Development of Energy-Based Impact Formula-Part II: Scabbing Depth, Scabbing Limit, and Perforation Limit
Abstract
:1. Introduction
2. Literature Review
3. Development of Scabbing Depth Formula
3.1. Scabbing-Resistant Energy
3.2. Derivation of Scabbing Depth Formula
3.3. Derivation of Scabbing Limit Formula
3.4. Derivation of Perforation Limit Formula
4. Verification of Energy-Based Impact Formula
4.1. Scabbing Depth Assessment
4.2. Scabbing Limit Assessment
4.3. Perforation Limit Assessment
5. Conclusions
- The scabbing depth formula is derived using the same concept as that of penetration depth, based on Hertzian contact theory, but is not applied with the energy concentration effect of the impact velocity and projectile shape. The scabbing depth formula is proposed and verified using the experimental data. The mean value of the tested-to-predicted scabbing depth ratio is 1.87 and the standard deviation is 1.22. The scabbing depth formula is less accurate than the penetration depth formula. This is because it is difficult to predict the scabbing depth due to the energy amplified by reinforcing bars and/or aggregate and reflection angle. Despite these challenges, in 52 of the 81 specimens (64%), the scattering ratio is 2 and the average ratio is 1.16. Therefore, the scabbing depth formula is good overall.
- The scabbing limit formula can be obtained from the scabbing depth formula. The scabbing limit thickness, which is equal to the thickness that makes the scabbing depth zero. The Hughes formula is the best for predicting perforation failure, while the proposed equation is the most conservative. However, the proposed formula is the best for predicting non-perforation, with 99% accuracy. The interface between perforation and non-perforation is properly divided.
- The perforation limit thickness can be obtained from the penetration depth, tunneling depth, and scabbing depth, whose sum is equivalent to the minimum thickness required to prevent perforation. This is equal to the perforation limit thickness. To prevent perforation, the slab thickness should be equal to or greater than the sum of the penetration depth, tunneling depth, and scabbing depth.
- A new formula for predicting the scabbing limit and perforation limit thickness is derived using the theoretical framework and verified using experimental data. The proposed formulae predict all scabbing failures. However, non-scabbing failure is predicted with an accuracy of 81%. This formula is found to be the most accurate.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Ratio Range | Number of Specimens | Average Ratio |
---|---|---|
Under 1 | 19 | 0.85 |
Under 1.5 | 43 | 1.05 |
Under 2 | 52 | 1.16 |
Over 2 | 29 | 3.14 |
Formula | Scabbing Failure (Predicted/Tested) | No Scabbing Failure (Predicted/Tested) |
---|---|---|
Proposed | 100% (75 of 75 specimens) | 81% (139 of 172 specimens) |
Modified NDRC | 100% (75 of 75 specimens) | 66% (113 of 172 specimens) |
Hughes | 100% (75 of 75 specimens) | 43% (74 of 172 specimens) |
ACE | 100% (75 of 75 specimens) | 66% (113 of 172 specimens) |
Formula | Perforation Failure | No Perforation Failure |
---|---|---|
Proposed | 63% (41 of 65 specimens) | 99% (180 of 182 specimens) |
Modified NDRC | 77% (50 of 65 specimens) | 93% (170 of 182 specimens) |
Hughes | 100% (65 of 65 specimens) | 67% (125 of 182 specimens) |
ACE | 88% (57 of 65 specimens) | 91% (166 of 182 specimens) |
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Kim, S.; Kang, T.H.-K. Development of Energy-Based Impact Formula-Part II: Scabbing Depth, Scabbing Limit, and Perforation Limit. Appl. Sci. 2020, 10, 5481. https://doi.org/10.3390/app10165481
Kim S, Kang TH-K. Development of Energy-Based Impact Formula-Part II: Scabbing Depth, Scabbing Limit, and Perforation Limit. Applied Sciences. 2020; 10(16):5481. https://doi.org/10.3390/app10165481
Chicago/Turabian StyleKim, Sanghee, and Thomas H.-K. Kang. 2020. "Development of Energy-Based Impact Formula-Part II: Scabbing Depth, Scabbing Limit, and Perforation Limit" Applied Sciences 10, no. 16: 5481. https://doi.org/10.3390/app10165481
APA StyleKim, S., & Kang, T. H.-K. (2020). Development of Energy-Based Impact Formula-Part II: Scabbing Depth, Scabbing Limit, and Perforation Limit. Applied Sciences, 10(16), 5481. https://doi.org/10.3390/app10165481