Deformation in Timber
DIMENSIONAL CHANGE IN TIMBER DUE TO MOISTURE
In timber it is customary to distinguish between those changes that occur when green timber is dried to very low moisture contents (e.g. 12%), and those that arise in timber of low moisture content due to seasonal or daily changes in the relative humidity of the surrounding atmosphere. The former changes are called shrinkage while the latter are known as movement.
Shrinkage in Timber
Removal of water from below the fibre saturation point occurs within the amorphous region of the cell wall and manifests itself by reductions in strength and elastic modulus, as well as inducing dimensional shrinkage of the material.
Anisotropy in Shrinkage
The reduction in dimensions of the timber, technically known as shrinkage, can be considerable but, owing to the complex structure of the material, the degree of shrinkage is different on the three principal axes; in other words, timber is anisotropic in its water relationships.
The variation in degree of shrinkage that occurs between different timbers and, more important, the variation among the three different axes within any one timber are illustrated in Table 1. It should be noted that the values quoted in the table represent shrinkage on drying from the green state (i.e. > 27%) to 12% moisture content, a level which is of considerable practical significance.
At 12% moisture content, timber is in equilibrium with an atmosphere having a relative humidity of 60% and a temperature of 20oC; these conditions would be found in buildings having regular but intermittent heating. From Table 1 it will be observed that shrinkage ranges from 0.1% to 10%, i.e. a 100fold range.
Longitudinal shrinkage, it will be noted, is always an order of magnitude less than transverse, while in the transverse plane radial shrinkage is usually some 60–70% of the corresponding tangential figure.
The anisotropy between longitudinal and transverse shrinkage, amounting to approximately 40:1, is due in part to the vertical arrangement of cells in timber and in part to the particular orientation of the microfibrils in the middle layer of the secondary cell wall (S2). Thus, since the microfibrils of the S2 layer of the cell wall are inclined at an angle of about 15o to the vertical, the removal of water from the matrix and the consequent movement closer together of the microfibrils will result in a horizontal component of the movement considerably greater than the corresponding longitudinal component (see Table 1).
Various theories have been developed over the years to account for shrinkage in terms of microfibrillar angle. The early theories were based on models that generally consider the cell wall to consist of an amorphous hygroscopic matrix in which are embedded parallel crystalline microfibrils that restrain swelling or shrinking of the matrix.
One of the first models considered part of the wall as a flat sheet consisting only of an S2 layer, in which microfibrillar angle had a constant value (Barber and Meylan, 1964). This model treated the cells as square in cross-section and there was no tendency for the cells to twist as they began to swell.
An improved model (Barber, 1968) treated the cells as circular in cross-section and embraced a thin constraining sheath outside the main cylinder, which acted to reduce transverse swelling; experimental confirmation of this model was carried out by Meylan (1968).
Later models have treated the cell wall as comprising two layers of equal thickness, having microfibrillar angles of equal and opposite sense, and these twoply models have been developed extensively over the years to take into account the layered structured of the cell wall, differences in structure between radial and tangential walls, and variations in wall thickness.
The principal researcher using this later type of model was Cave, whose models are based on an array of parallel cellulose microfibrils embedded in a hemicellulose matrix, with different arrays for each wall layer; these arrays of basic wall elements were bonded together by lignin microlayers.
Earlier versions of the model included consideration of the variation in the elastic modulus of the matrix with changing moisture content (Cave, 1972, 1975). The model was later modified to take account of the amount of highenergy water absorbed rather than the total amount of water (Cave, 1978a, b). Comparison with previously obtained experimental data was excellent at low moisture contents, but poorer at moisture contents between 15 and 25%.
All these theories are extensively presented and discussed by Skaar (1988) and more recently by Pang (2002) who, in addition, has modified the Barber and Meylan model to accommodate changes in lumen shape during shrinkage and the presence of layers of variable shrinkage in the wood.
The influence of microfibrillar angle on the degree of longitudinal and transverse shrinkage described for normal wood is supported by evidence derived from experimental work on compression wood.
Compression wood is characterised by possessing a middle layer to the cell wall, the microfibrillar angle of which can be as high as 45o, though 20–30o is more usual. The longitudinal shrinkage is much higher and the transverse shrinkage correspondingly lower than in normal wood, and it has been demonstrated that the values for compression wood can be accommodated on the shrinkage– microfibrillar angle curve for normal wood.
Differences in the degree of transverse shrinkage between tangential and radial planes (Table 1), are usually explained in terms of: first, the restricting effect of the rays on the radial plane; second, the increased thickness of the middle lamella on the tangential plane compared with the radial; third, the difference in degree of lignification between the radial and tangential cell walls; fourth, the small difference in microfibrillar angle between the two walls; and fifth, the alternation of earlywood and latewood in the radial plane which, because of the greater shrinkage of latewood, induces the weaker earlywood to shrink more tangentially than it would if isolated.
