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Size effects in polyurethane bonds: experiments, modelling and parameter identification

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Abstract

In this study we examine polyurethane bonds of varying thickness between anodised aluminium substrates. The performed shear tests showed an intriguing size effect of the kind “thinner equals softer”. This size effect occurs not only in the basic elasticity (relaxed state), but also in the viscoelastic behaviour of the tested material. The cause of such size effects is supposed to be found in the existence of so-called interphases or boundary layers, which may differ considerably from the bulk in terms of mechanical behaviour, thus having an enormous impact on thin bonds. In thick bonds, however, these interphases or boundary layers have a minor effect on the overall mechanical behaviour. To account for these experimental results in bond modelling, an extended phenomenological continuum mechanics-based model, which explicitly includes such size effects in its calculation, is developed and presented. For this purpose, an abstract structure parameter with its corresponding balance equation is established describing the formation of the interphases by means of a phase transition. This makes it possible to define the bond stiffness at a macroscopic level, without entering into the microstructure. The extended model brings up a set of model parameters, which are determined efficiently by an ES (evolution strategy). The study concludes with a summary and an outlook on our further research work.

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Notes

  1. The extreme absorptivity of anodised surfaces becomes already obvious at this point: it is not possible to remove the marker ink, not even with acetone.

References

  1. Bockenheimer C, Valeske B, Possart W (2002) Int J Adhes Adhes 22:349

    Article  CAS  Google Scholar 

  2. Fata D, Bockenheimer C, Possart W (2005) In: Possart W (ed) Adhesion-current research and applications. Wiley-VCH, Weinheim, p 479

    Google Scholar 

  3. Krüger JK, Possart W, Bactavachalou R, Müller U, Britz T, Santuary R, Alnot P (2004) J Adhesion 80:585

    Article  Google Scholar 

  4. Chung J, Munz M, Sturm H (2005) J Adhesion Sci Technol 19:1263

    Article  CAS  Google Scholar 

  5. Possart W, Krüger JK, Wehlack C, Müller U, Petersen C, Bactavatchalou R, Meiser A (2004) C R Chimie 9:60

    Article  Google Scholar 

  6. Bouchet J, Roche AA (2002) J Adhesion 78:799

    Article  CAS  Google Scholar 

  7. Roche AA, Bouchet J, Bentadjine S (2002) Int J Adhes Adhes 22:431

    Article  CAS  Google Scholar 

  8. Bouchet J, Roche AA, Jacquelin E (2002) J Adhesion Sci Technol 16:1603

    Article  CAS  Google Scholar 

  9. Bouchet J, Roche AA, Hamelin P (2002) Thin Solid Films 355:270

    Google Scholar 

  10. Vanlandingham MR, Dagastine RR, Eduljee RF, McCullough RL, Gillespie JW Jr (1999) Compos Part A: Appl Sci Manuf 30:75

    Article  Google Scholar 

  11. Wehlack C, Possart W, Krüger JK, Müller U (2007) Soft Mater 5:87

    Article  CAS  Google Scholar 

  12. Schlimmer M, Hennemann OD, Hahn O (2004) AiF project 76

  13. Schlimmer M, Bornemann J (2004) Berechnung und Dimensionierung von Klebverbindungen mit der Methode der Finiten Elemente und experimentelle Überprüfung der Ergebnisse. Forschungsbericht 1-2003, Schriftenreihe des Instituts für Werkstofftechnik der Universität Kassel, Kassel

  14. Schlimmer M, Hahn O, Hennemann OD (2006) Methodenentwicklung zur Berechnung und Auslegung geklebter Stahlbauteile im Fahrzeugbau bei schwingender Beanspruchung. Proc Gemeinsame Forschung in der Klebtechnik-6. Kolloquium 21./22. Februar

