Design Method Using Response Surface Model for CFRP Corrugated Structure under Quasistatic Crushing
Abstract
:1. Introduction
2. Methods
2.1. Material and Test Specimen
2.2. Quasistatic Compression Test
3. Test Results
Specimen Load Characteristics and Observed Results
4. Analysis and Discussion
4.1. Mathematical Model of Energy Absorption Efficiency
4.2. Mathematical Model of Crushing Force per Unit Length
4.3. Understanding the Phenomena Using the Stress Model of Corner Portions and Linear Portions
5. Conclusions
- In progressive crushing mode, EAE decreases with the increase in pitch.
- In progressive crushing mode, EAE increases with the increase in the number of stacks.
- In nonprogressive crushing mode, EAE significantly decreases.
- The energy absorption efficiency and average load generated in specimens with the varying number of stacks and pitch can be accurately represented by a linear response surface.
- As a result of examination by noting whether or not progressive crushing mode is observed, the corner portions largely contributed, with the predicted stress being 2.34 times larger than that of the linear portions.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Mechanical Property | Values | |
---|---|---|
Density [g/cm3] | 1.50 | |
Compression (SACMA SRM6) | Young’s modulus (GPa) | 59.49 |
Ultimate strength (Mpa) | 671.20 | |
Poisson’s ratio | 0.04 | |
Tension (ASTM D 3039) | Young’s modulus (GPa) | 62.47 |
Ultimate strength (Mpa) | 869.57 | |
Poisson’s ratio | 0.04 |
Number of Stacks (ply) | Lay-Up | Thickness (mm) | Pitch (mm) |
---|---|---|---|
8 | [0/90]8 | 1.82 | 5, 10, 15, 20 |
12 | [0/90]12 | 2.72 | Same |
16 | [0/90]16 | 3.63 | Same |
Explanatory Variable | Response Variable | |
---|---|---|
Number of Stacks (ply) | Pitch (mm) | EAE (J/g) |
8 | 5 | 51.3 |
10 | 47.0 | |
15 | 47.1 | |
20 | 45.3 | |
12 | 5 | 62.1 |
10 | 56.0 | |
15 | 54.8 | |
20 | 51.3 | |
16 | 5 | 52.9 |
10 | 64.9 | |
15 | 58.5 | |
20 | 55.6 |
Item | Partial Regression Coefficient (β0, β1, β2) | p Value | Std. Error | 95% Confidence Interval | |
---|---|---|---|---|---|
Lower | Upper | ||||
Intercept | 42.6 *** | p < 0.001 | 5.14 | 31.0 | 54.2 |
Number of stacks | 1.29 ** | 0.00564 | 0.356 | 0.481 | 2.09 |
Pitch | −0.332 | 0.145 | 0.208 | −0.803 | 0.139 |
Multiple R-squared (R2) | 0.634 | ||||
Adjusted R-squared (R’2) | 0.553 |
Item | Partial Regression Coefficient (β0, β1, β2) | p Value | Std. Error | 95% Confidence Interval | |
---|---|---|---|---|---|
Lower | Upper | ||||
Intercept | 42.0 *** | p < 0.001 | 2.47 | 36.3 | 47.7 |
Number of stacks | 1.71 *** | p < 0.001 | 0.187 | 1.28 | 2.14 |
Pitch | −0.601 *** | p < 0.001 | 0.111 | −0.857 | −0.345 |
Multiple R-squared (R2) | 0.925 | ||||
Adjusted R-squared (R’2) | 0.906 |
Explanatory Variable | Response Variable | |
---|---|---|
Number of Stacks (ply) | Pitch (mm) | CFL (kN/mm) |
8 | 5 | 0.275 |
10 | 0.255 | |
15 | 0.249 | |
20 | 0.234 | |
12 | 5 | 0.506 |
10 | 0.456 | |
15 | 0.437 | |
20 | 0.412 | |
16 | 5 | 0.527 |
10 | 0.710 | |
15 | 0.635 | |
20 | 0.605 |
Item | Partial Regression Coefficient (β0, β1, β2) | p Value | Std. Error | 95% Confidence Interval | |
