Mechanosorptive creep of wood laminate elements.

Obucina, Murco ; Dzaferovic, Ejub ; Bajramovic, Rasim 等

1. INTRODUCTION

Laminated elements made of veneer or wood laminates, glued together in longitudinal and perpendicular direction, have better mechanical and reologic properties and stability of shape compared to products made from single piece of wood. During exploitation these products are mainly exposed to constant loading and environmental effects. Considering the fact that wood is a viscoelastic material the logical consequence is the creep.

The least explained phenomenon is the wood creep appearing due to change of moisture. Deformation--deflection of loaded element, which goes through one or more moisturizing cycles, is higher than with the element exposed to one of two extreme moisture content conditions. Also, the amount of creep depends on the quantity and speed of moisture change. This phenomenon was explained by Grossman (Grossman, 1976) naming it "mechanosorptive creep". He described the difference between the creep under constant environmental conditions and mechanosorptive creep. Wood as a hygroscopic material has the ability to receive and to lose moisture depending on the difference between its own moisture and moisture in its environment, striving to create a balance with its environment. This phenomenon (absorption and desorption of moisture) is specially emphasized in hygroscopic moisture area and it is manifested through change in wood dimensions. Any movement of moisture in material is called moisture diffusion. If the cause is the gradient of potential of moisture then it is isothermal transfer of moisture and that phenomenon is called moisture conductivity. If the cause is the gradient of the temperature then the phenomenon can be called thermal-moisture conductivity.

2. METHODS

Moisture diffusion in the cross section of wood and wood products can be described by basic mass balance equation. This, together with constitutive relation of the initial and boundary condition, represents a mathematical model (Demirdzic et. al., 2005).

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Equations are valid for a whole body and for each body volume part V limited with surface S, with the outward-pointing surface vector n.

Equation (1) relates the mass change in the time unit and over the with the moisture diffusion. With the constant temperature the ratio between the moisture content and moisture potential is a linear function given as:

w = [c.sub.m]M (2)

where [rho] is density, w is moisture, [c.sub.m] is specific moisture, M is moisture potential, [q.sub.w] is mass flux, [S.sub.w] is moisture source in the time unit and over unit of mass.

If we assume isotropy and isothermal moisture transfer, then the relation between the mass flux [q.sub.w] and the moisture potential gradient M is given by the Fick's Law:

[q.sub.w] = -D gradM (3)

where D is the moisture diffusion coefficient

Boundary conditions for moisture diffusion are determined with the following equation (Srpcic et. al., 2001):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (4)

where [q.sub.w] is the flow of the moisture (mass flux) through the boundary surface (kg/[m.sup.2]s), [n.sub.i] are components of the normal to boundary surface, and [w.sub.p] is the given moisture content at boundary.

Boundary conditions for the moisture flow (4) can be simplified assuming that the water flow is a linear function of the difference between the water content at the boundary [w.sub.S] and equivalent water content in surrounding air [w.sub.A], which depends on relative humidity of surrounding air and the type of wood (Srpcic et. al., 2001):

[q.sub.w] = s([w.sub.A] - [w.sub.s]) (5)

where S is a coefficient of the transfer of moisture.

Creep test was done on a device with four-wheel load, where it was possible to simultaneously perform the creep test for 5 elements. Device was in a chamber where relative humidity was made constant by constant flow of air using axial fans over the container with salt. To preserve 94 % air humidity we used saturated solution of salt (Potassium Sulphate [K.sub.2]S[O.sub.4]) in water, and for 33 % humidity the Magnesium Chloride Mg[Cl.sub.2] x 6[H.sub.2]O. Room temperature was kept at 22.5 [+ or -] 0.5 oC.

Length of the cycle of different relative moistures was determined using the experience gained in the pre-experiment. Creep was monitored in four cycles of the air humidity change, two moistening (94 %) and two drying (33 %). The first cycle was moistening and it lasted 21 days, and the other three cycles were 14 days of sequential change of humidity in the chamber. Moisture of samples was measured using the gravimetric method. Each sample was cut to 26 samples of the same length of 18 mm. Then these were aligned one after another on a flat surface, the 3.2 mm thick veneer layer and put in a chamber along with the elements which were subjected to the creep test (Figure 1).

[FIGURE 1 OMITTED]

Samples were then quickly taken out of the chamber and were not returned in order to avoid the change of the relative humidity in the chamber as little as possible. The moisture determined in this manner was then used for the verification of the moisture content results through time, acquired by numerical model.

3. RESULTS

Analysis of experimental results shows the moisture influence on creep of laminated elements. The dominant influence on creep comes from the relative air humidity, i.e. moisture content of the laminated elements which were exposed to constant loading. After the initial elastic deformation which occurs under the loading, when we have a relatively high air moisture ([phi] =94 % [approximately equal to] w=21 %) then we get the deformation which increases with time (Figure 2).

With the increase of the moisture content in the hygroscopic area we have a decrease in the module of elasticity and increase of deformation (Obucina et.al., 2006). Diffusion of the moisture through time leads to tearing, transfer and reestablishment of active hydrogen bonds. This "tearing" of the bonds in the cell wall has as a consequence in the decrease of elastic properties, which leads to the deformation increase (Mukudai & Yata, 1986).

[FIGURE 2 OMITTED]

Most of the moisture is transferred by diffusion through a porous material. That is the reason why moisture content in the samples was assessed by diffusion in each time step and then the two-dimensional distribution of the moisture content was calculated over cross section (Figure 3). Material and physical parameters influencing the distribution of the water content were taken from literature.

[FIGURE 3 OMITTED]

In the above diagram we can observe that the highest diffusion of moisture in the cross section of the laminated elements happens at the start of exposure of laminated elements to different moisture. If the penetration depth of moisture throughout the cross section had influenced the creep then it would have taken much longer time to reach stabilization of the mechanosorptive creep. Moisture diffusion in the sample cross section is slowed down by glue layers and change of the wood properties due to increased temperature and pressure during the gluing process. This means that there is a significant difference in moisture of internal and external layers of the laminated elements. The speed of change of moisture influences the speed of change of deformation, but not its value.

Considering certain omissions during the definition of the numerical simulation of the moisture distribution over sample cross section we achieved good results, and the mentioned numerical model can be used to predict diffusion and distribution of moisture in wood and wood composites.

4. CONCLUSION

Change of moisture significantly influences the creep of laminated elements obtained by gluing of wood.

Outside layers of laminated elements had the highest moisture changes and that dominantly influenced mechanosorptive creep of laminated elements.

The used numerical model based on finite volumes can be successfully applied in prediction of the moisture gradient for cross section of the laminated elements.

5. REFERENCES

Demirdzic I.; Dzaferovic E. & Ivankovic A. (2005). Finite Volume Approach to Thermoviscoelasticity. Numerical Heat Transfer, Part B. 47: 213-237

Grosman P. U. A. (1976). Requirements for a model that exhibits mechano-sorptive Behavior. Wood Science and Technology, 10: 163-168

Mukudai. J. & Yata S. (1986). Modeling and simulation of viscoelastic behavior (tensile strain) of wood under moisture change. Wood Science and Technology, 20: 335-348

Obucina M.; Dzaferovic E.; Bajramovic R. & Resnik J. (2006). Influence of gluing technology on viscoelasticity properties of LVL. Wood Research. 51 (4): 11- 22

Srpcic S.; Turk G. & Srpcic J. (2001). Lon-term Behavior of Glulam Beams under Changing Humidity. Proceedings of First International Conference of the European Society for Wood Mechanics, Navi P. (Ed), pp. 167-176, Lausanne Switzerland