Tensile modulus, relationship with

Figures 20.13 and 20.14 describe the effect of dibutyltin dilaurate (DBTDL) on the tensile strength and tensile modulus for the 25/75 LCP/PEN blend fibers at draw ratios of 10 and 20 [13]. As expected, the addition of DBTDL slightly enhances the mechanical properties of the blends up to ca. 500 ppm of DBTDL. The optimum quantity of DBTDL seems to be about 500 ppm at a draw ratio of 20. However, the mechanical properties deteriorate when the concentration of catalyst exceeds this optimum level. From the previous relationships between the rheological properties and the mechanical properties, it can be discerned that the interfacial adhesion and the compatibility between the two phases, PEN and LCP, were enhanced. Hence, DBTDL can be used as a catalyst to achieve reactive compatibility in this blend system. This suggests the possibility of improving the interfacial adhesion between the immiscible polymer blends containing the LCP by reactive extrusion processing with a very short residence time.

For the majority of plastics (within the same group) the tensile modulus of elasticity increases approximately linearly with the degree of crystallinity [5], The data for linear and branched polymers follow the same approximate relationship. It is not clear whether the same molecular principles is applicable to WPCs (Table 8.13), but their tensile modulus of elasticity vary between different brands quite significantly. 

A typical example of recent studies of time-temperature-modulus relationships may be found in papers by Moehlenpah et al. (1970, 1971), who examined crosslinked epoxy resins filled with glass beads, fibers, or air bubbles. The initial tangent modulus in compression was seen to increase with a decrease in strain rate flexural and tensile moduli were reported to behave in a similar fashion. The WLF shift factor was essentially independent of the type of filler used and of the mode of loading. Kerner s equation was found to hold for the particulate composites in the glassy range. 

In the description of the basics of thermomechanical analysis in the first part of this section the mechanical properties were assumed to result from perfect elasticity, i.e., the stress is direcdy proportional to the strain and independent of the rate of strain. Hooke s law expresses this relationship with a constant modulus as sketched at the top of Fig. 4.157 for the example of tensile stress and strain. 

The main intention of the present contribution is to gain further inside into the relationship between disordered filler stmctures and the reinforcement of elastomers which is discussed mainly for the static and dynamic (shear or tensile) modulus. We will recognize that the classical approaches to (filled) mbber elasticity are not sufficient to describe the physics of such disordered systems. Instead, different theoretical methods have to be employed to deal with the various interactions and, consequently, reinforcing mechanisms on different length scales (see [1] and references therein). 

Figure 7.9 Effect of final heat treatment temperature on tensile modulus of PAN, mesophase and isotropic pitch fibers. PAN x MP1 [41] A MP2 IP [42]. Source Reprinted with permission from Matsumoto T, Mesophase pitch and its carbon fibers. Pure AppI Chem, 57(11), 1533,1985. Copyright 1985, Blackwell Publishers. Shen Z, Guo H etal, Carbon and Carbonaceous Composite Materials Stmclure-Property Relationship, Abstr and Proc, Malenovice, Czech Republic, 31, Oct 10-13,1995.

Source Reprinted with permission from Northolt MG, Veldhuizen LH, Jansen H, Tensile deformation of carbon fibres and the relationship with the modulus for shear between the basal planes. Carbon, 29,1267,1991. Copyright 1991, Elsevier. 

An interpolation procedure applied by Halpin and Tsai [17,18] has led to general expressions for the moduli of composites, as given by Eqs. (2.18) and (2.19). Note that for = 0, Eq. (2.18) reduces to that for the lower hmit, Eq. (2.8), and for = infinity, it becomes equal to the upper limit for continuous composites, Eq. (2.7). By empirical curve fitting, the value of = 2(l/d) has been shown to predict the tensile modulus of aligned short-fiber composites in the direction of the fibers, and the value of = 0.5 can be used for the transverse modulus. Other mathematical relationships for modulus calculations of composites with discontinuous fillers include the Takaya-nagi and the Mori-Tanaka equations [20]. 

In this paper, the BPDA-PFMB/PEI molecular composites were oriented by means of zone annealing/drawing slightly above the glass transition temperatures of the respective molecular composites (280 - 400 °C). The dependence of draw ratio on tensile modulus, crystal orientation, and birefringence was determined as a function of composition. The relationship between structure (crystal orientation) and tensile property (modulus) of drawn films has been examined by comparing crystal chain orientations with the prediction of affine deformation (12-16). 

