Complex moduli of aligned discontinuous fibre-reinforced polymer composites

This paper describes recent analytical and experimental efforts to determine the effects of fibre aspect ratio, fibre spacing, and the viscoelastic properties of constituent materials on the damping and stiffness of aligned discontinuous fibre-reinforced polymer matrix composites. This includes the analysis of trade-offs between damping and stiffness as the above parameters are varied. Two different analytical models show that there is an optimum fibre aspect ratio for maximum damping, and that the predicted optimum aspect ratios lie in the range of actual aspect ratios for whiskers and microfibres when the fibre damping is small. When the fibre damping is great enough, however, the optimum fibre aspect ratio corresponds to continuous fibre reinforcement. Experimental data for E-glass/epoxy specimens are presented for comparison with predictions.Nomenclature A _c,A_f,A_m Cross-sectional area of composite, fibre, and matrix, respectively - d Fibre diameter - E _c ^* ,E _f ^* ,E _m ^* Complex extensional modulus of composite, fibre, and matrix, respectively. - E_c,E_f,E_m Extensional storage modulus of composite, fibre, and matrix, respectively - E_c,E_f,E_m Extensional loss modulus of composite, fibre, and matrix, respectively - G_m Complex shear modulus of matrix - G_m Shear storage modulus of matrix - i –1^1/2 - K Defined in Equation A9 - K ₁ Defined in Equation A5 - l Fibre length - r Radial distance from centre of fibre - r ₀ Fibre radius - R Radius of representative volume element, or one-half of centre-to-centre fibre spacing - v _f,v _m Volume fraction of fibre and matrix, respectively - W _c Total strain energy stored in a unit volume of composite - W _f Strain energy stored in volumev _f of fibre - W _m Strain energy stored in a volumev _m of matrix - W _m Shear strain energy stored in a volumev _m of matrix - W _m Extensional strain energy stored in a volumev _m of matrix - w _rm Shear strain energy stored in the matrix inr ₀rR - w _f Extensional strain energy stored in a single fibre - x Distance along fibre from end of fibre - Defined in Equation 12 - Defined in Equation 2 - ^* Defined in Equation A2 - Extensional (longitudinal) strain - _c, _f, _m Extensional loss factor of composite, fibre, and matrix, respectively - _Gm Shear loss factor of matrix - Polar angle measured in a plane perpendicular to fibre axis - ¯gs _c,¯gs _f,¯gs _m Average longitudinal stress in composite, fibre, and matrix, respectively - _f Longitudinal stress in fibre - Shear stress in matrix - Defined in Equation 27