The regression design of carbon/glass hybrid fiber reinforced NASC can be defined as the design problem with three components which include reinforcing hybrid fiber (carbon/ glass hybrid fiber), elastic binding material (NBR) and filling material (compatibilization fiber and other stuffings). In consideration of the attribute for processing of the material, the component contents in NASC are in the following ranges:
0.12 < X, < 0.25, 0.4 < X2 < 0.8, 0.1 < X3 < 0.5 (2)
where Xі X2 and X3 are the contents of the elastic binding material, the reinforcing fiber and the filling material, respectively.
The stress relaxation rate y of NASC after ageing treatment at 573 K is used as an evaluating indicator, and the regression design of NASC is to obtain the regression equation by the experiments under the following conditions:
a, < X, < b,,(i = 1,2,3) and X, + X2 + X3 = 1 (3)
where ai and bi are the constraint conditions described in Eq. (2).
A symmetrical complex Z is established. The coordinate system z1x2x3 represents the actual design space of the components of NASC, and the coordinate system z1z2z3 represents the encoding space. Accordingly, the relationship between Z and X can be expressed by:
X1 = a1 + (b1 – a1 )z1/B, X2 = a 1+(b2 -a2)z2/B, X3 = 1 -(X1 + X2) (4)
where B=max(zij), i is the test number, and j the variable number. The coordinates of the actual test points are listed in Table 6, where the stress relaxation rates of the materials after ageing treatment at 573 K are also listed.
The stress relaxation rate of NASC after ageing at 573 K can be expressed by the coordinates of the encoding point, and the regression equation holds:
y = 63z1 + 77z2 + 120.8z3 – 137.6z1z2 + 0.49z1z3 – 261.6z2z3 (5)
|
NO. |
Encoding content of components |
Actual content of components |
Relaxation rate y (%) |
||||
|
z1 |
z2 |
z3 |
X1 |
X2 |
X3 |
||
|
1 |
0 |
1/2 |
1/2 |
0.12 |
0.667 |
0.213 |
51.6 |
|
2 |
1/2 |
0 |
1/2 |
0.207 |
0.4 |
0.393 |
32.9 |
|
3 |
1/2 |
1/2 |
0 |
0.207 |
0.667 |
0.127 |
43.9 |
|
4 |
1/4 |
1/4 |
1/2 |
0.163 |
0.533 |
0.303 |
34.6 |
|
5 |
1/4 |
1/2 |
1/4 |
0.163 |
0.667 |
0.17 |
42.3 |
|
6 |
1/2 |
1/4 |
1/4 |
0.207 |
0.533 |
0.26 |
31.3 |
|
7 |
3/4 |
1/8 |
1/8 |
0.25 |
0.467 |
0.283 |
58.4 |
|
8 |
1/8 |
3/4 |
1/8 |
0.142 |
0.8 |
0.058 |
52.4 |
|
9 |
1/8 |
1/8 |
3/4 |
0.142 |
0.467 |
0.392 |
43.1 |
|
Table 6. Experimental scheme and test results |
The purpose of prescription optimization is to improve the heat resistance and the attribute for processing of NASC, to reduce the self-cost of the raw materials of the product, and to ensure the stress relaxation rate of the material satisfying the index prescribed in the product standard. The prescription optimization of NASC is to obtain the optimal values of z1, z2 and z3 under the following conditions:
3
zi ^ 0′ Zzi = 1 z1 = Z1min/ Z2 = Z2min/y ^ 35 (* = 1,2,3) (6)
i=1
According to Eq. (5), the coordinates of the best theoretic design point of the contents of the components in NASC can be obtained, as z1=0.38, z2=0 and z3=0.63. From Eq. (4), the formulation is x1=0.186, x2=0.4 and x3=0.414.
Some NASC were prepared when the weight ratio (carbon fiber to glass fiber) equalled to 4:0, 3:1, 2:2, 1:2, 1:3 and 0:4 respectively. The experimental results of the transverse tensile strength and the stress relaxation rate of these materials after ageing treatment at 573 K for 5 hours are shown in Fig. 9. It can be found that the strength of the material is the highest and the relaxation rate is relatively low when the weight ratio is 2:3 (weight content of carbon fiber in hybrid fibers is 40%).
|
Weight content of carbon fiber in hybrid fibers /100% Fig. 9. The effect of carbon fiber content in hybrid fibers on transverse tensile strength and stress relaxation rate of NAFC |
Therefore, the optimization formulation of the NASC reinforced with carbon/glass hybrid fibers was obtained, as listed in Table 7.
|
Component |
Content (wt%) |
Component |
Content (wt%) |
|
|
NBR |
18.6 |
Accelerating agent |
0.22 |
|
|
Carbon fiber |
16.0 |
Zinc white |
0.48 |
|
|
Glass fiber |
24.0 |
Stearinic acid |
0.18 |
|
|
Sepiolite fiber |
10.3 |
Antiaging protective |
0.6 |
|
|
Phenolic resin |
8.38 |
Filling material |
Lime carbonate |
6.31 |
|
Hyperfine graphite powder |
7.44 |
Kaolin clay |
3.2 |
|
|
Vulcanized agent |
0.35 |
Soap stone powder |
1.6 |
|
|
Carbon black |
2.34 |
|
Table 7. Formulation of carbon/glass hybrid fibers reinforced NASC |
