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Macroscopical Modeling and Numerical Simulation for the Characterization of Crack and Durability Properties of Particle-Reinforced Elastomers

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Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 70))

Abstract

Numerical modeling of particle-reinforced or filled elastomers is a challenging task and includes the adequate representation of finite deformations, nonlinear elasticity, local damage as well as rate-dependent and rate-independent dissipative properties. On the structural scale, the permanent alteration of the material is visible as formation and propagation of discrete cracks, especially in the case of catastrophic crack growth and fatigue crack propagation. In this chapter, macromechanically formulated material models for finite viscoelasticity and endochronic elasto-plasticity of filled elastomers are presented in order to describe the material response of the undamaged continuum. On the FE-discretized structural scale, crack sensitivity of the material is assessed by the material force method. Material forces are used for the computational determination of fracture mechanical parameters of dissipative rubber material. Finally, arbitrary crack growth on the structural level is addressed by an adaptive implementation of cohesive elements. In a first application, crack propagation starting from an initial side notch in a tensile rubber specimen under mixed-mode loading is numerically predicted and compared to experimental observations. In a second example, averaged stress and energy based criteria are studied and compared with respect to their crack path predictability. In a third example, the durability of a tire design is numerically assessed by using the material force method.

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References

  1. Grambow, A.: Determination of Material Parameters for Filled Rubber Depending on Time, Temperature and Loading Condition. PhD thesis, Fakultät für Maschinenwesen, Rheinisch-Westfälische Technische Hochschule Aachen (2002)

    Google Scholar 

  2. Mooney, M.: A theory of large elastic deformation. Journal of Applied Physics 11, 582–592 (1940)

    Article  MATH  Google Scholar 

  3. Yeoh, O.: Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chemistry and Technology 63, 792–805 (1990)

    Article  Google Scholar 

  4. Arruda, E., Boyce, M.: A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. Journal of the Mechanics and Physics of Solids 41, 389–412 (1993)

    Article  Google Scholar 

  5. Miehe, C., Göktepe, S., Lulei, F.: A micro-macro approach to rubber-like materials. Part I: The non-affine micro-sphere model of rubber elasticity. Journal of the Mechanics and Physics of Solids 52, 2617–2660 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  6. Marckmann, G., Verron, E.: Comparison of hyperelastic models for rubberlike materials. Rubber Chemistry and Technology 79, 835–858 (2006)

    Article  Google Scholar 

  7. Kaliske, M., Heinrich, G.: An extended tube-model for rubber elasticity: Statistical-mechanical theory and finite element implementation. Rubber Chemistry and Technology 72, 602–632 (1999)

    Article  Google Scholar 

  8. Dal, H., Kaliske, M.: Bergström-Boyce model for nonlinear finite rubber viscoelasticity: Theoretical aspects and algorithmic treatment for the FE method. Computational Mechanics 44, 809–823 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Behnke, R., Dal, H., Kaliske, M.: An extended tube model for thermo-viscoelasticity of rubberlike materials: Parameter identification and examples. Proceedings in Applied Mathematics and Mechanics 11, 353–354 (2011)

    Article  Google Scholar 

  10. Behnke, R., Dal, H., Kaliske, M.: An extended tube model for thermo-viscoelasticity of rubberlike materials: Theory and numerical implementation. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber VII, pp. 87–92. CRC Press, Taylor & Francis Group (2011)

    Chapter  Google Scholar 

  11. Kaliske, M., Zopf, C., Brüggemann, C.: Experimental characterization and constitutive modeling of the mechanical properties of uncured rubber. Rubber Chemistry and Technology 83, 1–15 (2010)

    Article  Google Scholar 

  12. Dal, H., Kaliske, M., Zopf, C.: Theoretical and numerical modelling of unvulcanized rubber. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber VII, pp. 99–106. CRC Press, Taylor & Francis Group (2011)

    Chapter  Google Scholar 

  13. Green, M., Tobolsky, A.: A new approach to the theory of relaxing polymeric media. The Journal of Chemical Physics 14, 80–92 (1946)

    Article  Google Scholar 

  14. Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Clarendon Press, Oxford (1986)

    Google Scholar 

  15. Bergström, J., Boyce, M.: Constitutive modeling of the large strain time-dependent behavior of elastomers. Journal of the Mechanics and Physics of Solids 46, 931–954 (1998)

    Article  MATH  Google Scholar 

  16. Reese, S., Govindjee, S.: A theory of finite viscoelasticity and numerical aspects. International Journal of Solids and Structures 35, 3455–3482 (1998)

