Experimental values were obtained after tests as illustrated in Fig. 5 and 6 for tensile and impact strength respectively. RSM was applied to investigate linear, interaction & quadratic effect of independent parameters i.e.% infill density, layer thickness, and bed temperature on the impact energy (Ei) and tensile strength (σt) of PLA/PHA composite specimens printed with FDM process. Regression equations were established by the fitting of obtained experimental values to several models (linear, 2FI & quadratic). Various tests i.e. the sequential model sum of squares (SS), lack of fit (LF), and model summary statistics (MS) were used to estimate the adequacy of the model [17]. SS, LF test, and MS suggest the desired model for all responses, therefore, these tests were conducted for each response on prescribed processing parameters in Table 2.
X-Ray Powder Diffraction (XRD) was performed to analyze material homogeneity and composition. The results, depicted in Fig 7, showed an XRD peak of PLA/PHA specimen reported at 2θ = 16.5° which is consistent with the reported literature [18].
3.1. Tensile Strength
The sequential model with sum of squares was suggested based on p-value with P < 0.05 [19]. SS for the tensile test showed that p-value is less than 0.05 for both the linear and quadratic models as presented in Table 3.
Table 3: SS for Tensile Strength
Sources
|
Sum of squares
|
Df
|
Mean Square
|
F Value
|
P-value
|
|
Mean
|
11932.42
|
1
|
11932.42
|
|
|
|
Linear
|
410.93
|
3
|
136.98
|
2.87
|
0.0769
|
|
2FI
|
23.09
|
3
|
7.70
|
0.1290
|
0.9407
|
|
Quadratic
|
459.66
|
3
|
153.22
|
7.82
|
0.0123
|
Suggested
|
Cubic
|
108.98
|
3
|
36.33
|
5.15
|
0.0736
|
Aliased
|
Residual
|
28.19
|
4
|
7.05
|
|
|
|
Total
|
12963.28
|
17
|
762.55
|
|
|
|
LF test suggested the model based on p-value with P > 0.05 [20]. The model suggested for tensile strength by LF is the quadratic model. The quadratic model for tensile strength showed a non-significant lack of fit as its value is 0.0736 which is higher than 0.05 as presented in Table 4.
Table 4: Lack of Fit (LF) Tensile Strength
Sources
|
Sum. of Squares
|
Df
|
Mean Square
|
F-Value
|
P-value
|
|
Linear
|
591.73
|
9
|
65.75
|
9.33
|
0.0230
|
|
2FI
|
568.64
|
6
|
94.77
|
13.45
|
0.0126
|
|
Quadratic
|
108.98
|
3
|
36.33
|
5.15
|
0.0736
|
Suggested
|
Cubic
|
0.0000
|
0
|
|
|
|
Aliased
|
Pure Error
|
28.19
|
4
|
7.05
|
|
|
|
In model summary statistics (MS), from a previous study, it was found that an RS value greater than 0.75 is acceptable [19]. RS value is 0.8669 which is higher than 0.75 as shown in Table 5.
Table 5. Summary Statistics Tensile Strength Test
Source
|
Set.Dev.
|
RS
|
Adjusted RS
|
PRESS
|
|
Linear
|
6.91
|
0.3986
|
0.2599
|
1249.36
|
|
2FI
|
7.73
|
0.4210
|
0.0737
|
2865.61
|
|
Quadratic
|
4.43
|
0.8669
|
0.6958
|
1787.75
|
Suggested
|
Cubic
|
2.65
|
0.9726
|
0.8906
|
|
Aliased
|
3.2. Tensile Strength (ANOVA)
ANOVA for tensile test obtained data gives F-value of 5.07 which indicates the significance of the model as shown in Table 6. All terms whose p-value is less than 0.05 (P < 0.05) are significant. In this case, the linear effect of layer thickness and the quadratic effect of layer thickness is significant. Values greater than 0.05 demonstrate that terms did not affect the response. “Lack of Fit LF-value” of 0.073 suggests the Lack of Fit is non-significant.
