Creep-compliance technique

The creep-compliance technique has been used extensively by Sherman and co-workers for the study of ice cream, model emulsions, margarine, and butter (Sherman, 1966 Shama and Sherman, 1969 Vernon Carter and Sherman, 1980 Sherman and Benton, 1980). In these studies, the methodology employed was similar to that for ice cream, that is, the creep-compliance data on a sample were described in terms of mechanical models, usually containing four or six elements. Attempts were made to relate the parameters of the models to the structure of the samples studied. However, with increased emphasis on dynamic rheological tests and interpretation of results in terms of composition and structure, the use of mechanical models to interpret results of rheological tests has declined steadily. 

Measurements of glass transition temperatures at high pressure were made indirectly using, in particular, creep compliance [95, 96] or directly using differential scanning calorimetric techniques [97, 98]. The measured depression reaches values as high as 60°C for poly(methyl methacrylate) and polystyrene. 

One of the primary mechanical42) techniques for studying the dynamics of polymer fluids near the glass transition is the measurement of the creep compliance 7(f). At the initial time there is a finite compliance associated with the glasslike response of the liquid Jg. The value of the compliance at this point is typically near 1(T10 cm2/dyne. For an uncrosslinked liquid there will be a flow term given by tlrj. The total creep compliance can then be represented as... 

Rheological properties of mayonnaise have been studied using different rheological techniques steady shear rate-shear stress, time dependent shear rate-shear stress, stress growth and decay at a constant shear rate, dynamic viscoelastic behavior, and creep-compliance viscoelastic behavior. More studies have been devoted to the study of rheological properties of mayonnaise than of salad dressings, probably because the former is a more stable emulsion and exhibits complex viscous and viscoelastic rheological behavior. 

Rheological properties of salad dressings also were studied using the techniques steady shear rate-shear stress, stress growth and decay at a constant shear rate, dynamic viscoelastic behavior, and creep-compliance viscoelastic behavior. 

There are a great number of techniques for the experimental determination of viscoelastic functions. The techniques most frequently found in the literature are devoted to measuring the relaxation modulus, the creep compliance function, and the components of the complex modulus in either shear, elongational, or flexural mode (1-4). Although the relaxation modulus and creep compliance functions are defined in the time domain, whereas the complex viscoelastic functions are given in the frequency domain, it is possible, in principle, by using Fourier transform, to pass from the time domain to the frequency domain, or vice versa, as discussed earlier. 

Strictly speaking, there are no static viscoelastic properties as viscoelastic properties are always time-dependent. However, creep and stress relaxation experiments can be considered quasi-static experiments from which the creep compliance and the modulus can be obtained (4). Such tests are commonly applied in uniaxial conditions for simphcity. The usual time range of quasi-static transient measurements is limited to times not less than 10 s. The reasons for this is that in actual experiments it takes a short period of time to apply the force or the deformation to the sample, and a transitory dynamic response overlaps the idealized creep or relaxation experiment. There is no limitation on the maximum time, but usually it is restricted to a maximum of 10" s. In fact, this range of times is complementary, in the corresponding frequency scale, to that of dynamic experiments. Accordingly, to compare these two complementary techniques, procedures of interconversion of data (time frequency or its inverse) are needed. Some of these procedures are discussed in Chapters 6 and 9. 

Although creep-compliance (Kawabata, 1977 Dahme, 1985) and stress-relaxation techniques (Comby et al., 1986) have been used to study the viscoelestic properties of pectin solutions and gels, the most common technique is small-deformation dynamic measurement, in which the sample is subjected to a low-amplitude, sinusoidal shear deformation. The resultant stress response may be resolved into an in-phase and 90° out-of-phase components the ratio of these stress components to applied strain gives the storage and loss moduli (G and G"), which can be related by the following expression ... 

The four commonly used techniques to extract information on the viscoelastic behavior of suspensions are creep-compliance measurements, stress-relaxation measurement, shear-wave velocity measurements, and sinusoidal oscillatory testing (25-27). In general, transient measurements are aimed at two types of measurements, namely, stress relaxation, which is to measure the time dependence of the shear stress for a constant small strain, and creep measurement, which is to measure the time dependence of the strain for a constant stress. 

