Creep experiment

In this section we consider a different experimental situation the case of creep. In a creep experiment a is maintained at a constant value and the time dependence of the strain is measured. Thus it is the exact inverse of the relaxation... 

We shall follow the same approach as the last section, starting with an examination of the predicted behavior of a Voigt model in a creep experiment. We should not be surprised to discover that the model oversimplifies the behavior of actual polymeric materials. We shall continue to use a shear experiment as the basis for discussion, although a creep experiment could be carried out in either a tension or shear mode. Again we begin by assuming that the Hookean spring in the model is characterized by a modulus G, and the Newtonian dash-pot by a viscosity 77. ... 

It is interesting to note that the Voigt model is useless to describe a relaxation experiment. In the latter a constant strain was introduced instantaneously. Only an infinite force could deform the viscous component of the Voigt model instantaneously. By constrast, the Maxwell model can be used to describe a creep experiment. Equation (3.56) is the fundamental differential equation of the Maxwell model. Applied to a creep experiment, da/dt = 0 and the equation becomes... 

As we did in the case of relaxation, we now compare the behavior predicted by the Voigt model—and, for that matter, the Maxwell model—with the behavior of actual polymer samples in a creep experiment. Figure 3.12 shows plots of such experiments for two polymers. The graph is on log-log coordinates and should therefore be compared with Fig. 3.11b. The polymers are polystyrene of molecular weight 6.0 X 10 at a reduced temperature of 100°C and cis-poly-isoprene of molecular weight 6.2 X 10 at a reduced temperature of -30°C. 

The Maxwell and Voigt models of the last two sections have been investigated in all sorts of combinations. For our purposes, it is sufficient that they provide us with a way of thinking about relaxation and creep experiments. Probably one of the reasons that the various combinations of springs and dash-pots have been so popular as a way of representing viscoelastic phenomena is the fact that simple and direct comparison is possible between mechanical and electrical networks, as shown in Table 3.3. In this parallel, the compliance of a spring is equivalent to the capacitance of a condenser and the viscosity of a dashpot is equivalent to the resistance of a resistor. The analogy is complete... 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

Creep curves Creep experiments Creep resistance C9 reformate Cremin... 

Kelly, B.T. and Burchell, T.D., The analysis of irradiation creep experiments on nuclear reactor graphites. Carbon, 1994, 32, 119 125. 

The creep experiment lasted 1(K) s and then the load was removed for the recovery experiment. 

If the Boltzmann superposition principle holds, the creep strain is directly proportional to the stress at any given time, f Similarly, the stress at any given lime is directly proportional to the strain in stress relaxation. That is. the creep compliance and the stress relaxation modulus arc independent of the stress and slrai . respectively. This is generally true for small stresses or strains, but the principle is not exact. If large loads are applied in creep experiments or large strains in stress relaxation, as can occur in practical structural applications, nonlinear effects come into play. One result is that the response (0 l,r relaxation times can also change, and so can ar... 

Plazek (183) carried out very accurate creep experiments on natural rubber as a function of cross-linking. He found that data at different temperatures could be superimposed by the usual WLF shift factors which were developed for non-cross-linkcd poiymers (27). Temperature-superposed... 

In order to simplify the discussion and keep the derivation of the formulae tractable, a fibre with a single orientation angle is considered. In a creep experiment the tensile deformation of the fibre is composed of an immediate elastic and a time-dependent elastic extension of the chain by the normal stress ocos20(f), represented by the first term in the equation, and of an immediate elastic, viscoelastic and plastic shear deformation of the domain by the shear stress, r =osin0(f)cos0(f), represented by the second term in Eq. 106. 

The strength of a fibre is not only a function of the test length, but also of the testing time and the temperature. It is shown that the introduction of a fracture criterion, which states that the total shear deformation in a creep experiment is bounded to a maximum value, explains the well-known Coleman relation as well as the relation between creep fracture stress and creep fracture strain. Moreover, it explains why highly oriented fibres have a longer lifetime than less oriented fibres of the same polymer, assuming that all other parameters stay the same. 

It has been reported (4-6) that elastomers undergo very longterm relaxation processes in stress relaxation and creep experiments. The long time behavior of shear modulus can be represented by (18)... 

Table 3 shows values for the foam permeability to air, deduced from creep experiments. Verdejo (a.9) measured a value of 70 x lO m2 -i foam... 

Compressive creep experiments were performed on an EVAC foam from a rnnning shoe. The recovery process after creep is discussed. Modelling was performed of gas diffusion perpendicular to the stress axis and along the stress axis. 16 refs. 

A typical creep experiment involves measuring the extent of deformation, called the creep strain, e, over extended periods of time, on the order of thousands of hours, under constant tensile loads and temperature. The resulting plot of creep strain versus time (Figure 5.43) shows the resulting creep rate, e = dejdt, which is the slope of the... 

Using model concentrated suspensions of polyvinyl chloride and titanium dioxide particles in a Newtonian polybutene fluid, small amplitude oscillatory shear and creep experiments were described [2]. It was shown that the gel-like behaviour at very small strain, and strain hardening at a critical strain, are caused by particle interactions and the state of particle dispersion. 

The creep parameters J and y are obtained through transverse creep experiments. The initial compliance is the elastic response of the material (Equation 8.41). In general, the creep parameters J and y, and the shift factor aT may all be dependent on the cure state of the material. For the current process model the shift factor is assumed to be separable and, as such, is only temperature dependent. As a first approximation the creep parameters are represented as linear functions of the degree of cure. ... 

Figure H3.3.1 A creep experiment where a small constant stress (0) is applied to a food sample (step 1) for a period of time. Afterwards the applied stress is removed (step 2). The degree of deformation (strain, y) is measured during the experiment, and a typical response is shown. ...

The steady-state viscosity is a pragmatic way of predicting certain key properties of a sample. If the stresses used in the creep experiment are well chosen they will reflect the stresses applied to the sample by the action of gravity. Thus, the viscosity under these circumstances will help predict the ability of the material to resist sagging on a vertical surface (coatings). Other uses include prediction of sedimentation velocity or creaming velocity in two-phase dispersions. The ability of a paint to level out and therefore remove brush marks by... 

Because of the uncertainties involved in the decomposition, this procedure would not appear to be a practical way to determine the AHa value needed for Equation 8. It does, however, demonstrate three important points (1) it is the compliances of the mechanisms that are additive (2) T0 and AHa can be obtained from plots such as those shown in Figures 7 and 8 of shift data determined in either relaxation or creep experiments without decomposition of compliance master curves (3) Equation 8 describes time-temperature superposition in Kraton 102 adequately within the experimental accuracy. 

Figure 2.52 The creep experiment. Reprinted with permission from J. E. Mark, Physical Chemistry of Polymers, ACS Audio Course C-89, American Chemical Society, Washington, DC, 1986. Copyright 1986, American...

An important consequence of physical ageing is that, during a creep experiment or during creep in practice, the rate of creep is continuously reduced. Quantitative theories, supported by experimental results, give the picture as presented in Figure 7.10 the dotted lines indicate the creep as extrapolated from observations at higher temperatures the drawn lines are experimentally determined. The differences, in a favourable sense, are enormous ... 

In a creep experiment the Voigt-Kelvin element is instantaneously subjected to a stress [Pg.414]

The simplest model that can be used for describing a single creep experiment is the Burgers element, consisting of a Maxwell model and a Voigt-Kelvin model in series. This element is able to describe qualitatively the creep behaviour of viscoelastic materials... 

The results of creep experiments are usually expressed in the quantity creep compliance, the time-dependent quotient of strain and stress. 

---