Linear mechanical properties

S. K. Georgantzinos, G. I. Giannopoulos, D. E. Katsareas, P. A. Kakavas, N. K. Anifantis, Size-dependent non-linear mechanical properties of graphene nanoribbons., Computational Materials Science, vol. 50, pp. 2057-2062, 2011. 

Linear mechanical properties of the networks and gels discussed in this chapter are measured with the same methods of linear viscoelasticity as the polymer liquids (melts and solutions) discussed in Chapters 8 and 9. The various methods are described here, with examples pertaining to each class of materials. 

Non-linear mechanical properties were observed for rubber eomposites and referred to as the Payne effect. The Payne effeet was interpreted as due to filler agglomeration where the filler clusters formed eontained adsorbed rubber. The occluded rubber molecules within filler elusters eould not eontribute to overall elastic properties. The composites behaved similarly to rubber composites with higher filler loading. Uniform and stable filler dispersion is required for rubber composites to exhibit linear viscoelastic behaviour. Payne performed dielectric measurements on SBR vulcanizates containing silica or carbon black. The dielectric data were used to construct time-temperature superposition master curves. The reference temperature increased with crosslinking but not significantly with filler. Comparison of dynamic mechanical and dielectric results for the SBR blended with NR was made and interpreted. ... 

The above-mentioned complexity of the relationships between the structure and properties of textiles is further complicated by the non-linear mechanical properties of individual fibres caused by their visco-elastic behaviour, friction between fibres and threads, anisotropy, and statistical distribution of all properties. Modelling such complex materials requires application of a combination of experimental, analytical, and numerical methods, which will be considered in this chapter. 

When using rubbers, non-linear mechanical properties are encountered in all situations of practical interest. Rubbers exhibit large deformations even under comparatively weak external forces and thus are mostly found outside the range of small strains. 

The famous Williams-Landell-Ferry (WLF) equation [13] is useful for describing the temperature dependence of several linear mechanical properties of polymers (see Chapter 16). For the zero-shear viscosity, it may be written as... 

Most properties of linear polymers are controlled by two different factors. The chemical constitution of tire monomers detennines tire interaction strengtli between tire chains, tire interactions of tire polymer witli host molecules or witli interfaces. The monomer stmcture also detennines tire possible local confonnations of tire polymer chain. This relationship between the molecular stmcture and any interaction witli surrounding molecules is similar to tliat found for low-molecular-weight compounds. The second important parameter tliat controls polymer properties is tire molecular weight. Contrary to tire situation for low-molecular-weight compounds, it plays a fimdamental role in polymer behaviour. It detennines tire slow-mode dynamics and tire viscosity of polymers in solutions and in tire melt. These properties are of utmost importance in polymer rheology and condition tlieir processability. The mechanical properties, solubility and miscibility of different polymers also depend on tlieir molecular weights. 

Normalised fiber mechanical properties are expressed in terms of unit linear density. For example, in describing the action of a load on a fiber in a tensile test, units of N/tex or gram force per denier (gpd) are generally used. If this is done, the term tenacity should be used in place of stress. The tme units of stress are force per unit cross-sectional area, and the term stress should be reserved for those instances where the proper units are used. 

The first commercial PPS process by Phillips synthesized a low molecular weight linear PPS that had modest mechanical properties. It was usehil in coatings and as a feedstock for a variety of cured injection-molding resins. The Phillips process for preparing low molecular weight linear PPS consists of a series of nucleophilic displacement reactions that have differing reactivities (26). 

In addition to chemical analysis a number of physical and mechanical properties are employed to determine cemented carbide quaUty. Standard test methods employed by the iadustry for abrasive wear resistance, apparent grain size, apparent porosity, coercive force, compressive strength, density, fracture toughness, hardness, linear thermal expansion, magnetic permeabiUty, microstmcture, Poisson s ratio, transverse mpture strength, and Young s modulus are set forth by ASTM/ANSI and the ISO. 

Linear polyethylene (high density) was introduced in the late 1950s, with the development of coordination catalysts. Chlorosulfonation of these base resins gave products that were superior to the eadier, low density types in both chemical resistance and mechanical properties and with distinct advantages in mbber processibiUty (6,7). 

Figure 11.7 shows how the mechanical properties of normalised carbon steels change with carbon content. Both the yield strength and tensile strength increase linearly with carbon content. This is what we would expect the FejC acts as a strengthening phase, and the proportion of FojC in the steel is linear in carbon concentration (Fig. 11.6a). The ductility, on the other hand, falls rapidly as the carbon content goes up (Fig. 11.7) because the a-FejC interfaces in pearlite are good at nucleating cracks.

The above measurements all rely on force and displacement data to evaluate adhesion and mechanical properties. As mentioned in the introduction, a very useful piece of information to have about a nanoscale contact would be its area (or radius). Since the scale of the contacts is below the optical limit, the techniques available are somewhat limited. Electrical resistance has been used in early contact studies on clean metal surfaces [62], but is limited to conducting interfaces. Recently, Enachescu et al. [63] used conductance measurements to examine adhesion in an ideally hard contact (diamond vs. tungsten carbide). In the limit of contact size below the electronic mean free path, but above that of quantized conductance, the contact area scales linearly with contact conductance. They used these measurements to demonstrate that friction was proportional to contact area, and the area vs. load data were best-fit to a DMT model. 

The mechanical properties can be studied by stretching a polymer specimen at constant rate and monitoring the stress produced. The Young (elastic) modulus is determined from the initial linear portion of the stress-strain curve, and other mechanical parameters of interest include the yield and break stresses and the corresponding strain (draw ratio) values. Some of these parameters will be reported in the following paragraphs, referred to as results on thermotropic polybibenzoates with different spacers. The stress-strain plots were obtained at various drawing temperatures and rates. 

A polymer molecule may have just a linear chain or one or more hranches protruding from the polymer hackhone. Branching results mainly from chain transfer reactions (see Chain Transfer Reactions later in this chapter) and affects the polymer s physical and mechanical properties. Branched polyethylene usually has a few long hranches and many more short hranches... 

Mechanical properties of plastics are invariably time-dependent. Rheology of plastics involves plastics in all possible states from the molten state to the glassy or crystalline state (Chapter 6). The rheology of solid plastics within a range of small strains, within the range of linear viscoelasticity, has shown that mechanical behavior has often been successfully related to molecular structure. Studies in this area can have two objectives (1) mechanical characterization of... 

One of the main methods for improving the mechanical properties of linear polymers is their drawing that can be uniaxial (fibres), biaxial (films), planar symmetrical (films-membranes) etc. As a result of polymer deformation, the system changes into the oriented state fixed by crystallization. 

Since these double-base proplnts consist essentially of a single phase which bears the total load in any application of force, their mechanical property behavior is significantly different from composite proplnts. In the latter formulations, the hydrocarbon binder comprises only about 14% of the composite structure, the remainder being solid particles. Under stress, the binder of these proplnts bears a proportionately higher load than that in the single phase double-base proplnts. At small strain levels, these proplnts behave in a linear viscoelastic manner where the solids reinforce the binder. As strain increases, the bond between the oxidizer and binder breaks down... 

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