    Article  MATH  Google Scholar 

  17. Miehe, C., Keck, J.: Superimposed finite elastic-viscoelastic-plastoelastic stress response with damage in filled rubbery polymers. Experiments, modelling and algorithmic implementation. Journal of the Mechanics and Physics of Solids 48, 323–365 (2000)

    Article  MATH  Google Scholar 

  18. Miehe, C., Göktepe, S.: A micro-macro approach to rubber-like materials. Part II: The micro-sphere model of finite rubber viscoelasticity. Journal of the Mechanics and Physics of Solids 53, 2231–2258 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  19. Cohen, A.: A Padé approximant to the inverse Langevin function. Rheologica Acta 30, 270–273 (1991)

    Article  Google Scholar 

  20. Amin, A., Lion, A., Sekita, S., Okui, Y.: Nonlinear dependence of viscosity in modeling the rate-dependent response of natural and high damping rubbers in compression and shear: Experimental identification and numerical verification. International Journal of Plasticity 22, 1610–1657 (2006)

    Article  MATH  Google Scholar 

  21. Dal, H.: Approaches to the Modeling of Inelasticity and Failure of Rubberlike Materials. Theory and Numerics. PhD thesis, Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden (2012)

    Google Scholar 

  22. Kaliske, M., Rothert, H.: Constitutive approach to rate-independent properties of filled elastomers. International Journal of Solids and Structures 35, 2057–2071 (1998)

    Article  MATH  Google Scholar 

  23. Valanis, K.: A theory of viscoplasticity without a yield surface. Archives of Mechanics 23, 517–533 (1971)

    MathSciNet  MATH  Google Scholar 

  24. Kilian, H., Strauss, M., Hamm, W.: Universal properties in fillerloaded rubbers. Rubber Chemistry and Technology 67, 1–16 (1994)

    Article  Google Scholar 

  25. Netzker, C., Dal, H., Kaliske, M.: An endochronic plasticity formulation for filled rubber. International Journal of Solids and Structures 47, 2371–2379 (2010)

    Article  MATH  Google Scholar 

  26. Besdo, D., Ihlemann, J.: A phenomenological constitutive model for rubberlike materials and its numerical applications. International Journal of Plasticity 19, 1019–1036 (2003)

    Article  MATH  Google Scholar 

  27. Maugin, G.: Material Inhomogeneities in Elasticity. Chapman Hall, London (1993)

    MATH  Google Scholar 

  28. Gurtin, M.: Configurational Forces as Basic Concept of Continuum Physics. Springer, New York (2000)

    Google Scholar 

  29. Kienzler, R., Herrmann, G.: Mechanics in Material Space – with Application to Defect and Fracture Mechanics. Springer, Berlin (2000)

    Google Scholar 

  30. Morse, P.: Diatomic molecules according to the wave mechanics. II. Vibrational levels. Physical Review 34, 57–64 (1929)

    Article  MATH  Google Scholar 

  31. Dal, H., Kaliske, M.: A micro-continuum-mechanical model for failure of rubber-like materials: Application to ageing-induced fracturing. Journal of the Mechanics and Physics of Solids 57, 1340–1356 (2009)

    Article  MATH  Google Scholar 

  32. Treloar, L.: Stress-strain data for vulcanised rubber under various types of deformation. Transactions of the Faraday Society 40, 59–70 (1944)

    Article  Google Scholar 

  33. Hamdi, A., Naït Abdelaziz, M., Aït Hocine, N., Heuillet, P., Benseddiq, N.: Fracture criterion of rubber-like materials under plane stress conditions. Polymer Testing 25, 994–1005 (2006)

    Article  Google Scholar 

  34. Griffith, A.: The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London. Series A 221, 163–198 (1920)

    Article  Google Scholar 

  35. Rice, J.: A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379–386 (1968)

    Article  Google Scholar 

  36. Eshelby, J.: The elastic energy-momentum tensor. Journal of Elasticity 5, 321–335 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  37. Netzker, C., Horst, T., Reincke, K., Behnke, R., Kaliske, M., Heinrich, G., Grellmann, W.: Analysis of stable crack propagation in filled rubber based on a global energy balance. International Journal of Fracture (2013), doi:10.1007/s10704-013-9816-5

    Google Scholar 

  38. Näser, B., Kaliske, M., Müller, R.: Material forces for inelastic models at large strains: Application to fracture mechanics. Computational Mechanics 40, 1005–1013 (2007)

    Article  MATH  Google Scholar 

  39. Näser, B.: Zur numerischen Bruchmechanik dissipativer Materialien. PhD thesis, Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden (2009)

    Google Scholar 

  40. Behnke, R., Kaliske, M.: Computation of material forces for the thermo-mechanical response of dynamically loaded elastomers. Proceedings in Applied Mathematics and Mechanics 12, 299–300 (2012)

