Abstract
A composite test specimen in the shape of a semicircular curved bar subjected to bending offers an excellent stress field for studying the open-mode delamination behavior of laminated composite materials. This is because the open-mode delamination nucleates at the midspan of the curved bar. The classical anisotropic elasticity theory was used to construct a ‘multilayer’ theory for the calculations of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to end forces and end moments. The radial location and intensity of the open-mode delamination stress were calculated and were compared with the results obtained from the anisotropic continuum theory and from the finite element method. The multilayer theory gave more accurate predictions of the location and the intensity of the open-mode delamination stress than those calculated from the anisotropic continuum theory.
Keywords
- Middle Surface
- Radial Location
- Peak Shear Stress
- Effective Material Property
- Anisotropic Continuum
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Abbreviations
- a :
-
Inner radius of semicircular curved bar
- a i :
-
Outer radius of ith layer of semicircular curved bar
- a m :
-
Mean radius of semicircular curved bar, ½(a + b)
- A, B, C, D :
-
Arbitrary constants associated with F for loading case of end forces P
- A′, B′, C′, D′:
-
Arbitrary constants associated with F for loading case of end moments M
- Ā,\( \bar B\), \(\bar C\), \(\bar D\) :
-
Arbitrary constants associated with F for loading case of end moments M for isotropic materials
- b :
-
Outer radius of semicircular curved bar
- e :
-
Loading axis offset
- E L :
-
Modulus of elasticity of single ply in fiber direction
- E r :
-
Modulus of elasticity in r direction
- ET :
-
Modulus of elasticity of single ply transverse to fiber direction
- E θ :
-
Modulus of elasticity in θ direction
- E41:
-
Quadrilateral membrane element
- F :
-
Airy stress function
- G LT :
-
Shear modulus of single ply
- G r θ :
-
Shear modulus associated with r–θ system
- h :
-
Width of semicircular curved bar
- i :
-
Index associated with ith layer, i = 1,2,3,…, N
- k :
-
Anisotropic parameter, \(\sqrt {{E_\theta }/{E_r}}\)
- M :
-
Applied end moment
- N :
-
Total number of laminated layers
- P :
-
Applied end force
- r :
-
Radial distance
- r D :
-
Radial location of σD
- r m :
-
Radial location of (σ r )max
- r′m :
-
Radial location of (σ′ r )max
- r 0 :
-
Radial location of zero σθ
- u r :
-
Displacement in r direction
- u θ :
-
Displacement in θ direction
- x, y :
-
Rectangular Cartesian coordinates
- β:
-
Anisotropic parameter, \(\sqrt {1 + \left( {{E_\theta }/{E_r}} \right)\left( {1 - 2{v_{r\theta }}} \right) + {E_\theta }/{G_{r\theta }}}\)
- γrθ :
-
Shear strain in r–θ plane
- θ:
-
Composite ply thickness
- ε r :
-
Strain in r direction
- εθ :
-
Strain in θ direction
- θ:
-
Tangential coordinate
- νLT :
-
Poisson ratio of single-ply composite
- ν rz , ν zr , ν rθ, ν zθ, νθr ,vθz :
-
Poisson ratios
- σD :
-
Delamination stress in C-coupon
- σ r :
-
Radial stress
- (σ r )max :
-
Delamination stress for the case of end forces P,
- (σ′r)max :
-
Delamination stress for the case of end moments M, σr(r′m)
- σθ :
-
Tangential stress
- τ r θ :
-
Shear stress
- [](i) :
-
Quantity associated with ith layer
- [] i :
-
Quantity associated with ith layer
References
Ko, W. L., Delamination stresses in semicircular laminated composite bars. NASA TM-4026, 1988.
Tolf, G., Stresses in a curved laminated beam. Fiber Sci. and Technol., 19(4) (1983) 243–67.
Lekhnitskii, S. G., Anisotropic Plates. Gordon and Breach, New York, 1968.
Fung, Y. C., Foundations of Solid Mechanics. Prentice-Hall, Englewood Cliffs, New Jersey, 1965.
Whetstone, W. D., SPAR Structural Analysis System Reference Manual, System Level 13A, Vol. 1. Program Execution, NASA CR-158970-1, 1978.
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© 1989 Elsevier Science Publishers Ltd
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Ko, W.L., Jackson, R.H. (1989). Multilayer Theory for Delamination Analysis of a Composite Curved Bar Subjected to End Forces and End Moments. In: Marshall, I.H. (eds) Composite Structures 5. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1125-3_7
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DOI: https://doi.org/10.1007/978-94-009-1125-3_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6998-4
Online ISBN: 978-94-009-1125-3
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