Modelling long term deformation behaviour of polymers for finite element analysis

Abstract

Creep studies have been carried out under uniaxial tension and uniaxial compression on poly(oxymethylene). Measurements under tension have been modelled using a function with four material parameters. One of these parameters, related to a mean retardation time for the relaxation process responsible for creep, decreases with increasing stress, and this gives rise to non-linear creep behaviour. Measurements of creep under compression indicate that the retardation time parameter is determined by the stress state as well as the stress magnitude. A theoretical extension of the model has been proposed that relates stresses and strains under situations where the stress is not constant but varies with time. This is necessary for the model to be implemented in a finite element system to carry out design calculations that take proper account of the time dependent properties of polymers. The validity of the theory is evaluated through the use of the creep model to predict deformation for a variety of simple stress and strain histories under uniaxial tension. The close agreement between calculation and measurement supports the development of code, in future work, to obtain solutions for multiaxial stresses and strains using a finite element system.

Modeling nonlinear viscoelasticity in polymers for design using finite element analysis

“…Creep tests on the polyoxymethylene studied here have been reported in a previous article [11]. A comparison of creep tests under tension and compression at the same elevated stress (26 MPa) reveals that creep under compression occurs more slowly than under tension.…”

“…5 shows that the parameters μ and λ are related, and Eq . 5 thus becomes Also, under a uniaxial compressive stress −σ C so that σ C is positive By comparing tensile and compressive creep data at the same stress, a value of μ = 0.9 has been derived [11]. Using this value for μ in Eqs .…”

“…The time parameters t m and t 0 are measures of the molecular mobility and, the smaller are these values, the more rapid is the creep deformation. In most engineering plastics, these parameters are observed to decrease with stress leading to a dependence of creep compliance on stress and hence to nonlinear behavior [6–11]. The effect of elevated stress is therefore to increase molecular mobility so that the polymer creeps faster.…”

“…Second, a theoretical framework is needed to derive relationships between stress and strain for general stress or strain histories rather than the situation of constant stress used for the determination of materials properties. Progress with this second requirement has been described in a recent publication [11]. Relationships between stress and strain were developed for arbitrary stress or strain histories that are based on Eq .…”