Fracture Estimation in Ship Collision Analysis—Strain Rate and Thermal Softening Effects
Abstract
:1. Introduction
2. Material Model
2.1. Plasticity Model
2.2. Rate-Dependent Shell Element Fracture Initiation Model
3. Simulation of Panel Penetration Tests
4. Ship Collision Analysis
4.1. Collision Sceanario
4.2. Finite Element Modeling
5. Computational Results and Discussion
6. Conclusions
- Inclusion of strain rate hardening and thermal softening yields comparable results to the quasi-static simulation of ship collision problem. Therefore, these effects should be omitted from a practical assessment of ship structural crashworthiness analysis against collisions.
- Dynamic material behavior was considerably different from the quasi-static case; however, the plasticity and fracture strain-rate sensitivity lost their importance in low-velocity impact simulations of large-scale problems.
- The impact velocity has a minor effect on the structural response, which is observed only after a complete rupture of the outer shell plating and during the failure process of secondary members by buckling, folding, and tearing.
- Fracture preceded by localized necking is the dominant failure mode observed in ship-side collision. In the case of low-velocity impact, strain rate and thermal softening have a negligible influence on the fracture initiation of this type of failure.
- The commonly used Cowper–Symonds model for inclusion of strain rate effects and using a constant fracture strain yields a significant overestimation of absorbed energy by the struck ship, and the differences between quasi-static and dynamic simulations were significant. It is concluded that the common practice yields non-conservative results.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
Weighting factor in combined Swift-Voce hardening law | |
Voce hardening law parameter | |
Fracture strain rate sensitivity parameter | |
Reference strain rate for adiabatic condition | |
Localized necking strain under proportional loading | |
Fracture strain under proportional loading | |
Reference strain rate for isothermal condition | |
Pre-strain in Swift hardening law | |
Reference strain rate | |
Equivalent plastic strain | |
Equivalent plastic strain rate | |
Stress triaxiality | |
Taylor-Quinney coefficient | |
Lode angle parameter | |
Material density | |
Cauchy stress tensor | |
von Mises equivalent stress | |
Regulating term for transition from isothermal to adiabatic condition | |
A | Swift law parameter |
C | Strain-rate hardening sensitivity parameter |
Cp | Material specific heat |
D | Ductile fracture indicator |
E | Young’s modulus |
I1 | First invariant of stress tensor |
J2, J3 | Second and third invariants of deviatoric stress tensor |
N | Localized necking indicator |
Q | Voce law parameter |
T | Temperature |
Tm | Material melting temperature |
Tr | Reference temperature |
a, b, c | Hosford-Coulomb model parameters |
f2, f2, f3 | Lode angle-dependent functions in Hosford-Coulomb model |
g1, g2 | Stress triaxiality-dependent functions in DSSE model |
k | Deformation resistance function |
Strain hardening function | |
Strain-rate hardening function | |
Voce hardening law parameter | |
Swift hardening law | |
Thermal softening function | |
Voce hardening law | |
m | Thermal softening exponent |
n | Swift law exponent |
nf | Hosford-Coulomb model transformation coefficient |
pf | DSSE model exponent |
q | Cowper-Symonds model exponent |
References
- Liu, B.; Pedersen, P.T.; Zhu, L.; Zhang, S. Review of experiments and calculation procedures for ship collision and grounding damage. Mar. Struct. 2018, 59, 105–121. [Google Scholar] [CrossRef] [Green Version]
- Kim, J.H.; Baeg, D.Y.; Seo, J.K. Numerical investigation of residual strength of steel stiffened panel exposed to hydrocarbon fire. J. Ocean. Eng. Technol. 2021, 35, 203–215. [Google Scholar] [CrossRef]
- Ki, M.S.; Park, B.J. An experimental study on the h-beam under fire load in open space. J. Ocean. Eng. Technol. 2021, 35, 59–74. [Google Scholar] [CrossRef]
- Jeong, H.J.; Koo, W.; Kim, S.J. Numerical study on wave run-up of a circular cylinder with various diffraction parameters and body drafts. J. Ocean. Eng. Technol. 2020, 34, 245–252. [Google Scholar] [CrossRef]
