Modulus-composition curves

Figure 5. Modulus-composition curves for crass-polybutadiene-inier-cross-polystyrene semi-I and full IPNs (16). (a) Kerner equation (upper bound) (b) Budiansky model (c) Davies equation and (d) Kerner equation (lower bound). (Reproduced from ref. 23. Copyright 1981 American Chemical Society.)...

Plasticizer and Copolymerization change the glass transition temperature as discussed in Chapter 1. Plasticixers have little effect on Copolymerization can change although less strongly than 7 x. As a result, the basic modulus-temperature and modulus-time curves are shifted as shown in Figure 8 for different compositions. The shift in the modulus-temperature curve is essentially the same as the shift in TK. The shift in the modulus-time curve includes this plus the effect of any change in ()jr... 

Figure 8 Effect of plasticization or copolymerization on (A) the modulus-time and (B) modulus -temperature curves. The curves correspond to different plasticizer concentrations or to different copolymer compositions. Curve B is unplasticized homopolymer A is eithei a second homopolymer or plasticized B.

Figure 8 presents the storage and loss-modulus master curves obtained on all five samples of interest. The dashed lines indicate extensions of the master curves, using appropriately reduced data from the Rheovibron experiments in tension. Storage-modulus data in the rubbery plateau region vary systematically with composition, i.e., the... 

The temperature dependence of the relaxation modulus at 500 seconds of polycarbonate (7), polystyrene (8), and their blends (75/25, 50/50, and 25/75) was obtained from stress-relaxation experiments (Figure 4, full lines). In the modulus-temperature curves of the blends, two transition regions are generally observed in the vicinity of the glass-rubber transitions of the pure components. The inflection temperatures Ti in these transition domains are reported in Table I they are almost independent on composition. The presence of these two well-separated transitions is a confirmation of the two-phase structure of the blends, deduced from microscopic observations. 

Figure 13.22 Effect of crystallinity on the modulus-temperature curve. The numbers of the curves are rough approximations of the percentage of crystallinity. Modulus units = dynes/cm. (From Nielsen, L.E., Mechanical Properties of Polymers and Composites, Vol. 2, Marcel Dekker, New York, 1974. With permission.)...

Fig. 12.15 Modulus-temperature curves for two polyurethanes with different compositions. Note the two glass-transition temperatures for each polymer, corresponding to those of the hard and soft segments. (Adapted by permission of John Wiley Sons, Inc.)...

Thus far four composites listed in Table I have been studied. NbTi/Cu is discussed briefly here. From its microstructure and manufacture, a rectangular cross-section bar, it was assumed that this composite has orthorhombic (orthotropic) symmetry in its physical properties. Materials with this symmetry have nine independent elastic constants. While deviations from elastic behavior were small, nine independent elastic constants were verified. Four specimens were prepared (Fig. 16) and 18 ultrasonic wave velocities were determined by propagating differently polarized waves in six directions, (100) and (110). An example cooling run is shown in Fig. 17 for E33, Young s modulus along the filament axis. These data typify the composites studies a wavy, irregular modulus/temperature curve. 

Figure 3.31 shows temperature dependences of viscous-elastic functions of composites that include 45 vol% waterglass with various sihca modulus. Comparing curves 4 and 5 (M = 3 and M = 1.42), note that increase of sihca modulus leads to increase in the elastic modulus of the composite. 

Figure 12.2. Dependence of relative modulus (composite/polymer) on concentration for (A) the original Kerner equation (B) the modified Kerner equation (C) the Mooney equation. Circles correspond to experimental results. Solid curves are calculated with v = 0.35, Gf/Gp (relative modulus filler/polymer) = 25, and = 0.64.

The effect of temperature on the mechanical response of the polymer-leather composites remains to be treated. In Figure 20 are shown the torsional modulus-temperature curves for the three... 

From the relations among the viscoelastic functions, it follows that multiplication of any modulus function—(7"(w), G(l), E(t), etc.—by coTq/cT and plotting against war or will combine measurements at various temperatures to give a single composite curve which represents reduction of the data to Tq. Correspondingly, any compliance function multiplied by cT/cqTo can be reduced in a similar manner. Multiplication by the concentration-temperature ratio is often denoted by the subscript p. It should be emphasized that the ratio co/c differs from unity by only a very small amount associated with thermal expansion. 

The curves representing the temperature dependence of the real part of the complex modulus E curves measured by DMA are summarized in Figure 5 and Figure 6 for composite A and B respectively. In the above mentioned figures the reported curves are relative to both [0°] and [ 45 ]i4 lay up s. The tanS and E curves are not shown in the figures. The [ 45°]i4 specimens were submitted to successive DMA scans in order to check whether the Tg has changed after the heavy thermal treatment experienced by the sample in the first run (the maximum temperature reached was 250°C). 

The simply supported beam has a load applied centrally. The upper skin go into compression while the lower one goes into tension, and a uniform bending curve will develop. However, this happens only if the shear rigidity or shear modulus of the cellular core is sufficiently high. If this is not the case, both skins will deflect as independent members, thus eliminating the load-bearing capability of the plastic composite structure. 

---