Creep modulus behavior

Typical creep-modulus behavior is shown in Figure 1 viscoelastic parameters deduced from the master curve are given in Table II, and discussed below. 

Viscoelastic creep data are usually presented in one of two ways. In the first, the total strain experienced by the material under the applied stress is plotted as a function of time. Families of such curves may be presented at each temperature of interest, each curve representing the creep behavior of the material at a different level of applied stress. Below a critical stress, viscoelastic materials may exhibit linear viscoelasticity that is, the total strain at a given time is proportional to the applied stress. Above this critical stress, the creep rate becomes disproportionately faster. In the second, the apparent creep modulus is plotted as a function of time. 

Different viscoelastic materials may have considerably different creep behavior at the same temperature. A given viscoelastic material may have considerably different creep behavior at different temperatures. Viscoelastic creep data are necessary and extremely important in designing products that must bear long-term loads. It is inappropriate to use an instantaneous (short load) modulus of elasticity to design such structures because they do not reflect the effects of creep. Viscoelastic creep modulus, on the other hand, allows one to estimate the total material strain that will result from a given applied stress acting for a given time at the anticipated use temperature of the structure. 

Craze growth at the crack tip has been qualitatively interpreted as a cooperative effect between the inhomogeneous stress field at the crack tip and the viscoelastic material behavior of PMMA, the latter leading to a decrease of creep modulus and yield stress with loading time. If a constant stress on the whole craze is assumed then time dependent material parameters can be derived by the aid of the Dugdale model. An averaged curve of the creep modulus E(t) is shown in Fig. 13 as a function of time, whilst the craze stress is shown in Fig. 24. 

The creep behavior of 40% glass-filled polyphenylene sulfide Is summarized In Figure 5 which plots creep modulus against time for three sets of experimental conditions 23°C/5,000 psi, 66°C/5,000 psi, and 121°C/5,000 psi. Table II compares the per cent loss In apparent creep modulus at 1,000 hours and at 10,000... 

An interpretation of these results is that there is little effect of degradation crosslinking or other product formation on chain or group motions involved in the observed transition and modulus behavior up to about 160 hours exposure. This is a reflection of the relatively low crosslink density obtained up to that exposure time. It is anticipated that creep behavior, a low frequency response, would exhibit greater sensitivity to low levels of crosslinking. 

In a set of similar creep tests on the same material where the level of applied stress is varied at constant temperature, the effect of increasing stress normally is to decrease the creep modulus at corresponding test times. This is consistent with experience and with the theory of linear viscoelasticity. However, experimental data occasionally will show the opposite efl ect, or the creep curves at different stress levels will cross. This is probably due to experimental variation, and in such cases the experimental data may be regarded collectively as estimates of creep behavior over the range of the applied stesses involved. 

For the designer there is generally a less-pronounced curvature when creep and relaxation data are plotted log-log. Predictions can be made on creep behavior based on creep and relaxation data. This usual approach makes it easier to extrapolate, particularly with creep modulus and creep-rupture data. 

Figure 9.15 A W s isochronal creep modulus, measured at room temperature, as a function of draw ratio for a range of quenched (open symbols) and slowly cooled (closed symbols) samples of linear polyethylene drawn at 75°C. (m), Rigidex 140-60 (A, k), Rigidex 25 (D, M), Rigidex 50 (o, ), P40 (<>,- ), H020-54P. (Reproduced from Capaccio, Crompton and Ward (1976) Drawing Behavior of Linear Polyethylene. 1. Rate of Drawing As a Function of Polymer Molecular-weight and Initial Thermal-treatment I. Polym. Sci., Polym. Phys. Ed., 14, 1641. Copyright (1976).)...

