Dvořák, Zdeněk

Javořík, Jakub

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Chem. Listy 105, s233-s416 (2011) PMA 2011 & RubberCon 2011 Contributed Lectures Comparison of Young's modulus at BO°C 200 _,____~~~~~~~~~~~~~~~~~~ 180 +-~~~~~~~~~~~~~~~~-160 +-~~~~~~~~~~-+~-~ 140 ~~~--·~~~-I w 120 100 801-----~~~~_,____~-~~~~~-~~~~~~ Amount of crosslinked HOPE filler [%] Fig. 3. Comparison of modnlns of elasticity for mixtures of virgin LDPE and crosslinked HDPE at 80 °C Comparison of tensile strength at 80°C 140 135 +-~~~--·-~~~~--~~~~~~--T---130 +-~~~~~~~~~~~~~~~-I 125 +-~~~~---~~~~~~-.--~-+-~-Z 120 g. 115 110 +-~~~--~~~-+-~-105 +-~~~--I~~-100 +----+~~-"!II""---~-95 Amount of crosslinked HOPE filler [%] Fig. 4. Comparison of tensile strength for mixtures of virgin LDPE and crosslinked HDPE at 80 °C Opposite to this, higher amount of filler comes a In-crease tensile strength and modulus of elasticity. Another good result is the possibility of mixture LDPE and HDPE which are in normal state miscible with difficul-ties. . These results are significant for both the engineering practice, where product price can be reduced by the filler addition with increase in their properties, furthermore thus contribute to . a possibility of recycling the radiation cross-linked products and also consequently for the consumer. This article is financially supported by the Czech Ministry of Education, Youth and Sports in the R&D projects under the titles 'Modeling and Control of Processing Procedures of Natural and Synthetic Polymers', No. MSM 7088352102 and 'CEBIA Tech', No. CZ.l.0512.l.00103.0089 REFERENCES 1. Woods R. 1: Applied radiation chemistry: radiation processing, 1994. 2. Zyball A.: Strahlungsenergie zur Modification von Kunststoffen - Industrielle Anwendungen der Bestrah-s273 lungstechnik, In: Strahlenvemetzte Kunstoffe, Springer VDI verlag, Dusseldorf 2006. 3. Drobny J. G.: Radiation Technology for Polymers, CRC Press, Boca Raton 2003. 4. BGS - Beta-Ga=a-Service. [online]. http://www.bgs.de CL-I0 THE TESTING OF HYPERELASTIC PROPERTIES OF THE RUBBER MATERIALS JAKUB JA VORIK* and ZDENEK DVORAK Tomas Bata University in Zlin, nam. T.G. Masaryka 5555, 76001 Zlin, Czech Republic j avorik@ft.utb.cz Abstract The aim of our work is to set up nonlinear material pa-rameters of elastomers for numerical simulation of these ma-terials. For this purpose, it is necessary to test material in three different modes: uniaxial tension, equibiaxial tension and pure shear. The equibiaxial elastomer characterization is the object of this paper. A bubble inflation technique was used for this characterization. We use data from this test and from uniaxial test to create the FEM models of elastomer. Introduction Thanks their special properties we can find the elastom-ers in almost all areas of human doings (let us remember their sealing and damping properties)1,2. A need of exact descrip-tion of the highly nonlinear mechanics of this material arises still more often. Our aim is to set up nonlinear material parameters of elastomers for numerical simulations. The measuring the en-gineering constants for nonlinear material models is demand-ing more special equipment than the measuring the constants for previously used linear material models. For accurate evaluation of hyperelastic material constants we need to test material in all deformation modes that will occur during simu-lation. Usually three basic deformation modes are tested: uniaxial tension, equibiaxial tension and pure shea?.4. The uniaxial tension is easy to perform on standard testing machi-ness. But the special equipments are necessary for next two deformation modes. One of the suitable methods for equibiaxial characteriza-tion of elastomers is the bubble inflation technique in which an elastomer is inflated to the shape ofbubble6. Experimental A uniform circular specimen of elastomer is clamped at the rim and inflated using compressed air to one side. The specimen is deformed to the shape of bubble. The inflation of the specimen results in a biaxial stretching near the pole of the -----.---~~------Chem. Listy 105, s233-s416 (2011) PMA 2011 & RubberCon 2011 Contributed Lectures bubble and the planar tension near the rim. Thanks to the spherical symmetry we can consider equibiaxial stress at the pole of the bubble. The thickness of specimen is small and the ratio between the thickness of the inflated membrane t and the curvature radius r is small enough, then the thin shell assumption allows us to neglect the radial stress in the specimen. With consideration of mate-rial incompressibility we can express the thickness of inflated specimen as: where to is the initial thickness of specimen (unloaded state). Further we have to measure the stretch Aee at the pole of in-flated material. Generally stretch A is the ratio between the current length I and the initial length 10: We can use some of optical method for measurement of stretch Aee and curvature radius r (camera, video camera, laser etc.). Finally we can compute the hoop stress (Jee on the pole ofthe inflated specimen as ref.6: The specimen of 2 mm thin elastomer is fixed between two rings with inner diameter 40 mm. Rings are clamped in a support. Next function of the support is distribution of the com-pressed air to one side of the specimen. The current value of applied pressure is recorded using a pressure sensor. The in-flation of the specimen is recorded using a high resolution CCD video camera. A computer is used to control the pres-sure. The white strips were drawn in the central area of speci-men for stretch measurement. It is important to measure elon-gation and curvature radius only in the area near to pole (between the strips) of inflated specimen and not on entire bubble contour because only on the pole the equibiaxial state of stress occurs. The common SBR compound for tire manufacturing was tested. The material was loaded until failure. We obtained values of stretch ratios Aee and curvature radii r from image analysis of video record. Results The equibiaxial stress-strain diagram of tested material is shown in Fig. 1. Also the uniaxial stress data are presented in this diagram for comparison. We can see generally known face, when equibiaxial stress values are 1.5-2 times greater s274 16 ro D.. 6 14 4 2 4 Fig. 1. Stress-strain diagram of tested material than uniaxial. The FEM model of specimen inflation (based on 5-tenns Mooney-Rivlin hyperelastic model) was created and com-pared with experiment. Conclusions It is not possible to predict biaxial behaviour of elas-tomer from uniaxial data only. When both uniaxial and biaxial data are used, the material models closely follow both uniax-ial and biaxial experimental data6. The bubble inflation tech-nique is very suitable method for the equibiaxial tension test of elastomers and for the accurate description of hyperelastic behaviour of material. This work is financially supported by the Czech Ministry of Education, Youth and Sports in the R&D project under the title 'Modelling and Control of Processing Procedures of Natural and Synthetic Polymers', No. MSM7088352102. REFERENCES 1. Manas D., Stanek M., Manas M., Pata Y., Javorik J.: KGK, Kautsch. Gummi Kunstst. 62, 240 (2009). 2. Manas D., Manas M., Stanek M., Zaludek M., Sanda S., Javorik J., Pata, Y.: Chem. Listy. 103, 72 (2009). 3. Ogden R. W.: Non-linear Elastic Deformations, Dover Publications, Mineola 1997. 4. Kohnke P.: ANSYS - Theory reference, Ansys Inc., Canonsburg 1998. 5. Smith L. P.: The language of Rubber, Butterworth-Heinemann, Oxford 1993. 6. Reuge N., Schmidt F. M., Le Maoult Y, Rachik M., Abbe F.: Polymer Eng. Sci. 41,522 (2001). 

The testing of hyperelastic properties of the rubber materials

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The testing of hyperelastic properties of the rubber materials

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