    Article  Google Scholar 

  41. Mueller, R., Kolling, S., Gross, D.: On configurational forces in the context of the finite element method. International Journal for Numerical Methods in Engineering 53, 1557–1574 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  42. Steinmann, P., Ackermann, D., Barth, F.: Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting. International Journal of Solids and Structures 38, 5509–5526 (2001)

    Article  MATH  Google Scholar 

  43. Liebe, T., Denzer, R., Steinmann, P.: Application of the material force method to isotropic continuum damage. Computational Mechanics 30, 171–184 (2003)

    Article  MATH  Google Scholar 

  44. Menzel, A., Denzer, R., Steinmann, P.: On the comparison of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity. Computer Methods in Applied Mechanics and Engineering 193, 5411–5428 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  45. Zimmermann, D.: Material Forces in Finite Inelasticity and Structural Dynamics: Topology Optimization, Mesh Refinement and Fracture. PhD thesis, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart (2008)

    Google Scholar 

  46. Kaliske, M., Dal, H., Fleischhauer, R., Jenkel, C., Netzker, C.: Characterization of fracture processes by continuum and discrete modelling. Computational Mechanics 50, 303–320 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  47. Hiermaier, S.: Structures under Crash and Impact. Springer, Berlin (2008)

    Google Scholar 

  48. Belytschko, T., Black, T.: Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 45, 601–620 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  49. Neumann, J.: Anwendung von adaptiven Finite Element Algorithmen auf Probleme der Strukturdynamik. PhD thesis, Fakultät für Bauingenieur-, Geo- und Umweltwissenschaften, Institut für Mechanik, Universität Karlsruhe (2004)

    Google Scholar 

  50. Song, J.H., Wang, H., Belytschko, T.: A comparative study on finite element methods for dynamic fracture. Computational Mechanics 42, 239–250 (2008)

    Article  MATH  Google Scholar 

  51. Dugdale, D.: Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8, 100–104 (1960)

    Article  Google Scholar 

  52. Barenblatt, G.I.: The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7, 55–129 (1962)

    Article  MathSciNet  Google Scholar 

  53. Needleman, A.: A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 54, 525–531 (1987)

    Article  MATH  Google Scholar 

  54. Geißler, G.: The Cohesive Crack Tip Model within the Finite Element Method. Implementations, Enhancements, Applications. PhD thesis, Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden (2009)

    Google Scholar 

  55. Geißler, G., Kaliske, M.: Time-dependent cohesive zone modelling for discrete fracture simulation. Engineering Fracture Mechanics 77, 153–169 (2010)

    Article  Google Scholar 

  56. Kaliske, M., Rothert, H.: Formulation and implementation of three-dimensional viscoelasticity at small and finite strains. Computational Mechanics 19, 228–239 (1997)

    Article  MATH  Google Scholar 

  57. Geißler, G., Kaliske, M., Nase, M., Grellmann, W.: Peel process simulation of sealed polymeric film: Computational modelling of experimental results. Engineering Computations 24, 586–607 (2007)

    Article  Google Scholar 

  58. Nase, M., Langer, B., Baumann, H., Grellmann, W., Geißler, G., Kaliske, M.: Evaluation and simulation of the peel behavior of polyethylene/polybutene-1 peel systems. Journal of Applied Polymer Science 111, 363–370 (2009)

    Article  Google Scholar 

  59. Hillerborg, A., Modéer, M., Petersson, P.E.: Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 6, 773–781 (1976)

    Article  Google Scholar 

  60. Camacho, G., Ortiz, M.: Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 33, 2899–2938 (1996)

    Article  MATH  Google Scholar 

  61. Pandolfi, A., Ortiz, M.: Solid modeling aspects of three-dimensional fragmentation. Engineering with Computers 14, 287–308 (1998)

    Article  MATH  Google Scholar 

  62. Pandolfi, A., Ortiz, M.: An efficient adaptive procedure for three-dimensional fragmentation simulations. Engineering with Computers 18, 148–159 (2002)

    Article  Google Scholar 

  63. Papoulia, K., Sam, C.H., Vavasis, S.: Time continuity in cohesive finite element modeling. International Journal for Numerical Methods in Engineering 58, 679–701 (2003)

    Article  MATH  Google Scholar 

  64. Wells, G., Sluys, L.: A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 50, 2667–2682 (2001)

    Article  MATH  Google Scholar 

  65. Pidaparti, R., Yang, T., Soedel, W.: Plane stress finite element prediction of mixed-mode rubber fracture and experimental verification. International Journal of Fracture 45, 221–241 (1990)

