Maderas. Ciencia y tecnología. 4(1):77-99, 2002

NOTAS TECNICAS

CONTRIBUTION TO THE THEORY OF CELL COLLAPSE IN WOOD:
INVESTIGATIONS WITH EUCALYPTUS REGNANS♣

W. G. KAUMAN^1
1Ex Investigador de la Division of Forest Products, C.S.I.R.O., Melboume. Australia

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SUMMARY

Total collapse is considered as the sum of “liquid tension collapse” and “stress collapse”. An equation is derived giving total collapse as a linear function of wood temperature and, to a smaller extent, of collapse-free shrinkage. The parameters of the equation depend only on surface tension data and on structural and rheological properties of the wood.

To test the theory, Eucalyptus regnans cubes of 7/8 in. edge length were dried at temperatures ranging from 70 to 285°F, using two levels of humidity at each temperature. In addition, specimens measuring 7/8 by 7/8 by 3 in. were dried at 150°F and low humidity.

The results show good agreement with theoretical values for wood temperatures up to about 190°F. For higher temperatures or very low humidities collapse is found to be significantly time-dependent.

Collapse in small end-sealed cubes is shown to be of the same order as that in the thickness of boards of rectangular cross section, but the latter collapse less in width.

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INTRODUCTION

Collapse of the cells during drying is commonly observed in certain timber species and is particularly pronounced in some members of the genus Eucalyptus.

A widely accepted theory attributes this cell collapse to hydrostatic tensions acting in the water-filled capillary spaces of the wood structure (Tiemann 1915; Greenhill 1938). On the other hand, macroscopic stresses arising in the wood during drying have been suspected to contribute to collapse (Greenhill 1938) and have been claimed by some workers to be the sole cause of the phenomenon (Stamm and Loughborough 1942). Evidence has been presented that the intensity of collapse increases with increase in temperature during drying (Tiemann 1913; Greenhill 1938; Ellwood 1952; Ellwood et al. 1953). The relative humidity of the drying medium and the duration of the drying treatment have also been considered important in determining collapse intensity.

The present experiment was designed to investigate the mode of action of the collapse-inducing forces and their contribution to the observed collapse o ver a range of experimental conditions. The design also provided for possible differences between trees and positions within trees.

THEORETICAL CONSIDERATIONS

On the basis of earlier work as well as on the evidence of the present experiment, hydrostatic tensions and macroscopic drying stresses may be taken as the principal collapse-inducing forces. The corresponding components of the “total collapse” will be termed “liquid-tension collapse” and “stress collapse”.(Total collapse is defined as the difference between the total observed shrinkage and the "collapse-free shrinkage" determined on end-matched specimens measuring 1/32 in. in the fibre direction (Greenhill 1936)—see key to Figure 1)

The hydrostatic tension, P, is given by

(1)

where s = surface tension,

r₁, r₂ = principal radii of meniscus in largest opening in the cell wall of collapse-susceptible fibre.

To cause collapse, P must exceed the stress at the limit of plastic flow for the cell walls concerned. This property has never been directly measured. Because of the similarity in the appearance of collapsed cells to cells crushed by external compression (e.g. Tiemann 1948) it does not appear unreasonable to use instead, to a first approximation, results obtained for bulk wood, but even for bulk wood, data on the limit of plastic flow in compression perpendicular to the grain are not available. However, by analogy with other strength properties, the stress at the limit of plastic flow may be assumed to vary linearly with temperature. For instance, accurate measurements by Ellwood (1954) on American beech (Fagus spp.), whose strength properties generally do not differ excessively from Eucalyptus regnans, show that the proportional limit stress and the modulus of elasticity for short-term loading are related to temperature by highly significant linear regression equations. Similar

results were obtained by Kitahara and Suematsu (1955) for Japanese species. Taking account of the linear variation of surface tension with temperature (Eotvós relation), the collapse-inducing force due to liquid tension (FL) may therefore be represented by a linear relation,

FL = P-Q = ao + a1T

(2)

where
Q = stress at limit of plastic flow,
T = temperature of the wood,
a_o + a₁ = constants.

Liquid-tension collapse (C_L) is thus given by

CL = ØL ( FL) (1-fL (t))

(3)

where Ø_L is the time-independent functional relation between C_L and F_L, whereas f_L (t)(t = time) is of the nature of a creep function (cf. Grossman and Kingston 1955),

with
f_L (t) = 1 for t = O,
f_L (t) = O for t →∞

Stress collapse is induced during drying by the stresses acting in a plane perpendicular to the fibre direction. A full analytical calculation of stress collapse requires more detailed knowledge about the interaction of rheological properties with migration of heat and moisture than is at present available. However, a working hypothesis may be formulated along the following lines.

Due to the moisture gradient in a specimen being dried, the shell is stressed in tension during the collapse-susceptible stage. Earlier work (Kauman 1958) shows that this tension stress causes a reduction in total shrinkage in the shell parallel to the surface and an increase in total shrinkage in the shell perpendicular to the surface. (The latter effect is a viscoelastic analogy to the Poisson ratio.) The shell while stressed in tension exerts a compressive stress on the deeper parallel layers, resulting in increased total shrinkage in the core. A method for estimating these internal stresses from the results of mechanical testing experiments has been suggested by Ellwood (1954) for short-term static loading, but there are no suitable data for the estimation of stresses in E. regnans under the conditions of the present experiment.

