A generalized elastic solution for an arbitrarily propagating transient crack in functionally graded materials (FGMs) is obtained through an asymptotic analysis. The shear modulus and mass density of the FGM are assumed to vary exponentially along the gradation direction. The out-of-plane displacement field and its gradients about the crack tip were obtained in powers of radial coordinates, with the coefficients depending on the time rates of change of crack tip speed and stress intensity factor. The effects of the transient terms on the contours of constant out-of-plane displacement are duly discussed.

Keywords:
functionally graded materials, elastodynamics, crack-edge stress field analysis, fracture mechanics, shear modulus, internal stresses, density
Topics:
Fracture (Materials), Functionally graded materials, Transients (Dynamics), Stress, Displacement
1.
Niino
,
M.
,
Hirai
,
T.
, and
Watanabe
,
R.
,
1987
, “
The Functionally Gradient Materials
,”
J. Jap. Soc. Comp. Mater.
,
13:1
, p.
257
257
.
2.
Delale
,
F.
, and
Erdogan
,
F.
,
1983
, “
The Crack Problem for a Nonhomogeneous Plane
,”
J. Appl. Mech.
,
50
, pp.
67
–
80
.
3.
Schovanec
,
L.
, and
Walton
,
J. R.
,
1988
, “
On the Order of Stress Singularity for an Antiplane Shear Crack at the Interface of Two Bonded Inhomogeneous Elastic Materials
,”
ASME J. Appl. Mech.
,
55
, pp.
234
–
236
.
4.
Konda
,
N.
, and
Erdogan
,
F.
,
1994
, “
The Mixed Mode Crack Problem in a Nonhomogeneous Elastic Plane
,”
Eng. Fract. Mech.
,
47
, pp.
533
–
545
.
5.
Gu
,
P.
, and
Asaro
,
R. J.
,
1997
, “
Cracks in Functionally Graded Materials
,”
Int. J. Solids Struct.
,
34:1
, pp.
1
–
17
.
6.
Li
,
C. Y.
, and
Weng
,
G. J.
,
2002
, “
Antiplane Crack Problem in Functionally Graded Piezoelectric Materials
,”
J. Appl. Mech.
,
69
, pp.
481
–
488
.
7.
Rousseau
,
C. E.
, and
Tippur
,
H. V.
,
2000
, “
Compositionally Graded Materials With Cracks Normal to the Elastic Gradient
,”
Acta Mater.
,
48
, pp.
4021
–
4033
.
8.
Parameswaran
,
V.
, and
Shukla
,
A.
,
2002
, “
Asymptotic Stress Fields for Stationary Cracks Along the Gradient in Functionally Graded Materials
,”
Trans. ASME
,
69
, pp.
240
–
243
.
9.
Atkinson
,
C.
, and
List
,
R. D.
,
1978
, “
Steady State Crack Propagation Into Media With Spatially Varying Elastic Properties
,”
Int. J. Eng. Sci.
,
16
, pp.
717
–
730
.
10.
Wang
,
X. D.
, and
Meguid
,
S. A.
,
1995
, “
On the Dynamic Crack Propagation in an Interface With Spatially Varying Elastic Properties
,”
Int. J. Fract.
,
69
, pp.
87
–
99
.
11.
Nakagaki
,
M.
,
Sasaki
,
H.
, and
Hagihara
,
S.
,
1995
, “
A Study of Crack in Functionally Graded Materials Under Dynamic Loading
,”
PVP-Dynamic Fracture, Failure and Deformations, ASME
,
300
, pp.
1
–
6
.
12.
Parameswaran
,
V.
, and
Shukla
,
A.
,
1998
, “
Dynamic Fracture of a Functionally Fracture in Functionally Gradient Materials
,”
J. Mater. Sci.
,
33
, pp.
3303
–
3311
.
13.
Rousseau
,
C. E.
, and
Tippur
,
H. V.
,
2001
, “
Dynamic Fracture of Compositionally Graded Materials With Cracks Along the Elastic Gradient: Experiments and Analysis
,”
Mech. Mater.
,
33
, pp.
403
–
421
.
14.
Parameswaran
,
V.
, and
Shukla
,
A.
,
1999
, “
Crack-Tip Stress Fields for Dynamic Fracture in Functionally Gradient Materials
,”
Mech. Mater.
,
31
, pp.
579
–
596
.
15.
Jiang
,
L. Y.
, and
Wang
,
X. D.
,
2002
, “
On the Dynamic Crack Propagation in an Interphase With Spatially Varying Elastic Properties Under Inplane Loading
,”
Int. J. Fract.
,
114
, pp.
225
–
244
.
16.
Chalivendra
,
V. B.
,
Shukla
,
A.
, and
Parameswaran
,
V.
,
2002
, “
Dynamic Out of Plane Displacement Fields for an Inclined Crack in Graded Materials
,”
J. Elast.
,
69
, pp.
99
–
119
.
17.
Freund
,
L. B.
, and
Rosakis
,
A. J.
,
1992
, “
The Structure of the Near-Tip Field During Transient Elastodynamic Crack Growth
,”
J. Am. Soc. Mass Spectrom.
,
40
(
3
), pp.
699
–
719
.
18.
Gu
,
P.
, and
Asaro
,
R. J.
,
1997
, “
Cracks in Functionally Graded Materials
,”
Int. J. Solids Struct.
,
34
(
1
), pp.
1
–
17
.
19.
Freund, L. B., 1990, Dynamic Fracture Mechanics, Cambridge University Press, Cambridge, MA.
20.
G. R. Irwin, 1980, Series Representation of the Stress Field Around Constant Speed Cracks, University of Maryland Lecture Notes.
21.
Parameswaran
,
V.
, and
Shukla
,
A.
,
2002
, “
Near-Tip Out of Plane Displacement Fields for Dynamic Crack Propagation in Functionally Graded Materials
,”
Mech. Res. Commun.
,
29
, pp.
397
–
406
.
22.
Tippur
,
H. V.
,
Krishnaswamy
,
S.
, and
Rosakis
,
A. J.
,
1991
, “
A Coherent Gradient Sensor for Crack Tip Measurements: Analytical and Experimental Results
,”
Int. J. Fract.
,
40
, pp.
193
–
204
.
23.
Dally
,
J. W.
, and
Shukla
,
A.
,
1979
, “
Dynamic Crack Behavior at Initiation
,”
Mech. Res. Commun.
,
6
(
4
), pp.
239
–
244
.
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