Rubber viscoelasticity

Simulation of the Couette flow of silicon rubber - viscoelastic model... 

It is known that, in contrast to plastics, rubber chains break down only when they are fully stretched (Kinloch and Young, 1983 Kausch, 1987). An ultrasonic field creates high frequency extension-contraction stresses in crosslinked media. Therefore, the effects of rubber viscoelasticity have been incorporated into the description of dynamics of cavitation (Yashin and Isayev, 1999, 2000). The devulcanization of the rubber network can occur primarily around pulsating cavities due to the highest level of strain produced by the power ultrasound (Yashin and Isayev, 2000). 

Abstract The present chapter is written as an introduction towards this book on nonlinear viscoelasticity of rubber composites and nanocomposites. Rather than introducing the concept of the book to the readers this chapter reveals the basics behind rubber viscoelasticity and explains both linearity and nonlinearity from this behavior. Various filler reinforced rubbers are introduced emphasising the flow behavior of such nanocomposites. Major mathematical models proposed by Kraus, Huber and Vilgis and Maier and Goritz for the Payne Effect are briefly addressed based on the filler matrix interactions existing in the composite systems. 

Lubliner J (1985) A model of rubber viscoelasticity. Mech Res Commun 12 93-99... 

Raos G, Moreno M and Elli S (2006) Computational experiments on filled rubber viscoelasticity What is the role of particle-particle interactions , Macromolecules 39 6744-6751. 

The radiation and temperature dependent mechanical properties of viscoelastic materials (modulus and loss) are of great interest throughout the plastics, polymer, and rubber from initial design to routine production. There are a number of laboratory research instruments are available to determine these properties. All these hardness tests conducted on polymeric materials involve the penetration of the sample under consideration by loaded spheres or other geometric shapes [1]. Most of these tests are to some extent arbitrary because the penetration of an indenter into viscoelastic material increases with time. For example, standard durometer test (the "Shore A") is widely used to measure the static "hardness" or resistance to indentation. However, it does not measure basic material properties, and its results depend on the specimen geometry (it is difficult to make available the identity of the initial position of the devices on cylinder or spherical surfaces while measuring) and test conditions, and some arbitrary time must be selected to compare different materials. 

Petera, J. and Nassehi, V., 1996. Finite element modelling of free surface viscoelastic flows with particular application to rubber mixing. Int. J. Numer. Methods Fluids 23, 1117-1132. 

Keeping all of the flow regime conditions identical to the previous example, we now consider a finite element model based on treating silicon rubber as a viscoelastic fluid whose constitutive behaviour is defined by the following upper-convected Maxwell equation... 

International Rubber Hardness. The International mbber hardness test (ASTM D1415) (2) for elastomers is similar to the Rockwell test ia that the measured property is the difference ia penetration of a standard steel ball between minor and major loads. The viscoelastic properties of elastomers require that a load appHcation time, usually 30 seconds, be a part of the test procedure. The hardness number is read directly on a scale of 0 to 100 upon return to the minor load. International mbber hardness numbers are often considered equivalent to Durometer hardness numbers but differences ia iadenters, loads, and test time preclude such a relationship. 

In the earlier art, there was some consideration that partial incompatibility of the tackifier resin with the rubber was responsible for the appearance of tack, but this no longer is seriously held in light of continuing studies by many investigators. Aubrey [38] has addressed this in his review of the mechanism of tackification and the viscoelastic nature of pressure sensitive adhesives. Chu [39] uses the extent of modulus depression with added tackifier as a measure of compatibility. Thus in a plot of modulus vs. tackifier concentration, the resin that produces the deepest minimum is the most compatible. On this basis, Chu rates the following resins in order of compatibility for natural rubber rosin ester > C-5 resin > a-pinene resin > p-pinene resin > aromatic resin. 

