Amorphous strain rate

Fig. 3.14. The data is for a very broad range of times and temperatures. The superposition principle is based on the observation that time (rate of change of strain, or strain rate) is inversely proportional to the temperature effect in most polymers. That is, an equivalent viscoelastic response occurs at a high temperature and normal measurement times and at a lower temperature and longer times. The individual responses can be shifted using the WLF equation to produce a modulus-time master curve at a specified temperature, as shown in Fig. 3.15. The WLF equation is as shown by Eq. 3.31 for shifting the viscosity. The method works for semicrystalline polymers. It works for amorphous polymers at temperatures (T) greater than Tg + 100 °C. Shifting the stress relaxation modulus using the shift factor a, works in a similar manner.

The uniaxial failure envelope developed by Smith (95) is one of the most useful devices for the simple failure characterization of many viscoelastic materials. This envelope normally consists of a log-log plot of temperature-reduced failure stress vs. the strain at break. Figure 22 is a schematic of the Smith failure envelope. Such curves may be generated by plotting the rupture stress and strain values from tests conducted over a range of temperatures and strain rates. The rupture locus moves counterclockwise around the envelope as the temperature is lowered or the strain rate is increased. Constant strain, constant strain rate, and constant load tests on amorphous unfilled polymers (96) have shown the general path independence of the failure envelope. Studies by Smith (97) and Fishman (29) have shown a path dependence of the rupture envelope, however, for solid propellants. 

The change in the physical mechanism of deformation from elasticity, viscoelasticity to plasticity depends on the time scales in which the amorphous solid is measured and relaxed. The dependene of stress-strain relationship on relaxation time is conceptualized in Fig. 18, where the yield stress is defined. The yield occurs when the product of the relaxation time and the applied strain rate reaches a constant value [28, 38, 39]. Using Eq. (50) and replacing yield stress components ... 

In conclusion, the deformation behavior of poly(hexamethylene sebacate), HMS, can be altered from ductile to brittle by variation of crystallization conditions without significant variation of percent crystallinity. Banded and nonbanded spherulitic morphology samples crystallized at 52°C and 60°C fail at a strain of 0.01 in./in. whereas ice-water-quenched HMS does not fail at a strain of 1.40 in./in. The change in deformation behavior is attributed primarily to an increased population of tie molecules and/or tie fibrils with decreasing crystallization temperature which is related to variation of lamellar and spherulitic dimensions. This ductile-brittle transformation is not caused by volume or enthalpy relaxation as reported for glassy amorphous polymers. Nor is a series of molecular weights, temperatures, strain rates, etc. required to observe this transition. Also, the quenched HMS is transformed from the normal creamy white opaque appearance of HMS to a translucent appearance after deformation. 

The most common type of stress-strain tests is that in which the response (strain) of a sample subjected to a force that increases with time, at constant rate, is measured. The shape of the stress-strain curves is used to define ductile and brittle behavior. Since the mechanical properties of polymers depend on both temperature and observation time, the shape of the stress-strain curves changes with the strain rate and temperature. Figure 14.1 illustrates different types of stress-strain curves. The curves for hard and brittle polymers (Fig. 14.1a) show that the stress increases more or less linearly with the strain. This behavior is characteristic of amorphous poly-... 

Fig. 3. Tensile properties of notched blends at constant strain-rate (0.005 s ) and room temperature. Comparison between semi-crystalline (a) and amorphous PET (b) for different notches (X) Non-blended non notched PET, (+) Non-notched blend with 21 % of R, (O) Non-blended PET and 1 mm-radius notch, ( ) Non-blended PET and 0.25 mm-radius notch, ( ) PET blended with 21 % of R and 1 mm-radius notch, ( ) PET blended with 21 % of R and 0.25 mm-radius notch.

Fig. 9. Light mean free path, L, and stress vs. time during a tensile experiment at a constant strain rate of 5.10 s. Comparison between semi-cyistalline (a) and amorphous PET (b) both containing 21% of non-reactive modifier.

It is certain that the relaxation behavior of filled rubbers at large strains involves numerous complications beyond the phenomena of linear viscoelasticity in unfilled amorphous polymers. Breakdown of filler structure, strain amplification, failure of the polymer-filler bond, scission of highly extended network chains and changes in network chain configuration probably all play important roles in certain ranges of time, strain rate, and temperature. A clear understanding of the interplay of these effects is not yet at hand. 

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... 

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