Modelling of viscoelastic resins as matrices of fibre-reinforced polymeric composites
* Marian Klasztorny, ** Roman Gieleta * Politechnika Warszawska, Instytut Mechaniki i Konstrukcji, ul. Narbutta 85, 02-524 Warszawa ** Wojskowa Akademia Techniczna, Instytut Materiałoznawstwa i Mechaniki Technicznej, ul. Kaliskiego 2, 00-908 Warszawa
Annals 2 No. 3, 2002 pages 103-107
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abstract The study is devoted to viscoelastic modelling of resins (epoxy and polyester), applied as matrices of fibre-reinforced polymeric composites. This type of composites protects lower levels of stresses in the matrix, not exceeding 30% of the tensile strength of a resin material. The experiments, performed on bar resin samples tensioned uniaxially in a room temperature, have pointed that the creep processes are of the 1st rank type and reversible. Moreover, the directional strains are quasi- -proportional. The short lasting creep (SLC) can be simulated with good accuracy using the generating function in the form of a linear combination of the fractional and normal exponential functions. The long lasting creep (LLC) can be simulated with good accuracy using an additional normal exponential function. A new rheological model for resins (amorphous thermoharden materials), reflecting the above mentioned features, has been developed. This model, denoted with the symbol HWKK, is described by two elastic constants (E, ν ) and seven viscoelastic constants ( ω x 1, ω x2, ωy1, ωy2, τW, τK1, τK2). A mechanic representation of the HWKK model is shown in Figure 1. The parameters ω x1, ω x2 are coefficients for the SLC long-lasting time compliances, and ω x2, ω y2 denote coefficients for the LLC long-lasting time compliances. The parameters τW, τK1, τK2 denote the elastic sequence times related to the Wilczynski’s and Kelvin’s elements. The constants μ (a ratio defining the elastic-sequence-times distribution Λ (ξ; μ ) and γ (a fraction defining a linear combination of the generating functions Φ(t), F1(t)) are predefined and equal γ = 0.5, μ = 0.5 for both resins. Constitutive equations of viscoelasticity, governing the HWKK model, have been formulated (Eqs (3)-(6)). Classic creep of uniaxially tensioned bar samples has been described analytically and the directional creep functions derived (Eqs (7)-(9)). A computer aided algorithm for identification of 9 material constants has been formulated, programmed in Pascal and applied for estimation of the material constants for the Epidian 53 epoxy and Polimal 19 polyester. The main stages of the identification algorithm are illustrated graphically in Figures 2-4. The results of identification of the material constants are collected in Table 1. The HWKK rheological model for resins has been positively validated for selected loading programmes. This model enables simulating arbitrary viscoelastic processes with good accuracy, provided that the stress levels protect the 1st rank creep. Besides, this model can be applied for viscoelastic modelling of fibre-reinforced resin-matrix composites, applying a fully analytical method developed in Refs [4, 7].