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Fundamental aspects of timber seasoning, Exercises of Differential Equations

The aim of this investigation was to develop an economically viable method of seasoning back-sawn native. Tasmanian eucalypts and to reduce the seasoning time ...

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FUNDAMENTAL ASPECTS OF TIMBER SEASONING
by
RICHARD DENIS SCHAFFNER
B.E. (hons.)
Submitted in fulfilment of the requirements
for the degree of
MASTER OF ENGINEERING SCIENCE
in the
Faculty of Engineering
UNIVERSITY OF TASMANIA
AUSTRALIA
November 1981
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FUNDAMENTAL ASPECTS OF TIMBER SEASONING

by

RICHARD DENIS SCHAFFNER

B.E. (hons.)

Submitted in fulfilment of the requirements

for the degree of

MASTER OF ENGINEERING SCIENCE

in the

Faculty of Engineering

UNIVERSITY OF TASMANIA

AUSTRALIA

November 1981

ABSTRACT

The aim of this investigation was to develop an economically viable method of seasoning back-sawn native Tasmanian eucalypts and to reduce the seasoning time required for these timbers. The theory of unsteady state mass transfer based upon Fick's law of diffusion was used to study the drying process. The diffusion coefficients were measured directly by the diffusion cell method or deduced from a comparison of measured and calcul- ated drying curves. The relationship between shrinkage of wood fibre and moisture concentration was obtained by slowly drying thin strips of wood and regularly measuring deformations. (^) The effects of falling diffusivity and shrinkage with reducing moisturi concentration were found to effectively cancel one-another in the case of the timbers tested during this investigation. Drying stresses in wood were studied using the theory of elasticity in anisotropic bodies. (^) Airy stress functions were used when solving for stresses. For simplicity, sawn boards were approximated to orthotropic bodies and only boards cut with face-planes parallel/perpendicular to the principle material property directions were studied. Some elastic properties of native Tasmanian eucalypt timbers were measured on small sample populations and found to be similar to those of various North American hardwoods (with similar densities) reported by other authors. (^) The approximate elastic properties of Tasmanian eucalypts were deduced from this comparison. The theories of mass transfer and stress analysis were combined to form a model describing the development of drying stresses. The wood was assumed to be linearly elastic and to be free of the effects of hysteresis and creep. The governing differential equations were solved by numerical methods.. The model was used to assess the effectiveness of semi-permeable surface coatings in reducing drying stresses in timber. Tests on timber coated with animal glue (cologen) showed that checking (cracking) in Tasmanian eucalypts brought about by high drying stresses was reduced in severity or completely eliminated, depending upon the thickness of the coating.

CONTENTS

Page.

Preface vi Additional Publications xii Acknowledgements xiii

Chapter Chapter

Introduction. The structure of hardwoods

and sites of check formation. 8

Chapter 3: The^ theory^ of^ mass^ transfer^ in wood. 23

Chapter 4: The seasoning of hardwoods. 73

Chapter 5: Drying tests. 102

Chapter 6: The theory^ of^ elasticity^ of orthotropic materials. 154

Chapter 7: Th'e elastic properties and shrinkage behaviour of "Tasmanian Oak". 213

Chapter 8: Drying stresses. 249

Chapter 9: Conclusion. 272

i v

Contents ctd.

Appendix A: Nomenclature. (^) Al

Appendix B: 2-dimensional moisture transfer computer program. Notes, program listing, typical output. Bl Appendix (^) : Results from drying tests. Cl

Appendix D: The selection of suitable coating materials for backsawn "Tasmanian Oak". D

Appendix Ei (^) The elastic properties and shrinkage behaviour of "Tasmanian Oak": Test results. El

Appendix F: 1-dimensional moisture transfer and stress analysis computer program. Notes, program listin typical output. Fl

vi i

orthotropic materials with finite difference schemes and solving the resulting system of equations with the aid of a high-speed digital computer. The diffusion co-efficients of "Tasmanian Oak" in the radial direction (based on a constant diffusion co-efficient model) ranged from 110 -7 m 2 /hr

to 210 - 7^ m 2 /hr over the sample population tested. The most common value of the radial diffusion co-efficient or "diffusivity" encountered was 1.710 -7 m 2 /hr. The agreement between measured and calculated drying curves and moisture

distributions is remarkable considering the variability of the properties of wood.

