How the relationship between wood density and shrinkage depends on the microstructure of the cell wall

Transcription

1 How the reltionship between wood density nd shrinkge depends on the microstructure of the cell wll Klmn Schulgsser* nd Alln Witztum Deprtment of Mechnicl Engineering Deprtment of Life Sciences Ben-Gurion University of the Negev Beer Shev, Isrel * me Helsinki COS FP /8/11

2 Every discussion of wood shrinkge brings up two issues erly on: 1) Shrinkge is nisotropic, tngentil greter thn rdil. 2) Shrinkge (volumetric) is roughly proportionl to density. his figure is quntittively quite relistic for green to oven dry shrinkge of n verge conifer wood 2 his figure ppered in the first edition of the Wood Hndbook (1935) nd hs ppered in ll editions since nd in mny mny other publictions. Cption in first edition: Chrcteristic shrinkge nd distortion of flts, squres, nd rounds ( flt, squre nd round pieces since 1999) s ffected by the direction of the nnul rings. ngentil shrinkge is bout twice s gret s rdil.

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4 Wht bout the second question? Every discussion of wood shrinkge brings up two issues erly on: 1) Shrinkge is nisotropic, tngentil greter thn rdil. 2) Shrinkge (volumetric) is roughly proportionl to density. 4

5 J.A. Newlin nd..c. Wilson, he reltion of the shrinkge nd strength properties of wood to its specific grvity. USDA Bulletin No.676 (1919). No big discussion in text books, just simple sttement like: High density woods hve proportiontely more cell wll nd less lumen volume, nd so shrink nd swell more. J.C.F. Wlker, Primry Wood Processing Principles nd Prctice, 2 nd ed, Springer, 2006, p.98 End of story 5

6 ht just doesn t wsh! If the mtrix surrounding the pores hd no microstructure (or microstructure smll compred to pore dimensions) then ech of the four mteril bodies here would shrink (swell) to the sme outer dimensions. he fct tht denser woods tend to shrink more thn lighter woods must be relted to the microstructure of the wood t the geometric scle of the lumin. his ws clerly understood 50 yers go by Stmm nd Loughborough* nd nicely explined by them qulittively but they hve pprently been ignored. So I ll give it try. *A.J. Stmm nd W.K. Loughborough, Vrition in Shrinking nd Swelling of Wood. rns ASME (1942),

7 7 Circumferentil to cell wll stiffer nd shrinks less.

8 Now let s get nlyticl: Model the wood cells s cylindricl tubes*. We will homogenize the properties in the cross-section. nd here refer to rdil nd tngentil in the cell crosssection b We cn exctly clculte the shrinkge of the outer dimeter (= hlf the volumetric shrinkge) s function of the physicl prmeters of the cell wll mteril. hese re (considering the cell wll s mteril): rdil shrinkge, tngentil shrinkge E rdil elstic modulus, E tngentil elstic modulus, n nd n Poisson rtios We expect >> nd E >> E * N. Brber, A theoreticl model of shrinking wood. Holzforschung 22 (1968),

9 So we pply the equtions of liner elsticity. We get differentil eqution. We solve it. We pply the boundry conditions. We get b b n n c c 1 c 1 n n c 2 1 n n [b defined s reduction of rdius.] Here c is the rtio b/ nd mteril. c 1 1 V 2 where V is the volume frction of solid E E 9 And note tht wood specific grvity = 1.5 V. (he solid mteril hs density ~ 1.5 g/cm 3.) Further note tht the volumetric shrinkge will be twice the vlue given bove. his is n exct solution. Oh my goodness, so mny mteril prmeters! Wht mess. But we only wnt to know bout the nture of the shrinkge dependence on density.

10 So let s simplify the sitution. We will tke the Poisson rtio to be 0. his is specil cse, but lwys n is pprecibly less thn 1 nywy, so qulittively the sitution is not chnged. We get b b c 2c c 1 Now this is much better but not good enough! In ddition to nd nd of course c (which is directly relted to the volume frction V nd hence to the wood density) we still hve (the squre root of the rtio of elstic moduli) s confusing fctor. So let s get rid of (in terms of stiffness rtios) lso. 10

11 In cellulosic mterils t ll geometric levels, in plne of orthotropy, the following reltionship holds quite well. 1 2 Here 1 nd 2 re principl directions. ht this holds for whole wood (1 nd 2 re rdil nd tngentil directions) ws demonstrted nd rtionlized by Keyworth 1 ; tht this holds more generlly (lso pper nd prticle bord) nd tht there is sound physicl bsis for the reltionship cross the bord ws shown by Schulgsser 2,3 E E Keylwerth, Formänderungen in Holzquerschnitten. Holz ls oh- und Werkstoff 7 (1951), K. Schulgsser, herml expnsion of polycrystlline ggregtes with texture. Journl of the Mechnics nd Physics of Solids 35 (1987), K. Schulgsser, Moisture nd therml expnsion of wood, prticle bord nd pper. Pperi j Puu 70 (1988),

