Fillers modulus

The model for a filled system is different. The filler is, as before, represented by a cube with side a. The cube is coated with a polymer film of thickness d it is assumed that d is independent of the filler concentration. The filler modulus is much higher than that of the d-thick coat. A third layer of thickness c overlies the previous one and simulates the polymeric matrix. The characteristics of the layers d and c are prescribed as before, and the calculation is carried out in two steps at first, the characteristics of the filler (a) - interphase (d) system are calculated then this system is treated as an integral whole and, again, as part of the two component system (filler + interphase) — matrix. From geometric... 

Poor mechanical properties of rubber products may also be due to matrix separation [257], Just as in other systems, separation gives rise to cavities and initiates failure. These processes prevail in systems with poor adhesion and become more probable with the increasing filler modulus. 

Ep/E = modulus of filler/modulus of unfilled elastomer

volume fraction of filler... 

Young s Modulus. The Young s modulus, Ec, of the composite can be calculated from the matrix modulus, Em, the filler modulus, Ef, and the volume... 

Until recently, little attention has been given to predicting the modulus of polyblends. The first obvious distinction between polyblends and composites is that whereas the ratio of filler modulus to polymer modulus in composites is typically greater than 20, (20) the ratio of moduli for polyblends is very nearly equal to unity. For this reason of component modulus equivalency in polyblends, the form of the dependence of polyblend moduli on blend composition may be difficult to model in any meaningful manner within the limitation of typical scatter of experimental data. 

In the list, issues are defined in pragmatic engineering terms, but other aspects will be considered soon. Let as start from the third, the most general problem. Practically all previous theories, explicitly or as a silent aspect (to be accepted per se, implicitly), include condition that filler modulus... 

Concerning the modulus evaluatirai of the fillers is always problematic. The modulus has been evaluated. Different composites had been processed with increasing LCFo i content. The fillers modulus has been estimated by fitting a semiempiri-cal Halpin-Tsai model on the evolution of the composites Young s modulus as a function of fillers volume fraction. By extrapolation at 100% of fillers, we obtain the filler modulus which is estimated at 6.7 GPa. This value is coherent with wheat straw data given in the literature (Hornsby et al. 1997 KrtMibergs 2000). 

Unlike in the case of spherical inclusions where the rigid inclusions cause stiffening of the composite by excluding volume of a deformable mattix, the presence of an interphase layer affects the tme reinforcing efficiency of the inclusions. Hence, the effective filler modulus of the inclusions have to be calculated as a function of interphase thickness and elastic modulus. This can be done effectively using simple rule of mixture ... 

Modulus is the characterization of a rigid material. The elasticity modulus of plastic products made from pure resin is low, even for polyesters and polyamides with relatively higher elastic moduli, which is only 2.5%-10% of the metal elasticity modulus. The modulus of elasticity of filled plastics always increases with the addition of filler because the filler modulus is much larger than the modulus of polymers. For example, when 40 phr of magnesium sulfate whiskers are added to PVC, the breaking strength of the composite material increases by 62.43% and the modulus of elasticity increases by 52.38%.2o... 

Table 3 Experimentally measured (ySt) and theoretically predicted (y ax) positions of the stress overshoot as well as effective filler modulus (Gf) as functions of weight fraction ...

In Figure 5.23 the finite element model predictions based on with constraint and unconstrained boundary conditions for the modulus of a glass/epoxy resin composite for various filler volume fractions are shown. 

Resins filled with ground limestone to levels of 80% by weight are useful in soHd cast products. The fillers reduce sensitivity to brittle fracture and improve modulus, but have Httle effect on general strength properties (Table 8). 

Filler loading Volume, parts Mooney viscosity Optimum cure (at 141°C), min Modulus (at 300%), MPa Tensde strength, MPa Elongation, % Hardness, Shore A NBS abrasion (ASTMD1630) Rebound, %... 

Another difference between hot and cold elastomeric SBR latices is that hot types are carried to < 90% conversion and not normally shortstopped. The cold latices are usually shortstopped at ca 60—80% conversion. Again the desired physical properties of the contained copolymer are responsible for these differences. Cold latices are used in applications where the modulus, eg, in foam, or retention of physical properties at high filler loadings, eg, in fabric backing, are required. The cold latices are generally suppHed at a higher soHds concentration than the hot series because of these uses. 

Particulate fillers are divided into two types, inert fillers and reinforcing fillers. The term inert filler is something of a misnomer as many properties may be affected by incorporation of such a filler. For example, in a plasticised PVC compound the addition of an inert filler will reduce die swell on extrusion, increase modulus and hardness, may provide a white base for colouring, improve electrical insulation properties and reduce tackiness. Inert fillers will also usually substantially reduce the cost of the compound. Amongst the fillers used are calcium carbonates, china clay, talc, and barium sulphate. For normal uses such fillers should be quite insoluble in any liquids with which the polymer compound is liable to come into contact. 

When employed in elastomeric systems it is commonly observed that the finer the particle size the higher the values of such properties as tensile strength, modulus and hardness. Coarser particles will tend to give compounds less strong than compounds with the filler absent, but if the particle size is sufficiently fine there is an enhancement in the above-mentioned properties (at least up to an optimum loading of filler) and the phenomenon is known as reinforcement. The particle shape also has an influence for example, the somewhat plate-like china... 

Fibrous fillers are often embedded in a laminar form. The fibres used have higher moduli than the resins in which they are embedded so that when the composite of resin plus fibre is strained in the plane of the fibrous layer the bulk of the stress is taken up by the fibre. This results in an enhancement of both strength and modulus when compared with the unfilled resin. 

Excellent mechanical properties with very high values for tensile strength, flexural strength and modulus in the flow direction. This applies to unfilled materials and may be further enhanced by incorporation of fibrous fillers. Quoted data for these properties are in the following ranges ... 

Such is the anisotropy that flexural modulus may be four times as high in the flow direction as in the transverse directions. This difference may be reduced by incorporating fillers such as glass fibre or mica. 

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