3.4.2 FLEXURAL PROPERTIES (ASTM D-790)

3.4.2 FLEXURAL PROPERTIES (ASTM D-790):

The flexural strength test was performed as per the procedure explained in the chapter 2 and the results were tabulated as shown in table 3.6. The properties that were evaluated as a part of flexural strength test are flexural strength at peak load, flexural modulus, percentage elongation and Youngs modulus. From the results, regression analysis had been performed to get the regression equations, which are shown in the tables 3.7, 3.8, 3.9, 3.10. Then using the equations contour plots and response surfaces were generated for each of them as shown in the figures 3.5 to 3.12. The plots obtained are saddle shaped.

Table 3.6 Results for flexural properties for CaCO₃ – HDPE system:

Trial no.	X1	X2	Flex Strength @ peak load (kg/cm2)	%Elongation	Flex Modulus (M Pa)	Youngs Modulus (kg/cm2)
1.	60	5	4.4	15.7	182	16.2
2.	60	25	4.91	19	325	25.7
3.	80	5	4.96	21.4	288	22.8
4.	80	25	4.85	23.3	233	20.7
5.	56	15	4.63	16.4	292	25.9
6.	84	15	4.72	13.7	347	30.8
7.	70	1	4.67	23.6	363	32.2
8.	70	29	4.58	22.16	360	32
9.	70	15	4.86	22.9	416	36.9
10.	70	15	4.86	22.9	416	36.9
11.	70	15	4.86	22.9	416	36.9

Table 3.7 Estimated Regression Coefficients for Flexural Strength

Term	Coef	SE Coef	T	P
Constant	4.8581	0.07613	63.812	0.000
X1	0.07904	0.04686	1.687	0.152
X2	0.03460	0.04686	0.738	0.494
X1*X1	-0.05923	0.05626	-1.053	0.341
X2*X2	-0.08474	0.05626	-1.506	0.192
X1*X2	-0.155	0.06594	-2.351	0.066

S = 0.1319 R-Sq = 69.9% R-Sq (adj) = 39.8%

The regression equation is

Y = 4.8581+ 0.07904 X₁ – 0.03460X₂ - 0.05923X₁² - 0.08474X₂² -0.155X₁ X₂.

Table 3.8 Estimated Regression Coefficients for Flexural Modulus

Term	Coef	SE Coef	T	P
Constant	417.09	31.33	13.312	0.000
X1	11.49	19.29	0.596	0.577
X2	10.58	19.29	0.549	0.607
X1*X1	-70.69	23.15	-3.053	0.028
X2*X2	-49.26	23.15	-2.128	.087
X1*X2	-49.50	27.14	-1.824	0.128

S = 54.28 R-Sq = 75.0% R-Sq (adj) = 50.1%

The regression equation is

Y = 417.09+ 11.49 X₁ +10.58X₂ -70.69X₁² -49.26X₂² -49.50X₁ X₂.

Table 3.9 Estimated Regression Coefficients for Youngs Modulus

Term	Coef	SE Coef	T	P
Constant	37.0165	3.271	11.317	0.000
X1	1.0682	2.013	0.531	0.618
X2	0.8990	2.013	0.447	0.674
X1*X1	-6.6499	2.417	-2.751	0.040
X2*X2	-4.7366	2.417	-1.960	0.107
X1*X2	-2.9000	2.833	-1.024	0.353

S = 5.666 R-Sq = 68.0% R-Sq (adj) = 35.9%

The regression equation is

Y = 37.0165 +1.0682X₁ +0.8990X₂ - 6.6499X₁² - 4.7366X₂² -2.9X₁ X₂.

Table 3.10 Estimated Regression Coefficients for Percentage Elongation

Term	Coef	SE Coef	T	P
Constant	22.8871	1.4627	15.647	0.000
X1	0.7854	0.9004	0.872	0.423
X2	0.4020	0.9004	0.447	0.674
X1*X1	-3.7524	1.0808	-3.472	0.018
X2*X2	0.2425	1.0808	0.224	0.831
X1*X2	-0.3500	1.2669	-0.276	0.793

S = 2.534 R-Sq = 74.6% R-Sq (adj) = 49.2%

The regression equation is

Y = 22.8871+ 0.7854X₁ +0.4020X₂ -3.7524X₁² +0.2425X₂² -0.35X₁ X₂.