The principles behind the use of "pre-surfacing" (coating) treatments on timber used as a means of controlling surface checking during drying were thoroughly investigated. The basic requirement of this process is that high surface- fibre moisture concentrations greater than fibre saturation be maintained for a sufficiently long period of time early in drying to limit differential shrinkage in the timber, and hence the drying stresses to levels at which checking is not promoted. This method of controlling checking has been investigated by a number of researchers (for example, Rietz and Jenson (1966) and Harrison (1968) and unsuccessfully applied to the seasoning of back-sawn "Tasmanian Oak" by MacKay (1972) and Campbell (1975) ).

An approximate method of estimating the necessary combination of coating thickness and permeability (diffusivity) was developed. In^ this^ method,

v iii

it was assumed that no discontinuity in moisture concentration existed at the wood/coating interface and that the drying of sawn boards, particularly in the early stages, could be approximated to the drying of a semi-infinite slab. According to this simple model, the thickness of coating, d, (^) required to hold the surface fibres of a board above

the fibre saturation point for a time, t, is

where a = constant, dependant upon the initial moisture

concentration of the timber and the drying

conditions (typically, a = 8 for "Tasmanian

Oak").

V= coating^ diffusivity and Dw = (^) diffusivity of wood (in the appropriate direction).

It was estimated that surface tensile stresses generated during drying would be limited to a sufficiently low maximum by maintaining the surface fibres of back-sawn boards at a moisture concentration for a period of 5 days.

A mixture of animal glue ("collogen), talcum powder and water in the proportions

3.5 water : (^1) dry animal glue crystals : 1.9 talcum powder

(by weight) was found to have a mass diffusivity of approximately

A mathematical model describing the state of stress in anisotropic elastic bodies under conditions of plane strain and subjected to differential thermal or shrinkage strains was established. When this model was simplified for the isotropic case, the governing equation reduced to that derived for such materials by Timoshenko and Goodier (1970). The general relationship describing the state of stress in timber (an anisotropic material) was simplified by firstly approximating sawn boards to orthotropic bodies (principle material property axes orthogonal). The non-linear "elastic" behaviour of "Tasmanian Oak" was approximated by a linear model and the

. effects of creep, hysteresis and the development of checks were ignored.

To simplify the mathematics, the analysis of drying stresses was restricted to either purely back-sawn or purely quarter-sawn material. Furthermore, the boards were assumed to be very wide compared to their thickness. Under this assumption, the stresses acting in the direction perpendicular to the board faces are small at every point on the cross-section (away from the edges) and may be neglected; thus, drying stresses may be analysed using a one-dimensional model.

The relationship between moisture concentration and shrinkage, the permeability and the elastic constants of wood as well as the drying (boundry) conditions are the

major factors affecting drying stress levels in wood. A typical measured value of diffusivity and the measured mean shrinkage-moisture concentration relationships of "Tasmanian Oak" were used in the calculation of drying stresses in the simple linear model. The approximate elastic parameters of 9 Tasmanian^ Oak"^ used^ were^ deduced^ from^ a comparison of some (measured) properties of "Tasmanian Oak" with those published for various North American hardwoods. The simplified stress and moisture transfer equations were approximated by finite difference schemes and solved by digital computer.

From the calculated drying stress distributions in 25mm (nominal thickness) back-sawn "Tasmanian Oak" boards it was found that the maximum tensile stress in the surface fibres of boards coated to a thickness of 0.7mm with the animal glue - talcum powder mix were only one third of the maximum surface stress in matched uncoated boards dried under the same atmospheric conditions.