  15. Diebels S, Johlitz M, Steeb H, Batal J, Possart W (2007) J Phys: Conf Ser 62:34

    CAS  Google Scholar 

  16. Johlitz M, Steeb H, Diebels S, Batal J, Possart W (2007) Technische Mechanik, accepted

  17. Johlitz M, Steeb H, Diebels S, Chatzouridou A, Batal J, Possart W (2007) J Mat Sci 42:9894

    Article  CAS  Google Scholar 

  18. Steeb H, Diebels S (2004) Int J Solids Struct 41:5071

    Article  Google Scholar 

  19. Goodman M, Cowin S (1972) Arch Rat Mech Anal 44(4):249

    Article  Google Scholar 

  20. Helm D (2001) Formgedächtnislegierungen (Bericht-Nr. 3/2001 des Instituts für Mechanik, Kassel

  21. Helm D (20077) Int J Numer Meth Eng 69:1997

    Article  Google Scholar 

  22. Capriz G, Podio-Guidugli P, Williams W (1982) Meccanica 17:80

    Article  Google Scholar 

  23. Capriz G (1980) Continua with microstructures. Springer, New York

    Google Scholar 

  24. Svendsen B (1999) Continuum Mech Therm 4:247

    Article  Google Scholar 

  25. Svendsen B, Hutter K, Laloui L (1999) Continuum Mech Therm 4:263

    Article  Google Scholar 

  26. Coleman B, Noll W (1963) Arch Rat Mech Anal 13:167

    Article  Google Scholar 

  27. Coleman B, Gurtin ME (1967) J Chem Phys 47:597

    Article  CAS  Google Scholar 

  28. Chadwick P (1974) Phil Trans Roy Soc Lond A 276:371

    Article  CAS  Google Scholar 

  29. Alts T (1979) Prog Coll Pol Sci S 66:7367

    Google Scholar 

  30. Haupt P, Lion A, Backhaus E (2000) Int J Solids Struct 37:3633

    Article  Google Scholar 

  31. Haupt P, Lion A (2001) A generalisation of the Mooney-Rivlin model to finite linear viscoelasticity Constitutive Models for Rubber. Swets & Zeitlinger, London

    Google Scholar 

  32. Haupt P, Lion A (2002) Acta Mech 159:87

    Article  Google Scholar 

  33. Göktepe S, Miehe C (2005) J Mech Phys Solids 53:2259

    Article  Google Scholar 

  34. Miehe C, Keck J (2000) J Mech Phys Solids 48:323

    Article  Google Scholar 

  35. Miehe C, Göktepe S, Lulei F (2004) J Mech Phys Solids 52:2617

    Article  CAS  Google Scholar 

  36. Miehe C, Göktepe S (2005) J Mech Phys Solids 53:2231

    Article  CAS  Google Scholar 

  37. Keck J (1998) Zur Beschreibung finiter Deformationen von Polymeren, Experimente, Modellbildung, Parameteridentifikation und Finite-Elemente-Formulierung. Bericht-Nr. I-5 des Instituts für Mechanik (Bauwesen), Stuttgart

  38. Reese S (2001) Thermomechanische Modellierung gummiartiger Polymerstrukturen. F01/4 Institut für Baumechanik und Numerische Mechanik, Hannover

  39. Reese S, Govindjee S (1998) Mech Time-Depend Mater 1:357

    Article  Google Scholar 

  40. Reese S, Govindjee S (1998) Int J Solids Struct 35:3455

    Article  Google Scholar 

  41. Reese S, Wriggers P (1997) Comput Methods Appl Mech Eng 148:279

    Article  Google Scholar 

  42. Reese S, Wriggers P (1999) Modelling of the thermomechanical material behaviour of rubber-like polymers-micromechanical motivation and numerical simulation (Dorfmann & Muhr (eds) Rotterdam, 1999), p 13

