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
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.
Introduction Likelihood of failure vs. deterministic strength
No binary relation between stress and failure
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
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 Parameters: Overlap length, Adhesive layer thickness, Chamfering
Experimental investigations Characterization of timber
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.
Characterization of timber Off-axis tests were used to back-calculate shear strength and stiffness A confirmation was obtained using an alternative method3
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.
Numerical modeling sy txy txy 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 sy
Numerical investigations Sharp stress peaks of all stresses, at the locus of failure initiation
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
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 Weibull probabilistic
Numerical modeling Assuming a probability of failure of 50%
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
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.
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.
Numerical modeling CHAMFERED DLJ 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.
Beyond adhesives and/or timber Wood welding Vallee, Pichelin & Tannert: Strength predictionof wood-welded connection, to be submitted to WoodSciTech.
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.
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.
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
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.
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.
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