Electronic Journal of Polish Agricultural Universities (EJPAU) founded by all Polish Agriculture Universities presents original papers and review articles relevant to all aspects of agricultural sciences. It is target for persons working both in science and industry,regulatory agencies or teaching in agricultural sector. Covered by IFIS Publishing (Food Science and Technology Abstracts), ELSEVIER Science - Food Science and Technology Program, CAS USA (Chemical Abstracts), CABI Publishing UK and ALPSP (Association of Learned and Professional Society Publisher - full membership). Presented in the Master List of Thomson ISI.
Volume 7
Issue 2
Wood Technology
Available Online: http://www.ejpau.media.pl/volume7/issue2/wood/art-01.html


Andrzej Krauss



Swelling pressure in longitudinal direction has been determined on the basis of the time dependence of intensity of hygro-mechanical creep on the stretching, by the method of Moliński and Raczkowski [11]. The external stress needed for total inhibition of unidirectional spruce wood longitudinal swelling has been established. The maximum value of the swelling pressure determined on the basis of hygro-mechanical deformations of spruce wood samples simultaneously subjected to stretching in longitudinal direction and moistening is 14.4 MPa which is by 60% higher than the corresponding value found by the direct method of swelling inhibition for spruce wood sample of the same density. The probable reason for getting higher values of the maximum swelling pressure by the indirect method applied was the elimination of the sample buckling and a shortening of the time needed to reach the swelling pressure maximum, so reduction of the effects of the relaxation processes on the final result of swellin

Key words: hygro-mechanical creep, swelling pressure, spruce wood (Picea abies Karst.)..


It has been known for a long time that wetted wood exerts significant forces on obstacles restricting its free swelling. This phenomenon has been used even in antiquity for cleavage of rocks by insertion of dry wood wedges and then allowing them to absorb water. This phenomenon known as the swelling pressure of wood is common in all wood elements and constructions exposed to variable humidity conditions during exploitation. Perkitny [13] defined the swelling pressure as the pressure that must be exerted on the swelling wood from outside to preserve its original dry state size. The swelling pressure is the only experimentally determined parameter used to describe the inner stress in wood arising on its wetting [22].

The swelling pressure has been shown to depend on many factors, including the method of measurement applied [3, 7, 12, 14, 18, 19]. The observed wood capability of adsorption longitudinal elongation, under compressive stress even 2.5 times greater than the maximum swelling pressure in longitudinal direction [6] has aroused serious questions as to whether the hitherto applied methods of swelling pressure measurement are able to give the actual value of the swelling forces acting on wood moistening.

As follows from literature on swelling pressure, there are two main groups of the methods developed for its determination: the direct ones in which the swelling forces are measured [1, 3, 4, 13, 18, 19, 21] and the indirect ones in which some other parameters are measured [2, 11, 15, 17, 20]. The majority of the direct methods originate from the technique proposed by Perkitny [13] in which the sample permanent distortion on wetting is prevented and care is taken so that it only undergoes transient deformations. However, some of the methods from this group permit permanent deformations. Cyclic loading of the sample studied, required in the method proposed by Perkitny, is know [10] to intensify stress relaxation. In the methods allowing permanent swelling of the sample, it is not subjected to cyclic loading but the swelling is not totally inhibited. In view of the above it is reasonable to suppose that the maximum swelling pressure determined by the direct methods does not give actual val ues of the swelling forces in wood.

From among the experimentally verified indirect methods, an interesting one is that proposed by Moliński and Raczkowski [11, 12] and Moliński [10], in which the swelling pressure is determined from the time dependencies of hygro-mechanical wood deformation on applying mechanical loading of different values. The method permits determination of the stress needed for unidirectional inhibition of hygroscopic deformations and is based on the linear character of the dependence of viscoelastic properties of the sample on external load not exceeding 1/3 of its immediate resistance in the wet state. This method of determination of the adsorption stress in wood on the basis of the time dependence of its hygro-mechanical creep on stretching is devoid of the inconveniences of the traditional direct methods. No buckling of the sample or the cell walls occurs and in the measured section the stress is more or less uniform than in the direct method. In this method the adsorption stress is measured in the conditions of controlled aided swelling in contrast to the classical method in which the adsorption stress is measured on swelling inhibition. In the adsorption stress measurements on hygro-mechanical creep it is irrelevant whether the deformation of wetted wood is inhibited by compression or aided by stretching of the same strength [11], because the elasticity modulus in a given anatomical direction of wood determined on compressing and stretching takes the same values [5].