Tackifying resins enhance the adhesion of non-polar elastomers by improving wettability, increasing polarity and altering the viscoelastic properties. Dahlquist [31 ] established the first evidence of the modification of the viscoelastic properties of an elastomer by adding resins, and demonstrated that the performance of pressure-sensitive adhesives was related to the creep compliance. Later, Aubrey and Sherriff [32] demonstrated that a relationship between peel strength and viscoelasticity in natural rubber-low molecular resins blends existed. Class and Chu [33] used the dynamic mechanical measurements to demonstrate that compatible resins with an elastomer produced a decrease in the elastic modulus at room temperature and an increase in the tan <5 peak (which indicated the glass transition temperature of the resin-elastomer blend). Resins which are incompatible with an elastomer caused an increase in the elastic modulus at room temperature and showed two distinct maxima in the tan <5 curve. 

There are several ways in which the impact properties of plastics can be improved if the material selected does not have sufficient impact strength. One method is by altering the composition of the material so that it is no longer a glassy plastic at the operating temperature of the product (Chapter 6). In the case of PVC this is done by the addition of an impact modifier which can be a compatible plastic such as an acrylic or a nitrile rubber. The addition of such a material lowers the glass transition temperature and the material becomes a rubbery viscoelastic plastic with much improved impact properties. This is one of the methods in which PVC materials are made to exhibit superior impact properties. 

When rubbers eventually fracture, they do so by tearing. Fracture surface energies, using the Griffith equation, have been found to be of the order of 10 J m , whereas the true surface energies are only 0.1-1.0 J Hence, more energy is involved in fracture than is required to form new surfaces, and, as with other polymers, this extra energy is assumed to be used up in viscoelastic and flow processes that occur between the molecules immediately before the rubber breaks. 

Dynamic mechanical measurements for elastomers that cover wide ranges of frequency and temperature are rather scarce. Payne and Scott [12] carried out extensive measurements of /a and /x" for unvulcanized natural mbber as a function of test frequency (Figure 1.8). He showed that the experimental relations at different temperatures could be superposed to yield master curves, as shown in Figure 1.9, using the WLF frequency-temperature equivalence, Equation 1.11. The same shift factors, log Ox. were used for both experimental quantities, /x and /x". Successful superposition in both cases confirms that the dependence of the viscoelastic properties of rubber on frequency and temperature arises from changes in the rate of Brownian motion of molecular segments with temperature. 

Adsorption of rubber over the nanosilica particles alters the viscoelastic responses. Analysis of dynamic mechanical properties therefore provides a direct clue of the mbber-silica interaction. Figure 3.22 shows the variation in storage modulus (log scale) and tan 8 against temperature for ACM-silica, ENR-silica, and in situ acrylic copolymer and terpolymer-silica hybrid nanocomposites. 

Better cross-linking with the latter also improves post Tg viscoelastic responses of the rubber vulcanizates. Similar effect has also been observed with polychloroprene as investigated by Sahoo and Bhowmick [41]. Figure 4.8 represents the comparative tensile stress-strain behavior of polychloroprene rubber (CR) vulcanizates, highlighting superiority of the nanosized ZnO over conventional rubber grade ZnO [41]. 

Puskas, J.E., Paulo, C., and Altstadt, V. Mechanical and Viscoelastic Characterization of Hyperbranched Polyisobutylenes. Paper 76, ACS Rubber Division,160th Technical Meeting, October 16-19, Cleveland, OH, 2001. 

The specimen was prepared by the following method. After mixing HAF carbon black (50 phr) with natural rubber (NR) in a laboratory mixer, carbon gel was extracted from unvulcanized mixture as an insoluble material for toluene for 48 h at room temperamre and dried in a vacuum oven for 24 h at 70°C. We made the specimen as a thin sheet of the carbon gel (including carbon black) by pressing the extracted carbon gel at 90°C. The cured specimen was given by adding sulfur (1.5 phr) to the unvulcanized mixture and vulcanized for 30 min at 145°C. The dynamic viscoelastic measurement was performed with Rheometer under the condition of 0.1% strain and 15 Hz over temperatures. 

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

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