded as simply leading to a broadened constitutive model, which only applies to a small material neighborhood that is suffering surface separation. Further, and in contrast to conventional fracture mechanics, the form of the crack advance criterion does not restrict the material model that may be applied in the bulk continuum. The Exclusion Region theory has been implemented in a two-dimensional finite element code. The code uses a novel numerical procedure in which the moving separation front lies at the center of a translating, disc-shaped patch of elements. Compatibility at the interface between the mesh patch and the fixed background mesh is enforced weakly. Numerical studies have demonstrated complete correspondence between the new theory and linear elastic fracture mechanics. Preliminary results involving large deformations and extensive plastic deformation are also presented.

1.
Knowles
,
J. K.
, and
Sternberg
,
E.
, “
An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack
,”
Journal of Elasticity
3
, pp. 67–107,
1973
.
2.
Hutchinson
,
J. W.
, “
Singular behavior at the end of a tensile crack tip in a hardening material
,”
Journal of the Mechanics and Physics of Solids
16
, pp. 13–31,
1968
.
3.
Rice
,
J. R.
, and
Rosengren
,
G. F
, “
Plane strain deformation near a crack tip in a power-law hardening material
,”
Journal of the Mechanics and Physics of Solids
16
, pp. 1–12,
1968
.
4.
Ponte Castaneda
,
P.
, “
Asymptotic fields in steady crack growth with linear strainhardening
,”
Journal of the Mechanics and Physics of Solids
35
, pp. 227–268,
1987
.
5.
Hui
,
C.-Y.
, and
Riedel
,
H.
, “
The asymptotic stress and strain field near the tip of a growing crack under creep conditions
,”
International Journal of Fracture
17
, pp. 409–425,
1981
.
6.
Rice
,
J. R.
, “
A path-independent integral and the approximate analysis of strain concentration by notches and cracks
,”
Journal of Applied Mechanics
 0021-8936 
35
, pp. 379–386,
1968
.
7.
Knowles
,
J. K.
, and
Sternberg
,
E.
, “
On a class of conservation laws in linearized and finite elastostatics
,”
Archive for Rational Mechanics and Analysis
 0003-9527 
44
, pp. 187–211,
1972
.
8.
Budianski
,
B.
, and
Rice
,
J. R.
, “
Conservation laws and energy-release rates
,”
Journal of Applied Mechanics
 0021-8936 
40
, pp. 201–203,
1973
.
9.
Gurtin
,
M. E.
, and
Yatomi
,
C.
, “
On the energy release rate in elastodynamic crack propagation
,”
Archive for Rational Mechanics and Analysis
 0003-9527 
74
, pp. 231–247,
1980
.
10.
Liu
,
H. W.
,
Kunio
,
T.
,
Weiss
,
V.
, and
Okamura
,
H.
(eds.),
Fracture Mechanics of Ductile and Tough Materials and its Applications to Energy Related Structures
, proceedings of the USA-Japan joint seminar held at Hyama,
Japan
, November 12–16, 1979.
Martinus Nijhoff
,
The Hague
,
1981
.
11.
Moran
,
B.
, and
Shih
,
C. F.
, “
A general treatment of crack tip contour integrals
,”
International Journal of Fracture
35
, pp. 295–310,
1987
.
12.
Herrmann
,
A. G.
, and
Herrmann
,
G.
, “
On energy-release rates for a plane crack
,”
Journal of Applied Mechanics
 0021-8936 48, pp. 525–528,
1981
.
13.
Barenblatt
,
G. I.
, “
The mathematical theory of equilibrium cracks in brittle fracture
,”
Advances in Applied Mechanics
 0065-2156 
7
, pp. 55–129,
1962
.
14.
Dugdale
,
D. A.
, “
Yielding of steel sheets containing slits
,”
Journal of the Mechanics and Physics of Solids
8
, pp. 100–104,
1960
.
15.
Fager
,
L.-O.
,
Bassani
,
J. L.
,
Hui
,
C.-Y.
, and
Xu
,
D.-B.
, “
Aspects of cohesive zone models and crack growth in rate-dependent materials
,”
International Journal of Fracture
52
, pp. 119–144,
1991
.
16.
Knauss
,
W. G.
, and
Losi
,
G. U.
, “
Crack propagation in a nonlinearly viscoelastic solid with relevance to adhesive bond failure
,”
Journal of Applied Mechanics
 0021-8936 
60
, pp. 793–801,
1993
.
17.
Tvergaard
,
V.
, and
Hutchinson
,
J. W.
, “
The relation between crack growth resistance and fracture process parameters in elastic-plastic solids
,”
Journal of the Mechanics and Physics of Solids
40
, pp. 1377–1397,
1992
.
18.
Xia
,
L.
, and
Shih
,
C. F.
, “
Ductile crack growth - I. A numerical study using computational cells with microstructurally-based length scales
,”
Journal of the Mechanics and Physics of Solids
43
, pp. 233–259,
1995
.
19.
Xia
,
L.
, and
Shih
,
C. F.
, and
Hutchinson
,
J. W.
, “
A computational approach to ductile crack growth under large scale yielding conditions
,”
Journal of the Mechanics and Physics of Solids
43
, pp. 389–413,
1995
.
