V. I. Vettegren

New approach to the description of young's modulus for highly oriented polymers. I. Temperature–time dependences of young's modulus

Abstract A description of the relaxation of Youngs modulus (i.e., a decrease with increasing temperature and time) for highly oriented polymers is suggested and expressed by the equation where T is the absolute temperature, E is Youngs modulus, E0 is its value at T → 0, k is the Boltzmann constant, W0 is the activation energy of the relaxation of Youngs modulus, v is the rate of elastic deformation, and v0 is a constant. It was found that v0 = (1012-1014) Hz and that W0 coincides numerically with the activation energy of mechanical fracture determined from the temperature-time dependences of tensile strength. On the basis of these facts it was concluded that the relaxation of Youngs modulus and the failure strength of drawn polymers are substantially identical in nature.

Relation between strength and elastic properties of polymers

Formulae of the phonon theory of strength were examined; these formulae relate the activation energy of mechanical breakdown U0 and coefficient ψ of the formula of Zhurkov long-term strength with Youngs modulus and the Gruneisen coefficient. Oriented fibres based on aromatic para-polyamides, polyamidohydrazides, linear polyarimides and polyacrylnitrile were investigated. Experimental evaluation confirmed the validity of the formulae proposed and enabled dimensions of thermal fluctuations causing failure to be established.

New approach to the description of young's modulus for highly oriented polymers. ii. Relationship between young's modulus and thermal expansion of polymers over a wide temperature range

Abstract An empirical equation for Youngs modulus is proposed. It originates from thermal fluctuations and relates Youngs modulus for highly oriented polymers, E, to thermal expansion strain of the segments of macromolecular helices, eT, and to measurement time γ: where E 0 is the E value at eT → 0, C 0 is the heat capacity, k is the Boltzmann constant, e* ≅ 0.1, and t 0 = (10−12−10−l4)s. The equation may be used for description of the temperature dependences of Youngs modulus, E(T), at γ = constant over a wide temperature range: from cryogenic to melting temperatures. It was shown that omplicated (nonlinear) E(T) dependences were due to the variability of the γ(T) function because of the substitution of the Boltzmann statistics for the Bose one for both torsional and bending vibrational modes in a polymer solid.

Physical basis of temperature dependence of strength in polymers

The Zhurkov equation for long-term strength, σ(T, τ), is presented in the form σ(T, τ) = E(T, τ)e∗E0l/(κE0), where E(T, τ) is Youngs modulus as a function of temperature and time, E0 is the modulus averaged over the sample volume, E0l is the value of the modulus at the crack tip (both at 0 K), e∗ is that value of deformation for which the interatomic bonds loose their stability and begin to break, and κ is the stress concentration factor. Reasons for the deviations from linearity in the temperature dependence of strength have been investigated (at a fixed value of time-to-break, τ=const.), which are observed in the temperature region T⩽≡D/3 and T≌Tg (≡D is the Debye temperature and Tg the glass transition temperature). It has been established that the stress concentration factor does not vary in these regions (κ=const.); the deviations from linearity are explained by changes in the thermal expansion coefficient in these temperature intervals.

Strength of macromolecules of polyheteroarylenes containing an imide ring in the main chain

Abstract Data on the effective macromolecular tenacity, evaluated by means of IR spectroscopy, are presented for a number of polyheteroarylenes containing an imide ring in the main chain. The numerical values of these chain tenacities are compared to those previously obtained for flexible chain polymers. It is shown that the effective macromolecular tenacity of polyimides with a complex dianhydride fragment in the chain repeating unit is higher by a multiple of 1.5-2.0 than the corresponding value for flexible chain polymers; therefore the former polymer class includes a large reserve of macroscopic strength, which is still open to use.

A new approach to the description of the deformation kinetics and relaxation of mechanical properties of oriented polymers

The reduction of Youngs modulus and stress as well as the creep rate of highly oriented polymers with different chemical structure has been investigated. The kinetics of these processes are described by Arrhenius-type equations having the same activation parameters. The deformation and relaxation processes were assumed identical in their physical nature and functions of thermal fluctuation. Evidence for this assumption was obtained by investigating spectroscopically excited extended interatomic bonds of the macromolecules. The generation of excited bonds was found to determine the kinetics of these macroscopic processes in polymers.

The temperature-time dependence of the elastic modulus for oriented polymers☆

An experimental study was made of the temperature time dependence of the elastic modulus E for 30 oriented polymers differing in chemical structure. The formula derived to describe the temperature-time dependence of the elastic modulus is expressed as E=Eo1−kTW0lnττo, where Eo is the value of the modulus at T→0 K, k is Boltzmanns constant, Wo is the activation energy for relaxation of the modulus, and τo is a constant. It was found that τO≅(1012−10−14) sec, and that WO practically coincides with the activation energy of degradation determined from the temperature-time dependence of tensile strength. A common nature is postulated for temperature-time dependences of the elastic modulus and the strength of the oriented polymers.

Statistical spread of polymer Young's modulus values as a manifestation of their thermofluctuational nature☆

The statistical spread of Youngs modulus values [E-P(E)] in the mechanical testing of polymer samples under identical conditions is studied experimentally. The deviation of Youngs modulus values from the most probable one is directly related to the temperature. On the basis of this it is suggested that the spread of these values is determined by the heat fluctuation statistics. An analytical expression for P(E) is proposed.

Low temperature dependence of the strength of polyimide fibres

The authors have investigated the temperature dependence of strength σ(T) of 14 oriented polyimide fibres of varied chemical structure in the temperature interval 100–650 K and established that in the region of low temperatures T<ϑD/3 (ϑD is the effective Debye temperature) the dependence of strength on temperature is non-linear. It is assumed that the cause of the non-linearity of σ(T) is the variability of the thermal expansion coefficient in this temperature range as is confirmed by the results of spectroscopic investigations.

On the thermofluctuational nature of Young's modulus relaxation for oriented polymers

Abstract The formulas analyzed in this paper describe the temperature-time dependence of Youngs modulus for oriented polyimide fibres and the strain of interatomic bonds in strong negative density fluctuations known as dilatones. The experimental results show that Youngs modulus relaxation may be due to evolution of elongation of interatomic bonds in the dilatones.