36 Drying of Wood

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Second drying periodSecond drying periodEnd of dryingFSPTensilestressCompressivestressProngtest(a)(b)FIGURE 36.29 Appearance of drying stresses followingshrinkage. (Adapted from Perré , P., The numerical modelingof physical and mechanical phenomena involved inwood drying: an excellent tool for assisting with the studyof new processes, Tutorial, Proceedings of the Fifth InternationalIUFRO Wood Drying Conference, Qué bec, Canada,1996, 9–38.)where DW n is the activation energy associated toelement n.The mechanosorptive effect occurs as soon as themoisture content changes during load. The simplerway to express this effect consists in assuming thatthe strain rate depends linearly on both the stress fieldand the time derivative of the moisture content ḣ :_« msij ¼ m ijkl s kl (sign ḣ)ḣ (36:21)The mechanosorptive strain rate is always in the directionof the stress field, hence the factor sign _u inEquation 36.21.A three-dimensional resolution is very costly interms of calculation time and computer memoryspace. The need for such a cost is justified wheneverthe objective of the calculation lies in evaluating theoverall deformation of the board. In this way, theeffect of reaction wood, fiber angle, and propertyFSPX eq(a)End of drying(b)(c)(c)TensilestressCompressivestressFIGURE 36.30 Stress reversal due to the memory effect ofwood. (Adapted from Perré, P., The numerical modeling ofphysical and mechanical phenomena involved in wooddrying: an excellent tool for assisting with the studyof new processes, Tutorial, Proceedings of the Fifth InternationalIUFRO Wood Drying Conference, Québec,Canada, 1996, 9–38.)CupmethodFIGURE 36.31 Two experimental methods used to assessdrying stresses.variations can be analyzed. Good examples of thesepossibilities can be found in the literature (Dahlblomet al., 1994, 1996; Ormarsson, 1999). Nevertheless, tostudy the stress development within a section farfrom the ends of the board, a two-dimensional simulationis sufficient. A ‘‘planar displacement’’ formulationhas to be used in this case, assuming smalldisplacements (Perré and Passard, 1995; Chen et al.,1997a)orlargedisplacements(MaugetandPerré ,1999).36.2.4 .4 Stres s Deve lopm ent dur ing Dry ing:So me Exampl esAll examples presented in this section, except the nonsymmetriccase, refer to a flatsawn board of heartwood,20-mm thick and 40-mm wide. They have beencomputed using the computer code Transpore (Perréand Turner, 1996b and c, 1999; Mauget and Perré ,1999; Perré and Passard, 2002;). Figure 36.33 depictsthe moisture and stress fields calculated at differentdrying stages for quite severe conditions at a mediumtemperature level (T d ¼ 80 8C, T w ¼ 60 8C). After 6 hof drying, the external part of the section is within thehygroscopicrange,whichgivesrisetotensilestressduetoshrinkageinthezonesclosetotheexchangesurface.As a consequence of the mechanical equilibrium, internalzones undergo compressive stress. A negativeshear stress exists close to the edge (the right angleshavedecreased).Attheendofthedryingprocess(60h)the moisture content is almost equal to the EMC (7%)throughout the section. The stress reversal due to thememory effect of wood is clearly exhibited. It can benoted that the shear stress also changes in sign.When a face of a board is insulated, the dryingconditions are not symmetrical anymore andß 2006 by Taylor & Francis Group, LLC.
Element 1 Element 2 Element NElement 0FIGURE 36.32 Modeling the viscoelastic behavior of wood with the number of Kelvin elements in series.significant section deformations can be observed experimentally(Brandã o and Perré , 1996). Figure 36.34is an example of nonsymmetrical drying. In order toincrease the section deformation, a thin quartersawnboard has been simulated, here 5 mm by 80 mm. Thelarge displacement formulation is essential in thiscase. In this configuration, one part of the dryingstress is transformed into section deformation; hencethe stress-reversal phenomenon induces a negativefinal curvature.Thickness (cm)1.00.80.60.40.2Moisture content0.650.580.510.440.370.290.220.15Sigma xx0.00.00.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0Width (cm)Width (cm)Thickness (cm)1.00.80.60.40.21.541.240.930.630.320.01−0.29−0.60Thickness (cm)1.00.80.60.40.2Sigma xy0.00.0 0.5 1.0 1.5 2.0(a)Width (cm)0.150.090.03−0.03−0.09−0.15−0.21−0.28Thickness (cm)1.00.80.60.40.2Sigma yy0.00.0 0.5 1.0 1.5 2.0Width (cm)1.291.040.790.530.280.03−0.22−0.47Thickness (cm)Moisture content1.00.80.60.40.20.00.0 0.5 1.0 1.5 2.0Width (cm)0.080.080.070.070.070.070.070.07Thickness (cm)1.00.80.60.40.2Sigma xx0.00.0 0.5 1.0 1.5 2.0Width (cm)0.12−0.29−0.70−1.11−1.52−1.93−2.34−2.75aThickness (cm)1.00.80.60.40.2Sigma xy0.240.210.180.150.120.090.060.03Thickness (cm)1.00.80.60.40.2Sigma yy−0.10−0.35−0.60−0.86−1.11−1.36−1.62−1.870.00.0 0.5 1.0 1.5 2.0(b)Width (cm)0.00.0 0.5 1.0 1.5 2.0Width (cm)FIGURE 36.33 Moisture content and stress fields after (a) 6 h and (b) 60 h (T d ¼ 808C, T w ¼ 608C).ß 2006 by Taylor & Francis Group, LLC.
Page 1 and 2: 36Drying of Wood: Principlesand Pra
Page 3 and 4: Primary growthSecondannual ringFirs
Page 5 and 6: FIGURE 36.4 Wood is formed by cell
Page 7 and 8: TABLE 36.1Elementary Composition of
Page 9 and 10: FIGURE 36.8 Tension wood in Peduncu
Page 11 and 12: 36.2.1.3 Bound WaterBound moisture
Page 13 and 14: TABLE 36.6Order of Magnitude of Shr
Page 15 and 16: The transverse permeability and the
Page 17 and 18: FIGURE 36.14 Relative permeability
Page 19 and 20: Low moisture contentHigh moisture c
Page 21 and 22: Boundary layersExternal flowTP vHea
Page 23 and 24: HeatVaporVessel ortracheidLiquidPit
Page 25 and 26: Moisture content (%)15010050Sapwood
Page 27 and 28: to the history of that point (« me
Page 29: ConstantmoisturecontentTime t = 0 +
Page 33 and 34: Averaged moisture content (%)907560
Page 35 and 36: Moisture content (%)12010080604020A
Page 37: Second drying periodTensionParamete
Page 42 and 43: eaction wood produced by environmen
Page 44 and 45: where the boards butt up due to shr
Page 46 and 47: 1.2Normalized moisture content (Φ)
Page 48 and 49: set at a constant value at constant
Page 50 and 51: oards by conduction whereas the vac
Page 52 and 53: KilnSolarcollectorCondenserControlv
Page 54 and 55: Doe, P.E., Oliver, A.R., and Booker
Page 56 and 57: Perré P., 1992. Transferts couplé

36 Drying of Wood

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