It has been reported (5) that the elastic modulus of ABS resins prepared by either mass or emulsion polymerization can be represented by a single relationship with the dispersed phase volume fraction. This is in agreement with the theory that the modulus of a blend with dispersed spherical particles depends only on the volume fraction and the modulus ratio of particles to matrix phase. Since the modulus of rubber is almost 1000 times smaller than the modulus of the matrix SAN, the rubber particle volume fraction alone is the most important parameter controlling modulus values of ABS resins. Even for rubber particles containing a high occlusion level, as in ABS produced by mass polymerization, the modulus of the composite particle still remains imchanged from pure rubber, suggesting a unique relationship between modulus and dispersed phase volume fraction. Also, the modulus of a material is a small strain elastic property and is independent of particle size in ABS. The effects of rubber content on modulus and on tensile... 

Moduli of Binary Heterogeneous Blends. A linear stress-strain relationship, indispensable for modulus measurements, is granted only at very low strains, typically below 1%, where virtually all blends show interfacial adhesion sufficient for transmission of acting stress. At strains exceeding the hnearity limit, blend modulus (or compliance) decreases (or rises) with the strain. The tensile modulus of a two-component blend (Fig. 19) is given as (222)... 

This periodicity of about 500 nm has been reported for banded textures observed in both the thermotropic copolyesters and the aramids [407, 430, 439-445]. The lateral banded textures exhibited by some of the thermotropes and the pleated sheet textures exhibited by some of the aramids are observed only in materials which have a poorer degree of molecular orientation. The more highly oriented thermotropic and lyotropic fibers do not exhibit these textures. For instance, heat treated Vectran fibers do not exhibit any lateral banding. Likewise, Kevlar 149 exhibits a higher tensile modulus than Kevlar 49 [448], nearly 80-90% of theoretical predicted values. This is consistent with increased crystallinity and crystallite size, and without a pleated sheet structure. The relationship of the optical... 

Fig. 4 Relationship between extrudate (a) tensile modulus and (b) orientation parameter with die L/D. Samples prepared at extrusion temperatures 290°C (filled symbols) and 300 C (unfilled symbols) at draw ratio 4. Samples extruded from a 0.76-mm die at a wall shear rate of 720sec (Redrawn from Ref. 32.)...

FIfl. 5 Relationship between (a) tensile modulus, (b) tensile strength, and (c) orientation with spinline draw ratio of extrudate prepared using dies of L/D = 0.5 ( ), 10 (O). and 133 ( ) at extrusion temperature 290°C, Samples extruded from 0.76 mm-diameter dies at a wall shear rate of 720sec". (From Ref. 46.)... 

The relationship between tensile modulus and macromolecular orientation is plotted in Fig. 6 for these samples and along with the results of two other studies [34,43] to demonstrate similarity in results. No significant difference in the modulus-orientation angle relationship exists for samples prepared... 

Kontou and Spathis [44] carried out an investigation into the relationship between long-term viscoelasticity and viscoplastic responses of two types of ethylene-vinyl acetate metallocene-catalysed linear low-density polyethylene using DSC, DMTA and tensile testing. A relaxation modulus function with respect to time was obtained from values of relaxation spectra and treated as a material property. This relaxation modulus function was used to describe the corresponding tensile data and a constitutive analysis, which accounts for the viscoelastic path at small strains and the viscoplastic path at high strains, was employed to predict the tensile behaviour of the ethylene polymers (see also [45 9]). 

Some of the information in Tables 5.14 and 5.17 is shown graphically in Figures 5.7 and 5.8. The decrease in compressive strength and transverse tensile strength with increasing compressive and tensile moduli respectively is very marked. The relationship between tensile modulus and strength shows rather more scatter. 

Smith and Lemstra [186] studied the effect of molecular weight on the tensile strength of melt and solution spun, ultra drawn PE fibers. They showed that the tensile strength (s) and tensile modulus (E) of drawn fibers increases with molecular weight (Mw) based on an empirical relationship [186] ... 

With the rapid increase in numerical computing power, there have been attempts to formalize the different environmental contributions in order to provide a procedure to predict assembly durability (Crocombe 1997 Loh et al. 2002 Bordes et al. 2009). PigMre4S.IS shows a simple scheme. This is based on an initial identification of diffusion coefficients and mechanical parameters. The relationships between water content and properties such as tensile modulus, tensile strength, and interfacial fracture energy are then established. A coupled numerical model for the joint of interest is then constructed. This allows local water content to be defined and resulting changes in adhesive and interface properties to be predicted. At present, there are... 

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