Modulus values

Much more information can be obtained by examining the mechanical properties of a viscoelastic material over an extensive temperature range. A convenient nondestmctive method is the measurement of torsional modulus. A number of instmments are available (13—18). More details on use and interpretation of these measurements may be found in references 8 and 19—25. An increase in modulus value means an increase in polymer hardness or stiffness. The various regions of elastic behavior are shown in Figure 1. Curve A of Figure 1 is that of a soft polymer, curve B of a hard polymer. To a close approximation both are transpositions of each other on the temperature scale. A copolymer curve would fall between those of the homopolymers, with the displacement depending on the amount of hard monomer in the copolymer (26—28). 

The copolymer fiber shows a high degree of drawabiUty. The spun fibers of the copolymer were highly drawn over a wide range of conditions to produce fibers with tensile properties comparable to PPT fibers spun from Hquid crystalline dopes. There is a strong correlation between draw ratio and tenacity. Typical tenacity and tensile modulus values of 2.2 N/tex (25 gf/den) and 50 N/tex (570 gf/den), respectively, have been reported for Technora fiber (8). 

Content of Ot-Olefin. An increase in the a-olefin content of a copolymer results in a decrease of both crystallinity and density, accompanied by a significant reduction of the polymer mechanical modulus (stiffness). Eor example, the modulus values of ethylene—1-butene copolymers with a nonuniform compositional distribution decrease as shown in Table 2 (6). A similar dependence exists for ethylene—1-octene copolymers with uniform branching distribution (7), even though all such materials are, in general, much more elastic (see Table 2). An increase in the a-olefin content in the copolymers also results in a decrease of their tensile strength but a small increase in the elongation at break (8). These two dependencies, however, are not as pronounced as that for the resin modulus. 

Acoustic Measurements. Measurement of the propagation of ultrasonic acoustic waves has been found useful for determining the viscoelastic properties of thin films of adhesives. In this method, the specimen is clamped between transmitting and receiving transducers. The change in pulse shape between successive reverberation of the pulse is dependent on the viscoelastic properties of the transmitting material. Modulus values can be calculated (267,268). 

Fluids. The previous methods were designed for soHd specimens, although some can be used for fluids if a soHd support or carrier is used. The fluid must be highly viscoelastic for data to register, and absolute modulus values are difficult to determine because of the presence of the support. 

Different instmmentation is needed for the deterrnination of meaningful modulus values over wide viscosity and elasticity ranges. 

Although sealant manufacturer s Hterature commonly reports modulus values, these values must be interpreted carefully. Specimen sizes, test rate, cure conditions, and the time a sealant has been allowed to cure when tested can all have a significant effect on modulus. Therefore, for a tme comparison, sealants should be evaluated by a standard test that examines all sealants by the same procedure. In general, the longer a sealant has been allowed to cure, the more reaUstic the modulus data. 

Automated soldering operations can subject the mol ding to considerable heating, and adequate heat deflection characteristics ate an important property of the plastics that ate used. Flame retardants (qv) also ate often incorporated as additives. When service is to be in a humid environment, it is important that plastics having low moisture absorbance be used. Mol ding precision and dimensional stabiUty, which requites low linear coefficients of thermal expansion and high modulus values, ate key parameters in high density fine-pitch interconnect devices. 

The usefulness of this formula is restricted by the difficulty of obtaining good values to substitute in it. They must apply to the alloy selected, and be derived from carefully controlled tests on it. The stress value, S, reflects an engineer s Judgment in the selection of elastic limit or some arbitrary yield strength. The modulus value must match this. The restraint coefficent, K, is seldom known with any precision. 

On comparison of the yield strengths and elastic moduli of amorphous polymers well below their glass transition temperature it is observed that the differences between polymers are quite small. Yield strengths are of the order of 8000 Ibf/in (55 MPa) and tension modulus values are of the order of 500 000 Ibf/in (3450 MPa). In the molecular weight range in which these materials are used differences in molecular weight have little effect. 

The friction and wear of plastics are extremely complex subjects which depend markedly on the nature of the application and the properties of the material. The frictional properties of plastics differ considerably from those of metals. Even reinforced plastics have modulus values which are much lower than metals. Hence metal/thermoplastic friction is characterised by adhesion and deformation which results in frictional forces that are not proportional to load but rather to speed. Table 1.7 gives some typical coefficients of friction for plastics. 

A plastic beam is to be subjected to load for a period of 1500 hours. Use the 1500 hour modulus values given below and the data in Table 1.5 to decide which of the materials listed would provide the most cost effective design (on a stiffness basis). 

