3.4.4 HARDNESS (ASTM D 2240)

3.4.4 HARDNESS (ASTM D 2240):

SHORE – A:

The Shore – A Hardness test was performed as per the procedure explained in the chapter 2 and the results were tabulated as shown in table 3.15. From the results, regression analysis had been performed to get the regression equation, which is shown in the table 3.16. Then using the equation contour plots and response surfaces are generated which are shown in fig 3.21 and 3.22. The desired values of

Shore – A Hardness can be obtained at any combination within the optimized region as indicated in the contour plot. The value of X1 varies from 68 – 82 and X2 varies from 10 – 20 in the optimum region.

SHORE – D:

The Shore – A Hardness test was performed as per the procedure explained in the chapter 2 and the results were tabulated as shown in table 3.15. From the results, regression analysis had been performed to get the regression equation, which is shown in the table 3.17. Then using the equation contour plots and response surfaces are generated which are shown in fig 3.23 and 3.24. The desired values of

Shore – D Hardness can be obtained at any combination within the optimized region as indicated in the contour plot. The value of X1 varies from 55 - 67 and X2 17 - 25 varies from in the optimum region.

Table 3.15 Results of Shore – A and Shore – D Hardness tests for CaCO₃ – HDPE system:

TRIAL	X1	X2	SHORE – A HARDNESS	SHORE – D HARDNESS
1	60	5	76	54.3
2	60	25	79.0	56.0
3	80	5	81.0	58.3
4	80	25	78.3	56.3
5	56	15	78.3	59.0
6	84	15	80.3	58.0
7	70	1	78.0	57.3
8	70	29	80.6	57.3
9	70	15	81.0	57.6
10	70	15	81.0	57.6
11	70	15	81.0	57.6

Table 3.16 Estimated Regression Coefficients for Hardness- Shore A

Term	Coef	SE Coef	T	P
Constant	81.0095	0.4285	189.037	0.000
X1	0.9003	0.2638	3.413	0.019
X2	0.5119	0.2638	1.940	0.110
X1*X1	-1.0388	0.3166	-3.281	0.022
X2*X2	-1.0388	0.3166	-3.281	0.022
X1*X2	-1.4175	0.3712	-3.819	0.012

S = 0.7424 R-Sq = 90.3% R-Sq (adj) = 80.7%

The regression equation is

Y = 81.0095 +0.9003X₁ +0.5119X₂ -1.0388X₁² -1.0388X₂² -1.4175X₁ X₂.

Table 3.17 Estimated Regression Coefficients for Hardness- Shore D

Term	Coef	SE Coef	T	P
Constant	57.6223	0.8001	72.015	0.000
X1	0.3699	0.4925	0.751	0.486
X2	-0.0417	0.4925	-0.085	0.936
X1*X1	0.0210	0.5912	0.035	0.973
X2*X2	-0.5760	0.5912	-0.974	0.375
X1*X2	-0.9175	0.6930	-1.324	0.243

S = 1.386 R-Sq = 40.3% R-Sq (adj) = 0.0%

The regression equation is

Y = 57.6223 +0.3699X₁ -0.0417X₂ +0.0210X₁² -0.576X₂² -0.9175X₁ X₂.

Fig. 3.21 Contour Plot of Hardness – Shore A vs. X1, X2

Fig. 3.22 Response surface of Hardness – Shore A vs. X1, X2

Fig. 3.23 Contour plot of Hardness – Shore D vs. X1, X2

Fig. 3.24 Response surface of Hardness – Shore D vs. X1, X2

OVERLAYING OF CONTOUR PLOTS:

The individual contour plots were generated for each of the property and then simultaneous optimization of properties were carried out by overlaying the individual plots to obtain the overlaid contour plots.

The desired values of all these properties can be obtained at any given combination within the optimized region indicated by the white coloured region in the fig.3.20. The values of both X1 and X2 vary over a wide range in the optimized region.

The desired values of all these properties can be obtained at any given combination within the optimized region indicated by the white coloured region in the fig.3.13. The value of X1 varies from 77 – 80 and X2 varies from 5 – 17 in the optimized region.

Fig. 3.20 Overlaid Contour plot of Tensile Properties

Fig. 3.13 Overlaid contour Plot of Flexural Properties