Abstract
This paper investigates the delamination buckling of an orthotropic film with compressive prestress bonded to an orthotropic substrate. The buckled film detached from the film/substrate structure is solved in the closed form except for the resultant force and bending moment at the ends of the buckled film, which are obtained by matching the solutions for the buckled film and the film/substrate structure in which the buckled part of the film is removed. Special attention is paid to the effects of parameters of orthotropic materials on delamination buckling based on a numerical analysis. The energy release rate and mode mixity induced by buckling are evaluated, and the growth and arrest of the interface crack under mixed loading induced by buckling are discussed based on the energy criterion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- a ij :
-
dimensionless compliance coefficient
- B :
-
complex matrix
- b :
-
half debonding size
- D :
-
bending stiffness
- G :
-
energy release rate
- g i (z):
-
complex function
- H :
-
complex matrix
- h :
-
thickness of a film
- I :
-
identity matrix
- K i *, k :
-
stress intensity factor
- M, M 0 :
-
bending moment
- N, N 0 :
-
resultant force
- p, p i :
-
complex number
- S ij , S ij e :
-
conventional compliance component
- u i , u N , u M :
-
displacement
- Y(ζ 1, ζ 2):
-
matrix function
- α:
-
bimaterial matrix
- α 0 :
-
bimaterial parameter
- β:
-
bimaterial matrix
- β 0 :
-
bimaterial parameter
- Γ :
-
interface fracture toughness
- ΔN :
-
change in resultant force
- ε ij :
-
strain component
- ζ :
-
dimensionless resultant force
- θ 0 :
-
rotation angle
- κ ij :
-
thermal expansion coefficient
- λ, λ i :
-
orthotropic parameter
- ρ, ρ i :
-
orthotropic parameter
- σ :
-
stress
- φ(x 1, x 2):
-
complex function vector
- χ :
-
dimensionless bending moment
- ψ :
-
mode mixity
References
Whitcomb, J. D., “Parametric Analytical Study of Instability-Related Delamination Growth,” Composites Science and Technology, Vol. 25, No. 1, pp. 19–48, 1986.
Hutchinson, J. W. and Suo, Z., “Mixed Mode Cracking in Layered Materials,” Advances in Applied Mechanics, Vol. 29, pp. 63–191, 1991.
Choi, S. R., Hutchinson, J. W., and Evans, A. G., “Delamination of Multilayer Thermal Barrier Coatings,” Mechanics of Materials, Vol. 31, No. 7, pp. 431–447, 1999.
Bruno, D. and Greco, F., “An Asymptotic Analysis of Delamination Buckling and Growth in Layered Plates,” International Journal of Solids and Structures, Vol. 37, No. 43, pp. 6239–6276, 2000.
Cotterell, B. and Chen, Z., “Buckling and Cracking of Thin Films on Compliant Substrates under Compression,” International Journal of Fracture, Vol. 104, No. 2, pp. 169–179, 2000.
Yu, H. H. and Hutchinson, J. W., “Influence of Substrate Compliance on Buckling Delamination of Thin Films,” International Journal of Fracture, Vol. 113, No. 1, pp. 39–55, 2002.
Jeong, K. M. and Beom, H. G., “Buckling Analysis of an Orthotropic Layer Bonded to a Substrate with an Interface Crack,” Journal of Composite Materials, Vol. 37, No. 18, pp. 1613–1628, 2003.
Lu, T. Q., Zhang, W. X., and Wang, T., “The Surface Effect on The Strain Energy Release Rate of Buckling Delamination in Thin Film-Substrate Systems,” International Journal of Engineering Science, Vol. 49, No. 9, pp. 967–975, 2011.
Gurtin, M. E. and Murdoch, A. I., “A Continuum Theory of Elastic Material Surfaces,” Archive for Rational Mechanics and Analysis, Vol. 57, No. 4, pp. 291–323, 1975.
Beom, H. G., Cui, C. B., and Jang, H. S., “Dependence of Stress Intensity Factors on Elastic Constants for Cracks in an Orthotropic Bimaterial with a Thin Film,” International Journal of Solids and Structures, Vol. 49, No. 23, pp. 3461–3471, 2012.
Timoshenko, S. and Woinowsky-Krieger, S., “Theory of Plates and Shells,” McGraw-Hill New York, pp. 415–420, 1959.
Beom, H. G., Cui, C. B., and Jang, H. S., “Application of an Orthotropy Rescaling Method to Edge Cracks and Kinked Cracks in Orthotropic Two-Dimensional Solids,” International Journal of Engineering Science, Vol. 51, No. pp. 14–31, 2012.
Suo, Z. and Hutchinson, J. W., “Interface Crack between Two Elastic Layers,” International Journal of Fracture, Vol. 43, No. 1, pp. 1–18, 1990.
Beom, H. G. and Atluri, S. N., “Dependence of Stress on Elastic Constants in an Anisotropic Bimaterial under Plane Deformation and the Interfacial Crack,” Computational Mechanics, Vol. 16, No. 2, pp. 106–113, 1995.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhuo, X.R., Jang, H.S. & Beom, H.G. Delamination buckling of a thin film bonded to an orthotropic substrate. Int. J. Precis. Eng. Manuf. 16, 323–333 (2015). https://doi.org/10.1007/s12541-015-0043-z
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12541-015-0043-z