Considerable controversy reigns as to whether all five factors are actually involved and their relative significance. Comprehensive reviews of the evidence supporting these five possible explanations of differential shrinkage in the radial and tangential planes is to be found in Boyd (1974) and Skaar (1988).
Recently Kifetew (1997) demonstrated that the gross transverse shrinkage anisotropy of Scots pine timber, with a value approximately equal to 2, can be explained primarily in terms of the earlywood– latewood interaction theory by using a set of mathematical equations proposed by him; the gross radial and transverse shrinkage values were determined from the isolated early and latewood shrinkage values taken from the literature. Volumetric shrinkage, sv, is slightly less than the sums of the three directional components.
In order to avoid shrinkage of timber after fabrication, it is essential that it be dried down to a moisture content that is in equilibrium with the relative humidity of the atmosphere in which the article is to be located. A certain latitude can be tolerated in the case of timber frames and roof trusses, but in the production of furniture, window frames, flooring and sports goods it is essential that the timber is seasoned to the expected equilibrium conditions, namely 12% for regular intermittent heating and 10% in buildings with central heating, otherwise shrinkage in service will occur with loosening of joints, crazing of paint films, and buckling and delamination of laminates.
An indication of the moisture content of timber used in different environments is presented in Fig. 1.
So far only those dimensional changes associated with the initial reduction in moisture content have been considered. However, dimensional changes, albeit smaller in extent, can also occur in seasoned or dried wood owing to changes in the relative humidity of the atmosphere. Such changes certainly occur on a seasonal basis and frequently also on a daily basis.
Since these changes in humidity are usually fairly small, inducing only slight changes in the moisture content of the timber, and since a considerable delay occurs in the diffusion of water vapour into or out of the centre of a piece of timber, it follows that these dimensional changes in seasoned timber are small, considerably smaller than those caused by shrinkage.
To quantify such movements for different timbers, dimensional changes are recorded over an arbitrary range of relative humidities. In the UK, the standard procedure is to condition the timber in a chamber at 90% relative humidity and 25oC, then to measure its dimensions and to transfer it to a chamber at 60% relative humidity and 25oC, allowing it to come to equilibrium before re-measuring it; the corresponding average change in moisture content is from 21 to 12%. Movement values in the tangential and radial planes for those timbers listed in Table 1 are presented in Table 2.
The timbers are recorded in the same order, thus illustrating that although a broad relationship holds between values of shrinkage and movement, individual timbers can behave differently over the reduced range of moisture content associated with movement.
Since movement in the longitudinal plane is so very small, it is generally ignored. Anisotropy within the transverse plane can be accounted for by the same set of variables that influence shrinkage. Where timber is subjected to wide fluctuations in relative humidity, care must be exercised to select a species that has low movement values.
Moisture in timber has a very pronounced effect not only on its strength, but also on its elastic modulus, toughness and fracture morphology. Aware of the technological significance of the instability of wood under changing moisture content, many attempts have been made over the years to find a solution to the problem; although it has not been possible to achieve complete dimensional stabilisation, it has been possible through the effects of either heat treatment or chemical modification to reduce the dimensional movement in wood by about 50%.
Timber, like other materials, undergoes dimensional changes commensurate with increasing temperature. This is attributed to the increasing distances between the molecules as they increase the magnitude of their oscillations with increasing temperature. Such movement is usually quantified for practical purposes as the coefficient of linear thermal expansion, and values for certain timbers (and other substances) are listed in Table 3. Although differences occur between species these appear to be smaller than those occurring for shrinkage and movement.
The coefficient for transverse expansion is an order of magnitude greater than that in the longitudinal direction. This degree of anisotropy (10:1 on average) can be related to the ratio of length to breadth dimensions of the crystalline regions within the cell wall.
Transverse thermal expansion appears to be correlated with specific gravity, but somewhat surprisingly this relationship is not sustained in the case of longitudinal thermal expansion, where the values for different timbers are roughly constant (Weatherwax and Stamm, 1946).
The expansion of timber with increasing temperature appears to be linear over a wide temperature range; the slight differences in expansion that occur between the radial and tangential planes are usually ignored and the coefficients are averaged to give a transverse value, as recorded in Table 3.
For comparative purposes the coefficients of linear thermal expansion for glass- and carbon fibrereinforced plastic, two metals and two plastics are also listed. Even the transverse expansion of timber is considerably less than those of the plastics. The dimensional changes in timber caused by differences in temperature are small when compared with changes in dimensions resulting from the uptake or loss of moisture.
Thus for timber with a moisture content greater than about 3%, the shrinkage due to moisture loss on heating will be greater than the thermal expansion, with the result that the net dimensional change on heating will be negative. For most practical purposes thermal expansion or contraction can be safely ignored over the range of temperatures in which timber is generally employed.