Buckling Analysis of an Orthotropic Layer Bonded to a Substrate with an Interface Crack

Abstract

The buckling of an orthotropic layer bonded to a half-space with an interface crack subjected to compressive load under plane strain is analyzed. The theory of elasticity related to elastic stability is employed to investigate the buckling behavior of both the layer and the half-space. By the use of Fourier transforms, the boundary value problem is reduced to a system of homogeneous Cauchy-type singular integral equations of the second kind, which is solved numerically to determine the critical buckling loads. Numerical results are obtained for various geometric parameters and material properties of both the layer and the half-space. It is shown that the effect of orthotropy on the buckling load is to be distinct when the ratio of longitudinal modulus of the layer to the substrate is small or the ratio of layer thickness to the crack length is large.

Get full access to this article

View all access options for this article.

References

1. Gough, G.S., Elam, C.F. and de Bruyne, N.A. (1940). The Stabilization of a Thin Sheet by a Continuous Supporting Medium , J. Royal Aero. Soc., 44: 12-43 .

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, 17: 1069-1083 .

3. Bottega, W.J. and Maewal, A. (1983). Delamination Buckling and Growth in Laminates , ASME J. Appl. Mech., 50: 184-189 .

4. Rothschilds, R.J., Gillespie Jr., J.W. and Carlsson, L.A. (1988). Instability-Related Delamination Growth in Thermoset and Thermoplastic Composites , ASTM STP 972, 161-179 .

5. Peck, S.O. and Springer, G.S. (1991). The Behavior of Delaminations in Composites Plates-Analytical and Experimental Results , J. Comp. Materials, 25: 907-929 .

6. Kutlu, Z. and Chang, F.K. (1992). Modeling Compression Failure of Laminated Composites Containing Multiple Through-the-Width Delaminations , J. Comp. Materials, 26: 350-387 .

7. Sheinman, I., Kardomateas, G.A. and Pelegri, A.A. (1998). Delamination Growth During Pre- and Postbuckling Phases of Delaminated Composite Laminates , Int. J. Solids Structures, 35: 19-31 .

8. Bruno, D. and Greco, F. (2000). An Asymptotic Analysis of Delamination Buckling and Growth in Layered Plates , Int. J. Solids Structures, 37: 6239-6276 .

9. Dorris, J.F. and Nemat-Nasser, S. (1980). Instability of a Layer on a Half Space , ASME J. Appl. Mech., 47: 304-312 .

10.

10. Shield, T.W., Kim, K.S. and Shield, R.T. (1994). The Buckling of an Elastic Layer Bonded to an Elastic Substrate in Plane Strain , ASME J. Appl. Mech., 61: 231-235 .

11.

11. Hwang, S.F. (1998). The Buckling of an Orthotropic Layer on a Half-Space , Int. J. Mech. Sci., 40(7): 711-721 .

12.

12. Jeong, K.M. and Beom, H.G. (2000). Buckling Analysis of Two Isotropic Layers Bonded to a Semi-Infinite Substrate , Trans. Korean Soc. Mech. Engrs. A, 24: 2108-2114 (in Korean).

13.

13. Keer, I.M., Nemat-Nasser, S. and Oranaratnachai, A. (1982). Surface Instability and Splitting in Compressed Brittle Elastic Solids Containing Crack Arrays , ASME J. Appl. Mech., 49: 761-767 .

14.

14. 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., 40: 1023-1033 .

15.

15. Wang, W.X. and Takao, Y. (1995). Load Buckling of a Layer Bonded to a Half-Space With an Interface Crack , ASME J. Appl. Mech., 62: 64-70 .

16.

16. Washizu, K. (1968). Variational Methods in Elasticity and Plasticity, Pergamon Press, London .

17.

17. Flügge, W. (1972). Tensor Analysis and Continuum Mechanics, Springer-Verlag, New York .

18.

18. Erdogan, F. and Gupta, G.D. (1971). The Stress Analysis of Multi-Layered Composites with Flaw , Int. J. Solids Structures, 7: 39-61 .

19.

19. Muskhelishvili, N.I. (1958). Singular Integral Equations (Revised translation from Russian; In: Radok, J.R.M. (ed.), P. Noordhoff, Holland .

20.

20. Wang, W.X., Takao, Y. and Suhara, T. (1988). Interaction Between Cracks Perpendicular to and on the Interface in Composite Materials , JSME Int. J., Series I, 31: 201-208 .