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Stress model of a wood fibre in relation to collapse

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Summary

A wood fibre cell from a Tasmanian Eucalypt is typically cylindrical in shape with a length to diameter ratio of approximately 50∶1. Early in the process of seasoning for solid timber, when the fibre lumens are still saturated, internal tension within a fibre can rise to a value high enough to cause it to physically flatten, or collapse. A stress model of a fibre cell has been developed which predicts the stress and strain distributions within the fibre wall as a function of temperature, moisture content, and fibre wall strength properties and size in the early stages of drying. This model will be used together with measurement of the behaviour of collapse prone timbers to determine conditions which will avoid collapse during seasoning.

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Abbreviations

μ:

Poisson's ratio

E:

Young's modulus (Pa)

E⋆:

Instantaneous modulus, that is, ratio between increments of instantaneous stress and strain (Pa)

BD:

Basic density (kg/m3)

T:

Temperature (°C)

σ:

Local instantaneous stress (Pa)

ɛ:

Local instantaneous strain

k, K:

Constants

δ:

Signifies an increment

u:

Radial displacement of the fibre wall at a specified radius (m)

Ew :

Elastic modulus of water (Pa)

P0 :

Initial lumen pressure (Pa)

P1 :

Pressure in lumen (Pa)

P2 :

Pressure external to the fibre cell (Pa)

Vwrem :

Volume of water removed from fibre lumen per unit length of fibre (m3/m)

V1 :

Initial lumen volume per unit length of fibre (m3/m)

r1 :

Initial lumen radius (m)

r1n :

New lumen radius (m)

r:

radial direction

t:

tangential direction

z:

longitudinal direction

u:

ultimate

i:

instantaneous

y:

proportional limit

green:

refers to a property of the material in its “green” or saturated condition, that is, with a MC greater than FSP.

References

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  • Doe, P. E.; Oliver, A. R.; Booker, J. D. 1994: A non-linear strain and moisture content model of variable hardwood drying schedules. Paper presented at 4th International IUFRO wood drying conference, Rotorua, NZ, August 9–13, 1994

  • Ilic, J. 1987: Personal communication as cited in Oliver (1991)

  • Ilic, J. 1991: CSIRO Atlas of Hardwoods (Melbourne: Crawford House Press in association with the CSIRO)

  • Innes, T. C. 1992: Mechanical properties of Tasmanian Oak relevant to seasoning. B.E. Hons thesis, Department of Civil and Mechanical Engineering, University of Tasmania

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Authors

Additional information

The author is pleased to acknowledge the assistance of Emeritus Professor A. R. Oliver, Associate Professor P. E. Doe, University of Tasmania, and the Australian Furniture Research and Development Institute

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Innes, T.C. Stress model of a wood fibre in relation to collapse. Wood Sci.Technol. 29, 363–376 (1995). https://doi.org/10.1007/BF00202584

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  • DOI: https://doi.org/10.1007/BF00202584

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