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A constitutive model for rubbers providing temperature dependent behavior and self-heating
Published in Bertrand Huneau, Jean-Benoit Le Cam, Yann Marco, Erwan Verron, Constitutive Models for Rubber XI, 2019
The mechanical characteristics of rubber vary with temperature. For unfilled systems, Rey et al. (2013) experimentally confirm that the stiffness of elastomers above glass transition is nearly proportional to the absolute temperature ϑ. This can be explained by the entropic origin of rubber elasticity. Treloar (1973) gives a summary of the contributions that lead to the so-called kinetic theory of rubber. Figure 1 compares tensile tests of the rubber compound under investigation for -20°C and 80°C. Five repetitions at seven ascending amplitudes were performed on a static testing machine. The material exhibits a rather stable material stiffness in a broad temperature range. Further, all forms of inelasticity, such as set, hysteresis and strain- induced softening, are less pronounced at higher temperature.
Polymeric Materials
Published in Heinz K. Müller, Bernard S. Nau, Fluid Sealing Technology, 2019
Heinz K. Müller, Bernard S. Nau
The cross-links are formed during the curing process and limit the deformation that occurs when the material is under load. The thermal motion of the chain segments between cross-links provides the restoring force when the elastomer is strained. Curing is the chemical reaction that forms the cross-links, which are usually strong covalent bonds, and normally takes place in a metal mold at elevated temperature and pressure. FPM and FFPM, and sometimes other elastomers, also require a post-cure, during which they are heated to yet higher temperature at atmospheric pressure for some hours. This allows reaction gases to diffuse out. Examples of curing agents are organic peroxides (peroxide cure), amines, sulfur (the original vulcanising agent used for natural rubber), and bisphenols (in fluoroelastomers). The density of cross-linking affects the elastomer properties and is largely determined by the amount of curing agent used; properties are also affected by the choice of the curing agent. The nature of the relationship between cross-link density and elastic modulus was demonstrated in the discussion of constitutive models of rubber elasticity.
Phase and State Transitions and Transformations in Food Systems
Published in Dennis R. Heldman, Daryl B. Lund, Cristina M. Sabliov, Handbook of Food Engineering, 2018
In the glassy region, amorphous polymers are solid and brittle, and their modulus is fairly constant at 3 × 109 Pa (Sperling, 1992) or higher. Within the glass transition region, the modulus decreases by a factor of 103 over a temperature range of 20°C–30°C, although much variation of the glass transition temperature range is found across materials. The stiffness of amorphous materials in the glass transition region is very sensitive to changes in temperature, but the extent of the change in modulus is dependent on a number of factors, such as molecular weight, crystallinity, and the extent of cross-linking. The glass transition region represents the onset of long-range, coordinated molecular motions. The rubbery plateau (or viscous flow) region has not received much attention in the characterization of food materials, although its characterization is fundamental in the control of food solids properties and structure-properties relationships in food processing and storage. The rubbery plateau follows the glass transition of polymers, as their modulus levels off at an almost constant value of 2 × 106 Pa. For linear polymers, often the higher the molecular weight, the broader the rubbery plateau, although modulus increases with increasing crystallinity. Many amorphous, low molecular weight sugars and foods are transformed very rapidly to viscous liquids, syrups, or molasses, and they exhibit no rubbery plateau (Talja and Roos, 2001; Roos, 2010). Cross-linking improves rubber elasticity of polymers and extends their rubbery plateau. When polymers reach their rubbery flow region, they exhibit rubber elasticity at very short experimental times but flow in a long experiment. This region is followed by the liquid flow region in which polymers behave like molasses (Sperling, 1992). Obviously, low molecular weight food components are transformed extremely rapidly from the solid glassy state to the liquid flow region, and much discussion has taken place on the properties of amorphous water (Angell, 2014), the most important food component and plasticizer.
3D/4D-printed bending-type soft pneumatic actuators: fabrication, modelling, and control
Published in Virtual and Physical Prototyping, 2020
Ali Zolfagharian, M. A. Parvez Mahmud, Saleh Gharaie, Mahdi Bodaghi, Abbas Z. Kouzani, Akif Kaynak
Hyperelastic materials with high flexibility and capability of withstanding large strains, such as silicone and thermoplastic elastomers, are the most common materials used in the fabrication of 3D/4D-printed SPAs (Moseley et al. 2016). These materials demonstrate rubber elasticity with quite large and reversible nonlinear deformation, several times of their initial length, under a relatively low force. Their mechanical behaviour cannot be characterised by a constant elastic modulus (highlighted in Figure 10). They possess incompressible characteristics, which makes them retain their overall volume under applied stress (Hu et al. 2018; Hu 2019). The mechanical behaviour of hyperelastic materials is complex therefore warranting constitutive mathematical strain energy function models to be employed to predict their elastic behaviour via tensile test experimental data (Rivlin 1948; Ogden 1972; Ponte Castaneda 1989; Gent 1996). To estimate the nonlinear large deformation of these materials using FEA various strain energy models were employed and compared (Drozdov 2007; Kim et al. 2012; Marckmann and Verron 2006). Yet, not a single best model was reported as the selection of the best model is subjective to the application, and the material used in the SPA. Isotopic hyperelasticity models, including, Arruda-Boyce (Arruda and Boyce 1993) and Blatz-Ko, (Blatz and Ko 1962) were developed based on the incompressible hyperelastic material response at the molecular scale, while other models, including Mooney-Rivlin (Rivlin 1948), Ogden (Ogden 1972), Neo-Hookean (Ponte Castaneda 1989), and Yeoh (1993) reflect the rubber-like behaviour of these materials, known as extended-tube models. Further details of the comparison of these models are discussed in the following.