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Predicting The Strength Of Adhesively Bonded Timber Joints Using A Probabilistic Method
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Predicting The Strength Of Adhesively Bonded Timber Joints Using A Probabilistic Method


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  • 1. Predicting the Strength of Adhesively Bonded Timber Joints Using a Probabilistic Method
    Till Vallée, ProfessorThomas Tannert, Research FellowSimon Hehl, Research AssistantTimber & Composites LaboratoryBern University of Applied Sciences
  • 2. Outline
    Experimental investigations
    Numerical modeling
  • 3. Introduction
    Major issues related to strength prediction of bonded joints involving timber adherends
    • Timber has to be considered as a brittle material
    • 4. Timber mech props have a rel. high variability
    • 5. Stresses in the bonded splice are characterized by high peaks, especially both σy and τxy
    As a result
    • Any stress based prediction method is deemed to fail
  • Introduction
    The author1 has implemented a probabilistic method to overcome the major issues addressed
    Probabilistic methods
    • do not predict a deterministic strength value, but predict the likelihood that a given system will fail
    • 6. usually process the scattering of params
    • 7. usually implement size-effects
    1/T. Vallée, J. R. Correia, and T. Keller: „Probabilistic strength prediction for double lap joints composed of pultruded GFRP profiles – Part II: Strength prediction“, CompSciTech, 66(13), 1915-1930, 2006.
    „Probabilistic strength prediction for double lap joints composed of pultruded GFRP profiles – Part I: Experimental and numerical investigations“, CompSciTech, 66(13), 1903-1914, 2006.
  • 8. Introduction
    Likelihood of failure vs. deterministic strength
    • No binary relation between stress and failure
    • 9. For each stress-level, a probability of survival/failure, Ps/Pf
    • Strength of material is inversely related to the size of the sample on which it was determined
    • 10. Size effects is mathematically linked to the scattering of material props
  • Experimental investigations
    Very simple mechanical system considered
    Double lap joints (DLJ)
    Adherends: Spruce
    Adhesive: Epoxy
    Overlap length,
    Adhesive layer thickness,
  • 11. Experimental investigations
    Characterization of timber
    • Determination of all mechanical parameters
    {Ei}, {Gij} and {νij}
    • Off-axis tests
    • 12. Iosipescu tests
    Statistical characterization
    • Large number of individual tests
  • Characterization of timber
    Shear strength and stiffness on off-axis tests
    0°, 10°, 45° and 90°
    CNC cut from a board
    Determination following the Norris2 criterion
    2/Norris, G.B. 1950. Strength of orthotropic materials subjected to combined stress, Report No. 1816. US Department of Agriculture, Forest Research Laboratory. Madison, USA.
  • 13. Characterization of timber
    Off-axis tests were used to back-calculate shear strength and stiffness
    A confirmation was obtained using an alternative method3
    • Iosipescu test
    • 14. Good match obtained
    • 15. Caveat: Iosipescu test not fully adapted to timber
    3/ J. C. Xavier, N. M. Garrido, M. Oliveira, J. L. Morais, P. P. Camanho, F. Pierron, A comparison between the Iosipescu and off-axis shear test methods for the characterization of Pinus Pinaster Ait, Composites Part A: Applied Science and Manufacturing, 35(7-8), 2004, Pages 827-840.
  • 16. Experimental investigations
  • 17. Experimental modeling
  • 18. Experimental investigations
    The procedure described prior delivers the following: X = 98.21 MPa, Y = 4.46 MPa and S = 13.66 MPa, respectively
    • these values are in accordance with commonly encountered strengths in literature
    Weibull parameters for all experimentally gathered σF,i:
    • m = 3.717, and σF,0 = 1.124.