Consider the situation of a thin unidirectional lamina under a state of plane stress as shown in Fig. 3.9. The properties of the lamina are anisotropic so it will have modulus values of E and Ei in the fibre and transverse directions, respectively. The values of these parameters may be determined as illustrated above. 

In a short carbon fibre reinforced nylon moulding the volume ffacdon of the fibres is 0.2. Assuming the fibre length is much greater that the critical fibre length, calculate the modulus of the moulding. The modulus values for the fibres and nylon are 230 GN/m and 2.8 GN/m respectively. 

Shear modulus decreases rapidly in the preheated blends (Fig. 17) with an increase in Thiokol rubber. In the higher NBR region the two plots diverge, but they tend to converge at higher Thiokol levels. There is also a remarkable change in the trend observed at around 45-50% of Thiokol rubber. Preheating of the blend is accompanied by an increase in the shear modulus values. 

Table 5 compares the tensile properties of Vectra A950 in the form of dispersed fibers and droplets in the matrix by injection molding, microfibril by extrusion and drawing [28], injection molded pure thick sample and pure thin sample, and the pure drawn strand [28]. As exhibited, our calculated fiber modulus with its average of 24 GPa is much higher than that of the thick and thin pure TLCP samples injection molded. It can be explained that in cases of pure TLCP samples the material may only be fibrillated in a very thin skin layer owing to the excellent flow behavior in comparison with that in the blends. However, this modulus value is lower than that of the extruded and drawn pure strand. This can be... 

Figure 6 shows the shear modulus values for a series of neutral PAAm gels at different stages of deswelling [20]. The slopes of the dotted lines describing the deswelling of each sample are about 0.334, which perfectly agrees with the theory. 

This modulus value is often arbitrarily chosen, although several methods have been suggested for arriving at a suitable value. One is to plot a secant modulus based on 1% strain or that is 0.85% of the initial tangent modulus (Chapter 2, SHORT-TERM LOAD BEHAVIOR). However, for many plastics, particularly the crystalline TPs, this method is too restrictive, so in most practical situations the limiting strain is decided in consultation... 

In each case the section is designed to keep the deflection to less than 2 in. in 16 in. for a design life of 5 years and the extreme fiber stress is kept to a value less than the yield strength of the material. The first step in the analysis is to determine the necessary section to resist the bending load using the short-term tensile and compressive strength and modulus values. The extreme fiber stress is calculated for these sections to determine that the chair will not break when deflected. 

The frictional properties of TPs, specifically the reinforced and filled types, vary in a way that is unique from metals. In contrast to metals, even the highly reinforced plastics have low modulus values and thus do not behave according to the classic laws of friction. Metal-to-thermoplastic friction is characterized by adhesion and deformation resulting in frictional forces that are not proportional to load, because friction decreases as load increases, but are proportional to speed. The wear rate is generally defined as the volumetric loss of material over a given unit of time. Several mechanisms operate simultaneously to remove material from the wear interface. However, the primary mechanism is adhesive wear, which is characterized by having fine particles of plastic removed from the surface. 

FIGURE 20.12 (a) Top part shows variations of elastic modulus profile measured in different locations of the polypropylene (PP)-ethylene-propylene-diene terpolymer (EPDM) blend. The locations are shown by white dots in the blend phase image placed at the bottom. Vertical white dashed lines show the components borders and the elastic modulus value for this location. Vertical black dotted lines indicate the locations where elastic modulus E gradually changes between PP (E ) and EPDM (E )- These values are indicated with black arrows on the E axis, (b) LvP curves for PP-matrix, EPDM-domains, and one of interface locations. The approach curves are seen as solid black lines and the retract curves as gray lines. 

Tensile and Elongation. Samples of the belt wedge mbber, located between belts 1 and 2, were removed from both shoulders (serial side and opposite serial side) and buffed to a uniform thickness of 0.5-1.0 mm. Care was taken so that no signihcant heat was introduced to the samples by the buffing. Specimens were die-cut using an ASTM D 638 Type V dumbbell die and tested per ASTM D 412. Results obtained included modulus values at 100%, ultimate elongation, and tensile strength. Samples were tested at 20"/min (50.8 cm/min). 

Modulus of elasticity showed similar behaviour. Impregnated samples were found to have initially a higher modulus value than unimpregnated ones the decrease in modulus was less for the impregnated cements following the 88 days immersion in water. 

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