Deformations at Constant Strain Rate

If a polymer is deformed at constant strain-rate it is often possible to draw analogies between the observed response and the yield behaviour of metals, see Fig. 1(b). 

For a viscoelastic liquid in shear, the ratio oz t)/y in equations 56 to 58 is sometimes treated as a time-dependent viscosity J (r) which increases monoton-ically (provided the viscoelasticity is linear) to approach the steady-state viscosity Meissner has pointed out that, in an experiment involving deformation at constant strain rate followed by stress relaxation at constant deformation, viscoelastic information can be obtained without imposing the restriction in equation 11 of Chapter 1 that the loading interval is small compared with the time elapsed at the first experimental stress measurement. ... 

Tensile Stress Relaxation following Deformation at Constant Strain Rate... 

However, for / i, equation 1 reduces to equation 2, thus justifying the assumption implicit in experimental procedures that rapid loading is equivalent to instantaneous for practical purposes. Equation 1 has been discussed by Meissner and Smith in connection with combining deformation at constant strain rate with subsequent relaxation to obtain viscoelastic information, as mentioned in Section FI of Chapter 3. 

FIGURE 17.5 Examples of stress a versus strain e for various materials that are first compressed, then decompressed (both at constant strain rate). Examples are meant to illustrate various kinds of behavior. The hatched areas indicate the deformation energy that is dissipated (not recoverable). The scales are generally different for the various frames. 

Fig. 8.10. Stress-strain curves for ice single crystals deformed by basal shear at constant strain rate. In (a) the temperature is — is °C and the strain rate is given as a parameter in units of lO" s , while in (6) the strain rate is 1-3 x io s and the temperature is varied (Higashi et al. 1964).

Creep, stress relaxation and deformation under constant strain rate can be described assuming a viscoelastic response. Application of a constant strain can give rise to yield in thermoplastic materials. At yield the viscoelastic behaviour is non-linear, though the transition to non-linear is likely to occur prior to yield. 

In conjunction with the tensile fracture work W shown in the lower curves of Figure 8, the tensile strength (based on deformed cross section) and extensibility (nominal strain at break) were also measured. The cross plots of versus data for the CTBN modified epoxy resins of this study, tested at constant strain rate e = 0.09 min from T = -200 to 200 C are shown by the curves in Figure 9 as tensile failure envelopes. The upper extremity of the failure envelope curves of Figure 9 reflect a maximum tensile strength... 

If the applied shear stress varies during the experiment, e.g. in a tensile test at a constant strain rate, the relaxation time of the activated transitions changes during the test. This is analogous to the concept of a reduced time, which has been introduced to model the acceleration of the relaxation processes due to the deformation. It is proposed that the reduced time is related to the transition rate of an Eyring process [58]. The differential Eq. 123 for the transition rate is rewritten as... 

Figure 2.37 presents plots of elongational viscosities as a function of stress for various thermoplastics at common processing conditions. It should be emphasized that measuring elongational or extensional viscosity is an extremely difficult task. For example, in order to maintain a constant strain rate, the specimen must be deformed uniformly exponentially. In addition, a molten polymer must be tested completely submerged in a heated neutrally buoyant liquid at constant temperature. 

In most deformation experiments, the specimens have been deformed in compression at a constant strain-rate (10 -10 s ) under conditions of... 

The dislocation nucleation just discussed is a preyield phenomenon in any deformation experiment, it may occur (i) during any preconditioning treatment at temperature and pressure before the shear stress is applied, (ii) during the incubation period in a creep test, or (iii) during the nominally elastic region in a constant strain-rate experiment. Thus, the microstructure of the crystal immediately prior to the onset of deformation may not be the same as the microstructure of the as-grown crystal. 

In a constant strain-rate experiment, the rapid multiplication of dislocations following the yield point can produce more mobile dislocations than are necessary to maintain the imposed strain-rate and consequently the stress drops. The deformation will continue at a constant stress provided any decrease in u is compensated by an increase in iom, or vice versa. However, in general, the stress rises with increasing strain. The slope (dajdt) of the stress-strain curve is determined by the competition between two dislocation processes namely, work-hardening and recovery, which we now consider briefly. 

Figure 9.13. BF image (g = lOTl) of the dislocation tangles generated at the high-pressure water clusters in wet synthetic quartz deformed at a constant strain-rate at 475°C. (From McLaren et al. 1989.)...

Crystals deformed at a constant strain-rate (e = 10 s ) with a confining pressure of 300 MPa and 400 C in an orientation expected to activate the (100) [010] slip system, developed numerous microtwins in (100) and some dislocations that were not fully characterized. However, interesting dislocations and associated faults were observed in specimens scratched on a (110) surface. Figure 9.32 is typical of the dislocation microstructures observed in these specimens and shows segments of dislocation loops bounding planar defects on (100). 

Using these two types of samples, we performed uniaxial compression tests under constant strain rates from 2.8x10 to 2.9x1 O s in a cold room at -10°C. The experimental conditions used in this study are summarized in Table 1. Nine series of the deformation tests were performed so as to study the dependencies on each physical parameter. 

Fig. 6.17. Map of polycluster mechanical states. Region I elastic and anelastic (shaded area) deformations Region II inhomogeneous plastic deformation Region III homogeneous diffusional-viscous flow. Curves 1-3 show the temperature dependence of the stress at different constant strain rates...

On the map of mechanical states in region I, elastic and anelastic (shaded areas) deformations take place. In the region II, the inhomogeneous plastic deformation with the formation of shear bands takes place. The horizontal broken line corresponds to the theoretical yield stress of LRC. In the region III, the homogeneous diffusional-viscous flow takes place and, in the region IV, the mixed viscous flow is realized. Curves 1,2, 3 show the temperature dependence of the stress at different constant strain rates. The continuations of these curves in regions IV and II correspond to the mixed nonuniform plastic deformation. 

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