A NUMERICAL STUDY OF THE EFFECT OF GREEN-STATE MOISTURE CONTENT ON STRESS DEVELOPMENT IN TIMBER BOARDS DURING DRYING
Keywords:green state, non-linear, numerical, moisture transport, transient, timber drying, tangential stress
Timber boards manufactured with a traditional sawing pattern often contain both heartwood and sapwood. The difference in moisture content between heartwood (30-60%) and sapwood regions (120-200%) result in a radial moisture variation that can cause internal constraints during drying. However, the green state moisture content is seldom considered when evaluating kiln drying schedules. The developed numerical model is able to simulate stress development in timber boards, which are dried from green state to equilibrium moisture content. The model studied the effect of initial moisture content on stress development in timber boards during drying. The model operates on continuum level and consists of a coupled transient non-linear orthotropic moisture flow analysis, while a stress analysis considers elastic, hygroscopic and mechano-sorptive strain behaviour with use of the finite element method. The simulations were performed on four different timber board configurations, each defined by a unique pith location. The study shows that the green state moisture content does not necessarily lead to significant constraints, but has a positive effect on the maximum tensile stress found in tangential direction at the exchange surfaces in the beginning of the drying process. In this stage, stress development is mainly governed by shrinkage close to the surface, which is partly prevented due to regions still above the fibre saturation point. The initial MC can also influence the time when the maximum stress occurs, but not necessarily the location.
Absetz I (1999) The moisture equilibrium of softwoods above the fibre saturation point at the heartwood-sapwood boundary. Helsinki University of Technology, Espoo, TKK-TRT-101
Bramhall G (1971) The validity of Darcy's law in the axial penetration of wood. Wood Science & Technology, 5: 121 - 134.
Darcy H (1856) Les Fontaines Publiques de la ville de Dijon, exposition et application des principes a suivre et des formules a employer dans les questions de distribution d’eau. Qual des Augustins, Paris, Victor Dalmont Editeur, ISBN
Dinwoodie JM (2000) Timber: its nature and behaviour, Second Edition. E&FN Spon Taylor & Francis Group, ISBN 0-419-25550-8
Eitelberger J, Hofstetter K (2011a) A comprehensive model for transient moisture transport in wood below the fiber saturation point: Physical background, implementation and experimental validation. International Journal of Thermal Sciences, 50: 1861-1866.
Eitelberger J, Hofstetter K, Dvinskikh SV (2011b) A multi-scale approach for simulation of transient moisture transport processes in wood below the fiber saturation point. Composites Science and Technology, 71: 1727–1738.
Eriksson J (2005) Moisture transport and moisture induced distortion in timber – an experimental and numerical study. PhD Thesis, Department of Structural Engineering, Chalmers University of Technology, Gothenburg.
Eriksson J, Johansson H, Danvind J (2007) A mass transport model for drying wood under isothermal conditions. Drying Technology, 25: 433 - 439.
Fick A (1855, 1995) On liquid diffusion. Journal on Membrane Science, 100: 33 - 38.
Fortino S, Genoese A, Genoese A, Nunes L (2013) Numerical modelling of the hygro-thermal response of timber bridges during their service life: A monitoring case-study. Construction and Building Materials, 47: 1225 – 1234.
Krabbenhøft K (2003) Moisture transport in wood a study of physical & mathematical models and their numerical Implementation. PhD Thesis, Department of Civil Engineering, Technical University of Denmark, Copenhagen.
Larsen F (2013) Thermal/moisture-related stresses and fracture behaviour in solid wood members during forced drying: modelling and experimental study. PhD Thesis, Department of Civil Engineering, Technical University of Denmark, Copenhagen.
Larsen F, Ormarsson S (2012a) Numerical and experimental study of moisture-induced stress and strain field developments in timber logs. Wood Science & Technology.
Larsen F, Ormarsson S (2012b) A numerical and experimental study of temperature and moisture related fracture behaviour in timber logs. Holzforschung.
Nijdam JJ, Langrish TAG, Keey RB (2000) A high-temperature drying model for softwood timber. Chemical Engineering Science, 55: 3585-3598.
