The role of material properties for the mechanical

Authors: Karin Jungnikl Jürgen Goebbels Ingo Burgert Peter Fratzl

Publish Date: 2008/12/24

Volume: 23, Issue: 3, Pages: 605-610

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Abstract

Branch junctions are mechanically particularly interesting areas of trees because they have to withstand a combination of static and dynamic loads from the stem as well as from the branch In the present work the local adaptation of material properties at branch junctions was assessed by mapping microfibril angle and tissue density Images of the density distribution were obtained by computer tomography CT Wide angle Xray scattering WAXS was used to determine the microfibril angle distribution with highresolution around the junctions The stem tissue around the junctions showed increased density and microfibril angle which points towards an optimisation for fracture toughness The tissue at the branch bases showed low density combined with high MFA which provides deformability and flexibility and might act as protection of the stem against load transmission from the branchBranch junctions are structures that withstand strong static and dynamic loads for many years The mechanical design of a branch junction has to provide not only the stability and optimal functionality of the branch but also mechanical safety for the stem Another important property is damage tolerance when the branch is broken or shed eg defence against microorganisms at the defect Shigo 1989 To the tree the mechanical safety of the stem is of primary concern and has to be balanced versus the mechanical stability of the branches They are on the one hand necessary for photosynthesis but on the other hand increase the sail area creating a potential source of danger to the stem in the case of strong wind From the fracture mechanical perspective a branch junction also represents a notch in the stem Stem failure often occurs at damaged branch junctions or knots It was shown that force controlled optimisation of the shape of stem and branches is an essential tool for the control of the stress distribution at the surface Mattheck 1998 and also for introducing preferred points of failure as safety mechanism or for propagation purposes Niklas and Spatz 2000 Beismann et al 1997 A local change of the branch diameter at the branch collar Shigo 1989 or at a crotch Genenz et al 1997 were described as such ‘preferred points of failure’A study by electronic speckle pattern interferometry ESPI Müller et al 2006 provided a direct picture of the strain field in a longitudinal cross section of a junction A comparison was made between the strain field in a branch junction and polyester cast of the same shape The branch junction showed a homogeneous strain distribution within the stem while strain concentrations were observed in the polyester cast The homogeneous strain distribution in the wood sample implied a situation where ‘stress is high in zones of high modulus and low in zones of low modulus’ Müller et al 2006 From the results it was concluded that the distribution of the material properties should be adapted locally The aim of the present work was to show this adaptation directly by measuring the local distribution of material propertiesAt each growth increment the mechanical properties of the newly formed wood tissue are adapted to the local mechanical demands Microfibril angle MFA and tissue density have been shown to determine the stiffness and fracture behaviour of softwood Cave 1969 Reiterer et al 1999 The MFA has been shown to have a direct influence on energy absorption and tensile stiffness Reiterer et al 2001 It is known to be adapted in the course of diameter growth from pith to bark and along the length of stem and branches Lichtenegger et al 1998 Färber et al 2001 The direct influence of the tissue density on material strength and stiffness is eg visible in the mechanical properties of latewood LW and earlywood EW with similar MFA In the present study the contribution of the material properties to the mechanical stability of branch junctions was described by the local distribution of microfibril angle and tissue densityThe samples were collected from three young pine trees grown on a north facing slope in Waldviertel/Austria at around 900 m altitude All trees grew at the edge of a forest and were exposed to high snow loads during winter Two of them Tree I and II grew closer to the edge than the third Tree III which was taken from a more protected site in a clearing a few meters inwards the forest Trees I and III contained compression wood in the stem The examined branch junctions were selected at a height of the trees where the branches were alive the stem/branch diameter ratio comparable and the diameters high enough to suggest that the branch would produce significant loads on the stem The diameters of branch and stem without bark were for branch I 18 and 50 mm resulting in a diameter ratio of 035 for branch II 16 and 40 mm 040 and for branch III 14 and 45 mm 031 The number of growth rings in the stem above the branch was six Tree II and seven Trees I and III The angle between stem and branches was 45° directly at the stem for all samples but changed after a couple of centimeter where the branches started bending The selected junctions were facing the forest pointing uphill where no compression wood was formed in the stem All branches were bent at a couple of cm distally from the stem Branch I was bent sidewards by the westwind kept more or less the initial 45° angle with the stem throughout the length of the branch and had a pronounced branch collar Branch II and III were bent to an almost horizontal position and had less pronounced collars probably rather to be termed as stem collars Shigo 1989 The observed shape and pronouncedness of the collars correspond well with the classification by vitality due to shading described by Mattheck 1998CT of junction I a 3D view branch whorl carrying three branches and some rudimentary twigs Areas with high density appear bright Arrow pronounced compression wood CW opposite the examined junction b Stem cross section above and below the junction CW tissue with higher density arrow is highlighted with black lines At the underside the increased density and growth ring width is partially related to the other branches Above the branch the increased density is due to compression wood and a slight rotation in the course of the years can be seen c The branch is embedded at an angle of 45° Arrow “A” indicates the spatial restriction of the high density branch LW encircled areas “B” and “C” indicate areas of low density at the branch base see also Fig 1 and inside the stem The small arrows indicate the approximate positions of the sections in b In b and c the greyscale threshold of the reconstructed picture was adjusted to show the density gradient only within the latewood Areas with low density pith earlywood appear black

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