An analytical solution is presented for local buckling of a model of delaminated composites, that is, a layer bonded to a half-space with an interface crack. The layered system is subjected to compressive load parallel to the free surface. Basic stability equations derived from the mathematical theory of elasticity are employed to study this local buckling behavior. They are different from the conventional buckling equations used in most previous studies and based on the classical structural mechanics of beams and plates. A system of homogeneous Cauchy-type singular integral equations of the second kind is formulated by means of the Fourier integral transform and is solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for the buckling load and shape are presented for various delamination geometries and material properties of both the layer and half-space.

Issue Section:
Technical Papers
Topics:
Buckling, Fracture (Materials), Stress, Composite materials, Delamination, Elasticity, Integral equations, Materials properties, Plates (structures), Shapes, Stability, Structural analysis, Structural mechanics
1.
Bottega
W. J.
, and
Maewal
A.
,
1983
, “
Delamination Buckling and Growth in Laminates
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
50
, pp.
184
–
189
.
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 Structures
, Vol.
17
, pp.
1069
–
1083
.
3.
Dorris
J. F.
, and
Nemat-Nasser
S.
,
1980
, “
Instability of a Layer on a Half Space
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
47
, pp.
304
–
312
.
4.
Erdogan
F.
, and
Gupta
G. D.
,
1971
, “
Layered Composites with an Interface Flaw
,”
Int. J. Solids and Structures
, Vol.
7
, pp.
1089
–
1107
.
5.
Flugge, W., 1972, Tensor Analysis and Continuum Mechanics, Springer-Verlag, New York.
6.
Keer
L. M.
,
Nemat-Nasser
S.
, and
Oranratnachai
A.
,
1982
, “
Surface Instability and Splitting in Compressed Brittle Elastic Solids Containing Crack Arrays
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
49
, pp.
761
–
767
.
7.
Kutlu
Z.
, and
Chang
F. K.
,
1992
, “
Modeling Compression Failure of Laminated Composites Containing Multiple Through-the-Width Delaminations
,”
Journal of Composite Materials
, Vol.
26
, pp.
350
–
387
.
8.
Madenci
E.
, and
Westmann
R. A.
,
1991
, “
Local Delamination Buckling in Layered Systems
,”
ASME JOURNAL OF APPLIED MECHANICS
, Vol.
47
, pp.
157
–
166
.
9.
Muskhelishvili, N. I., 1958, Singular Integral Equations, (revised translation from Russian; edited by J. R. M. Radok), P. Noordhoff, Holland.
10.
Peck
S. O.
, and
Springer
G. S.
,
1991
, “
The Behavior of Delaminations in Composite Plates—Analytical and Experimental Results
,”
Journal of Composite Materials
, Vol.
25
, pp.
907
–
929
.
11.
Rothschilds, R. J., Gillespie, Jr., J. W., and Carlsson, L. A., 1988, “Instability-Related Delamination Growth in Thermoset and Thermoplastic Composites,” ASTM STP 972, pp. 161–179.
12.
Timoshenko, S. P., and Gere, J. M., 1961, Theory of Elastic Stability, McGraw-Hill, New York.
13.
Wang
W. X.
,
Shen
W.
,
Takao
Y.
,
Shen
Z.
, and
Chen
P.
,
1991
, “
An Analysis of Compressive Stability of Elastic Solids Containing a Crack Parallel to the Surface
,”
Eng. Fract. Mech.
, Vol.
40
, pp.
1023
–
1033
.
14.
Wang
W. X.
,
Takao
Y.
, and
Suhara
T.
,
1988
, “
Interaction Between Cracks Perpendicular to and on the Interface in Composite Materials
,”
JSME International Journal, I
, Vol.
31
, pp.
201
–
208
.
15.
Washizu, K., 1968, Variational Methods in Elasticity and Plasticity, Pergamon Press, London.
16.
Whitcomb
J. D.
,
1981
, “
Finite Element Analysis of Instability Related Delamination Growth
,”
Journal of Composite Materials
, Vol.
15
, pp.
403
–
426
.
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