7.3 Laws of Properties Change of FGM
209
where P −1 , P 0 , P 1 , P 2 , P 3 are experimentally estimated.
Table 7.1 reports the values of the mentioned coefficients for some chosen materials. The density of zirconium dioxide and nickel is 5680 and 8908 kg/m
3 , respectively.
The mentioned properties are obtained for each material component separately.
The values of the material properties are used to establish the dependence of the
beam material properties for different values z. In order to obtain the general material properties of the FGM beam, there is a need to take into account not only the
temperature dependence of the properties but also the influence of the volume parts
changes of separate materials with regard to thickness and length of the beam. The
effective material properties can be estimated in a reliable way by taking into account
the above-mentioned features.
Table 7.1 Constants of the cubic approximation (7.22) of properties of some materials
Property
Material
P 0
P −1
P 1
P 2
P 3
Young modulus E[Pa] Zirconium 244.27 ×
10 9
0
−1.37 ×
10 −3
1.21 ×
10 −6
−3.68 ×
10 −10
Nickel
223.95 ×
10 9
0
−2.79 ×
10 −4
−4 ×
10 −9
0
Aluminium 349.55 ×
10 9
0
−3.85 ×
10 −4
4.03 ×
10 −7
1.67 ×
10 −11
Steel
SUS304
201.04 ×
10 9
0
3.08 ×
10 −4
−6.53 ×
10 −7
0
Ceramics
Si3N4
348.43 ×
10 9
0
−3.07 ×
10 −4
2.16 ×
10 −7
−8.94 ×
10 −11
Thermal expansion
coefficient α[K −1 ]
Zirconium 17.76 ×
10 −6
0
−1.49 ×
10 −3
1.00 ×
10 −5
−6.78 ×
10 −11
Nickel
9.92 ×
10 −6
0
8.71 ×
10 −4
0
0
Aluminium 6.827 ×
10 −6
0
1.84 ×
10 −4
0
0
Steel
SUS304
12.33 ×
10 −6
0
8.08 ×
10 −4
0
0
Ceramics
Si3N4
5.87 ×
10 −6
0
9.09 ×
10 −4
0
0
Poisson’s coefficient ν Zirconium 0.29
0
1.13 ×
10 −4
0
0
Nickel
0.31
0
0
0
0
Aluminium 0.26
0
0
0
0
Steel
SUS304
0.32
0
−2.00 ×
10 −4
−3.8 ×
10 −7
0
Ceramics
Si3N4
0.24
0
0
0
0
Heat transfer [W/mK] Aluminium –14.08
–1123.6
−6.23 ×
10 −3
0
0