On the basis of the limited information available, a simple and convenient assumption is to consider stress collapse proportional to compressive stress, and compressive stress in turn proportional to the tensile stress in the shell. An indication of the magnitude of the tensile stress is given by the reduction of shrinkage in the shell parallel to the surface. This reduction may be taken as equal to the difference between the potential shrinkage of the unstressed shell and the actual shrinkage of the core at the time of maximum tension stress.

Stress collapse (C_s) may thus be written

(4)

where
S₀+C_L = potential shrinkage of unstressed shell,
S₀ = collapse-free shrinkage,
S_c = actual shrinkage of core at time of maximum tension stress.

The significance of the other symbols is analogous to equation (3). Superscripts i and j designate the tangential and radial directions.

Provided that the liquid-tension and stress components are additive, total collapse is given by the sum of (3) and (4).

EXPERIMENTAL PROCEDURE

(a) Material

The experimental material was selected from six sound mountain ash trees (E. regnans F. Muell.) aged 130 to 300 years, and grown in southern Tasmania. Ten sample blocks measuring about 6 by 3 by 4 in. were cut about 11/2 in. beneath the sapwood, comprising two blocks taken at different heights from each of four trees (Nos. 1, to 4) and one block from each of the other two trees (Nos. 5 and 6). Each block was sawn into 38 small cubes of 7/8 in. edge length (nominal) and 3 pairs of matched specimens of dimensions 7/8 by 7/8 by 3 in. approximately, the long axes of the specimens in the different pairs being in the tangential, radial, and longitudinal directions, respectively. In addition, a complete cross section measuring ^1/32 in. in the fibre direction was cut into 7/8 in. square specimens to determine collapse-free shrinkage.

(b) Experimental Tests

The experiment comprised:
(i) An investigation of the contribution to observed collapse by the liquid tension collapse and stress collapse-inducing forces over a range of experimental conditions (using 7/8 in. cubes.)

(ii) A limited study of the relation between collapse and the size and orientation of the specimen (using specimens measuring 7/8 by 7/8 by 3 in. approximately).

The 7/8 in. cubes were allotted at random to 38 test batches so that each batch . consisted of 10 specimens, including one from each sample block. Nineteen batches were allocated to the experimental treatments outlined in Table 1, the remainder being used for collateral tests and for repetitions. The 60 specimens in the study of collapse and specimen size were treated as one batch.

Drying treatments at dry-bulb temperatures of 110, 150, and 190°F were carried out in small research kilns using an air velocity of about 300 ft/min and tests at 75, 220, and 285°F in natural convection cabinets. The ^ in. specimens were dried at 75°F with natural convection.

Drying at the 4 and O per cent. equilibrium moisture content (e.m.c.) level was discontinued at an average moisture content of about 10 to 12 per cent. After the completion of drying, all specimens were conditioned to 12 per cent. Moisture content, then reconditioned (Reconditioning is a treatment in saturated steam at 212°F given to alleviate collapse) for 2 hr and again conditioned to 12 per cent. Although the optimum moisture content for reconditioning is about 17 per cent. (Greenhill 1938), scout tests showed that the small specimens used absorbed sufficient moisture during reconditioning to ensure recovery. The specimens were finally oven dried at 220°F.

The pore-size distribution in the wood structure was determined on 1/8 in. cubes by a mercury penetration technique based on a method first described by Ritter and Drake (1945).

The limit of proportionality in compression perpendicular to the grain was measured on green 2 in. cube specimens held at temperatures of either 70, 125, or 190°F throughout the test. The testing technique used was similar to that specified in B.S. No. 373 (1938). Measurements were taken in a standard testing machine using a loading rate of 0.024 in/min. Half the number of specimens was loaded on the tangential faces and the other half on the radial faces. After determining the limit of proportionality, each specimen was held at constant load to obtain a time- deformation curve. The constant loads selected in each case corresponded to the calculated hydrostatic tension assumed to act in the wood during drying above fibre saturation point at the same temperature.

(c) Measurements

Moisture contents were determined from weighings, and linear shrinkages from measurements of dimensions by a dial gauge fitted with conical anvils (the width of any checks intersecting the line of measurement being subtracted) at the following stages: (i) before drying; (ii) five times at suitable intervals during drying; (iii) after drying and conditioning to 12 per cent. moisture content; (iv) after reconditioning and conditioning to 12 per cent. moisture content; and (v) after oven drying. Volumetric shrinkages at 12 per cent. moisture content before and after reconditioning were measured with an Amsier mercury volume meter.

TABLE 1: SUMMARY OF EXPERIMENTAL TESTS

Test Group	Specimen size (nominal in.)	Specification of drying Medium
		Dry-Bulb Temperature	Wet-Bulb Temperature (ºF)	equilibrium moisture content (%)	Relative Humidity (%)
Liquid Tension and stress collapse	7/8 by 7/8 by 7/8	285 220 190 190 150 150 150£ 110 110 75	- - 185 150 144 112 112 103 78 66	0 0 15 4 15 4 4 15 4 12	- - 89 38 84 31 31 79 24 63
Collapse and orientation	7/8 by 7/8 by 3	150	112	4	31
Collpase-free shrinkage	7/8 by 7/8 by 1/32	75¥	6	12	63

¥: Specimens unsealed

£: Treated for 8 days in concentrated sodium chloride prior to drying. Specimens sealed after treatment (one batch only)

Each of the treatments listed was given to one test batch of specimens with the end grain sealed and one batch with the end grain unsealed

In tests dried al the 4 and 0 per cent. equilibrium moisture content levels, the wood temperature was measured by inserting thermocouples into the centre of specimens (provided from special batches) through 1/16 in. (dia.) holes sealed with wooden plugs.

