Prediction creep

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). 

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. 

This represents an exponential recovery of strain which is a reversal of the predicted creep. 

When plotted against time, these calculated values for the apparent modulus provide a simplified means of predicting creep at various stress levels (Fig. 2-32). For all practical purposes, curves of deformation versus time eventually tend to level oft Beyond a certain point, creep is small and may safely be neglected for many applications. 

Finally, there have been numerous attempts to develop formulas that could be used to predict creep information under varying usage conditions. In practically all cases the suggestions have been made that the calculated data be verified by actual test performance. Furthermore, numerous factors have been introduced to apply such data to reliable predictions of product behavior. 

In computing ordinary short-term characteristics of plastics, the standard stress analysis formulas may be used. For predicting creep and stress-rupture behavior, the method will vary according to circumstances. In viscoelastic materials, relaxation data can be used in Eqs. 2-16 to 2-20 to predict creep deformations. In other cases the rate theory may be used. 

Plastics, both thermoplastic and thermosetting, will deform under static load. This is known as creep. For this reason those materials whose prime function is mechanical are generally reinforced with mineral filler or short fibres, or else oriented by drawing. Many components have a limit on acceptable deformation, and the predicted creep strain at the end of life will be fed back to define either a maximum load, or mechanical dimensions large enough for the component to remain within the limitations on strain. Creep becomes more pronounced at higher temperatures. 

Figure 8.10 Fourth stage of SIM. The composite modulus curve of Figure 8.9 is inverted to yield the predicted creep curve for the reference temperature.

The model represents a liquid (able to have irreversible deformations) with some additional reversible (elastic) deformations. If put under a constant strain, the stresses gradually relax. When a material is put under a constant stress, the strain has two components as per the Maxwell Model. First, an elastic component occurs instantaneously, corresponding to the spring, and relaxes immediately upon release of the stress. The second is a viscous component that grows with time as long as the stress is applied. The Maxwell model predicts that stress decays exponentially with time, which is accurate for most polymers. It is important to note limitations of such a model, as it is unable to predict creep in materials based on a simple dashpot and spring connected in series. The Maxwell model for creep or constant-stress conditions postulates that strain will increase linearly with time. However, polymers for the most part show the strain rate to be decreasing with time [23-26],... 

Fig. 10.4 Curve showing the predicted creep crack growth rate versus stress intensity factor based on the model of Hui and Riedel.40...

A. Briefly explain the time-temperature superposition principle and how it can be used to predict creep properties. 

Such a curve of K, vs. d is naturally dependent on the material investigated and also on material specific parameters as molecular weight in PMMA this leads to a shift to lower K,-values or equivalently G -values with decreasing molecular weight It should be noted that slow crack propagation curves of quasi-brittle materials have been used by different authors [e.g. predict creep life curves ... 

These equations are used to convert a modulus to compliance in problem 6 of this chapter. The results of this calculation are depicted in Figure 2-16. In dealing with experimental results, the modulus is often available only as a set of discrete data gathered over a finite time interval. In this case, the transformation to a similar set of predicted creep data is a difficult numerical problem that can result in substantial errors.8,9 Commercial software packages are available that can do this and other "integral" transforms, but these should all be used with caution. A simplified example is suggested in problem 14. 

Figure 7.3 shows that the predicted creep of the Voigt model is a poor representation of the creep of a polyethylene. Better predictions can be obtained by combining, in series, Voigt models with different retardation... 

FIGURE 5-1 Predicted creep rates for alumina fibers as a function of aspect ratio using a two-dimensional model. Source Sabol, 1994. 

A S Mosallam and R E Chambers, Design procedure for predicting creep and recovery of pultruded composites , Proceedings of the 50th Annual Conference, Composites Institute, Cincinnati, USA, Paper 6-C. New York, The Society of the Plastics Industry, January 1995. 

The Larson-Miller parameter, P, in Eq. (6.102), is one of the useful parameters used for predicting creep life in metallic materials, but it is useful for ceramics as well. The LMP may be used to describe the stress-temperature-life relation in a SiC/SiC composite by means of the following expression ... 

Transient Response Creep. The creep behavior of the polsrmeric fluid in the nonlinear viscoelastic regime has some different features from what were found with the linear response regime. First, there are no ready means of relating the creep compliance to the relaxation modulus as was done in the linear viscoelastic case. In fact, the relationship between the relaxation properties and the creep properties depends entirely on the exact constitutive relationship chosen for the response of the material, and numerical inversion of the specific constitutive law is ordinarily necessary to predict creep response from the relaxation... 

Figure 4.6 Comparison of experimental and predictive creep strain for rPET...

Flexural creep testing on polymer concrete using an unsaturated polyester resin based on rPET was carried out to predict creep behaviour, and mechanical and empirical models were proposed using experiment results. The following conclusions were obtained from the results ... 

The viscoelastic behaviour of rPET polymer concrete is linear under stress levels up to 30% as a result, the two-point method of stress levels higher than 30% will probably lead to considerable error in the predicted creep deformation values. 

Repeating this extrapolation for different leads to a predicted creep curve. Figure 5.228 (d). 

Measured and predicted creep curves for examined TPU at 6 N/mm mean stress (f=0.35 Hz, iinear extrapoiation, power law)... 

Miyano et al. propose a method to predict creep strength Oc from the master curve for static strength using the linear cumulative damage law. fs(o) and 4(0) are static and creep failure time, respectively for stress 0. It is supposed that the material experiences a monotonic stress history o(f) for 0 < t < t where t is the failure time for this stress history. The linear cumulative damage law states ... 

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