ACKNOWLEDGEMENTS

Many people have assisted the author during the course of the research described in this document. To all of those people , no matter how small their contribution, the author extends his gratitude and appreciation. Special acknowledgement. is recorded for the following people:

Dr.P.E.Doe ,my supervisor, for his advice, assistance and enthusiasm. Dr.M.S.Gregory, joint supervisor, for his efforts in setting up the research program. Professor A.R.Oliver for his advice and support. Messrs. J.Hammond, J.Clark, the members of the Tasmanian Timber Promotion Board and the Board's staff for their initiative and support. Mr.S.Goodwin for his patience and dedication in the fabrication and maintainance of equipment. Lastly, my family for their patience and understanding, and for the typing.

,

APT -R 1

Quarier- board (^) satim

Bac.k — hoard

Eucalyptus regnans - average density = 630 kg/m 3 , Eucalytpus delegatensis - average density = 650 kg/m 3 , Eucalyptus obliqua - average density = 710 kg/m 3. These species together form what is commonly known as the "Tasmanian Oak" group of species; most of the sawn hardwood produced in Tasmania is marketed under this name.

In general, boards may be sawn from logs in two distinctly different ways. Quarter-sawn boards are cut with their wide faces essentially perpendicular to the seasonal or growth rings; that^ is,^ the^ wide^ faces^ are cut radially with respect to a log cross-section (see figure 1.1).

Figure 1.

Cross-section of a log showing quarter-sawn and back-sawn boards.

On the other hand, back-sawn boards are cut with their wide faces tangential to the growth rings. The growth

rings appear as linear markings on the faces of quarter- sawn boards which run in the longitudinal direction and are between 1.5 8. 3 mm apart in close-grained timbers such as those making up the "Tasmanian Oak" group. (^) However, the faces of back-sawn boards are heavily figured. (^) The difference in appearance is demonstrated in figure (1.2).

Back-sawn board Quarter - sawn board

Figure 1.

Figuring on the faces of back-sawn and quarter-sawn boards.

The faces of back-sawn boards are more visually appealing than those of quarter-sawn boards and consequently back- sawn material is in great demand for decorative applications including furniture, feature panelling and flooring.

Unfortunately, severe cracks or "checks" are formed on the faces of a large percentage (70 to 80%) of back-sawn "Tasmanian Oak" boards as they are dried from the "green" condition to equilibrium with the atmosphere. Badly-checked material is unsuitable for decorative applications and it is therefore uneconomic to produce back-sawn "Tasmanian Oak" using the methods currently

"Checks" are defined as cracks or fissures in wood fibre running in the longitudinal direction but not extending through the piece from one surface to another.

timber, in terms of both saw-dust and unmillable remainders, is high. In^ fact,^ the^ typical^ volumetric^ recovery^ of^ dry, rough-sawn boards from a given log intake ranges from 30 to 40% depending on log diameter and the amount of shrinkage during drying.

"Bark to bark" sawing (figure 1.4) produces a large percentage of wide back-sawn boards and recovery of dry, sawn material ranges from 50 to 65%.

Figure 1.

"Bark to bark" sawing.

This process involves less handling and is much faster than the quarter-sawing process. Gangs^ of^ parallel^ saw- blades are often used. Millers^ of^ "Tasmanian^ Oak"^ (and other Australian-grown eucalypt species) are at present unable to use the "bark to bark" sawing technique, primarily because of the excessive rate of degradation of back-sawn material during drying. To^ further^ complicate^ matters, hardwood millers in Tasmania face a reduction in the size and quantity of available sawlogs.

The future of the Tasmanian hardwood milling

industry therefore rests heavily upon the development of a method of reducing the level of degradation due to face- checking during the seasoning of back-sawn "Tasmanian Oak". In Australia, research on this particular problem has been pursued at various levels since the mid 1940's without an economic solution being reached. The research project described in this document was initiated by the Tasmanian Timber Promotion Board (T.T.P.B.) on behalf of the Tasmanian timber industry and backed financially by the T.T.P.B. and the Government of the State of Tasmania. The^ T.T.P.B. determined that a fresh attack should be made upon the problem at an institution with no previous connection with timber seasoning research, • thus avoiding any preconceptions or prejudices. However, great value was attached to the work of other researchers (both published and privately communicated) without reference to which this project would surely not have progressed at a satisfactory pace.