To determine the development of shrinkage in various positions within the specimen, a grid of lines, each about 5/1000 in. thick at 1/8 in. spacing, was traced with indelible pencil on the cross section of specimens selected from the top log of tree 2. The specimens of the lines were measured with a travelling microscope at suitable time intervals during drying. The collapse-free shrinkages in all positions on the cross section of each sample block were determined by measuring the shrinkage of sections of ¿g in. grain length dried at 75°F (Greenhill 1936).

Fig. 1. Dimensional changes observed on 7/8 in. cubes treated at 110, 150, and 190°F. BR, before reconditioning; AR, after reconditioning.

The expected standard error of moisture content was ±0.7 per cent. of the oven-dry weight, and of linear shrinkage about ± 0.2 per cent. of the green dimension. The standard deviation of a single volume measurement was 0.3 per cent. of the green dimension before reconditioning and 1.3 per cent. after reconditioning. Separate tests showed that the standard deviation of a single linear shrinkage determination in a particular position from measurements of grid spacing on the end grain was about ±0.5 per cent. of the green dimension.

The standard deviation of collapse-free shrinkage in all specimens was ± 1.2 per cent. and within sample blocks ±0.5 per cent. (average). These values are of the same order as those reported by Greenhill (1936) and are due to limitations of the technique and variability of the material.

Comparison of results in matched specimens indicated that thermocouple measurements of wood temperature were accurate to about ±2°F.

Fig. 2. Dimensional changes observed on 7/8 in. cubes treated at 75, 220, and 285°F and in specimens impregnated with sodium chaired. T, tangential; R, radial; V, volumetric; see Figure 1 for key to shading.

IV. RESULTS

(a) Study of Collapse-Inducing Forces

(i) Effect of Physical Variables. Dimensional changes observed in the drying experiments are shown in Figures 1 and 2 where the different components of total shrinkage are represented by differently shaded areas. The volumetric collapse-free shrinkages were calculated from the relation

V = Sr + St - SrSt/100

(5)

where
V = per cent. volumetric shrinkage,
S_r ,S_t = per cent. radial (r) and tangential (t) shrinkage, assuming longitudinal shrinkage to be negligible.

The mean total shrinkages and collapse for dry-bulb temperatures of 110, 150, and 190°F, for the two equilibrium moisture content levels used, and for sealed and unsealed specimens are summarized in Table 2. For the same dry-bulb temperatures, Table 3 gives the initial moisture contents, wood temperatures, drying times from the green condition to 30 per cent. average moisture content, and collapse recoveries. The lower initial moisture contents in sealed specimens are due to some unavoidable loss of moisture while drying the sealer coat. Changes in dimensions during the drying of the sealer coat were negligible.

TABLE 2:MEAN TOTAL SHRINKAGES, COLLAPSE RECOVERIES, AND TOTAL COLLAPSE AT DRY-BULB TEMPERATURES OF 110, 150, AND 190°F. Measured at 12 per cent. moisture content

Variable	Total Shrinkage before Reconditioning (%)			Collapse Recovery During Reconditioning			Total Collapse (%)
	Tan*.	Rad.	Vol.	Tan.	Rad.	Vol.	Tan.	Rad.	Vol. f
Dry-bulb temperature (°F) 190 150 110	21.6 17.9 14.5	13.9 11.8 9.7	29.2 25.2 20.9	12.0 10.2 7.3	8.1 7.0 5.2	14.6 12.7 8.5	14.8 11.0 7.9	10.0 7.8 5.7	19.1 14.9 10.9
End-sealing Sealed Not sealed	19.6 16.4	13.5 10.0	26.6 23.6	11.6 8.1	8.2 5.3	14.2 9.6	12.8 9.8	9.4 6.2	16.3 13.5
e.m.c. level (%)£ 15 4	18.1 17.9	11.6 12.0	25.8 24.4	9.7 10.0	6.5 7.0	12.0 11.9	11.6 11.0	7.6 8.0	15.8 14.0

* Tan.: tangential; Rad.: radial; VoL: volumetric.

f: Based on collapse-free shrinkages calculated from equation (5).

£ e.m.c: equilibrium moisture content.

Table 4 shows wood temperatures, drying times to 30 per cent. and collapse recoveries for drying tests at 75, 220, and 285°F and for specimens treated in sodium chloride.

The wood temperatures, after an initial heating period, tended to stabilize at some level between dry- and wet-bulb temperature until the average moisture content fell to within the vicinity of fibre saturation point, when they rose fairly rapidly towards the dry-bulb temperature (see Fig. 3). Wood temperatures in high humidity tests were estimated, within the limits of experimental error, from the dry- and wet-bulb temperatures of the drying atmosphere. Figure 4 shows the relation between collapse and wood temperature. The results for unsealed specimens dried at high humidity have been fitted by a straight line marked C_L.