    Article  Google Scholar 

  66. Gürses, E.: Aspects of Energy Minimization in Solid Mechanics: Evolution of Inelastic Microstructures and Crack Propagation. PhD thesis, Institut für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart (2007)

    Google Scholar 

  67. Kaliske, M., Özenç, K., Dal, H.: Aspects of crack propagation in small and finite strain continua. In: Jerrams, S., Murphy, N. (eds.) Constitutive Models for Rubber VII, pp. 137–142. CRC Press, Taylor & Francis Group (2011)

    Chapter  Google Scholar 

  68. Kaliske, M., Näser, B., Meiners, C.: Inelastic fracture mechanics for tire durability simulations. Tire Science and Technology 35, 239–250 (2007)

    Article  Google Scholar 

  69. Nasdala, L., Wei, Y., Rothert, H., Kaliske, M.: Lifetime prediction of tires with regard to oxidative aging. Tire Science and Technology 36, 63–79 (2008)

    Article  Google Scholar 

  70. Previati, G., Kaliske, M.: Crack propagation in pneumatic tires: Continuum mechanics and fracture mechanics approaches. International Journal of Fatigue 37, 69–78 (2012)

    Article  Google Scholar 

  71. Näser, B., Kaliske, M., Dal, H., Netzker, C.: Fracture mechanical behaviour of visco-elastic materials: Application to the so-called dwell-effect. Zeitschrift für Angewandte Mathematik und Mechanik 89, 677–686 (2009)

    Article  MATH  Google Scholar 

  72. Harbour, R., Fatemi, A., Mars, W.: The effect of a dwell period on fatigue crack growth rates in filled SBR and NR. Rubber Chemistry and Technology 80, 838–853 (2007)

    Article  Google Scholar 

  73. Näser, B., Kaliske, M., Mars, W.: Fatigue investigation of elastomeric structures. Tire Science and Technology 38, 194–212 (2010)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institut für Statik und Dynamik der Tragwerke, Technische Universität Dresden, Fakultät Bauingenieurwesen, 01062, Dresden, Germany

    Ronny Behnke & Michael Kaliske

  2. Institut für Mechanik (Bauwesen), Universität Stuttgart, Fakultät 2: Bau- und Umweltingenieurwissenschaften, Pfaffenwaldring 7, 70550, Stuttgart, Germany

    Hüsnü Dal

  3. DYNAmore GmbH Niederlassung, Donaustr. 7, 85049, Ingolstadt, Germany

    Gordon Geißler

  4. Dassault Systemes Deutschland GmbH, Joseph-Wild-Str. 20, 81829, München, Germany

    Bastian Näser

  5. EP/SPB, HPC X271, DaimlerChrysler AG, 71059, Sindelfingen, Germany

    Christiane Netzker

Authors
  1. Ronny Behnke
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  2. Hüsnü Dal
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  3. Gordon Geißler
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  4. Bastian Näser
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  5. Christiane Netzker
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  6. Michael Kaliske
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Editor information

Editors and Affiliations

  1. FB Werkstoffwissenschaften, Inst. Polymerwerkstoffe, Univ. Halle-Wittenberg, Geusaer Str. 88, Halle, 06099, Sachsen-Anhalt, Germany

    Wolfgang Grellmann

  2. Polymerforschung Dresden e.V., Leibniz-Institut für, Hohe Str. 6, Dresden, 01069, Sachsen, Germany

    Gert Heinrich

  3. Institute for Structural Analysis, Technische Universität Dresden, Nürnberger Straße 31a, Dresden, 01062, Germany

    Michael Kaliske

  4. Kautschuktechnologie e.V., Deutsches Institut für, Eupener Str. 33, Hannover, 30519, Germany

    Manfred Klüppel

  5. Dresden e.V., Leibniz-Institut für Polymerforschung, Hohe Str. 6, Dresden, 01069, Germany

    Konrad Schneider

  6. Polymer Research, Max-Planck-Institute for, Ackermannweg 10, Mainz, 55128, Germany

    Thomas Vilgis

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Behnke, R., Dal, H., Geißler, G., Näser, B., Netzker, C., Kaliske, M. (2013). Macroscopical Modeling and Numerical Simulation for the Characterization of Crack and Durability Properties of Particle-Reinforced Elastomers. In: Grellmann, W., Heinrich, G., Kaliske, M., Klüppel, M., Schneider, K., Vilgis, T. (eds) Fracture Mechanics and Statistical Mechanics of Reinforced Elastomeric Blends. Lecture Notes in Applied and Computational Mechanics, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37910-9_5

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  • DOI: https://doi.org/10.1007/978-3-642-37910-9_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-37909-3

  • Online ISBN: 978-3-642-37910-9

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