Creep kinetic parameters

Figure 67 shows the creep rate value and creep kinetic parameters vs total deformation plots obtained for poly(methyl methacrylate) (PMMA) and PVC. For these and other glassy polymers studied, the values of Go, and o determined from the various points of the creep curves were found to depend on the strain value in a similar way. At constant stress and temperature, these parameters reach their maximum values at deformation y thereafter they decrease, and their changes become insignificant at > 10-15%. Over the range = 20-40%, the value of activation volume a remains constant, while the activation energy Go decreases slightly. 

Remember that the activation energy of firacture is equal to that of creep Therefore, the molecular mechanism causing both processes may well have the same origin. Indeed, a comparison between the kinetic parameters for the generation of excited bonds, Uod and and those of creep, Uo, and y > listed in Table 1 for perfectly drawn polymers, shows Uoa = Uqs and y = y, as well as Xod = feos. Therefore, the average time for the generation of excited bonds controls the kinetics of deformation and fracture. 

Below we consider the results of our systematic research of deformation kinetics for glassy polymers over the wide ranges of temperatures and deformations, using the laser-interferometric technique under consideration [11,278,280-287], This research allowed us (1) to study the dependencies of kinetic parameters of creep on these factors, (2) to reveal the regular relations between the activation parameters of polymer creep, (3) to demonstrate their intimate connection with the parameters of relaxation transitions, and (4) to confirm directly the intermolecular physical nature of potential barriers of polymer plasticity. ... 

Fig. 67 Strain dependencies of the creep rates and kinetic parameters obtained in compression at 20°C for PMMA, ff=90MPa (a) and at tension for PVC, (7=50 MPa (b) [11]. The dashed curves relate to pre-strained samples...

Table 9 shows the satisfactory agreement between the activation parameters of deformation and relaxation transitions. Thus, the activation volumes of both processes coincide in the temperature region of P-relaxation with Kuhn segment volume m = mp = Ak. For PMMA, the main contribution to creep kinetics below -100°C is provided by small-scale kinetic units (w = 1 and Qo = 10-15kJmoD ) that corresponds to low-temperature 8-relaxation, namely, liberation of a monomer unit in PMMA [23,99]. AtT > Tp, approaching Tg, the kinetic parameters of deformation increase by a factor of 3. Curves 4 and 6 in Fig. 69 show that an w vs T plot practically repeats the plot of the activation volumes of the relaxation processes over the entire temperature range studied. 

Let us stress once more that, irrespective of the specific solid-state deformation model used [271-275,292], the values of creep activation parameters in polymers are interconnected and depend on the degree of deformation and temperature. Their changes are related in a regular manner to structural alterations in polymers and to their spectra of molecular motions. Due to the changeability of deformation kinetic... 

Table 10 Kinetic parameters of creep and effective energy of intermolecular interactions in PS and PS-co-MAA at 20°C [283]...

It was observed that the kinetic parameters (the sinh term exponent and apparent activation energy) were similar between Eq 16 and like parameters for the 96.5Sn-3.5Ag solder as shown in Eq 13. In fact, a direct comparison of creep rates between the higher-order Pb-firee solders and 96.5Sn-3.5Ag solders at similar stresses and temperature indicated that the former were only slightly more creep resistant than the binary alloy. Quantitatively, that difference stemmed from the relatively small variations in a and the A constant. Mechanistically, it indicates that the AgjSn and Cu Snj phases did not have a significant role in the creep deformation, either explicitly or even indirectly, such as by altering the Sn-rich matrix microstructure. 

For a crossllnked rubber sample, one simple parameter which can be used to roughly characterize the material is the crosslink density (v) or the average molecular weight between crosslinks (Mg a 1/v). It should be clear that this single parameter cannot completely represent a network in general. Nevertheless, it is well known that the viscoelastic behavior of a polymer network will vary with crosslink density as schematically depicted in Figure 1 for the creep behavior of a polymer at two crosslink densities < Vq. Here the kinetic theory of rubber elasticity... 

The analysis of full rheological curve illustrates how the complex mechanical behavior can be subdivided into several regions, and how within each of these regions it can be represented by a simple model that utilizes only one or two constant parameters. For this reason, such phenomena as Schwedov s creep and Bingham s viscoplastic flow, whose molecular mechanisms are so different, can be described by substantially different parameters within otherwise the same model. Such subdivision of complex behavior into a finite number of simpler constituents with particular quantitative characteristics illustrates the universal role of macrorheology. At the same time, detailed description of a mechanism involved in each of these elementary stages requires the use of molecular-kinetic concepts and may be characterized as a microrheological approach. 

A basic property is the melting temperature since it is known that materials parameters which characterize the deformation behavior are well correlated with the melting temperature (Frost and Ashby, 1982). Examples are the elastic moduli which not only control the elastic deformation, but are also important parameters for describing the plastic deformation, and the diffusion coefficients which control not only the kinetics of phase reactions, but also the kinetics of high-temperature deformation, i.e. creep. Furthermore, the melting temperature is intuitively regarded as a measure of the phase stability since it limits the application temperature range. 

In this Section, the process of deformation, relaxation, and fracture are examined only within a restricted temperature range between the main 0 and a) relaxational transitions, Tp < T < T. The kinetics of creep, relaxation of stress and Young s modulus, and fracture are investigated experimentally as a function of the external stress applied to a sample and/or the increase in temperature. It is shown that the kinetics of the processes considered are described by Arrhenius-type equations. Then, the activation parameters (the energy and the volume) of the kinetic equations are calculated and compared with each other. This procedure demonstrates the identical physical nature of these processes. 

A comparison between Eq. (7), for the kinetics of the steady-state creep, with Eq. (3), for the kinetics of the decelerating creep, leads to the conclusion the kinetics of creep m both stages may be expressed by a uniform equation. Moreover, the energetic parameters, Uqs and Uop, are numerically identical Uo, = Uop = Uq. Hence, the mechamsm of creep in both stages is uniform, and the increase in deformation in both stages is a continuous process [16, 20, 23]. 

Creep rate, Young s modulus, and tensile strength are also shown to be connected with the mode parameters (the Griineisen parameter and the maximum frequency) of the fundamental vibrations. We suggest, that this relation reflects the participation of different vibrational modes in the generation of excited bonds. Therefore, powerful energy fluctuations seem to play a decisive role in the deformation, relaxation, and fracture in oriented polymers, their formation controls the kinetics of the macroscopic processes considered. 

Gas Flow In Nanochannels, Fig. 3 Thermal creep coefficient versus rarefaction parameter 6 solid lines, kinetic equation solution [11] pointed line, free-molecular value based on Eqs. 12 and 15 dashed line, Navier-Stokes solution Eq. 19... 

Note that if the super-index ch or tb is omitted the quantity is referred to both channel and tube. The coefficient Gj describes a gas flow due to a temperature gradient and it is called the thermal creep coefficient. The coefficients Gp and Gt are introduced so that they are always positive. They are calculated from the kinetic equation and determined by the rarefaction parameter... 

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