Figure 4: Relation of total collapse to wood temperature. High humidity: ▲selead; Δ unsealed. Low humidity: ● sealed; ○ unsealed. CL, experimental liquid-tension collapse (see Section V(a) (i))

Figure 5 illustrates the development and distribution of total shrinkage in f in. cube specimens dried at 190°F, based on microscope measurements of the spacing of grid lines traced on the end grain. At this temperature, the effects of end sealing and humidity were very pronounced. Values in equivalent positions on both sides of the center were averaged to overcome matching difficulties due to differences in collapse in early and late wood. The enhanced shrinkage in positions 1 and 2 is caused by tension stress in the shell parallel to the surface, as discussed in Section II.

TABLE 3: INITIAL MOISTURE CONTENTS, STABILIZED WOOD TEMPERATURES, DRYING TIMES, AND COLLAPSE RECOVERIES AT DRY-BULB TEMPERATURES OF 110, 150, AND 190°F

Drying Conditions		End-Grain Sealing*	Initial Moisture Content (%)	Stabilized Wood Temperature (°F)	Drying Time to 30% Average Moisture Content (hr)	Collapse Recovery (% of total collapse)
Dry Bulb Temperature (°F)	e.m.c. Level of Drying Atmosphere (%)					Tan.	Rad.
190 190 190 190 150 150 150 150 110 110 110 110	15 15 4 4 15 15 4 4 15 15 4 4	S U S U S U S U S U S U	100 125 104 136 93 117 101 124 97 128 100 131	187f 185f 176 160 147f 145f 135 120 107f 105f 100 95	19 14 7 3 42 25 12 4 75 12 33 5	83 69 91 76 91 85 104 96 92 88 93 101	76 78 87 82 90 88 90 87 91 93 93 99

* S: end grain sealed; U: end grain not sealed.

f: Wood temperatures estimated from dry- and wet-bulb temperatures.

The average collapse free shrinkages to 12 per cent. moisture content were 6.5 per cent. tangential and 3.8 per cent. radial. Shrinkages per 1 per cent. Moisture change during oven drying from 12 per cent. after reconditioning did not vary sensibly between different tests, average Values for all tests being 0.254 per cent. tangential and 0.184 per cent. radial. These Values are substantially the same as the collapse-free shrinkages (per 1 per cent. moisture change) which were 0.266 per cent. tangential and 0.168 per cent. radial. This observation indicated the absence of any appreciable heat stabilization.

The stress at the limit of proportionality in compression perpendicular to the grain in the tangential direction at 70, 125, and 190°F was found to be 235, 150, and 55 lb/in², respectively. Corresponding Values in the radial direction were 300, 200, and 75 lb/in². These results may be represented by the linear regression equations

q(tang)= 335-1.48T (lb/in2),	(6)
q(rad) = 435 – 1.89T (lb/in2)

Deformation for loading beyond the proportional limit are given in table 5, and some typical creep curves are shown in Figure 6. The pore-size distribution determined by mercury penetration is shown in Figure 7. The figure also includes the approximate differential pore-size distribution calculated by the Kelvin equation from sorption data for E. regnans extracted with water and ethanol (Christensen and Kelsey 1958). Although the latter method of calculation is not very accurate and extracted material not strictly comparable with untreated JET. regnans, the result does provide a check of the order of magnitude of pore sizes.

Figure 5: Development and distribution of total shrinkage in specimen cubes from the top log of tree n° 2 dried at 190°F

TABLE 4:STABILIZED WOOD TEMPERATURES, DRYING TIMES, AND COLLAPSE RECOVERIES FOR DRYING TESTS AT 75, 220, AND 285°F AND FOR SPECIMENS IMPREGNATED WITH SODIUM CHLORIDE

Drying Conditions		End Grain Sealing*	Stabilized Wood Temperature (°F)	Drying Time to 30% Average Moisture Content (hr)	Collapse Recovery (% of total collapse)
Dry-Bulb Temperature (°F)	e.m.c Level Of Drying Atmosphere (%)				Tang.	Rad.
285 285 220 220 75 75 150£	0 0 0 0 12 12 4	S U S U S U £	203 165 195 150 73 70f -	1¼ 1 2¾ 2 130 78 15	104 92 94 94 90 103 108	92 87 98 91 102 102 120

* S: end grain sealed; U: end grain unsealed.

f: Wood temperatures estimated from dry- and wet-bulb ternperatures.

£: Treated fbr 8 days in concentrated sodium chioride, then end-sealed, and dried.

 

Fig. 6:Deformation beyond limit of proportionality at constant load in tangential direction. Loads stated represent stresses beyond limit of proportionality. Rate of deformation during loading to proportional limit =1.2 per cent./min.

TABLE 5: DEFORMATIONS INDUCED BY MECHANICAL LOADING COMPARED WITH LIQUID-TENSION COLLAPSE. Deformations and collapse expressed in per cent. of green dimensions

Wood Temp. (ºF)	Direction	Calculated Collapse Inducing Force* (ºF) (lb/in2)	Mechanical Strength Test					Drying Experiment	Ratio D/F kL¥
			Appiled Load Beyond Proport. Limit (lb/in2)	Deformation of Loading (min)	Creep
					Duration of Loading (min)	Total Deform. (%)	Residual Deform. after Unloading (D) (%)	Exp. Liquid Tension £ Collapse (%)
70	Tan. Rad	85 14	85 14	0.9 0.5	120 120	2 1	1.0 0.5	4.3 2.3	0.012 0.036
70	Tan. Rad	85 14	180 180	1.4 0.8	60 60	7 2	5.5 1.4	4.3 2.3	- -
125	Tan. Rad	135 85	135 85	5.5 2.0	20 -	15 10	7.7 5.9	8.1 5.3	0.057 0.069
190	Tan. Rad.	208 188	208 188	16.0 14.0	7 7	25 22	13.7 10.6	13.0 9.0	0.066 0.056

* From equation (2), using the stress at the proportional limit (as discussed in section V (a)).

