Creep-temperature relationships

Not only are the creep compliance and the stress relaxation shear modulus related but in turn the shear modulus is related to the tensile modulus which itself is related to the stress relaxation time 0. It is therefore in theory possible to predict creep-temperature relationships from WLF data although in practice these are still best determined by experiment. 

It was previously mentioned that the constants of the materials were temperature dependent. It has been shown that the form of the creep curves obtained at elevated temperatures match those taken for longer periods of time at lower temperature. In other words, there is a time-temperature relationship such that creep tests taken for relatively short periods of time at one temperature can substitute for much longer term tests at lower temperatures. This concept is the WLF relationship developed by William, Landel, and Ferry. It is based on a system of reduced variables. The general input from the relationship is that if the creep curves are plotted on a logarithmic scale, the effect of the temperature will be to shift the curve by an amount equal to... 

Larson, F. R., and Miller, J. A. A Time-Temperature Relationship for Rupture and Creep Stresses. Transactions, ASME, Vol. 175, 1952. 

F.R. Larson, J. Miller, A time-temperature relationship for rupture and creep stresses, Trans. ASME (1952) 765-775. 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

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. 

The variation of creep with time as a function of both load and temperature is illustrated in Figure 5.44. Arrhenius-type relationships have been developed for steady-state creep as a function of both variables such as... 

Hardness and a ductile-to-brittle transition temperature (DBTT) have also been noted to follow a Hall-Petch relationship (Meyers, and Chalwa, 1984). Ductility increases as the grain size decreases. Decreasing grain size tends to improve fatigue resistance but increases creep rate. Electrical resistivity increases as grain size decreases, as the mean free path for electron motion decreases. 

Despite the large number of creep and creep rupture mechanisms,91,92 the lifetime of structural materials at elevated temperatures is often a simple function of the creep rate. This relationship was first noted by Monkman and Grant114 who presented an empirical relationship between rupture life and... 

Suppose that one conducts a series of experiments to determine the stress and temperature dependence of creep behavior for the fibers and matrix these experiments would provide curves such as those shown schematically in Fig. 5.6a and b. Conducting these experiments over a range of temperatures and stresses would provide a family of curves that could be combined to provide a relationship between strain rate, stress, and temperature. Such a temperature and stress dependence of constituent intrinsic creep rates, together with the intrinsic creep mismatch ratio, is schematically illustrated in Fig. 5.6c. In this plot, the creep equations for the two constituents at a given temperature and stress are represented by planes in (1 IT, logo-, logs) space, with different slopes, described by <2/> Qm and ny, nm. The intersection of the two planes represents the condition where CMR = 1, which separates temperature and stress into two regimes CMR< 1 and CMR> 1. 

Fig. 5.6 Relationship between the creep rate of a composite and the stress and temperature dependence of the creep parameters of the constituents.31 (a) Temperature dependence of constituent creep rate, (b) Stress dependence of constituent creep rate, (c) Intrinsic creep rate of constituents as a function of temperature and stress illustrating the temperature and stress dependence of the creep mismatch ratio. In general, load transfer occurs from the constituent with the higher creep rate to the more creep-resistant constituent, (d) Composite creep rate with reference to the intrinsic creep rate of the constituents. The planes labeled kf and em represent the intrinsic creep rates of the fibers and matrix, respectively.

In the preceding sections, we have looked at the various types of relaxation processes that occur in polymers, focusing predominantly on properties like stress relaxation and creep compliance in amorphous polymers. We have also seen that there is an equivalence between time (or frequency) and temperature behavior. In fact this relationship can be expressed formally in terms of a superposition principle. In the next few paragraphs we will consider this in more detail. First, keep in mind that there are a number of relaxation processes in polymers whose temperature dependence we should explore. These include ... 

The search for quantitative structure-property relationships for the control and prediction of the mechanical behaviour of polymers has occupied a central role in the development of polymer science and engineering. Mechanical performance factors such as creep resistance, fatigue life, toughness and the stability of properties with time, stress and temperature have become subjects of major activity. Within this context microhardness emerges as a property which is sensitive to structural changes. 

A common practice is to reduce relaxation or creep data to the temperature Tg thus, the reference temperature is picked as the glass transition temperature measured by some slow technique such as dilatometry. The reason for choosing Tg as the reference temperature is founded on the idea that all amorphous polymers at their glass transition temperature will have similar viscoelastic behavior. This type of corresponding states principal is often expressed in terms of a hopefully universal mathematical relationship between the shift factor aT at a particular temperature and the difference between Tg and this temperature. Perhaps the most well known of these relationships is the WLF equation... 

Fig. 38 shows a set of curves fitted to plateau creep data on the basis of the two-process model, and the corresponding activation parameters are shown in Table 1. The activation volume for ther 2 dashpot is in the range of 100 A3, and, as remarked by Wilding and Ward, this comparatively small activation volume could be consistent with a slip process in the crystalline regions. Support for this hypothesis comes from examination of the temperature dependence of this process. Results for selected samples show that there is a good linear relationship between log ep and 1/T. At high stress levels the behaviour corresponds to that of an apparent single activated process, with... 

Creep tests have been carried out on single lap joints at different temperatures and loads as indicated in Fig. 33.4. The resulting shear strain y versus time relationships appear as straight lines in a double-logarithmic plot which show the same slope but are shifted by a factor. This indicates that creep data may be represented by a power law of the form of Eq. (2), where t is time and Aq, n and m denote material parameters [9]. 

If we consider the case of tests at ambient temperatures and moderate times, then the elTects measured are principally physical. Creep and stress relaxation tests under these conditions may need extrapolating to longer times. Ignoring any possible degradation effects, it is commonly found with rubbers that a plot of modulus against log of time will yield a linear relationship, which makes extrapolation very easy. With plastics, the log... 

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