Abstract
The objective of this paper is to determine theoretically the material damping of short fibre-reinforced polymer matrix composites. The major damping mechanism in such composites is the viscoelastic behaviour of the polymer matrix. The analysis was carried out by developing a finite-element program which is capable of evaluating the stress and strain distribution of short fibre composites under axial loading (see Fig. 1a). Using the concept of balance of force we can express the modulusE x along the loading direction as a function of the mechanical properties of the fibre and matrix materials, fibre aspect ratio,l/d, loading angle,θ, and fibre volume fraction,V f. Then we apply the elastic-viscoelastic correspondence principle to replace all the mechanical properties of the composite, fibre and matrix materials such asE x,E f,E m,G m, by the corresponding complex moduli such asE ′x +iE ″x , andE ′f +iE ″f . After separation of the real and imaginary parts, we can expressE x/t'' andE t"x as functions of the fibre aspect ratio,l/d, loading angle,θ, stiffness ratio,E f/E m, fibre volume fraction,V f, and damping properties of the fibre and matrix materials such asη f andη m. Numerical results of the composite storage modulus,E ′x , loss modulus,E ″x , and loss factor (damping),η C, are plotted as functions of parameters such asl/d,θ,V f, and are discussed in terms of variations ofl/d,θ, andE f/E m, in detail. It is observed that for a given composite, there exist optimum values ofl/d andθ at whichE ″x andη c are maximized. The results of this paper can be used to optimize the performance of composite structures.
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Abbreviations
- A c,A f,A m :
-
cross-sectional area of composite, fibre and matrix, respectively
- d :
-
fibre diameter
- E L :
-
longitudinal modulus of composite (along the fibre direction) (see Fig. 1a)
- E T :
-
transverse modulus of composite (see Fig. 1a)
- E x :
-
modulus of composite along thex-direction (see Fig. 1b)
- E f :
-
tensile modulus of fibre
- E m :
-
tensile modulus of matrix
- G m :
-
shear modulus of matrix
- G LT :
-
in-plane shear modulus of composite (see Fig. 1a)
- l :
-
fibre length
- m :
-
tip to tip distance between fibres
- i :
-
(−1)1/2
- R :
-
one-half of centre-to-centre fibre spacing
- V f :
-
fibre volume fraction
- x :
-
distance along fibre from end of fibre
- α :
-
defined in Equation 22
- β :
-
defined in Equation 3
- β * :
-
defined in Equation 19
- ε L :
-
extensional (longitudinal strain) of composite
- ε f,ε m :
-
extensional (longitudinal strain) of fibre and matrix, respectively
- η c,η f,η m :
-
extensional loss factor of composite, fibre and matrix respectively
- η G m :
-
shear loss factor of matrix
- θ :
-
angle between fibre and thex-direction
- ¯σ c, ¯σ f, ¯σ m :
-
average longitudinal stress in composite, fibre and matrix, respectively
- σ :
-
longitudinal stress in fibre
- τ :
-
shear stress at fibre-matrix interface
- Ψ :
-
defined in Equation 23
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Sun, C.T., Gibson, R.F. & Chaturvedi, S.K. Internal material damping of polymer matrix composites under off-axis loading. J Mater Sci 20, 2575–2585 (1985). https://doi.org/10.1007/BF00556089
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DOI: https://doi.org/10.1007/BF00556089