£ ollapse in unsealed specimens dried at high humidity is termed “experimental liquid-tension collapse” (cf. Section V(a) (i)).

¥ kL may be taken to present the linear terms of the liquid-tension collapse function Ø L (see eqn. (3) and Section V(a) (i)).

Fig 7: Pore-size distribution in E. Regnans, determined by mercury penetration and from sorption data.

Fig. 8: Dimensional changes observed on 7/8 in. cubes in different logs. See Figure 1 for key to shading.

(ii) Differences Between Trees and Positions. Average experimental results for each of the 10 sample blocks used in the experiment are shown graphically in Figure 8.

(iii) Statistical Analysis.—Analyses of variance were carried out to determine the significance of the effect of drying temperature, humidity and end-grain sealing as well as of trees and positions in trees on the various dimensional changes observed during drying. The analyses did not include data from trees 5 and 6 which only provided one sample block each and thus did not yield information on effect of position in tree. Estimates of error were obtained using all tests, but the significance of drying variables was calculated from a sub analysis of the batches dried at 110, 150, and 190°F.

TABLE 6: STATISTICAL SIGNIFICANCE OF THE EFFECT OF PHYSICAL VARIABLES

Dimensional change	Direction	Variable			Significant Difference between two Means
		Temp.	Humidity	End-Grain Sealing	5% Level	1% Level
Total shrinkage to 12 per cent. moisture content before reconditioning	Tan. Rad. Vol.	** ** **	n n *	** ** **	3.5 1.7 2.6	4.6 2.3 3.5
Total shrinkage to 12 per cent. moisture content after reconditioning	Tan. Rad. Vol	* * **	n n *	n ** **	1.3 0.8 1.8	1.8 1.1 2.4
Total shrinkage to oven dry state after reconditioning	Tan. Rad.	** **	* n	n *	1.3 0.9	1.7 1.2
Reconditioning recovery	Tan. Rad.	** **	n n	** **	3.2 1.5	4.2 2.0
Total collapse	Tan. Rad.	** **	n n	** **	3.5 1.7	4.6 2.3
Residual collapse	Tan. Rad.	** **	** *	n *	1.0 0.7	1.4 0.9
Recovery as per cent of total collapse	Tan. Rad.	** **	** n	n n	13 14	17 19

* :Significant at 5 per cent. level.

**: Significant at 1 per cent. level.

n : not significant.

The results of the analysis for the different physical variables are summarized in Table 6, and for trees and positions in trees in Table 7. The effect of end sealing, where significant, was, in general, greater for drying at low humidity than at high humidity. Temperature was, in most cases, of greater effect in end-sealed than in unsealed specimens. None of the drying variables had any significant effects on the average shrinkage per 1 per cent. moisture change between 12 and O per cent. Moisture content.

(b) Relation between Collapse and Specimen Size and Orientation

Tests on the influence of the size and orientation of the specimen on collapse were carried out apart from the main series of experiments, and were not included m the statistical analysis, The results are given in Figure 9.

TABLE 7: STATISTICAL SIGNIFICANCE OF THE EFFECT OF TREE AND POSITION IN TREE

Dimensional change	Direction	Variable			Significant Difference between two Means
		Temp.	Position	Tree/ position Inter action	5% Level	1% Level
Total shrinkage to 12 per cent. moisture content before reconditioning	Tan. Rad. Vol.	n n n	** n *	n ** **	2.1 1.0 1.6	2.8 1.4 2.1
Total shrinkage to 12 per cent. moisture content after reconditioning	Tan. Rad. Vol	n n n	n n n	** ** **	0.8 0.5 1.1	1.0 0.6 1.4
Total shrinkage to oven dry state after reconditioning	Tan. Rad.	n n	n n	** **	0.8 0.5	1.0 0.7
Reconditioning recovery	Tan. Rad.	* *	** n	n *	1.9 0.9	2.6 1.2
Total collapse	Tan. Rad.	** *	** n	n *	2.1 1.0	2.8 1.4
Residual collapse	Tan. Rad.	n n	n *	n n	0.6 0.4	0.8 0.6
Recovery as per cent. of total collapse	Tan. Rad.	* n	n n	n n	7.8 8.6	10.2 11.4
Average shrinkage per 1 per cent. moisture change between 12 and 0 per cent mpisture	Tan. Rad.	* n	* n	n **	0.035 0.030	0.046 0.040

* :Significant at 5 per cent. level.

**: Significant at 1 per cent. level.

n : not significant.

V. DISCUSSION

(a) Comparison on Theory with Experimental Results

(i) Liquid-Tension Collapse.—Liquid-tension collapse may be numerically predicted from the theory in Section II.

