Constitutive compliance/stiffness equations of viscoelasticity for resins
Marian Klasztorny Politechnika Warszawska, Instytut Mechaniki i Konstrukcji, ul. Narbutta 85, 02-524 Warszawa
Annals 3 No. 7, 2003 pages 243-249
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abstract A modified rheological model HWKK for resins has been developed, taking into consideration the results of analysis of the experimental investigations. This model makes possible to simulate short-, medium- and long-lasting viscoelastic processes in epoxy or polyester resin, provided that the processes are reversible and of the first-rank type. These assumptions are satisfied for fibrous polymeric composites. Constitutive compliance equations of linear viscoelasticity have been formulated, in the shear-bulk version (3)1. The shear (distorsional) deformations are simulated with three linearly independent stress-history functions (3)2,3. The bulk (voluminal) deformations are simulated as ideally elastic. The HWKK rheological model for resins has been positively validated for selected stress programmes. The modified HWKK model is described with two constants of elasticity and 6 constants of viscoelasticity, i.e. 3 long-lasting creep coefficients and 3 retardation times. An algorithm for identification of constants of viscoelasticity has been developed (4, 5) and these constants have been estimated for Epidian 53 epoxy as well as Polimal 109 polyester resin (Table 1). The experimental results and the optimally simulated creep processes are illustrated in Figure 1 for selected resin. An analytic method for reversal of the constitutive compliance equations of viscoelasticity has been developed. The method uses the approximate constitutive stiffness equations of viscoelasticity of the HWKK model (9)1, which simulate time histories of the deviatoric stresses with three linearly independent strain-history functions. In the stiffness equations there occur 2 constants of elasticity (the same as in the compliance equations) as well as 6 constants of viscoelasticity of clear physical interpretation (3 long-lasting relaxation coefficients and 3 relaxation times). The axiatoric stresses are simulated as ideally elastic. The constants of viscoelasticity, describing the stiffness equations, are derived from the condition of coincidence of the exact and approximate shear complex stiffnesses (21)-(25). The results of reversal of the constitutive compliance equations are illustrated in Figure 2, presenting the exact and approximate shear complex stiffnesses for selected resin. Key words: resins, constitutive compliance/stiffness equations, material constants, identification