This paper investigates an approach for calculating the cyclic J-integral through a new industrial application. A previously proposed method is investigated further with the extension of this technique through a new application of a practical three-dimensional (3D) notched component containing a semi-elliptical surface crack. Current methods of calculating the cyclic J-integral are identified and their limitations discussed. A modified monotonic loading (MML) concept is adapted to calculate the cyclic J-integral of this 3D semi-elliptical surface crack under cyclic loading conditions. Both the finite element method (FEM) and the extended finite element method (XFEM) are discussed as possible methods of calculating the cyclic J-integral in this investigation. Different loading conditions including uniaxial tension and out-of-plane shear are applied, and the relationships between the applied loads and the cyclic J-integral are established. In addition, the variations of the cyclic J-integral along the crack front are investigated. This allows the determination of the critical load that can be applied before crack propagation occurs, as well as the identification of the critical crack direction once propagation does occur. These calculations display the applicability of the method to practical examples and illustrate an accurate method of estimating the cyclic J-integral.

References

References
1.
Irwin
,
G.
,
1957
, “
Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate
,”
ASME J. Appl. Mech.
,
24
, pp.
361
364
.
2.
Griffith
,
A. A.
,
1921
, “
The Phenomena of Rupture and Flow in Solids
,”
Philos. Trans. R. Soc. London A
,
221
, pp.
163
198
.10.1098/rsta.1921.0006
3.
Rice
,
J. R.
,
1968
, “
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
,”
ASME J. Appl. Mech.
,
35
(
2
), pp.
379
386
.10.1115/1.3601206
4.
Wells
,
A. A.
,
1963
, “
Application of Fracture Mechanics at and Beyond General Yielding
,”
Br. Weld. J.
,
10
, pp.
563
570
.
5.
Broek
,
D.
,
1986
,
Elementary Engineering Fracture Mechanics
, 3rd ed.,
Martinus Nijhoff
,
Springer, Dordrecht, The Netherlands
.10.1007/978-94-009-4333-9
6.
Anderson
,
T. L.
,
2005
,
Fracture Mechanics: Fundamentals and Applications
, 2nd ed.
CRC Press
,
Boca Raton, FL
.
7.
Ainsworth
,
R. A.
,
1999
,
R5: An Assessment Procedure for the High Temperature Response of Structures
, Procedure R5: Issue 2,
British Energy Generation Ltd
,
Gloucester
.
8.
Milne
,
I.
,
Ainsworth
,
R. A.
,
Dowling
,
A. R.
, and
Stewart
,
A. T.
,
1988
, “
Assessment of the Integrity of Structures Containing Defects
,”
Int. J. Pressure Vessels Piping
,
32
, pp.
3
104
.
9.
Begley
,
J. A.
, and
Landes
,
J. D.
,
1972
, “
The J-Integral as a Fracture Criterion
,”
ASTM STP
,
514
, pp.
1
20
.
10.
Kishimoto
,
K.
,
Aoki
,
S.
, and
Sakata
,
M.
,
1980
, “
On the Path Independent Integral-J
,”
Eng. Fract. Mech.
,
13
(
4
), pp.
841
850
.10.1016/0013-7944(80)90015-6
11.
Bucci
,
R. J.
,
Paris
,
P. C.
,
Landes
,
J. D.
, and
Rice
,
J. R.
,
1972
, “
J Integral Estimation Procedures
,”
ASTM STP
,
514
, pp.
40
69
.
12.
Dowling
,
N. E.
,
1976
, “
Geometry Effects and the J-Integral Approach to Elastic–Plastic Fatigue Crack Growth
,”
ASTM STP
,
601
, pp.
19
32
.
13.
Zhu
,
X.-K.
, and
Joyce
,
J. A.
,
2012
, “
Review of Fracture Toughness (G, K, J, CTOD, CTOA) Testing and Standardization
,”
Eng. Fract. Mech.
,
85
, pp.
1
46
.10.1016/j.engfracmech.2012.02.001
14.
Dassault Systems Simulia Corporation
,
2012
, Version 6.12-3.
15.
Paris
,
P.
, and
Erdogan
,
F.
,
1963
, “
A Critical Analysis of Crack Propagation Laws
,”
ASME J. Fluids Eng.
,
85
(
4
), pp.
528
534
.
16.
Sumpter
,
J. D. G.
, and
Turner
,
C. E.
,
1976
, “
Method for Laboratory Determination of JC
,”
ASTM STP
,
601
, pp.
3
18
.
17.
Dowling
,
N. E.
, and
Begley
,
J. A.
,
1976
, “
Fatigue Crack Growth During Gross Plasticity and the J-Integral
,”
ASTM-STP
,
590
, pp.
82
103
.
18.
Chattopadahyay
,
J.
,
2006
, “
Improved J and COD Estimation by GE/EPRI Method in Elastic to Fully Plastic Transition Zone
,”
Eng. Fract. Mech.
,
73
(
14
), pp.
1959
1979
.10.1016/j.engfracmech.2006.03.012
19.
Miller
,
A. G.
, and
Ainsworth
,
R. A.
,
1989
, “
Consistency of Numerical Results for Power Law Hardening Materials and the Accuracy of the Reference Stress Approximation
,”
Eng. Fract. Mech.
,
32
(
2
), pp.
233
247
.10.1016/0013-7944(89)90296-8
20.
Moës
,
N.
,
Dolbow
,
J.
, and
Belytschko
,
T.
,
1999
, “
A Finite Element Method for Crack Growth Without Remeshing
,”
Int. J. Numer. Methods
,
46
(
1
), pp.
131
150
.10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J
21.
Chen
,
W.
, and
Chen
,
H.
,
2013
, “
Cyclic J-Integral Using the Linear Matching Method
,”
Int. J. Pressure Vessels Piping
,
108–109
, pp.
72
80
.10.1016/j.ijpvp.2013.04.011
22.
Tanaka
,
K.
,
1983
, “
The Cyclic J-Integral as a Criterion for Fatigue Crack Growth
,”
Int. J. Fract.
,
22
(
2
), pp.
91
104
.10.1007/BF00942715
23.
Leidermark
,
D.
,
Moverare
,
J.
,
Simonsson
,
K.
, and
Sjöström
,
S.
,
2011
, “
A Combined Critical Plane and Critical Distance Approach for Predicting Fatigue Crack Initiation in Notched Single-Crystal Superalloy Components
,”
Int. J. Fatigue
,
33
(
10
), pp.
1351
1359
.10.1016/j.ijfatigue.2011.05.009
You do not currently have access to this content.