Assuming cylindrical capillaries of constant radius and using the Eötvös relation, equation (1) becomes

(7)

The collapse-inducing force depends on the radius of the largest pore present in the cell wall. The pore size distribution curves determined by mercury penetration and calculated from sorption data (see Fig. 7) indicate that the largest micropores have radii of the order of 1500 Å. In the absence of data on the limit of plastic flow, Q (eqn. (2)), the stress at the limit of proportionality determined by mechanical tests, q (eqn. (6)), will be used. Although the ratio Q/q may be of the order of 2/3 or lower (Ivanov 1941), errors introduced by this substitution may be corrected by incorporating this ratio in the function f_L (eqn. (3)). Substituting for P, q, and r in equation (2), the liquid-tension force over the temperature range 70 to 190°F is:

FL = 59+0.92T (lb/in2) (tan.)= -41+1.32T (lb/in2) (rad.)

(8)

Fig. 9: Comparison of dimensional changes in 7/8 in. cubes and specimens measuring 7/8 by 7/8 by 3 in. after drying at 150°F and low humidity.

R, radial; T, tangential; L, longitudinal; *S', sealed; U, unsealed; See Figure 1 for key to shading.

Investigations by Ellwood (1954) on American beech, by Youngs (1957) on red oak (Quercus rubra L.), and mechanical tests on E. regnans in the present experiment (Fig. 6) indicate that the creep function f_L<(t) in equation (3) is probably of an exponential form. Although the asymptotic value may only be reached after a long time, the work mentioned above shows that for stresses of collapse-inducing magnitude, ( ∂f_L/ ∂t) < l within about 10 hr after the start of loading at 70° F, and within 1 to 2 hr at 180°F. It thus seems reasonable to take 1 - f_L (t) approximately constant, except possibly in thin veneer and during very rapid drying, or during drying at very low temperatures. Furthermore, to a first approximation, terms above the first order in the liquid-tension collapse function f _L (eqn. (3)) will be neglected. f_L may then be replaced by the product k_LF_L where k_L is a parameter which can be calculated from the residual deformation for a given applied load (D) measured by the mechanical tests shown in Table 5. Although k_L is a function of temperature, the data show that the variation o ver the range 125 to 190°F is small. Similar results were reported by Barnard-Brown and Kingston (1951) and by Ellwood (1954). k_L will thus be taken as 0-06 over the temperature range 110 to 190°F. It should be noted that k_L = k_L∞ (1—f_L), where k_L is the value of C_LF_L for t→∞ , and f_L is the creep function which has been assumed constant. Furthermore, k_L incorporates the ratio q/Q.

With these assumptions, theoretical liquid-tension collapse is given from (3) by the relations, valid over the range 110 to 190°F,

CL (tan)=3.5+0.055 T per cent,	(theor.) (r=1500Å)	(9)
CL (tan)=2.5+0.079 T per cent,

Collapse ordinarily does not occur in sections thin enough to be dried free from infernal drying stresses, and liquid-tension collapse can therefore not be directly measured. It can, however, be approximated by careful, slow drying through exposed end grain so that moisture gradients are kept to a minimum. The observed distribution of shrinkage (see Fig. 5) shows that the smallest gradients occurred in unsealed specimens dried at high humidity. Collapse in these specimens thus constitutes the closest approach to pure liquid-tension collapse realized in the present experiment and will hereinafter be called “experimental liquid-tension collapse”.

Experimental liquid-tension collapse over the temperature range 110 to 190°F is given by the regression equations (significant at the 1 per cent. level)

CL (tan)=-1.8+0.080 T per cent,	(expt)	(10)
CL (tan)=-1.7+0.057 T per cent,

as represented by the lines marked “C_L” in Figure 4.

Liquid-tension collapse calculated from (9) is somewhat higher than the values given by (10). A better fit is obtained by using a value of r deduced from the observations.

(ii) Calculation of Capillary Radius.—From Figure 4 it appears that the extrapolations of C_{L (tan)} and C_{L (tan)} tend to zero at T = 22 and 29°F, respectively.

When C_L = 0, P = Q, and hence, from (6) and (7) (taking T = 25.5°F and using q for Q) r = 6.54xl0^-6 in. = 1664 Å. This result is in remarkably good agreement with the value r = 1500 Å estimated from the pore-size distribution determined by two different methods. Substitution of Q instead of q would not change the order of magnitude of r.

Using r = 1664 Å, equations (9) become

CL(rad) = -4.8+0.084T per cent.	(theor) r =1664 Å	(11)
CL (tan)= 1.2+0.059T per cent,

Detailed comparison of (10) and (11) shows that the differences between theoretical and experimental values over the temperature range 110 to 190°F are well below the 5 per cent. level of significance except for radial collapse at wood temperatures above 178°F.

(iii) Stress Collapse. To compute stress collapse from equation (4), the following Values will be assumed for the parameter S_c, the actual shrinkage of the core at the time of maximum tension stress

S_c =: (S₀+C_L) for unsealed specimens dried at high humidity (small moisture gradient),
S_c =: 1/2 (S₀+C_L) for unsealed specimens dried at low humidity (moderate moisture gradient),
S_c = 0 for sealed specimens (severe moisture gradient),

where S₀ is the collapse-free shrinkage. It should be noted that the value of S_c depends mainly on the amount of drying through exposed end grain, and only to a smaller extent on humidity. S_c is negligible when end grain drying can be neglected.

Proceeding as for liquid-tension collapse, stress collapse will be considered as approximately time-independent and the tensor will be replaced by a matrix with constant elements . Evidence from an earlier investigation (Kauman 1958) and the present experiment is consistent with the condition which seems to indicate that the viscoelastic “Poisson effect” mentioned in Section II is more important than stress transfer between parallel layers. However, the accuracy of the results does not yet permit of the conclusive determination of the relative influence of each of these factors. To a first approximation, the terms containing will be neglected.

