Elasticity of Wood-Based Materials

All of the materials presented above have three mutually perpendicular principal axes, defining their orthogonal anisotropy. Usually, it is assumed, however, that the thickness of boards is small in relation to other dimensions, and the elastic prop­erties of the wood-based materials in question adopt extreme values in the mutually orthogonal directions, while perpendicular to the thickness of the board. In other words, in two mutually perpendicular directions, the elastic properties of wood-based materials assume extreme values that is the largest in one direction and the smallest in the other direction. These directions correspond to the axes of symmetry of elastic properties, and it has been adopted to call them the main directions of anisotropy. Materials with such properties are called orthotropic. Therefore, Hooke’s law for the orthotropic body in a system of rectangular Cartesian coordinates, overlapping with the main directions of anisotropy (Fig. 4.20), can be written in the form:

where

Ex, Ey linear elasticity modules in the main directions of anisotropy, vx, vy Poisson’s ratios in the main directions of anisotropy,

Gxy shear elasticity module in the anisotropic plane,

ex, sy normal strains in the main directions of anisotropy and

Yxy shear strains in the anisotropic plane,

whereby the following dependency applies here

mxy myx

EX= Ey;

Tables 4.5, 4.6 and 4.7 show examples of values of mechanical properties of different types of wood-based materials.

Property

Unit

Value

Density

kg/m3

550-680

Young’s modulus Ey

MPa

3080

Young’s modulus Ex

MPa

2530

Poisson’s ratio vyx

0.207

Poisson’s ratio vxy

0.282

Shear modulus Gyx

MPa

794

Bending strength kgy

MPa

13.3

Bending strength kgx

MPa

11.9

Splitting strength kr

MPa

0.15-0.20

Table 4.5 Properties of chipboards (Wilczynski and Kociszewski 2000)

Property

Unit

Value

Density

kg/m3

510-710

Young’s modulus Ey

MPa

4000

Young’s modulus Ex

MPa

3850

Poisson’s ratio vyx

0.30

Poisson’s ratio vxy

0.30

Shear modulus Gyx

MPa

G = E/2(1 + v)

Bending strength kgy

MPa

34.5

Bending strength kgx

MPa

32.2

Splitting strength kr

MPa

0.31

Table 4.6 Properties of MDF boards (Wilczynski et al. 2001; Schulte and Fruhwald 1996)

Property

Unit

Value

Density

kg/m3

550-800

Young’s modulus Ey

MPa

3500-10,000

Young’s modulus Ex

MPa

500-700

Poisson’s ratio vyx

0.439

Poisson’s ratio vxy

0.031

Shear modulus Gyx

MPa

822, G = E/2(1 + v)

Bending strength kgy

MPa

30-100

Stretching strength krx

MPa

30-60

Shearing strength kgy

MPa

25-50

Table 4.7 Properties of plywood