  • Experimental investigations
    Mechanical characterization of the adhesives
    SikaDur330, SikaForce7851, SikaFast5221…
    Direct determination of axial and shear properties
  • 19. Experimental results
    Independently on all parameters
    • Failure always triggered in the timber
    • 20. Failure occurred in a brittle manner
    • 21. Scattering around 15%
  • Experimental results
  • 22. Numerical modeling
    All configurations were numerically modeled
    Using Ansys v11,
    Including the orthotropic properties of timber
    Determination of all stress components that trigger failure
    σx,σy, τxy… since they appear in the FC
  • 23. Numerical investigations
    Sharp stress peaks of all stresses, at the locus of failure initiation
  • 24. Numerical modeling
    Strength prediction using a purely stress based approach, i.e. based on the most stressed element, does systematically underestimate the strength
    • Possibility to overcome this by implementing pseudo-plasticity, or considering stress-at-a-distance; which is arbitrary
    • 25. Stress based approach are conceptually flawed
    Additionally, relatively important scattering of strength data would add additional blur
  • 26. Numerical modeling
    Probabilistic method
    • Strength data is Weibull-distributed
    • 27. Knowing the Weibull modulus, m, allows to simply formulate size-effects
  • Numerical modeling
    Each element has a different volume, Vi, compared to the specimen on which strength was determined, V0
    Its strength is thus different…
    Each of the elements i has a probability of survival
    …determined using Weibull
    …Ps of joint = ΣPs,i
    Size effects
  • 28. Numerical modeling
    Assuming a probability of failure of 50%
  • 29. Numerical modeling
    A very good agreement can be found between experimental and predicted results
    Assuming a probability of failure of 50%, which basically means: half specimen survive, half fail (see next slide)
    Further, as the probabilistic method predicts likelihoods, it is directly possible to predict corresponding quantile-values
    e.g. 5% or 95%, usually needed for design as characteristic values
    Quantile-values not necessarily according to normal pdf
  • 30. Numerical modeling
    Till Vallée, Thomas Tannert and Simon Hehl Implementation of probabilistic dimensioning methods for adhesively bonded joints in codes and standards, IABSE, 2010, Dubrovnik.
  • 31. Results of strength prediction: adh’ thickness
    See also regarding optimum thickness: Till Vallée, João R. Correia, and Thomas Keller, Optimum Thickness of Joints made of GFRP Pultruded Adherends and Polyurethane Adhesive, ICCM17, Edinburgh/UK, July 2009.
  • 32. Numerical modeling
    Stresses reduced
    Till Vallée, Juan Murcia, Thomas Tannert and David Quinn, Influence of stress reduction methods on the strength of adhesively bonded composed of brittle adherends, subm. To Int. JourAdh&dh.
  • 33. Beyond adhesives and/or timber
    Wood welding
    Vallee, Pichelin & Tannert: Strength predictionof wood-welded connection, to be submitted to WoodSciTech.
  • 34. Beyond adhesives and/or timber
    T. Vallée, J. R. Correia, and T. Keller, „Probabilistic strength prediction for double lap joints composed of pultruded GFRP profiles, part II: Strength prediction“, Composites Science and Technology, vol. 66, no. 13, pp. 1915-1930, 2006.
  • 35. Beyond adhesives and/or timber
    Successful application to rounded dovetail connections
    Which also exhibit significant stress peaks
    T. Tannert, T. Vallée and F. Lam; Probabilistic strength prediction for rounded dovetail connections, Part II: Strength prediction, submitted to WoodSciTech.
  • 36. Simon Hehl, Till Vallée and Yu Bai, Experiments and Strength Prediction of a Joint Composed of a Pultruded FRP Tube bonded to an FRP Lamella, 8th international conference on fracture and damage mechanics (FDM09), Malta, Sept. 2009.
    Beyond adhesives and/or timber
  • 37. Conclusions
    Study clearly shows that probabilistic strength prediction methods are possible for adhesively bonded timber joints
    The obtained quality in the strength prediction justifies the extensive experimental tests for the material description
    Possible improvements are possible with applying other strength distributions and/or failure criteria
    T. Vallée, T. Keller, G. Fourestey, B. Fournier and J. R. Correia, Adhesively bonded joints composed of pultruded adherends: Considerations at the upper tail of the material strength statistical distribution, Probabilistic Engineering Mechanics, 24(39), pp. 358–366, 2009.
  • 38. Conclusions & outlook
    Ongoing work includes application to entire structures
    T. Vallée, T. Tannert and M. Schwendimann
    T. Vallée, T. Tannert and M. SchwendimannAdhesively bonded timber trusses:
    Experimental and numerical investigation, WCTE2010, Italy.
  • 39. Thank you for your attention
    I’m happy to answer your questions