  43. Lion A (1996) Continuum Mech Therm 8:153

    Article  Google Scholar 

  44. Lion A (1997) Acta Mech 123:1

    Article  Google Scholar 

  45. Lion A (1999) Rubber Chem Technol 72:410

    Article  CAS  Google Scholar 

  46. Lion A (2000) Thermomechanik von Elastomeren. Bericht-Nr. 1/2000 des Instituts für Mechanik, Kassel

  47. Sedlan K (2001) Viskoelastisches Materialverhalten von Elastomerwerkstoffen, Experimentelle Untersuchung und Modellbildung. Berichte des Instituts für Mechanik (2/2001), Universität Gesamthochschule Kassel, Kassel

  48. Amin AFMS, Alam MS, Okui Y (2002) Mech Mater 34:75

    Article  Google Scholar 

  49. Amin AFMS, Alam MS, Okui Y (2003) J Test Eval 31(6):524

    Google Scholar 

  50. Amin AFMS, Lion A, Sekita S, Okui Y (2006) Int J Plasticity 22:1610

    Article  CAS  Google Scholar 

  51. Laiarinandrasana L, Piques R, Robisson A (2003) Int J Plasticity 19:977

    Article  CAS  Google Scholar 

  52. Bergstrom JS, Boyce MC (1998) J Mech Phys Solids 56(5):931

    Article  Google Scholar 

  53. Boyce MC, Arruda EM (2000) Rubber Chem Technol 73:504

    Article  CAS  Google Scholar 

  54. Bergstrom JS, Boyce MC (2001) Macromolecules 34(3):614

    Article  Google Scholar 

  55. Bergstrom JS, Boyce MC (2001) Mech Mater 33:523

    Article  Google Scholar 

  56. Bergstrom JS, Boyce MC (2000) Mech Mater 32:627

    Article  Google Scholar 

  57. Besdo D (2003) Int J Plast 19:1001

    Article  CAS  Google Scholar 

  58. Besdo D (2003) Int J Plast 19:1019

    Article  CAS  Google Scholar 

  59. Ihlemann J (2002) Kontinuumsmechanische Nachbildung hochbelasteter technischer Gummiwerkstoffe. Institut für Mechanik (Maschinenbau) Universität Hannover, Hannover

    Google Scholar 

  60. Lubliner J (1985) Mech Res Commun 12:93

    Article  Google Scholar 

  61. Tallec PL, Kaiss A, Rahier C (1994) Int J Numer Meth Eng 37:1159

    Article  Google Scholar 

  62. Kröner E (1960) Arch Ration Mech Anal 4:273

    Article  Google Scholar 

  63. Lee EH, Liu DT (1967) J Appl Phys 38:19

    Article  CAS  Google Scholar 

  64. Lee EH (1969) J Appl Mech 36:1

    Article  Google Scholar 

  65. Mooney M (1940) J Appl Phys 11:582

    Article  Google Scholar 

  66. Rivlin RS (1948) Phil Trans Roy Soc Lond A 241:379

    Article  Google Scholar 

  67. Cahn JW, Hilliard J (1958) J Chem Phys 28:258

    Article  CAS  Google Scholar 

  68. Scheday G (2003) Theorie und Numerik der Parameteridentifikation von Materialmodellen der finiten Elastizität und Inelastizität auf der Grundlage optischer Feldmessmethoden. Bericht-Nr. I-11 des Instituts für Mechanik (Bauwesen), Stuttgart

  69. Schwefel HP (1995) Evolution and Optimum Seeking. Wiley, New York

    Google Scholar 

  70. Rechenberg I (1973) Evolutionsstrategie: optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, Stuttgart

Download references

Acknowledgements

The authors are grateful to the DFG (Deutsche Forschungsgemeinschaft—German Research Foundation) for financial support under grant numbers Di 430/5-1 to 5-3 and Po 577/15-1.

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Correspondence to Holger Steeb.

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Johlitz, M., Diebels, S., Batal, J. et al. Size effects in polyurethane bonds: experiments, modelling and parameter identification. J Mater Sci 43, 4768–4779 (2008). https://doi.org/10.1007/s10853-008-2674-2

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  • DOI: https://doi.org/10.1007/s10853-008-2674-2

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