Creep strain recovery

X. Wu and J. W. Holmes, Tensile Creep and Creep-Strain Recovery Behaviour of Silicon Carbide Fiber/Calcium Aluminosilicate Matrix Ceramic Composites, J. Am. Cerartu Soc. 76, 2695-2700 (1993). 

Table 6.1 summarizes the experimental details together with symbols (designations) including values for applied load, load time, strain, strain rate and the creep-strain recovery ratio, R r. 

Creep describes time-dependent permanent deformation of materials resulting from constant structural stress. The creep of polymers can be divided into two main stages primary creep and steady-state creep. The creep strain rate decreases with time in the primary creep and is constant in the steady-state creep. Strain recovery occurs with the removal of external load after a creep time. Therefore, the total strain (e) consists of three separate parts el, e2, and e3. The el and e2 are the immediate elastic deformation and delayed elastic deformation, respectively. The e3 is the Newtonian flow. It was found that the el and e2 decreased with increasing clay contenf indicating lower creep recovery with the addition of C20A. The creep compHance J, the ratio of strain and applied load, can be expressed as... 

Figure 36 is representative of creep and recovery curves for viscoelastic fluids. Such a curve is obtained when a stress is placed on the specimen and the deformation is monitored as a function of time. During the experiment the stress is removed, and the specimen, if it can, is free to recover. The slope of the linear portion of the creep curve gives the shear rate, and the viscosity is the appHed stress divided by the slope. A steep slope indicates a low viscosity, and a gradual slope a high viscosity. The recovery part of Figure 36 shows that the specimen was viscoelastic because relaxation took place and some of the strain was recovered. A purely viscous material would not have shown any recovery, as shown in Figure 16b. 

Creep strain when load is removed Recovery time... 

Creep and Recovery Behaviour. Plastics exhibit a time-dependent strain response to a constant applied stress. This behaviour is called creep. In a similar fashion if the stress on a plastic is removed it exhibits a time dependent recovery of strain back towards its original dimensions. This is illustrated in... 

For a linear viscoelastic material in which the strain recovery may be regarded as the reversal of creep then the material behaviour may be represented by Fig. 2.49. Thus the time-dependent residual strain, Sr(t), may be expressed as... 

Extensive tests have shown that if the final creep strain is not large then a graph of Fractional Recovery against Reduced Time is a master curve which... 

If there have been N cycles of creep and recovery the accumulated residual strain would be... 

Tests have shown that when total strain is plotted against the logarithm of the total creep time (ie NT or total experimental time minus the recovery time) there is a linear relationship. This straight line includes the strain at the end of the first creep period and thus one calculation, for say the 10th cycle allows the line to be drawn. The total creep strain under intermittent loading can then be estimated for any combinations of loading/unloading times. 

The total creep strain after the stress of 10.5 MN/m has been applied for the 11th time would be 0.121 -I- 0.747 = 0.868%. Now tests have shown that a plot of total creep strain plotted against the logarithm of the total creep time (i.e. ignoring the recovery times) is a straight line which includes the point edT). 

Recovery is the strain response that occurs upon the removal of a stress or strain. The mechanics of the recovery process are illustrated in Fig. 2-34, using an idealized viscoelastic model. The extent of recovery is a function of the load s duration and time after load or strain release. In the example of recovery behavior shown in Fig. 2-34 for a polycarbonate at 23°C (73°F), samples were held under sustained stress for 1,000 hours, and then the stress was removed for the same amount of time. The creep and recovery strain measured for the duration of the test provided several significant points. 

First the sample, that was loaded to about 20% of its short-term yield strength or 13.8 MPa (2,000 psi), recovered almost completely one hour after the release of the load, the net strain being 0.03%. Second, the sample loaded to 66%of its short-term yield strength, or 41.4 MPa (6,000 psi), retained a strain of 0.8% at 1,000 hours after the release of the load. The initial strain was 2.8%, the strain from the 1,000 hour creep an additional 1.7%. Thus only about one-half the creep strain was recovered. Visually extrapolating the recovery curve reveals that even after a year (104 hr.), about one-third of the creep strain (0.6%) will remain. 

Fig. 3-6 An example of intermittent loading involving successive creep strain and recovery.

In order to obtain a general model of the creep and recovery functions we need to use a Kelvin model or a Kelvin kernel and retardation spectrum L. However, there are some additional subtleties that need to be accounted for. One of the features of a Maxwell model is that it possesses a high frequency limit to the shear modulus. This means there is an instantaneous response at all strains. The response of a simple Kelvin model is shown in Equation 4.80 ... 

As shown by Fig. 3.11 for an applied force, the creep strain is increasing at a decreasing rate with time because the elongation of the spring is approaching the force produced by the stress. The shape of the curve up to the maximum strain is due to the interaction of the viscosity and modulus. When the stress is removed at the maximum strain, the strain decreases exponentially until at an infinite time it will again be zero. The second half of this process is often modeled as creep recovery in extruded or injection-molded parts after they cool. The creep recovery usually results in undesirable dimensional changes observed in the cooled solid with time. 

