Kinetics of creep

Equation 6.14 provides a formal connection between creep crack growth and the kinetics of creep deformation in that the steady-state crack growth rates can be predicted from the data on uniaxial creep deformation. Such a comparison was made by Yin et al. [3] and is reconstructed here to correct for the previously described discrepancies in the location of the crack-tip coordinates (from dr/2 to dr) with respect to the microstructural features, and in the fracture and crack growth models. Steady-state creep deformation and crack growth rate data on an AlSl 4340 steel (tempered at 477 K), obtained by Landes and Wei [2] at 297, 353, and 413 K, were used. (AU of these temperatures were below the homologous temperature of about 450 K.) The sensitivity of the model to ys, N, and cr is assessed. 

The occurrence of creep-controlled crack growth, in an inert environment, has been demonstrated. It can occur even at modest temperatures, and has been linked to localized creep deformation and rupture of ligaments isolated by the growth of inclusion-nucleated voids ahead of the crack tip. Landes and Wei [2] and Yin et al. [3] have made a formal connection between the two processes, and provided a modeling framework and experimental data to link the kinetics of creep to creep-controlled crack growth. Further work is needed to develop, validate, and extend this understanding. In particular, its extension to high-temperature applications needs to be explored. 

Nowadays, the kinetics of polymer deformation is often supposed to be specific for the different stages in the evolution of deformation. For instance, this seems to be the case for three types of the kinetics of creep decelerating, steady state, and accelerating creep [6]. 

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]. 

A well-known example of this time-temperature equivalence is the steady-state creep of a crystalline metal or ceramic, where it follows immediately from the kinetics of thermal activation (Chapter 6). At a constant stress o the creep rate varies with temperature as... 

An instrument for measuring the mechanical properties of rubbers in relation to their use as materials for the absorption and isolation of vibration. These properties are resilience, modulus (static and dynamic), kinetic energy, creep and set. The introduction of an improved version has recently been announced. 

Creep and fracture in crystals are important mechanical processes which often determine the limits of materials application. Consequently, they have been widely studied and analyzed in physical metallurgy [J. Weertmann, J.R. Weertmann (1983) R.M. Thomson (1983)]. In solid state chemistry and outside the field of metallurgy, much less is known about these mechanical processes [F. Ernst (1995)]. This is true although the atomic mechanisms of creep and fracture are basically independent of the crystal type. Dislocation formation, annihilation, and motion play decisive roles in this context. We cannot give an exhaustive account of creep and fracture in this chapter. Rather, we intend to point out those aspects which strongly influence chemical reactivity and reaction kinetics. Illustrations are mainly from the field of metals and metal alloys. 

Ultimately, a knowledge of kinetics is valuable because it leads to prediction of the rates of materials processes of practical importance. Analyses of the kinetics of such processes are included here as an alternative to a purely theoretical approach. Some examples of these processes with well-developed kinetic models are the rates of diffusion of a chemical species through a material, conduction of heat during casting, grain growth, vapor deposition, sintering of powders, solidification, and diffusional creep. 

Equation 13.3 was first obtained by Herring and is useful in modeling the kinetics of diffusional creep [5] and sintering [6] in pure metals. 

The first quantitative study of deformation mechanisms in ABS polymers was made by Bucknall and Drinkwater, who used accurate exten-someters to make simultaneous measurements of longitudinal and lateral strains during tensile creep tests (4). Volume strains calculated from these data were used to determine the extent of craze formation, and lateral strains were used to follow shear processes. Thus the tensile deformation was analyzed in terms of the two mechanisms, and the kinetics of each mechanism were studied separately. Bucknall and Drinkwater showed that both crazing and shear processes contribute significantly to the creep of Cycolac T—an ABS emulsion polymer—at room temperature and at relatively low stresses and strain rates. 

The effect of stress upon the kinetics of crazing can be represented by two rate quantities obtainable from the creep data. The linear portion at the end of the volume strain-time curve defines a maximum rate of... 

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. 

TiAl/SiC composite by interface reactions has recently been studied (Ochiai et al., 1994). The kinetics of the phase reactions is determined by interdiffusion, which has been studied in the case of TiAl-Mo (Zhang etal., 1992a). It has been shown that both the creep resistance and the toughness of a TiAl matrix composite can be improved by using coated fibers with weak fiber/matrix interfaces (Weber et al., 1993). 

Upon cessation of cooling below Tg the enthalpy and volume slowly but incessantly decrease toward their equilibrium values. During this decrease other kinetic properties, such as the rate of creep, slow down. This deceleration of kinetic processes is called physical aging and is reflected in Figure 5.1 by the... 

However, if the creep compliance curves are compared at their respective TgS,we see in Figure 5.16 that the softening dispersions are, within experimental uncertainty, at the same place in the time scale of response. Specifically the positions of the four Jpit/ar) curves at a compliance level of 1.0 x 10 Pa appear to be spread on a time scale by not much more than one decade of time. Relative uncertainties of Tg values of 1.5°C can account for this spread in positions. Until more precise relative TgS can be measured we can tentatively surmise that at Tg all polymers at the same rate are deep in the softening zone. This conclusion appears reasonable when we consider that short-range chain dynamics should determine both creep rates just above the glassy level as well as changes in the local liquid structure, the kinetics of which determine Tg. 

Beckmann, J., McKenna, G. B., Landes, B. G., Bank, D. H., and Bubeck, R. A., Physical aging kinetics of syndiotactic polystyrene as determined from creep behavior, Polym. Eng. ScL, 37,1459-1468 (1997). 

In this paper, general principles of physical kinetics are used for the descnption of creep, relaxation of stress and Young s modulus, and fracture of a special group of polymers The rates of change of the mechanical properties as a function of temperature and time, for stressed or strained highly oriented polymers, is described by Arrhenius type equations The kinetics of the above-mentioned processes is found to be determined hy the probability of formation of excited chemical bonds in macromolecules. The statistics of certain modes of the fundamental vibrations of macromolecules influence the kinetics of their formation decisively If the quantum statistics of fundamental vibrations is taken into account, an Arrhenius type equation adequately describes the changes in the kinetics of deformation and fracture over a wide temperature range. Relaxation transitions m the polymers studied are explained by the substitution of classical statistics by quantum statistics of the fundamental vibrations. 

Therefore, the kinetics of decelerating creep for oriented polymers in the range between the main relaxation transitions can be described by an Arrhenius type equation in the form of Eq. (3). 

Figures 2 and 3 also present the expenmental results of the examination of steady-state creep. They are similar to those for primary creep. Therefore, the kinetics of deformation in the secondary creep stage may be expressed by an Arrhenius type equation analogous to that for the primary stage [24]...

Since the tertiary creep stage, accelerating creep, embraces a short time region, compared with the previous stages, it is difficult to investigate the kinetics of deformation on this stage. The next Section will be devoted to the final phenomenon of creep evolution, the fracture. 

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. 

Equations (52)-(54) show that finite rates of creep, relaxation of Young s modulus, and fracture at T - 0 are conditioned by tunneling of the atoms through the potential barrier and the existence of zero-point vibrations. These phenomena are not taken into account in the classic Arrhenius-type equations. The tunneling contribution in the kinetics of the processes examined depends on the characteristic temperature. 

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. 

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