PSI - Issue 34

Atefeh Rajabi Kafshgar et al. / Procedia Structural Integrity 34 (2021) 71–77 Atefeh Rajabi Kafshgar et al./ Structural Integrity Procedia 00 (2021) 000 – 000

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Table 3. Proposed level with Taguchi method Responses Infill Density (A)

Extrusion Temperature (B)

Raster Angle (C)

Layer Thickness (D)

Ultimate Tensile Stress Elongation at Break Modulus of Elasticity

60 60 60 60 60

220 200 220 220 200

90 45 90 90 45

0.1 0.2 0.1 0.1 0.2

Yield Strength Toughness

According to Table 2, if 60, 220, 90, and 0.1 are chosen for A, B, C, and D, respectively (for instance), the value of properties (or responses) would be unknown from the Taguchi method. To solve this problem, regression model can be used to predict the response values. 2.2. Regression model For more investigation, a regression model is fitted to each mechanical property. Equations 2-6 present regression models that show the relationship between the predictors (printing parameters) and responses (mechanical properties). Negative coefficients indicate a negative effect and positive coefficients indicate a positive effect on the response variable (i.e. the mechanical properties) by increasing the independent variables (printing parameters). The larger the coefficients, the greater their impact. The degree of the impact and the type of impact (positive or negative) are consistent with the results obtained from the Taguchi method. These equations can be applied to optimize factors and predict response variables.

(2) (3) (4) (5) (6)

8.13 0.1876 0.1204 0.0166 12.48 UltimateTensileStress A B C D =− + + + − 6.19 0.01806 0.00892 0.01581 1.92 Elongationat Break A B C D = + − − + 0.436 0.00656 0.00533 0.002741 0.700 Modulusof Elasticity A B C D = − + + + −

11.4 0.1286 0.1042 0.0389 11.4 Yield Strength A B C D = − + + + − 1.897 0.00825 0.0065 0.004889 1.167 Toughness A B C D = + − − +

Moreover, each property is optimized by the response optimizer in Minitab software. Solutions are reported in Table 4. The results help us to understand that what response value (fit), confidence interval (CI), and prediction intervals (PI), could be provided by suggested levels. CI shows an interval for the estimation of the true value of the mean of response variable (mechanical property). If these tests are repeated many times, 95% of the CIs would contain the mean of mechanical property's value. PI presents an interval for the estimation of a new individual observation. It is expected that if the process is repeated infinitely, in 95% of cases PI includes the value of mechanical properties of the new sample produced according to the specific 3D printing parameters. For example, if 60, 200, 45, and 0.2 are chosen for A, B, C, and D, respectively, the toughness of the new sample will be between 0.944J and 1.266J with a confidence of 95%. However, there is a conflict with proposing a unique printing configuration. Regression equations and decision-maker preferences can be used to select appropriate levels. Considering the importance of stress and toughness, we examined these two properties in the next step. Table 4. The results of single-objective optimization Response Lower Target A B C D Fit 95% CI 95% PI Ultimate Tensile Stress 17.67 29.43 60 220 90 0.1 29.8675 (28.352, 31.383) (27.165, 32.570) Elongation at Break 3.33 5.51 60 200 45 0.2 5.16125 (4.659, 5.663) (4.266, 6.057) Modulus of Elasticity 0.72 1.22 60 220 90 0.1 1.30792 (1.188, 1.427) (1.095, 1.521) Yield Strength 10.96 21.27 60 220 90 0.1 21.5925 (18.29, 24.89) (15.70, 27.48) Toughness 0.46 1.19 60 200 45 0.2 1.10500 (1.015, 1.195) (0.944, 1.266)