The process of physical aging is accompanied by a gradual change in a number of physical parameters of the solid under study. In this paper we show that by correlating the excess enthalpy with the excess volume, bulk modulus, K, data of reasonable magnitude are obtained for polystyrene, PS, and poly(vinyl acetate), PVAc. The underlying reasoning is based on standard equilibrium thermodynamics. For PVAc the time dependence of K during the aging process is discussed in terms of corresponding data calculated from dynamic mechanical measurements at varying frequency. Examples are also given of calculations of K from uniaxial stress relaxation data obtained with polyethylene samples where both the volume and the con comitant stress changes were determined. The calculation of K was based on the usual formula relating pressure (1/3rd of the uniaxial stress) to the corresponding volume change. The K data obtained were somewhat lower than those normally reported, an effect likely to be related to the time scale involved.
There exist large amounts of experimental evidence on stress relaxation for metals and their alloys, synthetic and natural polymers, glasses and frozen non-polymeric organic liquids. The results, typically presented as curves a (log t) of relaxation of stress aas a function of logarithmic time t, exhibit common features, apparently independent of the type of Material. All curves consist of three regions: initial, nearly horizontal, starting at σ0; central, descending approximately linearly; and final, corresponding to the internal stress σi = σ(>). We discuss briefly the experimental evidence as well as the main features of the cooperative theory which does not involve specific features of different classes of Materials. The bulk of the paper deals with computer simulations. Simulation results obtained with the method of molecular dynamics are reported for ideal metal lattices, Metal lattices with defects, and for polymeric systems. In agreement with both experiments and the cooperative theory, the simulated σ (log t) curves exhibit the same three regions. In agreement with the theory, the slope of the simulated central part is proportional to the initial effective stress σ0* = σ0 - σi. The time range taken by the central part is strongly dependent on the defect concentration: the lower the defect concentration, the shorter the range. IMposition in the beginning of a high strain ε destroys largely the resistance of a material to deformation, resulting in low values of the internal stress σo. Since the cooperative theory assumes for particles (atoms, polymer chain segments) the existence of two states, unrelaxed and relaxed, and has a formal connection to the Bose-Einstein (B-E) distribution, we first simulate B-E systems, recording the formation of relaxed clusters of particles of different sizes. Differences in cluster sizes predicted from a B-E Model and those obtained from the simulations are recorded and analyzed. On the joint basis of experimental, theoretical
The possibility of describing transient phenomena associated with flow and consolidation of solids, such as stress relaxation or physical aging, in terms of a kinetic mechanism comprising spontaneous and induced events is discussed. The starting point is the differential equation dṅ/dt=−aṅ[1−(b/a)ṅ], with n denoting the number of relaxed entities and ṅ=dn/dt (a,b are constants, t is time), yielding an ṅ(t) function reminiscent of a Bose–Einstein distribution. The corresponding n(t) relation describes the linear variation of n with log t, and the exponential dependence of ṅ on n, as often found experimentally. Replacing ṅ in the starting equation by the relative rate ṅ/n yields a power-law-type ṅ(n) dependence. A further modification, where the induction term ṅ/n is not linear but raised to a power ≳1, finally produces a generalized version of the stretched exponential. When interpreted formally in terms of a spectrum of relaxation times τ, all three equations produce response functions with discrete τ distributions, provided a≠0.
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