Axisymmetric buckling, initial post-buckling and growth of a circular delamination bridged by nonlinear fibers in three-dimensional composites are studied by a perturbation method. The through-thickness fibers are assumed to provide nonlinear restoring traction resisting the deflection of the delaminated layer. A closed-form solution for the central deflection of the delamination due to on applied compressive stress during initial post-buckling is obtained. In addition, some simple formulas for calculating the strain energy release rate and the mixed mode stress intensity ratio (i.e., Mode II versus Mode I) at the delamination crack tip are also established. Some interesting conclusions arising directly from the perturbation solutions are drawn. These include: (1) initial post-buckling behavior of a circular delamination is unstable for a softening bridging model; this may result in initial delamination growth for some materials with lower fracture toughness when the delamination buckles rather than post-buckles. However, stable growth is obtained for a hardening bridging model; (2) with an increase of the nonlinear fiber bridging parameter β¯, the residual stiffness of a three-dimensional composite structure with a circular delamination increases gradually; (3) bridging force changes the catastrophic nature of the delamination growth and increases the stability of the delamination. The range and the dynamic effect of the unstable delamination growth diminish or disappear as the bridging parameters increase; (4) for the bridged delamination, the higher the material fracture toughness, the higher the stability of the delamination growth, and the smaller the range and dynamic effect of its unstable growth. [S0021-8936(00)03203-7]

1.
Kardomateas
,
G. A.
, and
Schmueser
,
D. W.
,
1988
, “
Buckling and Postbuckling of Delaminated Composites under Compressive Loads Including Transverse Shear Effects
,”
AIAA J.
,
26
, pp.
337
343
.
2.
Chai
,
H.
,
Babcock
,
C. D.
, and
Knauss
,
W. G.
,
1981
, “
One Dimensional Modeling of Failure in Laminated Plates by Delamination Buckling
,”
Int. J. Solids Struct.
,
17
, pp.
1069
1083
.
3.
Bottega
,
W. J.
, and
Maewal
,
A.
,
1983
, “
Delamination and Buckling in Laminates
,”
ASME J. Appl. Mech.
,
50
, pp.
185
189
.
4.
Evans
,
A. G.
, and
Hutchinson
,
J. W.
,
1984
, “
On the Mechanics of Delamination and Spalling in Compressed Films
,”
Int. J. Solids Struct.
,
20
, pp.
455
466
.
5.
Yin
,
W.-L.
,
1985
, “
Axisymmetric Buckling and Growth of a Circular Delamination in a Compressed Laminate
,”
Int. J. Solids Struct.
,
21
, pp.
503
514
.
6.
Chai
,
H.
,
1990
, “
Three Dimensional Fracture Analysis of Thin Film Debonding
,”
Int. J. Fract.
,
46
, pp.
237
256
.
7.
Chai
,
H.
,
1990
, “
Buckling and Post-Buckling Behavior of Elliptical Plates: Part I—Analysis, Part II—Results
,”
ASME J. Appl. Mech.
,
57
, pp.
981
994
.
8.
Suo
,
Z.
,
1990
, “
Delamination Specimens for Orthotropic Materials
,”
ASME J. Appl. Mech.
,
57
, pp.
627
634
.
9.
Peck
,
S. O.
, and
Springer
,
G. S.
,
1991
, “
The Behavior of Delaminations in Composite Plates: Analytical and Experimental Results
,”
J. Compos. Mater.
,
25
, pp.
907
929
.
10.
Kardomateas
,
G. A.
,
1993
, “
The Initial Postbuckling and Growth Behavior of Internal Delaminations in Composite Plates
,”
ASME J. Appl. Mech.
,
60
, pp.
903
910
.
11.
Giannakopoulos
,
A. E.
,
Nilsson
,
K. F.
, and
Tsamasphyros
,
G.
,
1995
, “
The Contact Problem at Delamination
,”
ASME J. Appl. Mech.
,
62
, pp.
989
996
.
12.
Zhang
,
X.
, and
Yu
,
S.
,
1996
, “
An Analysis of Axisymmetric Buckling and Growth of Circular-Shaped Delamination
,”
Acta Mech. Solida Sinica
,
9
, pp.
201
209
.
13.
Shu
,
D.
, and
Mai
,
Y.-W.
,
1993
, “
Effect of Stitching on Interlaminar Delamination Extension in Composite Laminates
,”
Compos. Sci. Technol.
,
49
, pp.
165
171
.
14.
Cox
,
B. N.
,
1994
, “
Delamination and Buckling in 3D Composites
,”
J. Compos. Mater.
,
28
, pp.
1114
1126
.
15.
Cox
,
B. N.
, and
Marshall
,
D. B.
,
1994
, “
Concepts for Bridged Cracks in Fracture and Fatigue,” Overview No. 111
,
Acta Metall. Mater.
,
42
, pp.
341
363
.
16.
Li
,
S.
,
Huang
,
Y.
,
Hu
,
Y.
, and
Zhong
,
W.
,
1997
, “
Analysis on Buckling and Postbuckling of Delamination in 3D Composites
,”
Acta Mech. Solida Sinica
,
10
, pp.
212
219
.
17.
Li
,
S.
,
Hu
,
Y.
,
Huang
,
Y.
, and
Zhong
,
W.
,
1997
, “
The Fracture Analysis of a Bridged Delamination in 3D Composites
,”
Acta Mech. Solida Sinica
,
18
, No.
3
, pp.
94
99
(in Chinese).
18.
Hu
,
Y.
,
Huang
,
Y.
,
Li
,
S.
, and
Zhong
,
W.
,
1999
, “
The Effects of Bridging in a 3D Composite on Buckling, Postbuckling and Growth of Delamination
,”
Arch. Appl. Mech.
,
69
, pp.
419
428
.
19.
Massabo
,
R.
, and
Cox
,
B. N.
,
1999
, “
Concepts for Bridged Mode II Delamination Cracks
,”
J. Mech. Phys. Solids
,
47
, No.
6
, pp.
1265
1300
.
20.
Li
,
S.
,
Huang
,
Y.
,
Hu
,
Y.
, and
Li
,
D.
,
1998
, “
Effects of Fiber Bridge on the Delamination Buckling in 3D Composites
,”
Eng. Mech.
,
15
, No.
4
, pp.
127
132
(in Chinese).
21.
Li
,
S.
,
Li
,
D.
,
Huang
,
Y.
, and
Hu
,
Y.
,
1998
, “
Analysis on Stability Characteristics of Quasi-Static Growth of a Bridged Delamination in 3D Composites
,”
Acta Mater. Compos. Sinica
,
15
, No.
4
, pp.
143
150
(in Chinese).
22.
Xu, Z., 1982, Theory of Elasticity (II), Higher Education Press, Beijing, (in Chinese).
23.
Gu, D., 1993, Perturbation Method, Higher Education Press, Beijing (in Chinese).
24.
Hutchinson
,
J. W.
, and
Suo
,
Z.
,
1992
, “
Mixed Mode Cracking in Layered Materials
,”
Adv. Appl. Mech.
,
29
, pp.
63
191
.
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