An Analytical Solution for Anisotropic Composite Plate of Crack under Bending and Twisting

Abstract:

Analysis of mechanical behaviors near crack tip for linear elastic anisotropic composite plate under bending loadings and twisting loadings was done. By introducing proper deflection function, the mechanical problem reduced to the boundary value problem of partial differential equation. The mixed mode stress intensity factor at the crack tip were presented under bending loadings and twisting loadings at infinity. By solving boundary value problem of partial differential equation and using a complex variable function method, the expressions for bending moments, strains and displacements near crack tip are derived. The obtained results are used to the theoretical research and experimental analysis of the fracture problems of composite plate.

• Periodical: Advanced Materials Research (Volumes 197-198)
• Pages: 1567-1572
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.197-198.1567
• Online since: February 2011
• Authors: Xue Xia Zhang, Xiao Chao Cui, Wei Yang Yang, Wen Bin Zhao
• Keywords: Anisotropic Plate, Complex Variable Function Method, Crack, Stress Intensity Factor (SIF)

References

[1] Lekhnitskii: Theory of Elasticity of an Anisotropic Elastic Body (transl. H.C. Hu in Chinese, Science Press, China 1963).

[2] N．I．Muskhelishvili: Some Basic Problems of the Mathematical Theory of Elasticity (Noordhof Press, Groningen1953).

[3] M.L. Williams: J. appl. mech. Vol. 28 (1961), p.78.

[4] G.C. Sih, P.C. Paris and F. Erdogan: J. Appl. Mech. Vol. 29 (1962), p.306.

[5] G.C. Sih: Mechanics of Fracture, Vol. 3 (Noordhoff Press, leyden 1977).

[6] J.K. Lu: Complex Variable Methods in Plane Elasticity (WuHan University Press, China 2005).

[7] H.T. Cai J.K. Lu: App1. Math. Mech. Vol. 30 (2009), p.1429.

[8] K. Wang and R.J. Tang: J. LanZhou. Univ. Vol. 15 (1979), p.36.

[9] C.T. Liu, C.P. Jiang: Fracture Mechanics for Plates and shells( national defence industrial press, China 2000).

[10] C.T. Liu, Y.Z. Li: Adv. Mech. Vol. 12(1982), p.346.

[11] W.Y. Yang, S.Q. Zhang, X.X. Zhang and Y.L. M: Math. Acta. Vol. 24 (2004), p.45.

[12] W.Y. Yang and S.Q. Zhang: App1. Math. Mech. Vol. 20 (1999), p.205.

[13] S. Q. Zhang, Y.Z. Zhu and W.Y. Yang: Engi. Frac. Mech. Vol. 43 (1992), p.797.

[14] W.Y. Yang, J.L. Li and X.X. Zhang: Complex Variable Method in Theory of Fracture for Composite Materials (Science Press, Beijing 2005).

[15] J. H. Guo and G. T. Liu: Chin. Phy. B. Vol. 17 (2008), p.2610.