Creep response

In the linear viscoelastic range, the parameters of this series do not depend on the level of the applied load. 

For creep under applied constant stress Oq, the material response is  

In the nonlinear range the dependence on the level of the applied load can be expressed by multiplying the linear parameters by so-called nonlinearity factors which, of course, are load-, time- and temperature-dependent [22,23]. The 

the following equation can be also expressed in terms of creep compliance  

Time-Temperature Superposition In order to predict the long-term creep behavior based on short-term creep measurements, it is generally assumed that the polymer does not change its structure with time, and consequently the time-temperature superposition (TTS) principle can be adopted. ITS has been used to obtain the master curves for creep compliance against time. According to TTS, the creep at a given temperature (To) is related to the creep at another temperature 

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Figure 5.105 Creep response of SMC-R50 composite at various temperatures. Reprinted, by permission, from P. K. Mallick and S. Newman, eds.. Composite Materials Technology, p. 62. Copyright 1990 by Carl Hanser Verlag.

A power-law expression of the form of Eq. (5.115) adequately describes the creep properties of SMC composites. The creep response of the SMC-R50 composite at various temperatures shown in Figure 5.105 is representative of this behavior. Among the material variables, fiber content once again has the greatest influence on the creep strain. At a given temperature and stress level, creep strain is higher if the fiber content is reduced. 

Figure H3.3.5 The creep response of a food (circles) was fitted to a Burger model with one Kelvin-Voight unit. The goodness of fit is shown as the continuous curve and the standard error. The values of compliance and viscosity of the respective springs and dashpots were outcomes of the fitting process.

Linear viscosity is that when the function is splitted in both creep response and load. All linear viscoelastic models can be represented by a classical Volterra equation connecting stress and strain [1-9] ... 

Fig. 5.2 Comparison of creep behavior and time-dependent change in fiber and matrix stress predicted using a 1-D concentric cylinder model (ROM model) (solid lines) and a 2-D finite element analysis (dashed lines). In both approaches it was assumed that a unidirectional creep specimen was instantaneously loaded parallel to the fibers to a constant creep stress. The analyses, which assumed a creep temperature of 1200°C, were conducted assuming 40 vol.% SCS-6 SiC fibers in a hot-pressed SijN4 matrix. The constituents were assumed to undergo steady-state creep only, with perfect interfacial bonding. For the FEM analysis, Poisson s ratio was 0.17 for the fibers and 0.27 for the matrix, (a) Total composite strain (axial), (b) composite creep rate, and (c) transient redistribution in axial stress in the fibers and matrix (the initial loading transient has been ignored). Although the fibers and matrix were assumed to exhibit only steady-state creep behavior, the transient redistribution in stress gives rise to the transient creep response shown in parts (a) and (b). After Wu et al 1...

Fig. 8.14 Comparison of compressive creep response of MoSi2/SiC composites tested in air and in inert atmospheres.42...

Wilding and Ward showed that the creep and recovery behaviour of the low molecular weight samples could be represented to a good approximation by the model representation shown in Fig. 35(b), which consists of a Maxwell and Voigt element in series, on the basis that the parameters E, E, r and r), are dependent on the stress level. Data for the creep response of the samples under discussion at a constant applied stress Op were therefore fitted to the equation... 

The critical stress can now be seen to be essentially an experimental limitation. The smallest strain reading on our present creep apparatus is 5x 10 . The anticipated plateau strain rate of 10" s for a typical sample with a critical stress of 0.2 GPa would therefore only produce a measurable creep response after 500 days, which is on the limit of the time scale of present creep tests at Leeds University. 

Recent work has shown that the creep and recovery behaviour of ultra high modulus polypropylenes is very similar to that of LPE. Again the Sherby-Dorn plots form a good entry to the detailed examination of the creep response. Plateau creep behaviour similar to that of LPE has been observed, and the high stress process correlates well with the a-relaxation process in terms of its activation energy. 

After the irradiation was extinguished, the creep experiment was continued for the usual period. Finally, after complete recovery, the creep response of the network at the new crosslink density... 

Thus, the aim of the present paper is not to review the bulk of the results published to date relating to the creep response of various magnesium-based composites. Instead of such an approach this paper provides a comprehensive report on the extensive experimental results obtained by authors in an investigation of the high temperature creep behavior of the two magnesium alloys, AZ 91 and QE 22, and their discontinuous composites. The objective of the present research is a further attempt to clarify the direct and indirect strengthening effects of short-fiber and particulate reinforcements in creep of magnesium-matrix composites. 

Figure 6.8 Creep compliance curve showing polymer creep-response behavior.2...

Once the creep response of a pad has been determined, it can be superimposed on the characteristic stress impulse graph to identify which... 

Figure 3-2. Creep response of a Maxwell body displayed using linear (left) and...

In other words, the lifetime of a part should decrease exponentially with increasing temperature as well as with increasing applied stress both predictions are borne out by experiments. It is worth noting that Eqs. (12.42) to (12.44) are only valid if the rate of damage generation was controlled by the bulk creep response of the material and steady-state conditions are established during the experiment. 

Neither the simple Maxwell nor Voigt model accurately predicts the behavior of real polymeric materials. Various combinations of these two models may more appropriately simulate real material behavior. We start with a discussion of the four-parameter model, which is a series combination of the Maxwell and Voigt models (Figure 14.9). We consider the creep response of this model. 

Figure 14.10 Creep response of the four-parameter model.

The generalized Voigt element or the Voigt-Kelvin model is a series arrangement of an arbitrary number of Voigt elements (Figure 14.12). Under creep, the creep response of each individual element is given by... 

The creep response of polyethylene in Fig. 7.3 can be adequately reproduced by using Eq. (7.6) with retardation times that differ by powers of 10, i.e. Ti = 1 s, T2 = 10 s, T3 = 100 s, etc. Thus, polyethylene has a spectrum of retardation times. The spectrum, determined by curve fitting the creep response, can be used to predict other forms of viscoelastic behaviour. 

The creep response depends mainly on the temperature and the cross-link density. At temperatures below T, cross-linking has little effect on the properties of the material, but above T, the secondary creep, arising from irreversible viscous flow, is reduced or eliminated by cross-hnking. 

When the strains or the strain rates are sufficiently small, the creep response is Unear. In this case, when the time-dependent strain is divided by the fixed stress, a unique creep compUance curve results that is, at each time there is only one value for this ratio, which is the compliance—y(t)lao = J t). The unique shear creep compliance function J t) (Pa or cm /dyne, 1 Pa = 0.1 cm /dyne) obtained for an amorphous polymer has the usual contributions... 

In order to verify some of the predictive capabilities of the finite element model described in the previous sections, the transverse creep response of a IM7/5260 composite investigated in a earlier study [8] was used as a benchmark case. Two separate load histories were considered (1) transverse creep and recovery of a [90]i6 specimen under isothermal conditions, and (2) transverse creep of a [90]i6 specimen subjected to cyclic thermomechanical loading for extended periods of time. 

Figure 2.12 a Creep of a viscoelastic polymer subjected to a constant stress, Oq the creep response is usually represented by the creep compliance, ] = elOq, where e is the measured strain. 

The response functions g t—x) and h(t—x) can be written in terms of a, b and c in (19), and can further be used to describe completely the creep response through the analogue of (20). In other words, the complete non-linear viscoelastic response should be describable in terms of these two functions only. Certain features of this representation can be checked very quickly against the experimental data. For example, it can be shown that for a creep experiment with or = 0 for r < 0, and 0, then... 

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