# Volumetric Analysis in Mechanical Behaviour and Physical Ageing of Polymers

[Doktorsavhandling]

Volumetric changes associated with the deformation of ideal elastic solids depends on elastic constants of the solid and applied strain. Their magnitude is easily determined from the corresponding Poisson's ratios. In real solids, where viscous effects are superimposed on elastic deformation, the situation becomes more complicated, since the changes in volume and the corresponding Poisson's ratios depend on time. Due to practical difficulties inherent in volumetric measurements on viscoelastic materials, experimental data of this type are scarce, often lacking sufficient reliability. This is reflected in incomplete theoretical treatment of phenomena of this type in relevant literature.

The present thesis aims at providing reliable volumetric results recorded for poly(methyl methacrylate), PMMA, and polycarbonate, PC, during creep, and for low density polyethylene, LDPE, and linear low density polyethylene, LLDPE, during stress relaxation. Measurements of dynamic mechanical characteristics for poly(vinyl acetate), PVAc, during physical ageing, that is during thermally induced volume relaxation following temperature steps of varying direction and magnitude, are also presented.

In the creep measurements on PMMA and PC, the volume of the loaded specimen was found to increase in the initial part of the process. After reaching a maximum, the volume began to diminish at a relatively low rate. The position of the maximum was successfully interpreted in terms of a viscous Poisson's ratio used in connection with common mechanical models of viscoelasticity.

Measurements in the stress relaxation mode using specially constructed extensometers and liquid stress dilatometer yielded volume values decreasing monotonically during the entire process. At low initial deformations of the LDPE and LLDPE specimens the volume was found to vary linearly with the relaxing stress, allowing an apparent bulk modulus to be determined. The values of this modulus were lower, but of the same order of magnitude, as data reported in the literature. At higher deformations the volume-stress diagrams became non-linear.

The thermally induced physical ageing process in PVAc was followed both by dilatometer and by dynamic-mechanical measurements, including the determination of the relevant mechanical parameters. The variation of the storage/loss moduli and the loss tangent reflected the level of structure consolidation during the ageing process. In the evaluation of the results, attention was given to the question of the timescales characterizing the evolution of various physical quantities and the influence of the mechanical stimuli on the ageing rate. The results presented in this thesis support the notion that the timescales exhibit significant differences. In the first place, this applies to the rates at which the volume and mechanical parameters appear to reach their equilibrium levels. Also, the presented results show that small strains can reduce the ageing rate, and that although weak, this influence is clear for ageing temperatures lower than T_{g}-3 °C, for PVAc.

The volumetric data pertaining to the ageing experiments were analysed using a modified Doolittle free volume approach. While fair agreement was reached by using less than unity B values of the Doolittle equation for ageing experiments following temperature down-jumps and the ageing rate was fairly well predicted at lower ageing temperatures, this approach failed to reproduce the up-jump results. When employing the KAHR model, both types of experiments could be accurately accommodated in the formalism.

**Nyckelord: **volume changes, creep, stress relaxation, dynamic mechanical properties, physical ageing, dilatometry, Poisson's ratio, Gr neisen parameter, bulk modulus, timescale, ageing rate, Doolittle's equation, KAHR model

Denna post skapades 2006-09-19. Senast ändrad 2007-04-17.

CPL Pubid: 1120