Strona 2_redak - Instytut Agrofizyki im. Bohdana Dobrzańskiego ...

46
Multiple wetting and drying of grain causes internal cracks in the grain endosperm
structure, which reduces the values of modulus of elasticity even by 40% [171]. In the
case of corn kernels, modulus of elasticity decreases with increasing moisture, from
600 MPa at moisture content of 10% to 50 MPa at moisture of 35% [86]. Modulus of
elasticity of rape seeds at moisture content of 6-8% is about 40 MPa, and with
increasing seed moisture drops to the level of several MPa [158]. Modulus of
elasticity of pea seeds falls within the range of 100-400 MPa depending on the
cultivar and the seed moisture content [43].
Direct linking of the modulus of volumetric elasticity of a granular material with
the elastic properties of elementary grains by means of a quantitative mathematical
formula is extremely complicated. Theoretical studies are usually focused on the search
for general conditions that would permit the determination of modulus of volumetric
elasticity of a system of elastic granules. Walton [168] derived the relationship of
effective modulus of volumetric elasticity of a random system of spheres K on the basis
of elastic reactions taking place within the area of elementary contact:
where:
K
1
2 2 3
1 ⎛ 3υ N
t
1 2 2 2 ⎟ ⎞
= ⎜
6
⎝ π (1 − ν ) ⎠
K = K E
,
2
3
1
p
1
3
(6.5)
3
4πR
n
υ = ,
3V
E – Young modulus,
K 1 – material parameter,
n – number of granules in volume V,
N t – mean number of contacts per individual granule,
p – pressure,
R – radius,
V – volume,
υ – solid fraction,
ν – Poisson constant.
For the description of the stress-strain relation within the area of elementary
contact of the bodies he applied the Hertz formula that is commonly used for the
case of contact of an elastic sphere with flat rigid surface [104, 105 162].