12 And wht we get is simply : b b c 2 2c c where now It is importnt to emphsize tht this is n exct solution, lbeit when certin (resonble) reltionships exist between physicl prmeters. b c = b/ 12

13 b b c 2 2c 2 c First off let s look t the two limiting cses: c 1 (i.e. V, nd thus density, very very low). We find b b Not surprising. (Any thin-wlled network of ny cell shpe would give this.) Next consider c (i.e. V pproches 1 nd density 1.5). We find b b And the impliction is (since > ) tht s density increses shrinkge increses. b c = b/ But wht if hd been smller thn???? 13

14 Percent volumetric shrinkge Now let s look t how shrinkge ctully depends on density. As n exmple we will tke / = 25 nd / = Shrinkge = 28 x sp.gr. (Newlin) Dt rnge = 2.4 (%) (0.3) 0.4 (0.6) 0.6 (0.9) 0.8 (1.2) 1 (1.5) 14 Volume frction (specific grvity)

15 In other words the fit should indeed be more or less liner in the rnge of interest but should not be forced to go through zero. J.A. Newlin nd..c. Wilson, he reltion of the shrinkge nd strength properties of wood to its specific grvity. USDA Bulletin No.676 (1919). 15

16 And we lern nother interesting thing. As microfibril ngle decreses in the S 2 lyer (which generlly corresponds to incresing ring number) the would probbly not chnge perceptively, but will increse somewht (S 2 microfibrils less oriented in circumferentil direction), nd our model predicts tht this should increse shrinkge. Now with incresing ring number, generlly density lso increses, but the shrinkge observed seems to be somewht greter thn tht ttributble simply to the proportionl increse of density*. * See for instnce the dt in: M. Grekin nd E. Verkslo, Vritions in bsic density, shrinkge nd shrinkge nisotropy of Scots pine wood from mture minerl soil stnds in Finlnd nd Sweden. Bltic Forestry 16 (2010),

17 Percent volumetric shrinkge For instnce consider typicl cse (volume fction 0.31 corresponding to density 0.46) for = 50% we clculte the volumetric shrinkge s increses (do to decresing microfibril ngle) from 2% to 3%. We see tht volumetric shrinkge does increse, but not rdiclly. And this would be dditive to shrinkge increse do to greter density In other words 50% increse of would cuse n increse of bout 17% in shrinkge (%) 17

18 Now just out of curiosity let s sk how the lumen dimeter chnges on drying. (his, of course, does not influence wood globl shrinkge.) We find c 2 2c 2 c 1 [ defined s reduction of rdius.] 1 1 b 18 Agin let s look t the two limiting cses: c 1 (i.e. V, nd thus density, very very low). We find Agin not surprising. (Any thin-wlled network of ny cell shpe would give this.) Next consider c (i.e. V pproches 1 nd density 1.5). We find c = b/ Note: here is only teensy weensy difference between this expression nd the one for b/b on slide #15. he + in the exponent of the middle term of the numertor ws there. Agin, the sme s before. NO, NO, NO, wit minute, the sign hs chnged! At some point when density increses, even though the wood shrinks the lumen dimeter increses. Is this possible!?

19 Percent reduction of lumen volume Not only is it possible, it is exctly wht hppens. For exmple, Boutelje* found tht for Scots pine on drying, the lumen volume decresed in erlywood (thin cell wlls) s expected but incresed in ltewood (thick cell wlls) not t ll obvious. Similr observtions were mde by Beiser** for spruce nd beech his is predicted by the current model Clcultions for / = 25 nd / = 16 Lumen volume decreses on drying. Lumen volume increses on drying (0.3) (0.6) (0.9) (1.2) (1.5) Volume frction (specific grvity) = 2.4 (%) 19 *J. Boutelje, On the reltionship between structure nd the shrinkge nd swelling of the wood in Swedish pine (Pinus sylvestris) nd spruce (Pice bies). Svensk Ppperstidning 76 (1973), ** W.Beiser, Mikrophotgrphische Quellungsuntersuchungen von. Kolloid-Zeitschrift 65 (1933),

20 A Necessry Disclosure After prepring this tlk I cme cross pper by. Nkno* in which the density dependence of shrinkge/swelling is lso considered vi cylindricl model. his model is essentilly geometricl, not mechnicl. It ssumes tht there exists physicl prmeter for wood dependent on chnge of moisture content, h/b, [ h is the cell wll thickness (b ) ]. he model results in liner reltionship between shrinkge/swelling nd density the slope being dependent on the vlue chosen for this physicl prmeter. (In short, the model indirectly ssumes reltionship between density nd shrinkge in order to demonstrte reltionship between density nd shrinkge.) *. Nkno, Anlysis of cell wll swelling on the bsis of cylindricl model. Holzforschung 62 (2008),

21 High density woods hve proportiontely more cell wll nd less lumen volume, nd so shrink nd swell more. High density woods hve proportiontely more cell wll nd less lumen volume; they shrink nd swell more due to the unique nture of the microstructure. End of Story hnks for listening. 21