- Jones, N. Some recent developments in the dynamic inelastic behaviour of structures. Ships Offshore Struct. 2006, 1, 37–44. [Google Scholar] [CrossRef]
- Paik, J.K. Practical techniques for finite element modeling to simulate structural crashworthiness in ship collisions and grounding (Part I: Theory). Ships Offshore Struct. 2007, 2, 69–80. [Google Scholar] [CrossRef]
- Samuelides, M. Recent advances and future trends in structural crashworthiness of ship structures subjected to impact loads. Ships Offshore Struct. 2017, 10, 488–497. [Google Scholar] [CrossRef]
- Storheim, M.; Amdahl, J. On the sensitivity to work hardening and strain-rate effects in nonlinear FEM analysis of ship collisions. Ships Offshore Struct. 2017, 12, 100–115. [Google Scholar] [CrossRef]
- Storheim, M.; Alsos, H.S.; Amdahl, J. Evaluation of nonlinear material behaviour for offshore structures subjected to accidental actions. J. Offshore Mech. Arctic Eng. 2018, 140, 041401. [Google Scholar] [CrossRef] [Green Version]
- Gruben, G.; Sølvernes, S.; Berstad, T.; Morin, D.; Hopperstad, O.S.; Langseth, M. Low-velocity impact behaviour and failure of stiffened steel plates. Mar. Struct. 2017, 54, 73–91. [Google Scholar] [CrossRef]
- Cerik, B.C.; Shin, H.K.; Cho, S.R. On the resistance of steel ring-stiffened cylinders subjected to low-velocity mass impact. Int. J. Impact Eng. 2015, 84, 108–123. [Google Scholar] [CrossRef]
- Cowper, G.; Symonds, P. Strain hardening and strain rate effects in the loading of cantilever beams. In Technical Report, No. 28; Division of Applied Mathematics, Brown University: Providence, RI, USA, 1957. [Google Scholar]
- Jones, N. Dynamic inelastic response of strain rate sensitive ductile plates due to large impact, dynamic pressure and explosive loadings. Int. J. Impact Eng. 2014, 74, 3–15. [Google Scholar] [CrossRef]
- Choung, J.; Nam, W.; Lee, J.Y. Dynamic hardening behaviors of various marine structural steels considering dependencies on strain rate and temperature. Mar. Struct. 2013, 32, 49–67. [Google Scholar] [CrossRef]
- Johnson, G.R.; Cook, W.H. A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In Proceedings of the 7th International Symposium on Ballistics, The Hague, The Netherlands, 19–21 April 1983; pp. 541–547. [Google Scholar]
- Ko, Y.G.; Kim, S.J.; Sohn, J.M.; Paik, J.K. A practical method to determine the dynamic fracture strain for the nonlinear finite element analysis of structural crashworthiness in ship-ship collisions. Ships Offshore Struct. 2018, 13, 412–422. [Google Scholar] [CrossRef] [Green Version]
- Cerik, B.C.; Lee, K.; Park, S.J.; Choung, J. Simulation of ship collision and grounding damage using Hosford-Coulomb fracture model for shell elements. Ocean. Eng. 2019, 173, 415–432. [Google Scholar] [CrossRef]
- Cerik, B.C.; Park, S.J.; Choung, J. Use of localized necking and fracture as a failure criterion in ship collision analysis. Mar. Struct. 2020, 73, 102787. [Google Scholar] [CrossRef]
- Storheim, M.; Alsos, H.S.; Hopperstad, O.S.; Amdahl, J. A damage-based failure model for coarsely meshed shell structures. Int. J. Impact Eng. 2015, 83, 59–75. [Google Scholar] [CrossRef]
- Park, S.J.; Choung, J. Punching fracture experiments and simulations of unstiffened and stiffened panels for ships and offshore structures. J. Ocean. Eng. Technol. 2020, 34, 155–166. [Google Scholar] [CrossRef]
- Cerik, B.C.; Choung, J. Rate-dependent combined necking and fracture model for predicting ductile fracture with shell elements at high strain rates. Int. J. Impact Eng. 2020, 146, 103697. [Google Scholar] [CrossRef]
- Cerik, B.C.; Ringsberg, J.W.; Choung, J. Revisiting MARSTRUCT benchmark study on side-shell collision with a combined localized necking and stress-state dependent ductile fracture model. Ocean. Eng. 2019, 187, 106173. [Google Scholar] [CrossRef]
- Roth, C.C.; Mohr, D. Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets. Int. J. Impact Eng. 2014, 56, 19–44. [Google Scholar] [CrossRef]
- Swift, H. Plastic instability under plane stress. J. Mech. Phys. Solids 1952, 1, 1–18. [Google Scholar] [CrossRef]