To be able to get more realistic values of the sorption stress in wood, the swelling pressure in longitudinal direction in the wood samples wetted in humid air was determined. The aim of the study was to derive the values of swelling pressure of wood in longitudinal direction on the basis of the time dependence of the hygro-mechanical creep on the sample stretching.


The study was performed for spruce wood samples (Picea abies Karst.). The samples were cut out in the shape of double oars of the size 100 mm in longitudinal direction, 6 mm in the radial direction and 2 mm in the tangential direction. The narrowed section in the middle of the sample (the measuring base) was 66 mm long measured in longitudinal direction (Figure 1). The samples were made of the bolt from the central log of 63 mm in thickness, seasoned in laboratory conditions. The mean moisture content of the log was 8%. From the circumferential zone of the bolt, some slabs of the cross-section of 20(T) x 15(R) mm were cut out and subjected to curving and milling in order to give them the desired shape of oars. The samples selected for the study were those of the grains parallel to the longitudinal axis and the same number of annual rings.

Fig.1. The shape and size of the sample

The swelling pressure in longitudinal direction was measured according to the method proposed by Moliński and Raczkowski [11] and using the equipment they described. The density of wood samples in the oven-dry state was in the range 415±15 kg/m3. The hygro-mechanical creep was measured on moistening the samples from the oven-dry state in the air of relative humidity close to 98% and at 294±1°K. The stretching load applied was 0.01, 0.13, 0.26 and 0.32 of the immediate resistance to stretching in longitudinal direction in the wet state. The absolute values of the stretching stress applied were 0.65, 10, 20 and 25 MPa. Each measurement was three times repeated. All the measurements were performed in 6 hours. Apart from the hygro-mechanical deformations, on the twinned samples the hygroscopic deformations were observed, and their moisture content was measured at the time needed to reach the maximum swelling pressure. The absolute deformation was always re ferred to the initial sample measuring base.


The time dependence of the hygro-mechanical sample deformations of spruce wood moistened in humid air and stretched in longitudinal direction are presented in Table 1 and Figure 2. The data used to illustrate this dependence are mean values because of a small scatter of the experimental results. As follows from the experimental data, the hygroscopic deformations are proportional to the stretching stress applied. This observation is confirmed by the isochoric dependencies of hygro-mechanical creep on the stretching stress presented in Figure 3.

Table 1. The size of the hygro-mechanical deformations of the wood samples studied

Time, t [h]

Deformation, epsylon hm [%]

Mechanical stress , sigma [MPa]
















































Fig.2. Time dependence of hygro-mechanical deformations of spruce wood under longitudinal stretching stress and simultaneously moistened in air

Fig.3. Mechanical stress versus the time of its application and hygro-mechanical deformations of spruce wood under longitudinal stretching stress and simultaneously moistened in air (a) and the adsorption stress obtained from these dependencies (b)

The linear dependencies of the hygro-mechanical deformations on the stress (epsylon hm = f(sigma)) were approximated by the equations of linear regression. The lines obtained on the basis of these equations were found to cut the ordinate axis at the points corresponding to the experimentally obtained values of free hygroscopic deformations. In this way a series of linear equations of the type epsylon(t i) = m(t i)sigma + b(t i) was obtained, in which:

The equations and the corresponding correlation coefficients are given in Table 2. The Table also presents the numerical values of the stress calculated from the regression equations that, if applied, would not permit the sample swelling in a given anatomical direction, despite wetting. As follows from the dependencies shown in Figure 3, the values of stress needed for total inhibition of swelling have the negative sign. This is the compressive stress whose intensity changes in a continuous way on wetting (Fig. 3b). The time dependence of the adsorption stress determined in the above described way is in a qualitative agreement with that of the swelling pressure determined by the classical direct method [8, 14, 16].

