Eyring reduced time model

Relationship Between Strength and Load Rate Derived from the Eyring Reduced Time Model... 

Fig. 63 The Eyring reduced time model involves the activated site model for plastic and viscoelastic shear deformation of adjacent chains...

Fig. 64 Creep and creep failure can be modelled by the time-dependent shear deformation as described by the Eyring reduced time model...

The Eyring reduced time model provides the framework for the derivation of the creep equation of polymer fibres [10]. The creep shear strain of a domain... 

The proposed model for creep rupture based on the condition of maximum shear strain and the Eyring reduced time model explain the observed relations concerning the lifetime of aramid, polyamide 66 and polyacrylonitrile fibres. However, with increasing temperatures, in particular above 300 °C, chemical degradation of PpPTA also determines the lifetime. Furthermore, the model... 

For a more complete description of the time and the temperature dependence of the fibre strength a theoretical description of the viscoelastic and plastic tensile behaviour of polymer fibres has been developed. Baltussen (1996) has shown that the yielding phenomenon, the viscoelastic and plastic extension of a polymer fibre can be described by the Eyring reduced time model. This model uses an activated site model for the plastic and viscoelastic shear deformation of adjacent chains in the domain, in which the straining of the intermolecular bonding is now modelled as an activated shear transition between two states, separated by an energy barrier. It provides a relation between the lifetime, the creep load and the temperature of the fibre, which for PpPTA fibres has been confirmed for a range of temperatures (Northolt et al., 2005). 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

As shown in Sect. 2, the fracture envelope of polymer fibres can be explained not only by assuming a critical shear stress as a failure criterion, but also by a critical shear strain. In this section, a simple model for the creep failure is presented that is based on the logarithmic creep curve and on a critical shear strain as the failure criterion. In order to investigate the temperature dependence of the strength, a kinetic model for the formation and rupture of secondary bonds during the extension of the fibre is proposed. This so-called Eyring reduced time (ERT) model yields a relationship between the strength and the load rate as well as an improved lifetime equation. 

If the applied shear stress varies during the experiment, e.g. in a tensile test at a constant strain rate, the relaxation time of the activated transitions changes during the test. This is analogous to the concept of a reduced time, which has been introduced to model the acceleration of the relaxation processes due to the deformation. It is proposed that the reduced time is related to the transition rate of an Eyring process [58]. The differential Eq. 123 for the transition rate is rewritten as... 

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