Creep behavior is similar to viscous flow. The behavior in Equation 14.17 shows that compliance and strain are linearly related and inversely related to stress. This linear behavior is typical for most amorphous polymers for small strains over short periods of time. Further, the overall effect of a number of such imposed stresses is additive. Non-creep-related recovery... 

The response of different materials to a stress applied at time t = t0 followed by removal of that stress at t = tl, ie, creep and recovery, is shown in Figure 16 (145). For an elastic material (Fig. 16a), the resulting strain is instantaneous and constant until the stress is removed, at which time the material recovers and the strain immediately drops back to zero. In the case of the viscous fluid (Fig. 16b), the strain increases linearly with time. When the load is removed, the strain does not recover but remains constant. Deformation is permanent. The response of the viscoelastic material (Fig. 16c) draws from both kinds of behavior. An initial instantaneous (elastic) strain is followed by a time-dependent strain. When the stress is removed, the initial strain recovery is elastic, but full recovery is delayed to longer times by the viscous component. 

The rheological properties of gum and carbon black compounds of an ethylene-propylene terpolymer elastomer have been investigated at very low shear stresses and shear rates, using a sandwich rheometer [50]. Emphasis was given to measurements of creep and strain recovery at low stresses, at carbon black flller contents ranging between 20 and 50% by volume. The EPDM-carbon black compounds did not exhibit a zero shear rate viscosity, which tended towards in-Anity at zero shear stress or at a finite shear stress (Fig. 13). This was explained... 

In Chap. 13 the creep recovery of a Burgers element was discussed and from Fig. 13.18 it becomes clear that the recoverable shear creep strain is in the present terms equal to... 

The loss of modulus caused by crazing becomes less pronounced as the draw ratio is increased, especially in tests carried out at lower stress levels. This observation supports earlier conclusions drawn from creep studies on other rubber-toughened plastics (6) if the specimen can reach a strain of 5% largely or entirely by shear mechanisms, the loss of modulus resulting from the creep and recovery program is quite small if, on the other hand, crazing is the dominant mechanism, the loss in modulus is large. 

Fig. 1. Tensile creep and recovery of rubber-modified plastics, showing axial strain (x), lateral contraction ( ), and volume strain (o) for ASA polymer and polypropylene copolymer at 20 °C...

Strain from a creep experiment with constant applied stress cr followed by a creep recovery experiment (starting at t — 0) with zero applied stress, for a viscoelastic solid (lower curves) and a viscoelastic liquid (upper curves). The recoverable compliance can be determined from either creep or recovery. All deformation is recovered for solids but only the elastic part of the deformation is recovered for liquids. 

Rheological measurements were performed in shear using a stress controlled rheometer (Carri-Med CSL 100) operating in cone-plate geometry. Each sample is submitted successively to a first frequency sweep in range 10 3-40 Hz under 3% strain, to a creep and recovery test, and finally to a second frequency sweep identical to the first one. The dynamical strain amplitude (3%) and the value of the creep stress (chosen so as to keep the maximum strain below 10%) were set in order to remain within the linear viscoelasticity domain. Creep and creep recovery were recorded during 20 h and 80 h, respectively, times which allowed the steady state to be reached in all cases. A fresh sample was used for each solvent/temperature combination. 

On removal of the applied stress, the material experiences creep recovery. Figure 14.5 shows the creep and the creep recovery curves of the Maxwell element. It shows that the instantaneous application of a constant stress, Oo, is initially followed by an instantaneous deformation due to the response of the spring by an amount Oq/E. With the sustained application of this stress, the dashpot flows to relieve the stress. The dashpot deforms linearly with time as long as the stress is maintained. On the removal of the applied stress, the spring contracts instantaneously by an amount equal to its extension. However, the deformation due to the viscous flow of the dashpot is retained as permanent set. Thus the Maxwell element predicts that in a creep/creep recovery experiment, the response includes elastic strain and strain recovery, creep and permanent set. While the predicted response is indeed observed in real materials, the demarcations are nevertheless not as sharp. 

Isochronous curves, on the other hand, are more advantageously obtained by direct experiments because they are less time consuming and require less specimen preparation than creep testing. The experiments actually involve a series of mini creep and recovery tests on the material. Thus a stress is applied to a specimen of the material, and the strain is recorded after a time t (typically 100 sec). The stress is then removed and the material is allowed to recover. This procedure is repeated unit there are sufficient points to plot the isochronous curve. 

When plastics are unloaded, the creep strain is recoverable. This contrasts with metals, where creep strains are permanent. The Voigt linear viscoelastic model predicts that creep strains are 100% recoverable. The fractional recovered strain is defined as 1 — e/cmax, where e is the strain during recovery and Cmax is the strain at the end of the creep period. It exceeds 0.8 when the recovery time is equal to the creep time. Figure 7.9 shows that recovery is quicker for low Cmax and short creep times, i.e. when the creep approaches linear viscoelastic behaviour. 

Rg. 7.6 Creep and recovery. The upper graph shows the applied stress as a function of time and the lower graph the resulting strain. 

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