The maximum value of swelling pressure determined from the measurements of hygro-mechanical creep in longitudinal direction is on average 14.4 MPa, which is by about 60% higher than the corresponding value obtained by the direct method (converted per the same wood density) [8]. This fact can be explained by elimination of the buckling of the whole sample and its particular anatomical elements in the indirect method. Moliński [10, 11] reported the swelling pressure values determined for the directions across to the grains by about 40% higher than those obtained by the direct method. A possible reason for getting the swelling pressure values in the longitudinal direction by over 50% higher than those obtained by the classical method can be a different kinetics of moistening. In the measurements by the indirect method the maximum swelling pressure was noted after 4 hours of moistening, whereas in the direct method after 24h of moistening [8]. The mean moisture contents of the samples at the t ime of the maximum swelling pressure did not differ significantly in the two experiments 12.5% and 13.5%. The indirect method, in contrast to the classical one, permits the use of very thin samples, for which the time needed for reaching the maximum swelling pressure is shorter and the relaxation processes have much lower effect on the final result of measurement.

Table 2. Regression equations describing the dependence of the deformation of the samples on the value of the tensile stress at the selected moments of the hygro-mechanical creep process

Time, t

Regression equation

Correlation coefficient, r

Stress corresponding to zero deformation, sigma* [MPa]








e = 0.0169s – 0.0023

e = 0.0192s + 0.1228

e = 0.0204s + 0.2251

e = 0.0219s + 0.2843

e = 0.0225s + 0.3235

e = 0.0237s + 0.3381

e = 0.0243s + 0.3452















In order to determine the maximum swelling pressure disregarding the effect of the stress relaxation, so the so-called pure swelling pressure, the method proposed by Mishiro [9] was applied. In this method the swelling pressure is obtained from the slope of the linear section of the swelling pressure dependence on the swelling. The linear section is extrapolated to intersect the line parallel to the axis of ordinates and passing through the point of abscissa corresponding to the maximum swelling pressure [alpha(sigma* msp)]. The ordinate of this point is the pure swelling pressure (sigma*psp). The pure swelling pressure value read out from the dependence shown in Figure 4 is 16 MPa and is only by 11% higher than the maximum swelling pressure (sigma*msp).

Fig.4. The swelling pressure of spruce wood along the grain as a function of swelling on moistening in humid air

The maximum swelling pressure in longitudinal direction converted into the swelling pressure of wood substance reaches 52 MPa, while the pure swelling pressure after analogous conversion is 58 MPa. In the experiment reported in this paper, only the unidirectional value of the swelling pressure was determined, and it is only part of the total energy of wood swelling. The swelling pressure of wood substance on the submicroscopic level calculated from the Katz equation reaches about 160 MPa [18]. Tarkow and Turner [21] have reported that the wood of 1440 kg/m3 density on two-directional inhibition of its swelling caused by moistening in the air of relative humidity varying from 30 to 100%, generates the swelling pressure of over 77 MPa. In view of the above, it is reasonable to suppose that the swelling pressure values determined in this study are close to the real ones.


The method of wood swelling pressure determination from the measurements of hygro-mechanical creep on stretching and simultaneous moistening in humid air can be applied for measurements of swelling pressure of wood in longitudinal direction. It is devoid of some of the inconveniences of the direct method, which is of particular importance in the measurements in longitudinal direction. The method permits determination of the swelling pressure values close to the real ones and by about 60% higher than those obtained by the direct method of swelling inhibition.


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Andrzej Krauss
Faculty of Wood Technology
The August Cieszkowski Agricultural University of Poznań
Wojska Polskiego 38/42, 60-627 Poznań, Poland
e-mail: akrauss@au.poznan.pl

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