20.
Rashid
,
M. M.
, “
Computational simulation of surface formation in solid continua
,” in
Proc. 1995 Conf. on Computational Engineering Science
(
Atluri
S. N.
,
Yagawa
G.
,
Cruse
T. A.
, eds.),
Mauna Lani, Hawaii
, July 30 – August 3, pp. 1709–1714,
1995
.
21.
Rashid
,
M. M.
, “
A new theory for free-surface formation in solid continua
,”
International Journal of Solids and Structures
 0020-7683 
34
, pp. 2303–2320,
1997
.
22.
Keegstra
,
P. N. R.
,
Head
,
J. L.
, and
Turner
,
C. E.
, “
A two-dimensional dynamic linear-elastic finite-element program for the analysis of unstable crack propagation and arrest
,” in
Numerical Methods in Fracture Mechanics
,
Luxmoore
A. R.
and
Owen
D. R. J.
(eds.),
University College
,
Swansea
, pp. 634–647,
1978
.
23.
Yagawa
,
G.
,
Sakai
,
Y.
, and
Ando
,
Y.
, “
Analysis of a rapidly propagating crack using finite elements
,” in
Fast Fracture and Crack Arrest
, ASTM STP 627,
Hahn
G. T.
and
Kanninen
M. F.
(eds.),
American Society for Testing and Materials
,
West Conshohocken, PA
, pp. 109–122,
1977
.
24.
Kobayashi
,
A. S.
,
Mall
,
S.
,
Urabe
,
Y.
, and
Emery
,
A. F.
, “
A numerical dynamic fracture analysis of three wedge-loaded DCB specimens
,” in
Numerical Methods in Fracture Mechanics
,
Luxmoore
A. R.
and
Owen
D. R. J.
(eds.),
University College
,
Swansea
, pp. 673–684,
1978
.
25.
Malluck
,
J. F.
, and
King
,
W. W.
, “
Fast fracture simulated by finite-element analysis which accounts for crack-tip energy dissipation
,” in
Numerical Methods in Fracture Mechanics
,
Luxmoore
A. R.
and
Owen
D. R. J.
(eds.),
University College
,
Swansea
, pp. 648–659,
1978
.
26.
Aoki
,
S.
,
Kishimoto
,
K.
,
Kondo
,
H.
, and
Sakata
,
M.
, “
Elastodynamic analysis of crack by finite element method using singular element
,”
International Journal of Fracture
14
, pp. 59–68,
1978
.
27.
Nishioka
,
T.
,
Stonesifer
,
R. B.
, and
Atluri
,
S. N.
, “
An evaluation of several moving singularity finite element procedures for analysis of fast fracture
,”
Engineering Fracture Mechanics
15
, pp. 205–218,
1981
.
28.
Thesken
,
J. C.
, and
Gudmundson
,
P.
, “
Application of a moving variable order singular element to dynamic fracture mechanics
,”
International Journal of Fracture
52
, pp. 47–65,
1991
.
29.
Lee
,
C. K.
, and
Lo
,
S. H.
, “
An automatic adaptive refinement finite element procedure for 2D elastostatic analysis
,”
International Journal for Numerical Methods in Engineering
 0029-5981 
35
, pp. 2189–2210,
1992
.
30.
Potyondy
,
D. O.
,
Wawrzynek
,
P. A.
, and
Ingraffea
,
A. R.
, “
An algorithm to generate quadrilateral or triangular element surface meshes in arbitrary domains with application to crack propagation
,”
International Journal for Numerical Methods in Engineering
 0029-5981 
38
, pp. 2677–2701,
1995
.
31.
Belytschko
,
T.
,
Lu
,
Y. Y.
, and
Gu
,
L.
, “
Element-free Galerkin methods
,”
International Journal for Numerical Methods in Engineering
 0029-5981 
37
, pp. 229–256,
1994
.
32.
Belytschko
,
T.
,
Organ
,
D.
, and
Krongauz
,
Y.
, “
A coupled finite element — elementfree Galerkin method
,”
Computational Mechanics
 0178-7675 
17
, pp. 186–195,
1995
.
33.
Belytschko
,
T.
,
Lu
,
Y. Y.
,
Gu
,
L.
, and
Tabbara
,
M.
, “
Element-free Galerkin methods for static and dynamic fracture
,”
International Journal of Solids and Structures
 0020-7683 
32
, pp. 2547–2570,
1995
.
34.
Rashid
,
M. M.
, “
The arbitrary local mesh replacement method: an alternative to remeshing for crack propagation analysis
,”
Computer Methods in Applied Mechanics and Engineering
154
, pp. 133–150,
1998
.
35.
Fish
,
J.
, and
Markolefas
,
S.
, “
Adaptive s-method for linear elastostatics
,”
Computer Methods in Applied Mechanics and Engineering
104
, pp. 363–396,
1993
.
36.
Fish
,
J.
, “
The s-version of the finite element method
,”
Computers and Structures
 0045-7949 
43
, pp. 539–547,
1992
.
37.
Hood
,
P.
, “
Frontal solution program for unsymmetric matrices
,”
International Journal for Numerical Methods in Engineering
 0029-5981 
10
, pp. 379–399,
1976
.
38.
Irons
,
B. M.
, “
A frontal solution program for finite element analysis
,”
International Journal for Numerical Methods in Engineering
 0029-5981 
2
, pp. 5–32,
1970
.
39.
Rashid
M. M.
, “
Incremental kinematics for finite element applications
,”
International Journal for Numerical Methods in Engineering
 0029-5981 
36
, pp. 3937–3956,
1993
.
This content is only available via PDF.
You do not currently have access to this chapter.
Close Modal

or Create an Account

Close Modal
Close Modal