The value of over the temperature range of about 110 to 190°F is deduced from the earlier investigation mentioned above as = O.32, = O.15, where superscripts t, r indicate the tangential and radial directions, respectively. The Values obtained by fitting equation (4) to the results of the present experiment are = 0.30, = 0.17.

(iv) General Equation for Collapse.—It will be assumed that liquid-tension collapse and stress collapse are independent, except as provided in equation (4). In the simplified case where f _L and f _s may be taken as linear and the creep function as constant, total collapse (C) over the temperature range 110 to 190°F is thus given by addition of C _L and C_S,

C (tan) = -0.3+1.5n+(0.059+0.027(1-n))T+0.32(1-n)S0rad per cent.	(12)
C (rad) = -4.6-0.17n+(0.084+0.0088(1-n))T+0.15(1-n)S0tan per cent.

where

n=	O for sealed specimens,
	1/2 for unsealed specimens dried at low humidity.
	1 for unsealed specimens dried at high humidity.

These equations show that the wood temperature, T, is the most important variable determining total collapse. The influence of the collapse-free shrinkage, SQ, and of %, though in many instances significant, is of less importance. The accuracy of the calculated Values as compared with observed collapse is shown in Table 8. For temperatures outside the range 110º to 190°F, equations (12) have been extrapolated, disregarding any deviations of the e.m.c. levels from the standard Values of 4 and 15 per cent. In fact, stress collapse is a function of the e.m.c. level, and a more accurate version of (12) would contain e.m.c. (or humidity) as a variable. The extrapolation yields good results for tangential collapse but appears to be incorrect for radial collapse.

Nearly all the significant differences occur at a zero per cent. e.m.c. level and high temperature. under these conditions, instead of taking the creep function f_L(t) (eqn. (3)) constant, it is probably more correct to write

where g_L = 1, g_L (¥ ) = l-k_L¥ ana similarly for f_s(t). (This correction may be taken to include temperature variation of k_L). Then, if g_L = g_s = 0.173 is substituted for the treatments mentioned above most of the discrepancies are eliminated (see Table 8).

In addition to the time-dependence of the creep function, collapse depends on time in yet another way. Greenhill (1938) was the first to observe that wood heated in the green state to temperatures above about 110°? will collapse more than unheated controls, the extent of the increased collapse depending on both temperature and time of exposure. Specimens dried at high temperatures are effectively exposed to a heat treatment in the green state until they reach fibre saturation point, and collapse is therefore increased. In the author’s opinion, this increase in collapse is due to weakening of the cell wall by hydrolysis or other chemical changes (cf. Stamm 1956). In the present experiment, the greatest amount of collapse due to this factor, 2-8 per cent. tangential and 1-6 per cent. radial, was statistically not significant. It occurred in sealed specimens dried at 190°F and high humidity.

(b) Reconditioning Recovery, .Residual Collapse, and Effect of Impregnation with Sodium Chloride

Reconditioning recoveries and residual collapse showed increases with drying temperature significant at the 1 per cent. level, but recovery expressed as percentage of total collapse generally decreased with increase in temperature (see Table 6, also Tables 3 and 4, and Figs. 1 and 2). The increase in actual recovery is, of course, a reflection of the greater collapse at high temperatures, whereas the decrease in relative recovery and increase in residual collapse may be attributed to the effect of heating of the green wood which causes chemical degradation. Greenhill observed similar decreases in relative recovery after heat treatments (Greenhill 1938).

Residual collapse was greater by a highly significant difference and relative recovery lower after drying at high humidity as compared with low humidity tests.

TABLE 8:COMPARISON OF OBSERVED TOTAL COLLAPSE WITH THEORETICAL VALUES PREDICTED FROM EQUATIONS (12)

Experimental Conditions			Total collapse (%)
			Tangential			Radial
Dry-bulb Temp. (ºF)	e.m.c	Sealingf	Obs	Calculated		Obs.	Calculated
				g(t)=0y	g(t)=0.17y		g(t)=0y	g(t)=0.17y
285	0 0	S u	17.4 10.3	18.4 13.0	15.2 10.8	12.6 7.7	15.0** 10.4**	12.4 8.6
190	15 15 4 4	S U S U	17.4 12.6 17.2 12.1	16.9 12.1 16.1 12.6	14.0 - - -	10.5 9.1 12.6 7.7	13.6** 10.7 12.5 9.9*	11.2 - - -
150	15 15 4 4	S U S U	12.7 10.8 10.8 9.8	13.6 9.8 12.5 9.7	- - - -	8.8 6.4 10.1 5.9	9.8 7.5 8.7 6.4	- - - -
110	15 15 4 4	S U S U	9.6 6.2 8.8 7.0	10.1 7.4 9.5 8.0	- - - -	7.2 3.9 7.5 4.1	6.2 4.2 5.5* 4.2	- - - -
75	12 12	S U	8.3 4.2	7.2 5.3	- -	5.7 2.9	2.9** 1.3	- -

* Difference between observed and calculated Values significant at 1 per cent. level.

f S, end grain sealed; U, end grain unsealed. ψ g(t), corrected creep function (see Section V(o) (iv)).