In order to predict the creep behavior and possibly the ensuing failure a number of approaches have been proposed. These are based respectively on the theory of viscoelasticity — including the concept of free volume — or on empirical representations of e(t) or of the creep modulus E(t) = ao/e(t). The framework of the linear theory of viscoelasticity permits the calculation of viscoelastic moduli from relaxation time spectra and their inter conversion. The reduction of stresses and time periods according to the time-temperature superposition principle frequently allows establishment of master-curves and thus the extrapolation to large values of t (cf. Chapter 2). The strain levels presently utilized in load bearing polymers, however, are generally in the non-linear range of viscoelasticity. This restricts the use of otherwise known relaxation time spectra or viscoelastic moduli in the derivation of e (t) or E (t). 

Creep data are invaluable for predicting die long-term functional behavior of a material or product. However, the current body of data (seldom, if ever, reported on product data sheets) cannot be compared for a series of material candidates. Polymers must be tested exactly the same way ( test mode, initial stress level, time, and temperature) in order to have a valid comparison, without relying on mathematical adjustments. The concept of the use of creep modulus has been widely adopted. However, one must still adhere to the paradigms of linear viscoelasticity to allow valid comparisons of different polymeric materials. 

While the standard linear model does not precisely describe creep or stress relaxation behavior because of the assumption of a single relaxation time, the above arguments still ly to actual polymer behavior, where Dc (t) < Dr ) . Thus, for constant load applications, the creep compliance or its inverse, the so-called effective creep modulus should be used, whereas for constant displacement (e.g., a plastic nut and bolt), the relaxation modulus should be used. 

Since extrapolation to a 50 year creep compliance or creep modulus depends critically on the short-term behavior, the moisture effects can potentially give significant errors, particularly if there is a one-time absorption of moisture into initially dry specimens. In tensile creep tests conducted over a two-year time period [7], the moisture fluctuations in the... 

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. ... 

Master curves can be used to predict creep resistance, embrittlement, and other property changes over time at a given temperature, or the time it takes for the modulus or some other parameter to reach a critical value. For example, a mbber hose may burst or crack if its modulus exceeds a certain level, or an elastomeric mount may fail if creep is excessive. The time it takes to reach the critical value at a given temperature can be deduced from the master curve. Frequency-based master curves can be used to predict impact behavior or the damping abiUty of materials being considered for sound or vibration deadening. The theory, constmction, and use of master curves have been discussed (145,242,271,277,278,299,300). 

The Maxwell model is also called Maxwell fluid model. Briefly it is a mechanical model for simple linear viscoelastic behavior that consists of a spring of Young s modulus (E) in series with a dashpot of coefficient of viscosity (ji). It is an isostress model (with stress 5), the strain (f) being the sum of the individual strains in the spring and dashpot. This leads to a differential representation of linear viscoelasticity as d /dt = (l/E)d5/dt + (5/Jl)-This model is useful for the representation of stress relaxation and creep with Newtonian flow analysis. 

The tensile modulus is an important property that provides the designer with information for a comparative evaluation of plastic material and also provides a basis for predicting the short-term behavior of a loaded product. Care must be used in applying the tensile modulus data to short-term loads to be sure that the conditions of the test are comparable to those in use. The longer-term modulus is treated under the creep test (Chapter 2). 

For elastomers, factorizability holds out to large strains (57,58). For glassy and crystalline polymers the data confirm what would be expected from stress relaxation—beyond the linear range the creep depends on the stress level. In some cases, factorizability holds over only limited ranges of stress or time scale. One way of describing this nonlinear behavior in uniaxial tensile creep, especially for high modulus/low creep polymers, is by a power... 

Biaxially oriented films, made by stretching in two mutually perpendicular directions, have reduced creep and stress relaxation compared to unoriented materials. Part ot the effect is due to the increased modulus, but for brittle polymers, the improved behavior can be due to reduced crazing. Biaxial orientation generally makes crazing much more difficult in all directions parallel to the plane of the film. 

The viscoelastic behavior of concentrated (20% w/w)aqueous polystryene latex dispersions (particle radius 92nm), in the presence of physically adsorbed poly(vinyl alcohol), has been investigated as a function of surface coverage by the polymer using creep measurements. From the creep curves both the instantaneous shear modulus, G0, and residual viscosity, nQ, were calculated. 

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)... 

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