Abstract
The paper presents a simple mathematical model of drying that permits evaluation of moisture content distribution in dried wood during the constant and falling drying rate periods and, in particular, estimation of stresses generated from the moment when the moisture content at the body surface reaches the fibre saturation point (FSP). The acoustic emission method (AE) is used for monitoring the state of stress in dried wood. The numerically evaluated drying induced stresses are compared with the number of acoustic signals and their energy monitored on line during drying tests. It can be stated that the enhanced emission of acoustic signals occurs at those moments when the drying induced stresses approach their maximum. Both the numerical calculus and the experimental tests were conducted on a pine-wood sample in the form of a disk.
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Abbreviations
- A :
-
Elastic bulk modulus [MPa]
- B = kR/Λ:
-
Coefficient of mass exchange (Biot number) [1]
- D :
-
Coefficient of diffusion [m2/s]
- e ij :
-
Strain deviator [1]
- J 0, J 1 :
-
Bessel functions of first kind of zero and first order
- k :
-
Coefficient of convective vapour exchange [kg/ m2·s]
- M :
-
Elastic shear modulus [MPa]
- r, R :
-
Cylinder radius [m]
- s ij :
-
Stress deviator [Pa]
- t :
-
Time [s]
- T :
-
Temperature [K]
- u :
-
Radial displacement vector [m]
- W :
-
Mass flux of moisture [kg/m2·s]
- X :
-
Dry basis moisture content [1]
- Y :
-
Vapour content in drying air [1]
- α,β:
-
Ratios of mechanical modules [1]
- κ:
-
Viscous bulk modulus [Pa·s]
- κ(T) :
-
Coefficient of thermal expansion [1/K]
- κ(X) :
-
Coefficient of humid expansion [1]
- \(\varepsilon_{ij}\) :
-
Strain tensor [1]
- \(\varepsilon\) :
-
Volumetric strain [1]
- λ n , α n :
-
Eigenvalues [1]
- σ ij :
-
Stress tensor [Pa]
- σ:
-
Spherical stress [Pa]
- ρ:
-
Mass density [kg/m3]
- η:
-
Shear viscoelastic modulus [Pa·s]
- Ω,ω:
-
Parameters [1]
- \(\vartheta=TT_r\) :
-
Relative temperature [°C]
- θ = X − X r :
-
Relative moisture content [1]
- τ:
-
Retardation time [s]
- Λ:
-
Mass transport coefficient [kg·s/m3]
References
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Kowalski, S.J., Smoczkiewicz-Wojciechowska, A. Stresses in dried wood. Modelling and experimental identification. Transp Porous Med 66, 145–158 (2007). https://doi.org/10.1007/s11242-006-9011-5
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DOI: https://doi.org/10.1007/s11242-006-9011-5