** Difference between observed and calculated Values significant at 6 per cent. level.

This is probably due to the longer drying time at high humidity levels which results in a more prolonged exposure of the moist wood to high temperatures. There was also a trend for residual collapse to be higher in unsealed than in sealed specimens which may indicate that the stress distribution is not without influence on this variable. The greater actual recovery in sealed specimens is, of course, due to the greater collapse incidence in this material.

Impregnation with sodium chloride yielded a decrease in collapse in both the radial and tangential direction, although the latter was statistically not significant. This decrease may be attributed to the lower stresses in the impregnated specimens due to reduced collapse-free shrinkage (Stamm 1934) and reduced moisture gradients resulting from the depression of the evaporation rate. Collapse in this material was, in fact, comparable to that in unsealed specimens dried at the same temperature where similarly small moisture gradients may be expected.

(c) Tree and Position Effects

From Figure 8 and Table 7 it can be seen that significant differences in total collapse occurred between different trees and between the two positions in each tree, the butt logs invariably collapsing more severely than top logs. Tree-position interaction gave significant differences over a greater range of dimensional variables than either tree or position alone; this might be due to the fact that specimens were taken at non-uniform heights in the various trees.

(d) Specimen Dimension and Orientation in Tree

Figure 9 shows that dimensional changes observed in 7/8 in. cubes were comparable to those in the thickness (measured at the midpoint of the 3 in. dimension) of specimens of rectangular cross section, but that the latter collapsed considerably less in width, irrespective of orientation in the tree. It has been shown by Greenhill (1938) that collapse in end-sealed, 1 in. long, rectangular specimens is of the same order as that in a long board of similar cross section. Collapse in the small cubes used in the present experiment can therefore be considered similar to that in the thickness, but not in the width of a long board.

VI. CONCLUSIONS

Total collapse may be theoretically expressed as a function of wood temperature and collapse-free shrinkage by an equation of the form

(13)

The parameters a_k, b_k, c_k depend only on surface tension data and structural and rheological properties of the wood. The parameter n depends mainly on the proportion of end-grain drying and to a smaller extent on the humidity of the drying medium. When end-grain drying is negligible, n may be neglected; when end-grain drying is preponderant, n may be taken as unity. In these limiting cases, equation (13) reduces to the form

Ci = a01 + a11T + a21S0j (n=0)	(14)
Ci =a02 + a12T (n=1)

The theoretical results calculated from (13) are in good quantitative agreement with the experimental results. For high temperatures and very rapid drying, (13) contains a time-dependent factor of the form 1- f(t) (cf. eqns. (3), (4)).

The values of the parameters in equation (13), and hence the total collapse, are particularly sensitive to variations in the compressive stress perpendicular to the grain at the limit of plastic flow and in the effective radius of the largest opening in the wall of a collapse-susceptible cell. For example, when these two properties vary by about ± 10 per cent., total tangential collapse in an end-sealed specimen at 150°F may vary by up to 62 per cent., as shown in Table 9.(Compressive stresses in Table 9 are Values at the proportional limit (q) instead of the limit of plastic flow (Q). Calculated collapse Values are not affected by this, since the parameters in equation (12) incorporate the ratio q/Q.) It is suggested that even small variations in compressive strength and capillary radii may largely account for the marked variations in collapse from tree to tree and within trees.

TABLE 9:CALCULATED TOTAL TANGENTIAL COLLAPSE IN SEALED SPECIMENS AT 150°F WOOD TEMPERATURE CORRESPONDING TO VARIATIONS OF ±10 PER CENT. IN COMPRESSIVE STRESS AT PROPORTIONAL LIMIT AND RADIUS OF LARGEST OPENING IN CELL WALL

Radius (Å)	Compressive Stress (lb/in2)
	Tangential 102 Radial 137 (-10%)	Tangential 113* Radial 152*	Tangential 124 Radial 167 (+10%)
1500 (-10%) 1664* 1830 (+10%)	17.0 14.6 12.5	16.0 13.6* 11.5	15.1 12.7 10.5

* Mean Values in present experiment.

Although the liquid-tension collapse theory presented in this paper considers phenomena in an idealized single cell, the quantitative agreement with experimental results suggests that the basic operational unit in wood undergoing collapse behaves largely like a single cell, even though it may, in fact, be composed of many cells. A more elaborate theory would have to consider statistically the interactions between cells and take account of the distribution functions of effective capillary radii and strength properties.

Collapse in small cubes is comparable to that observed in the thickness of specimens of rectangular cross section, and in the case of end-sealed cubes to that in the thickness of long, i in. thick boards of rectangular cross section. Rectangular specimens and boards, however, collapse to a smaller extent in width.

NOTE
Publicado originalmente en Australian Journal of Applied Science 2(1): 122-145. 1960

VII. ACKNOWLEDGMENTS

The author gratefully acknowledges Mr. E. R. Pankevicius' assistance with the experimental work and the help of Miss N. Ditchburne, Division of Mathematical Statistics, C.S.I.R.O., who carried out the statistical analysis. Thanks are also due to Mr. R. L. Newman of the Australian Newsprint Mills for the collection of the specimens, to Mr. O. G. Ingles, C.S.I.R.O. Chemical Research. Laboratories, for carrying out the mercury penetration measurements, and to Mr. N. H. Kioot of the Division of Forest Products, G.S.I.R.O., for arranging the mechanical strength and creep tests.

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