Ormarsson S (1999) Numerical analysis of moisture related distortion in sawn timber. PhD Thesis, Department of Structural Mechanics, Chalmers University of Technology, Gothenburg.
Ormarsson S, Dahlblom O, Petersson H (1998) A numerical study of the shape stability of sawn timber subjected to moisture variation part 1: Theory. Wood Science & Technology, 32: 325-334.
Ormarsson S, Dahlblom O, Petersson H (1999a) A numerical study of the shape stability of sawn timber subjected to moisture part 2: Simulation of drying board. Wood Science & Technology, 33.
Ormarsson S, Dahlblom O, Petersson H (1999b) A numerical study of the shape stability of sawn timber subjected to moisture variation part 3: Influence of annual ring orientation. Wood Science & Technology, 33.
Ottosen N, Petersson H (1992) Introduction to the Finite Element Method. Prentice Hall, ISBN 0-13-473877-2
Pang S, Keey RB, Langrish TAG (1995) Modelling the temperature profiles within boards during the high-temperature drying of Pinus radiata timber: the influence of airflow reversals. International Journal of Heat & Mass Transfer, 38(2): 189-205.
Perré P (2007) Fundamentals of wood drying. A.R.BO.LOR: Nancy, France, European COST, ISBN
Perré P, Turner IW (1999) A 3-D version of TransPore: a comprehensive heat and mass transfer computational model for simulating the drying of porous media. International Journal of Heat & Mass Transfer, 42: 4501-4521.
Rémond R, Perré P, Mougel E (2005) Using the concept of thin dry layer to explain the evolution of thickness, temperature, and moisture content during convective drying of Norway Spruce boards. Drying Technology, 23(1,2): 249-271.
Rosenkilde A (2002) Moisture content profiles and surface phenomena during drying of wood. PhD Thesis, Building materials, KTH Royal Institute of Technology, Stockholm.
Salin J-G (1992) Investigation of heartwood/sapwood and wood anisotropy influence on timber drying by a two-dimensional simulation model. 8th International Drying Symposium, August 2-5, Montreal, Quebec, Canada.
Salin J-G (2006a) Modelling of the behaviour of free water in sapwood during drying. Wood Material Science & Engineering, 1(1): 4 - 11.
Salin J-G (2006b) Modelling of the behaviour of free water in sapwood during drying. Wood Material Science & Engineering, 1(2): 45 - 51.
Salin J-G (2008) Drying of Liquid Water in Wood as Influenced by the Capillary Fiber Network. Drying Technology, 26: 560–567.
Salin J-G (2010) Problems and solutions in wood drying modelling: History and future. Wood Material Science & Engineering, 5(2): 123-134.
Samuelsson A, Arfvidsson J (1994) Measurement and calculation of moisture content distribution during drying. 4th Internation IUFRO Wood Drying Conference, 1994, August 9-13, Rotorua, New Zealand.
Siau JF (1995) Wood: influence of moisture on physical properties. Virginia, Virginia Polytechnic Institute and State University, ISBN 0-9622181-0-3
Siau JF, Avramidis S (1996) The surface emission coefficient of wood. Wood & Fiber Science, 28(2): 178-185.
Skaar C (1988) Wood-water relations. Springer series in wood science, Berlin, Springer-Verlag, ISBN 3-540-19258-1
Spolek GA, Plumb OA (1981) Capillary pressure in softwoods. Wood Science & Technology, 15: 189-199.
Wiberg P (1996) CT-scanning during drying. Moisture distribution in Pinus Silvestris. 5th International IUFRO Wood Drying Conference, August 13-17, Quebec, Canada.
Wiberg P (1998) CT-scanning of moisture distributions and shell formation during wood drying. Thesis, Division of Wood Physics, Luleå University of Technology, Skellefteå.
Wiberg P, Morén TJ (1999) Moisture flux determination in wood during drying above fibre saturation point using CT-scanning and digital image processing. Holz als Roh- und Werkstoff, 57: 137-144.
Yeo H, Smith WB (2005) Development of a convective mass transfer coefficient conversion method. Wood & Fiber Science, 37(1): 3–13.
Zienkiewicz OC, Taylor RL (1991) The Finite Element Method. London, McGraw-Hill, ISBN
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