- Voce, E. The relationship between stress and strain from homogenous deformation. J. Inst. Met. 1948, 74, 537–562. [Google Scholar]
- Mohr, D.; Marcadet, S.J. Micromechanically-motivated phenomenological Hosford-Coulomb model for predicting ductile fracture initiation at low stress triaxialities. Int. J. Solids Struct. 2015, 67–68, 40–55. [Google Scholar] [CrossRef]
- Cerik, B.C.; Park, B.; Park, S.J.; Choung, J. Modeling, testing and calibration of ductile crack formation in grade DH36 ship plates. Mar. Struct. 2019, 66, 27–43. [Google Scholar] [CrossRef]
- Park, S.J.; Lee, K.; Cerik, B.C.; Choung, J. Comparative study on various ductile fracture models for marine structural steel EH36. J. Ocean. Eng. Technol. 2019, 33, 259–271. [Google Scholar] [CrossRef]
- Pack, K.; Mohr, D. Combined necking & fracture model to predict ductile failure with shell finite elements. Eng. Fract. Mech. 2017, 182, 32–51. [Google Scholar]
- Gruben, G.; Langseth, M.; Fagerholt, E.; Hopperstad, O. Low-velocity impact on high-strength steel sheets: An experimental and numerical study. Int. J. Impact Eng. 2016, 88, 153–171. [Google Scholar] [CrossRef] [Green Version]
- Liu, K.; Liu, B.; Villavicencio, R.; Wang, Z.; Guedes Soares, C. Assessment of material strain rate effects on square steel plates under lateral dynamic impact loads. Ships Offshore Struct. 2018, 13, 217–225. [Google Scholar] [CrossRef]
- Liu, K.; Wang, Z.; Tang, W.; Zhang, Y.; Wang, G. Experimental and numerical analysis of laterally impacted stiffened plates considering the effect of strain rate. Offshore Eng. 2015, 99, 44–54. [Google Scholar] [CrossRef]
- Hong, L.; Amdahl, J.; Wang, G. A direct design procedure for FPSO side structures against large impact loads. J. Offshore Mech. Arct. Eng. 2009, 131, 031105-1. [Google Scholar] [CrossRef]
- Paik, J.K.; Park, J.H.; Samuelides, E. Collision-accidental limit states performance of double-hull tanker structures: Pre-CSR versus CSR designs. Mar. Tech. 2009, 46, 183–191. [Google Scholar]
- Haris, S.; Amdahl, J. Analysis of ship-ship collision damage accounting for bow and side deformation plates. Mar. Struct. 2013, 32, 18–48. [Google Scholar] [CrossRef]
- Liu, B.; Villavicencio, R.; Zhang, S.; Guedes Soares, C. Assessment of external dynamics and internal mechanics in ship collisions. Ocean. Eng. 2017, 141, 326–336. [Google Scholar] [CrossRef]
- Cerik, B.C.; Choung, J. Ductile fracture behavior of mild and high-tensile strength shipbuilding steels. Appl. Sci. 2020, 10, 7034. [Google Scholar] [CrossRef]
- Klepaczko, J.R.; Rusinek, A.; Rodríguez-Martinez, J.A.; Pęcherski, R.B.; Arias, A. Modelling of thermo-viscoplastic behaviour of DH-36 and Weldox 460-E structural steels at wide ranges of strain rates and temperatures, comparison of constitutive relations for impact problems. Mech. Mat. 2009, 41, 599–621. [Google Scholar] [CrossRef] [Green Version]
- Nam, W. Numerical analysis of iceberg impact interaction with ship stiffened plates considering low-temperature characteristics of steel. J. Ocean Eng. Technol. 2019, 33, 411–420. [Google Scholar] [CrossRef] [Green Version]
- Son, Y.M.; Kim, J.D.; Oh, H.K.; Kim, Y.-T.; Park, S.-B.; Lee, J.M. Analysis of shear behavior and fracture characteristics of plywood in cryogenic environment. J. Ocean. Eng. Technol. 2019, 33, 394–399. [Google Scholar] [CrossRef] [Green Version]
- Lee, D.J.; Shin, S.B.; Kim, M.H. Modeling of the temperature-dependent and strain rate-dependent dynamic behavior of glass fiber-reinforced polyurethane foams. J. Ocean. Eng. Technol. 2019, 33, 547–555. [Google Scholar] [CrossRef] [Green Version]
- Park, W.C.; Song, C.Y. Evaluation on sensitivity and approximate modeling of fire-resistance performance for A60 class deck penetration piece using heat-transfer analysis and fire test. J. Ocean. Eng. Technol. 2021, 33, 141–149. [Google Scholar] [CrossRef]
- Park, W.C.; Song, C.Y. Heat transfer characteristics of bulkhead penetration piece for A60 Class compartment II: Fire resistance test for piece material and insulation types. J. Ocean. Eng. Technol. 2019, 33, 340–349. [Google Scholar] [CrossRef] [Green Version]
A (MPa) | ε0 | n | k0 (MPa) | Q (MPa) | β | α |
---|---|---|---|---|---|---|
582.2 | 0.0009016 | 0.1727 | - | - | - | 1.0 |
C | (s−1) | Tr (K) | