Creep time-temperature shear

Figure 10.10 Time-temperature shear creep compliance master curve (Sullivan). 

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. 

The phenoxy resins can form strong bonds to metals in seconds at temperatures from 315 to 340°C. At these bonding conditions, a tensile lap shear strength of 3500 to 4000 psi can be obtained on aluminum. The same bond can be made in 2 to 3 min at 260°C and in 30 min at 190°C due to the thermoplastic phenoxy s time-temperature creep characteristics and relatively low softening temperature (100°C).8... 

As an example of the concentration dependence of viscoelastic properties in Fig. 16.11 the shear creep compliance of poly(vinyl acetate) is plotted vs. time for solutions of poly(vinyl acetate) in diethyl phthalate with indicated volume fractions of polymer, reduced to 40 °C with the aid of the time temperature superposition principle (Oyanagi and Ferry, 1966). From this figure it becomes clear that the curves are parallel. We may conclude that the various may be shifted over the time axis to one curve, e.g. to the curve for pure polymer. In general it appears that viscoelastic properties measured at various concentrations may be reduced to one single curve at one concentration with the aid of a time-concentration superposition principle, which resembles the time-temperature superposition principle (see, e.g. Ferry, General references, 1980, Chap. 17). The Doolittle equation reads for this reduction ... 

Use the shear creep data in Figure 4.4, together with the method of time-temperature superposition, to estimate the shear creep compliance for linear polyethylene at 20°C and a creep time 10 s. Ust the assumptions that you make in this long extrapx>lation of the creep data. 

Creep curves in shear were measured at different stages of the gelation process. At temperatures above 0°C the rate of gelation was too small for a reasonable measurement. Initially, the creep curves showed liquidlike behaviour, whereas after some time, depending on temperature, rubberlike behaviour... 

Rheological measurements were performed in a stress rheometer fixture with a 2-cm cone and plate having a 1° cone angle and gap of 27 pm. Dynamic shear moduli were measured at 0.5% strain between 0.1 and 100 rad/s. Creep compliance was measured with a constant applied stress in the range of 0.1 to 5 kPa. Both measurements were performed over a series of temperatures to obtain data for time-temperature superposition. 

For a homogeneous viscoelastic material that is confined to a temperature range within which there is no phase change, the effects of time and temperature can be interchangeable. In other words, if we apply a stress or strain to the material, we can choose either to wait for it to relax or creep at the fixed test temperature or we can get the same response faster by raising the test temperature. This principle is called time-temperature superposition and is widely used in linear viscoelasticity. Taking into account any small variation of the plateau modulus, we can express the principle mathematically (say, in steady shear) as... 

The creep rate under shear loading increases with both time and temperature. Similar curves are obtained for tensile creep and other fibre angles. Using a transformation equation, it was possible to superpose these curves to form a master curve. 

Simple fracture is the separation of a body into two or more pieces in response to an imposed stress that is static (i.e., constant or slowly changing with time) and at temperatures that are low relative to the melting temperatnre of the material. Fracture can also occur from fatigue (when cyclic stresses are imposed) and creep (time-dependent deformation, normally at elevated temperatnres) the topics of fatigue and creep are covered later in this chapter (Sections 8.7 throngh 8.15). Althongh applied stresses may be tensile, compressive, shear, or torsional (or combinations of these), the present discussion wiU be confined to fractnres that resnlt from uniaxial tensile loads. For metals, two fracture ductile fracture, modes are possible ductile and brittle. Classification is based on the ability of a material... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

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. 

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