Table 6: ANOVA for Tensile Strength
Source
|
Sum of Squares
|
Df
|
Mean Square
|
F-value
|
P-value
|
|
Model
|
893.69
|
9
|
99.30
|
5.07
|
0.0219
|
Significant
|
A- Layer thickness
|
370.06
|
1
|
370.06
|
18.88
|
0.0034
|
|
B- Infill density
|
40.86
|
1
|
40.86
|
2.09
|
0.1920
|
|
C- Bed Temperature
|
0.0171
|
1
|
0.0171
|
0.0009
|
0.9773
|
|
AB
|
7.98
|
1
|
7.98
|
0.4072
|
0.5437
|
|
AC
|
3.31
|
1
|
3.31
|
0.1690
|
0.6933
|
|
BC
|
11.80
|
1
|
11.80
|
0.6021
|
0.4632
|
|
A2
|
411.67
|
1
|
411.67
|
21.01
|
0.0025
|
|
B2
|
16.08
|
1
|
16.08
|
0.8208
|
0.3951
|
|
C2
|
51.20
|
1
|
51.20
|
2.61
|
0.1501
|
|
Residual
|
137.18
|
7
|
19.60
|
|
|
|
Lack of Fit
|
108.98
|
3
|
36.33
|
5.15
|
0.0736
|
Not significant
|
The obtained regression equation w.r.t coded factors to predict the influence of layer thickness, infill density, and bed temperature on tensile strength without non-significant parameters, is given below:
σt = 28.59 + 6.80 × A +2.26 × B + 0.04 × C - 1.41 × A × B - 0.91 × A × C - 1.72 × B × C - 1.72 × B × C - 9.89 × A² + 1.95 × B² + 3.49 × C² Eq (1)
According to ANOVA, layer thickness and % infill density play a vital role in the tensile strength of printed samples shown in Fig. 8 and table 6.
3.3. Impact Strength
The sequential model with sum of squares was. suggested on the basis of p-value with P < 0.05 [21]. SS indicates that for impact strength the p-value is less than 0.05 for the quadratic model as shown in Table 7.
Table 7: SS for Impact Strength
Sources
|
Sum of squares
|
Df
|
Mean Square
|
F Value
|
P-value
|
|
Mean
|
1412.87
|
1
|
1412.87
|
|
|
|
Linear
|
93.57
|
3
|
31.19
|
1.76
|
0.2042
|
|
2FI
|
24.05
|
3
|
8.02
|
0.3886
|
0.7638
|
|
Quadratic
|
153.46
|
3
|
51.15
|
6.78
|
0.0177
|
Suggested
|
Cubic
|
34.32
|
3
|
11.44
|
2.48
|
0.2008
|
Aliased
|
Lack of fit test suggests the model based on p-value with P > 0.05 [22]. The model suggested for impact strength by Lack of fit is the quadratic model as shown in Table 8. The quadratic model for impact strength showed a non-significant lack of fit as its value is 0.2008 which is higher than 0.05.
Table 8: Lack of Fit Test for Impact Strength
Sources
|
Sum of Squares
|
Df
|
Mean Square
|
F-Value
|
P-value
|
|
Linear
|
211.83
|
9
|
23.54
|
5.09
|
0.0659
|
|
2FI
|
187.78
|
6
|
31.30
|
6.77
|
0.0426
|
|
Quadratic
|
34.32
|
3
|
11.44
|
2.48
|
0.2008
|
Suggested
|
Cubic
|
0.0000
|
0
|
|
|
|
Aliased
|
Earlier it was reported that RS value greater than 0.75 is acceptable in model summary statics (MS) [23]. The model suggested for impact strength by summary statistics is the quadratic model as presented in Table 9.
