PSI - Issue 26

N.A. Fountas et al. / Procedia Structural Integrity 26 (2020) 139–146 Fountas et al. / Structural Integrity Procedia 00 (2019) 000–000

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During testing, the crosshead speed was maintained at 5 mm/min for PLA as specified in ASTM D638 standard for recording stable material deformation before failure. The crosshead motion continued until the fracture or the catastrophic failure of the specimens. Experimental results including tensile stress (MPa) - tensile strain (%), as well as load (kN) - elongation (mm) data; see Fig. 1b were collected and recorded through the data acquisition system of Bluehill ® 2 environment. 3. Statistical analysis and regression model generation The analysis of the data obtained from the customized RSM design coupled with the L 16 factorial design was performed on MINITAB ® R17 software using the full quadratic response surface model as given by Eq.3. Where y is the response i.e., load (kN) and x i is the i th parameter. For significance check, F-value given in ANOVA table is used. Probability of F-value greater than calculated F value due to noise is indicated by p -value. If p -value is less than 0.05, significance of corresponding term is established. For lack of fit, p -value should be greater than 0.05. An insignificant lack of fit is desirable because it indicates that any term excluded by the model is insignificant and that the developed model fits well. Anderson–Darling normality test is used to verify the suitability of the model corresponding to the tensile strength for practical applications. If p value for the Anderson–Darling test is lower than the chosen significance level (0.05 in the current study), it is concluded that the data do not follow a normal distribution. In this research, ANOVA indicates that the quadratic model generated, is suitable for predicting the tensile strength of PLA specimens in terms of load (kN) with regression p -value less than 0.05 (i.e. 0.001) and lack of fit more than 0.05 (i.e. 0.25>0.05). Based on p -value, it has been concluded that the tensile strength of PLA specimens is mainly influenced by the linear terms and interaction terms followed by square terms in general. The individual significance of each term is calculated by t-test at 95% confidence level, thus; terms having p -value less than 0.05 are significant. The coefficient of determination ( R 2 ) which indicates the percentage of total variation in the response explained by the terms in the model has been found equal to 96.95 %. It was evident that infill density and orientation angle had the largest effect on the response of load (kN). Results for the regression model are shown in Fig.2. Fig. 2a illustrates a graphical comparison among experimental and predicted results. Fig.2b verifies the model’s adequacy in predicting the response. Since p -value of the normality plot is found to be far beyond 0.05 (i.e. 0.250) it indicates that residuals follow a normal distribution and prediction made by the regression model are in good agreement with experimental results. 0 1 1 k k i i x       ii i i x x ij i j x x i i i j  y         (3)

(a) Experimental vs predicted results for Load (kN)

(b) Normality of residuals at 95% C.I.

99 90 80 76 00

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Shape 1.162 Scale 0.05708 N 16 AD 0.178 P-Value >0.250

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Fig. 2. (a) Experimental vs predicted results for load (kN); (b) Probability plot of residuals at 95% c.i. (Anderson-Darling test).