Physical aging viscoelastic functions

A unified approach to the glass transition, viscoelastic response and yield behavior of crosslinking systems is presented by extending our statistical mechanical theory of physical aging. We have (1) explained the transition of a WLF dependence to an Arrhenius temperature dependence of the relaxation time in the vicinity of Tg, (2) derived the empirical Nielson equation for Tg, and (3) determined the Chasset and Thirion exponent (m) as a function of cross-link density instead of as a constant reported by others. In addition, the effect of crosslinks on yield stress is analyzed and compared with other kinetic effects — physical aging and strain rate. 

In the solid state deformation, the nonlinear viscoelastic effect is most clearly shown in the yield behavior. The activation volume tensor is a key parameter. In addition to the well known dependence of yield stress on temperature and strain rate, the functional relationships between yield, stress field, and physical aging are presented. 

The nonlinear viscoelasticity modulus E t, e) is a function of time, t and strain, e. The compound behaviour is nonlinear even at very small deformation [9]. As described in Chapter 6, the presentation of modulus data requires t and e axes. The plot is a curved surface. When we consider the property changes resulting from physical ageing and from various deformational history [14], the separability of time and strain does not hold and linearisation of nonlinear data will not work. 

Creep, stress relaxation and set are all methods of investigating the result of an applied stress or strain as a function of time. Creep is the measurement of the increase of strain with time under constant force stress relaxation is the measurement of change of stress with time under constant strain and set is the measurement of recovery after the removal of an applied stress or strain. It is important to appreciate that there are two distinct causes for the phenomena of creep, relaxation and set, the first physical and the second chemical. The physical effect is due to rubbers being viscoelastic, as discussed in Chapter 9, and the response to a stress or strain is not instantaneous but develops with time. The chemical effect is due to ageing of the rubber by oxidative chain scission, further crosslinking or other reaction. 

The present article focuses on 5ueld and crazing in polymers and does not deal directly with the viscoelastic response, though it is recognized that jdeld and viscoelasticity share many of the same features—strain rate and temperature dependence (1) and even concepts such as time-temperature superposition (2) (see Viscoelasticity Aging, Physical). We first present a summary of conventional yield criteria, these being methods to quantify the yield stress as a function of... 

The effects of a number of environmental factors on viscoelastic material properties can be represented by a time shift and thus a shift factor. In Chapter 10, a time shift associated with stress nonlinearities, or a time-stress-superposition-principle (TSSP), is discussed in detail both from an analytical and an experimental point of view. A time scale shift associated with moisture (or a time-moisture-superposition-principle) is also discussed briefly in Chapter 10. Further, a time scale shift associated with several environmental variables simultaneously leading to a time scale shift surface is briefly mentioned. Other examples of possible time scale shifts associated with physical and chemical aging are discussed in a later section in this chapter. These cases where the shift factor relationships are known enables the constitutive law to be written similar to Eq. 7.53 with effective times defined as in Eq. 7.54 but with new shift factor functions. This approach is quite powerful and enables long-term predictions of viscoelastic response in changing environments. 

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