Creep critical value

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 viscoelastic creep modulus may be determined at a given temperature by dividing the constant applied stress by the total strain prevailing at a particular time. Since the creep strain increases with time, the viscoelastic creep modulus must decrease with time (Fig. 2-23). Below its critical stress for linear viscoelasticity, the viscoelastic creep modulus versus time curve for a material is independent of the applied stress. In other words, the family of strain versus time curves for a material at a given temperature and several levels of applied stress may be collapsed to a single viscoelastic creep-modulus-time-curve if the highest applied stress is less than the critical value. 

The model is based on the idea that the glassy phase is composed of two layers - a normal glassy phase layer behaving in a Newtonian way, embedded into an over-condensed layer with non-Newtonian behaviour. Thus, for stresses lower than the critical stress, the creep is controlled by the normal glassy phase (n= 1), and when the stress exceeds a critical value, the squeeze of this phase makes the two over-condensed layers come into contact, thus the material creeps in a non-Newtonian way (n = 0.5). The creep rate is written ... 

If the association is extensive enough a weak solid is formed that will exhibit a yield point. The data in Fig. 24 illustrate the properties observed with such an aggregated solution. For strains less than a critical value Yy of about 5% the creep was fully recoverable and fitted by the cube-root, or Andrade, creep relation for the compliance y(t)/a ... 

The power law approximation of the voltage current characteristic for superconductors above Ic has been known for some time (64). Such studies have been made in Y-Ba-Cu-O (65) with results similar to those shown in Figure 16. The value of n in V In has been found to decrease as the magnetic field is increased, and of course becomes ohmic above Hc2. Another representation of the current voltage data is shown in Figure 17 from Enpuku et al. (66), log V vs 1/T for increasing currents (above critical). The expected near straight line arises from the flux creep model of Tinkham for T/Tc 1. 

Figure 14-5 defines the creep below the critical shear stress. It is called anelastic creep and is to a large extent recoverable. The anelastic strain for a given stress below °crk approaches its equilibrium value u0 as... 

Concerning the above-mentioned critical quantities the authors have in fact established (i) that irrespective of stress level damage is apparently initiated at a critical creep strain ec of 3 to 3.5% (ii) that a notable deviation of creep data from the potential law starts just at this strain level and (iii) that although the strain rate dev/df is a function of stress, the minimum in the Sherby-Dorn plot also occurs (for the tubular specimens) at ec. The postulated changes in sample morphology at about the time when the strain values started to deviate from Findley s equation, were in fact seen by these and other authors [42,52], who detected in U PVC deformed micro-cavities later... 

Viscoelastic creep data can be presented by plotting the creep modulus (constant applied stress divided by total strain at a particular time) as a function of time [23-26], Below its critical stress, the viscoelastic creep modulus is independent of stress applied. A family of curves describing strain versus time response to various applied stress may be represented by a single viscoelastic creep modulus versus time curve if the applied stresses are below the material s critical stress value. 

For practical purposes the lower limit of the critical strain can be used as a criterion. This value appears, moreover, to be not much dependent on temperature, so that it can be considered as a material constant. It varies from -03% for PS to 2.2 % for PP. From creep isochrones a stress level can now quite easily be detected at which, within a given time of usage, no damage to the material is to be expected. This stress level is, of course, much lower than the one we found from Figure 7.20. 

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