Simulation of rheological processes in resins described by HWKK/H model
Marian Klasztorny Politechnika Warszawska, Instytut Mechaniki i Konstrukcji, ul. Narbutta 85, 02-524 Warszawa
Quarterly No. 1, 2006 pages 32-38
DOI:
keywords: resins, rheological processes, stress control, numerical simulation
abstract The paper concerns simulation of rheological processes in hardening plastics (resins) with stress control. Service conditions of the material have been assumed as follows: the material works in the glassy state and in the normal conditions; rheological processes are quasi-static and isothermal; the reduced stress levels do not exceed 30% of the immediate tensile strength of the material. The experiments performed at these service conditions have pointed out that the material can be treated as uniform, isotropic and linearly viscoelastic. The shear strains are viscoelastic and reversible. Short-term, medium-term and long-term shear strains can be distinguished, respectively described by fractional exponent and two normal exponents as stress-history functions. The bulk strains are elastic. Above mentioned empiric observations are satisfied by the HWKK/H rheological model of resins (Fig. 1). The standard constitutive equations (2) of viscoelasticity related to the HWKK/H model are presented. The model is described by 2 elastic constants and 6 viscoelastic constants, i.e. 3 long-term shear creep coefficients and 3 retardation times of shear strains. A numerical algorithm for simulation of rheological processes in resins has been developed, which is unified for all stress-history functions used in the model. In the algorithm, the Boltzmann superposition rule, the simulation result of classic creep as well as a high-rank Gauss quadrature have been used (Eqs (14, 18-20)). An optional continuous stress function is approximated with the staircase function (Eq (19)). Constitutive equations (2) have been transformed into the algorithmic form (20). The problem of quasi-exact calculation of double-improper integral (14)1 has been solved effectively. The algorithm, concerning simulation of arbitrary rheological processes with stress control, has been programmed in Pascal and tested on Epidian 53 epoxy resin. Three stress programmes in uni-directional tension have been considered (Fig. 3). The results of the simulation are presented in Table 2 and in Figures 4-6. It has been pointed out that the algorithm developed in the study is general, simple for programming and yields quasi-exact solutions in very short times. So, it is useful in practice.