Table 9: Summary Statistics of Impact Strength
Source
|
Set.Dev.
|
RS
|
Adjusted RS
|
Predicted RS
|
PRESS
|
|
Linear
|
4.21
|
0.2889
|
0.1248
|
-0.3248
|
429.10
|
|
2FI
|
4.54
|
0.3632
|
-0.0190
|
-1.5915
|
839.37
|
|
Quadratic
|
2.75
|
0.8370
|
0.6273
|
-0.7847
|
578.04
|
Suggested
|
Cubic
|
2.15
|
0.9429
|
0.7717
|
|
|
Aliased
|
3.4. Impact Strength (ANOVA)
From ANOVA for impact test obtained data, the model’s F-value of 3.99 suggests the model is significant as shown in Table 10. All terms of the model whose p-value is less than 0.05 are termed as significant as shown in Table 4-9. The linear effect of layer thickness in significant terms compares to the remaining terms. P > 0.05 demonstrates that terms are non-significant. The "Lack of Fit F-value" of 2.48 suggests that lack of fit is non-significant.
Table 10: ANOVA for Impact Strength
Source
|
Sum of Squares
|
Df
|
Mean Square
|
F-value
|
P-value
|
|
Model
|
271.08
|
9
|
30.12
|
3.99
|
0.0407
|
Significant
|
A- Layer thickness
|
76.20
|
1
|
76.20
|
10.10
|
0.0155
|
|
B- Infill density
|
15.88
|
1
|
15.88
|
2.10
|
0.1901
|
|
C- Bed Temperature
|
1.50
|
1
|
1.50
|
0.1984
|
0.6695
|
|
AB
|
9.77
|
1
|
9.77
|
1.29
|
0.2926
|
|
AC
|
0.2209
|
1
|
0.2209
|
0.0293
|
0.8690
|
|
BC
|
14.06
|
1
|
14.06
|
1.86
|
0.2144
|
|
A2
|
81.06
|
1
|
81.06
|
10.75
|
0.0135
|
|
B2
|
52.40
|
1
|
52.40
|
6.95
|
0.0336
|
|
C2
|
19.91
|
1
|
19.91
|
2.64
|
0.1482
|
|
Residual
|
52.81
|
7
|
7.54
|
|
|
|
Lack of Fit
|
34.32
|
3
|
11.44
|
2.48
|
0.2008
|
Not significant
|
Regression equation, w.r.t coded factors to predict influence of layer thickness, print bed temperature, and Infill density on impact strength without non-significant parameters, is given below:
Ei =11.818 + 3.08625 * A + 1.40875 * B + -0.4325 * C + 1.5625 * AB + -0.235 * AC + 1.875 * BC + -4.38775 * A^2 + -3.52775 * B^2 + 2.17475 * C^2 Eq (2)
Analysis of Variance reported that % infill density and layer thickness has a substantial effect on the impact strength of printed notched specimens as shown in Fig. 9.
3.5. Process Parameter Optimization
Numerical optimization was used to find out optimum levels of independent parameters. By using the desirability function (DF), RSM identified an arrangement of parameters to optimize several responses [19] and provide the responses which are most significant and will give the maximum tensile and impact strength at optimized parameters as presented in table 11.
Table 11: prediction of responses
Factor
|
Na.me
|
Optimize Level.
|
Low level.
|
High level.
|
Tensile strength
MPa
|
Impact strength
J/m
|
A.
|
Layer thickness.
|
0.4443
|
0.0800
|
0.6000
|
35.27
|
14.51
|
B
|
Infill density
|
44.76
|
20.00
|
55.00
|
|
C
|
Bed temperature
|
20.00
|
20.00
|
60.00
|
|
3.6. Verification of Experiment
RSM suggested the optimum levels of layer thickness, % infill density & bed temperature which were 0.44mm, 44.76 %, and 20 °C temperature respectively. These predicted values were verified to check the competence of the obtained equations. Predicted and experimental values of tensile and impact strength at optimal conditions are shown in Table 12. The stress-strain curve for tensile test specimen under the optimal level of parameters is depicted in Fig 10.
Table 12: Verification of experiments
Sr. No
|
Responses
|
Predicted Value
|
Experimental Value
|
Percentage Error
|
1
|
Tensile Strength (MPa)
|
35.27
|
32.99
|
6.0%
|
2
|
Impact Strength (J/m)
|
14.51
|
14.13
|
2.68%
|