Modulus-Temperature Relations

As the temperature is raised the thermal agitation becomes sufficient for segmental movement and the brittle glass begins to behave in a leathery fashion. The modulus decreases by a factor of about 10- over a temperature range of about I0-20°C in the glass-to-rubber transition region. 

Modulus-temperature behavior of amorphous polymers is also affected by admixture with plasticizers. These are the soluble diluents described briefly in Section 12.3.2. As shown in Fig. 11-11, the incorporation of a plasticizer reduces Tg and makes the polymer more flexible at any temperature above Tg. In polyfvinyl chloride), for example, T can be lowered from about 85°C for unplaslicized material to —30°C for blends of the polymer with 50 wt % of dioctyl phthalate plasticizer. A very wide range of mechanical properties can be achieved with this one polymer by variations in the type and concentration of plasticizers. 

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Fig. 11-10. Modulus-temperature relations for amorphous and partially crystalline versions of the same polymer.

Modulus-temperature relations for amorphous polymers in static test reveal a sharp drop of modulus in the glass-to-rubber transition region (see Figure 1.19). Since the storage modulus G (oj) behaves like a modulus measured in a static test, it decreases in the glass transition region. However, the loss modulus G"((jj) and tan 6 go through a maximum under the same conditions. 

Fig. 11-9. Effect of cross-linking on modulus-temperature relation for an amorphous polymer.

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

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. 

Thus all the different temperature related data in Fig. 2.58 could be shifted to a single master curve at the reference temperature (7 ). Alternatively if the properties are known at Tref then it is possible to determine the property at any desired temperature. It is important to note that the shift factor cannot be applied to a single value of modulus. This is because the shift factor is on the horizontal time-scale, not the vertical, modulus scale. If a single value of modulus 7, is known as well as the shift factor ar it is not possible to... 

A common feature of the three PTEB samples is that the yield stress decreases as the drawing temperature increases (Table 2), whereas it does not change significantly with the strain rate. The Young modulus does not change with the strain rate but it decreases and the break strain increases as the drawing temperature increases. The main conclusion is that the behavior of PTEB-RT is intermediate between the other two samples, with the advantage of a considerable increase in the modulus in relation to sample PTEB-Q and without much decrease in the break strain (Table 2). 

The general need is to understand the response of a material to an applied stress. The stress may be applied externally or induced by altering other parameters such as temperature (which can cause a phase transformation). The fundamental idea is the link to bonding. In Chapter 4 we described how the Young s modulus is related directly to the bond-energy curve. In Chapter 12 we described the nature of dislocations in ceramics. 

Figure 2.39 shows the response of the modulus to stress. The nylon fibers are characterized by an initial modulus at elongation —> 0 that is proportional to the ratio at which the fibers were drawn. This initial modulus is related to the glass transition temperature of the amorphous region and consequently to the mobility of the chain segments in these regions. It depends therefore on factors such as temperature and water content, which affect the mobility of the chain segments. 

Forced-vibration instruments drive specimens at specific frequencies and determine the response, usually over a range of temperatures. Storage and loss moduli or related parameters are determined. Series of modulus-temperature curves can be generated by making measurements at several different fi equencies. Because thermal and mechanical transitions are functions of frequency as well as temperature, data from such curves can be used to calculate activation energies of transitions. In addition, frequencies can be chosen to represent or approximate polymer processing effects and use conditions. 

The inclusion of rubber in polymers does, nevertheless, reduce the elastic modulus and the yield stress [53]. The phase separation between the polymer and the rubber is an important requirement, and mechanical resistance increases if the rubber has low elastic modulus in relation to the matrix, good adhesion to the matrix, adequate crosslinking, optimized average particle size and distribution, and low glass transition temperature [54]. The separating distance between the elastomeric zones also plays an important role in the toughening mechanisms. 

Bulk Modulus. Bulk modulus (K) at room temperature is about 106 to 108 GPa (15.4 to 15.7 X 10 psi) for pure titanium. The bulk modulus is related to Young s modulus as follows ... 

Walters reached a similar conclusion from his experimental results. He obtained the friction-temperature relations at constant sliding speed. The temperature of maximum friction at a constant speed, increases linearly with the glass transition temperature. It appeared however, that in a graphical plot of the linear relation the point corresponding to the results obtained with butyl rubber falls distinctly outside the line. In our work with butyl rubber such an anomalous behaviour has been confirmed. Instead of relating the speed of maximum friction to Tg, Grosch related it to the frequency at which the loss modulus is a maximum. That correlation has been found to be valid to several rubbers includ ing butyl rubber. On the other hand, it is not surprising to expect that besides Tg, there are other parameters which have an important influence upon friction properties. 

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