Abstract
Large strain fixed-end torsion of circular solid rubber bars is studied semi-analytically. The analyses are based on various non-Gaussian network models for rubber elasticity, some of which were proposed very recently. Results are presented in terms of predicted torque vs. twist curves and axial force vs. twist curves. In some cases, the predicted stress distributions are also given. The sensitivity of the second-order axial force to the employed models is considered. The predicted results are compared with experimental results found in the literature.
Key Words
rubber network model large strain torsionPreview
Unable to display preview. Download preview PDF.
References
- [1]White CS, Bronkhorst CA and Anand L. An improved isotropic-kinematic hardening model for moderate deformation metal plasticity.Mech Mater, 1990, 10: 127–147CrossRefGoogle Scholar
- [2]Khen R and Rubin MB. Analytical modelling of second order effects in large deformation plasticity.Int J Solids Structures, 1992, 29: 2235–2258CrossRefGoogle Scholar
- [3]Wu PD and Van der Giessen E. On large strain inelastic torsion of glassy polymers.Int J Mech Sci, 1993, 35: 935–951MATHCrossRefGoogle Scholar
- [4]Poynting JH. On pressure, perpendicular to the shear planes in finite pure shears and on lengthening of loaded wires when twisted.Proc R Soc Lond, 1909, A82: 546–559MATHGoogle Scholar
- [5]Neale KW and Shrivastava SC: Analytical solutions for circular bars subjected to large strain plastic torsion.J Appl Mech, 1990, 57: 293–306Google Scholar
- [6]Wu PD and Van der Giessen E. Analysis of elastic-plastic torsion of circular bars at large strains.Arch Appl Mech, 1991, 61: 89–103MATHGoogle Scholar
- [7]Van der Giessen E, Wu PD and Neale KW. On the effect of plastic spin on large strain elastic-plastic torsion of solid bars.Int J Plast, 1992, 8: 773–801MATHCrossRefGoogle Scholar
- [8]Rivlin RS and Saunders DW. Large elastic deformations of isotropic materials VII. Experiments on the deformation of rubber.Phil Trans R Soc, 1951, A243: 251–288MATHGoogle Scholar
- [9]Ogden RW, Chadwick P. On the deformation of solid and tubular cylinders of incompressible isotropic elastic materials.J Mech Phys Solids, 1972, 20: 77–90CrossRefGoogle Scholar
- [10]Ogden RW, Chadwick P and Haddon EW. Combined axial and torsional shear of a tube of incompressible isotropic elastic material.Quart Journ Mech and Applied Math, 1973, XXVI: 23–41Google Scholar
- [11]Kuhn W and Grun F. Beziehuugen zwischen elastischen konstanten uud dehuugsdoppelbrechung hochelastischer stoffe.Kolloidzeitschrift, 1942, 101: 248–271CrossRefGoogle Scholar
- [12]James HM and Guth E. Theory of the elastic properites of rubber.J Chem Phys, 1943, 11: 455–481CrossRefGoogle Scholar
- [13]Wu PD and Van der Giessen E. On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers.J Mech Phys Solids, 1993, 41: 427–456MATHCrossRefGoogle Scholar
- [14]Arruda EM and Boyce MC. Evolution of plastic anisotropy in amorphous polymers during finite straining. In: Boehler J-P and Khan AS eds. Anistotropy, and Localization of Plastic Deformation. London: Elsevier Applied Science, 1991. 483–488Google Scholar
- [15]Arruda EM and Boyce MC. A three-dimensional constitutive model for large stretch behaviour of rubber materials.J Mech Phys Solids, 1993, 41: 389–412CrossRefGoogle Scholar
- [16]Dahoun A, G'Sell C, Molinari A and Canova GR. Plastic behaviour and deformation textures of poly (ether ether ketone) under uniaxial tension and simple shear 1993 (submitted for publication, 1993)Google Scholar
- [17]Wu PD and Van der Giessen E. On improved 3-D non-Gaussian network models for rubber elasticity.Mech Res Comm, 1992, 19: 427–433CrossRefGoogle Scholar
- [18]Wu PD and Van der Giessen E. On network descriptions of mechanical and optical properties of rubbers. (submitted for publication)Google Scholar
- [19]Treloar LRG and Riding G. A non-Gaussian theory for rubber in biaxial strain. I. Mechanical properties.ProcR Soc Lond, 1979, A369: 261–280CrossRefGoogle Scholar
- [20]Dahoun A. Comportement Plastique et Textures de Deformation des Polymeres Semi-crystallins en Traction Uniaxiale et en Cisaillement Simple. Ph D Thesis. Institut National Polytechnique de Lorraine, Nancy, France, 1992Google Scholar
- [21]Wang MC and Guth E. Statistical theory of networks of non-Gaussian flexible chains.J Chem Phys, 1952, 20: 1144–1157MathSciNetCrossRefGoogle Scholar
- [22]Mark JE and Erman B. Rubberlike Elasticity: A Molecular Primer. New York: Wiley, 1988Google Scholar
- [23]Ball RC, Doi M, Edwards SF and Warner M. Elasticity of entangled network.Polymer, 1981, 22: 1010–1018CrossRefGoogle Scholar
- [24]Gao J and Weiner JH. Chain force concept in systems of interacting chains.Macromolecules, 1991, 24: 5179–5191CrossRefGoogle Scholar
- [25]Wu PD and Van der Giessen E. Large strain visco-plastic torsion of circular bars of glassy polymers. In: Lee WB ed. Advances in Engineering Plasticity and its Applications. Amsterdam: Elsevier Science Publishers BV, 1993. 477–484Google Scholar
Copyright information
© Chinese Society of Theoretical and Applied Mechanics 1994