The viscoelastic behavior is evaluated by means of two types of methods static tests and dynamic tests. In the first calegtuy a step change of stress or strain is applied and the stress or strain response is recorded as a function of time. Stress relaxation, creep compliance, and creep recovery are static methods. The dynamic tests involve the imposition of an oscillatory strain or stress. Every technique is described in the following sections. 

The most common technique employed to date has been that of creep in uniaxial tension. It was shown above that with the inclusion of lateral strain measurements this is a powerful technique giving access to up to 6 independent creep compliance functions. This is more than for any other known method. It further has the overwhelming advantage over many methods, such as say torsional or flexural creep, that the stress is sensibly uniform over the working volume of the specimen. This advantage is paramount in studies of materials displaying non-linear behaviour in creep since analysis of the non-uniform stress situation in non-linear systems is not well developed. Attempts to overcome the non-uniform stress situation in torsion, by recourse to, say, torsion of thin walled tubes, lead to severe difSculties in specimen preparation in oriented materials, when anisotropy of behaviour is to be studied. 

Notwithstanding the inherent advantages of the controlled-stress technique in yield studies, it should be borne in mind that an interpretation of the results of creep-compliance measurements in terms of a real yield stress (i.e. a stress below which the sample exhibits Hookean elastic behaviour) is subject to the usual experimental limitations of machine resolution (i.e. of angular displacement) and the role of time-scale in the sample s response to applied stress. 

Schapery [16, 17] has used the theory of the thermodynamics of irreversible processes to produce a model that may be viewed as a further extension of Leaderman s. Schapery continued Leaderman s technique of replacing the stress by a function of stress /(a) in the superposition integral, but also replaced time by a function of time, the reduced time ip. The material is assumed to be linear viscoelastic at small strains, with a creep compliance function of the form [17]... 

Methods exist which, in principle, permit all of the transient and dynamic moduli to be calculated from the results of any one of the analyses described above. For example, from the stress relaxation test it should be possible to calculate creep compliance and dynamic moduli. In practice, however, these calculations are not so simple. They require accurate stress relaxation data over a wide range of time, including times close to zero. The calculation procedures involve convolution techniques which are not very successful if the data are inaccurate or incomplete. 

A number of small strain experiments are used in rheology. Some of the more common techniques are stress relaxation, creep, and sinusoidal oscillations. In the linear viscoelastic region all small strain experiments must be related to one another through G(t), as indicated by the basic constitutive equation, eq. 3.2.7, or through M(t), eq. 3.2.4. Different experimental methods are used because they may be more convenient or better suited for a particular material or because they provide data over a particular time range. Furthermore, it is often not easy to transform results from one type of linear viscoelastic experiment to another. For example, transformation from the creep compliance J t) to the stress relaxation modulus G(t) is generally difficult. Thus both functions are often measured. 

Recently, a method based on the determination of a dynamic properly, the absolute biaxial creep compliance, has been developed in our lab [5]. The method is a scaled down version of the classic bubble inflation technique [6-7], and is capable of measuring the biaxial creep comphance response of films as thin as 13 nm. In the foUowing we summarize this method and some of the prior results on ultrathin polymer films. In addition, we present new results of creep recovery in bubble deflation experiments as well as show images of rupturing... 

For orthorhombic symmetry on the other hand, tensile creep and lateral compliance measurements on specimens cut from oriented sheet will yield only 6 of the 9 required creep functions those not accessible by this method being Suit), Sssit) and S66(t)- The two shear compliances 555(1) and Seeit) can be obtained by torsional creep experiments, but these need to be carefully designed and involve complex experimental procedures. The only possibility for measurement of Su(t) on sheet appears to be by compressive creep techniques, however, one would expect substantial experimental difficulties largely associated with strain measurement and specimen geometry. There appears to be no reported evaluation of the full characterisation of creep for the case of orthorhombic synunetry. 

Tensile and torsional creep methods will be discussed below. For discussion of the very specialised techniques which have been used for studies of anisotropy of compliance in fibres and monofilaments, such as the Hertzian contact technique by Hadley et al and Pinnock et readers are referred to the original papers and to Ward. It should be noted that such methods are not well adapted to creep measurement and are mainly used for determination of isochronous parameters. They suffer from all the limitations, referred to above, associated with non-uniform stress situations. 

Some of the viscoelastic or rheological properties that can be measured using this technique include viscosity, modulus tensile compliance, creep-stress relaxation, gel time and gel temperature, tensile compliance, and stress-strain properties. 

---