---|---|---|---|---|---|
Lower | Upper | ||||
Intercept | −0.0847 | 0.215 | 0.0635 | −0.228 | 0.0589 |
Number of stacks | 0.0458 *** | p < 0.001 | 0.00440 | 0.0358 | 0.0557 |
Pitch | −0.00181 | 0.500 | 0.00257 | −0.00762 | 0.00401 |
Multiple R-squared (R2) | 0.923 | ||||
Adjusted R-squared (R’2) | 0.906 |
Item | Partial Regression Coefficient (β0, β1, β2) | p Value | Std. Error | 95% Confidence Interval | |
---|---|---|---|---|---|
Lower | Upper | ||||
Intercept | −0.0919 ** | 0.00594 | 0.0248 | −0.149 | −0.0348 |
Number of stacks | 0.0512 *** | p < 0.001 | 0.00188 | 0.0468 | 0.0555 |
Pitch | −0.00528 ** | 0.00146 | 0.00111 | −0.00784 | −0.00271 |
Multiple R-squared (R2) | 0.989 | ||||
Adjusted R-squared (R’2) | 0.987 |
Case | Explanatory Variable | Response Variable | ||
---|---|---|---|---|
Number of Stacks (ply) | Pitch (mm) | Corner Area (CA) (mm2) | Straight-Line Area (LA) (mm2) | MCF (kN) |
8 | 5 | 72.4 | 242 | 48.8 |
10 | 45.2 | 204 | 35.7 | |
15 | 36.2 | 209 | 34.4 | |
20 | 27.1 | 196 | 29.3 | |
12 | 5 | 108.0 | 363 | 89.6 |
10 | 67.8 | 306 | 63.8 | |
15 | 54.3 | 313 | 60.2 | |
20 | 40.7 | 294 | 51.8 | |
16 | 10 | 90.5 | 408 | 99.4 |
15 | 72.4 | 418 | 87.5 | |
20 | 54.3 | 393 | 75.9 |
Item | Partial Regression Coefficient (β1, β2) | pValue | Std. Error | 95% Confidence Interval | |
Lower | Upper | ||||
Corner area (CA) | 0.163 | 0.196 | 0.118 | −0.0989 | 0.425 |
Straight-line area (LA) | 0.171 *** | p < 0.001 | 0.0269 | 0.111 | 0.231 |
Multiple R-squared (R2) | 0.987 | ||||
Adjusted R-squared (R’2) | 0.985 |
Item | Partial Regression Coefficient (β1, β2) | p value | Std. Error | 95% Confidence Interval | |
---|---|---|---|---|---|
Lower | Upper | ||||
Corner area (CA) | 0.332 * | 0.0234 | 0.122 | 0.0565 | 0.608 |
Straight-line area (LA) | 0.142 *** | p < 0.001 | 0.0256 | 0.0843 | 0.200 |
Multiple R-squared (R2) | 0.991 | ||||
Adjusted R-squared (R’2) | 0.989 |
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Gomi, T.; Ayuzawa, S.; Urushiyama, Y.; Misaji, K.; Takahashi, S.; Motoyama, K.; Suzuki, K. Design Method Using Response Surface Model for CFRP Corrugated Structure under Quasistatic Crushing. Appl. Sci. 2021, 11, 10178. https://doi.org/10.3390/app112110178
Gomi T, Ayuzawa S, Urushiyama Y, Misaji K, Takahashi S, Motoyama K, Suzuki K. Design Method Using Response Surface Model for CFRP Corrugated Structure under Quasistatic Crushing. Applied Sciences. 2021; 11(21):10178. https://doi.org/10.3390/app112110178
Chicago/Turabian StyleGomi, Tetsuya, Shotaro Ayuzawa, Yuta Urushiyama, Kazuhito Misaji, Susumu Takahashi, Keiichi Motoyama, and Kosuke Suzuki. 2021. "Design Method Using Response Surface Model for CFRP Corrugated Structure under Quasistatic Crushing" Applied Sciences 11, no. 21: 10178. https://doi.org/10.3390/app112110178
APA StyleGomi, T., Ayuzawa, S., Urushiyama, Y., Misaji, K., Takahashi, S., Motoyama, K., & Suzuki, K. (2021). Design Method Using Response Surface Model for CFRP Corrugated Structure under Quasistatic Crushing. Applied Sciences, 11(21), 10178. https://doi.org/10.3390/app112110178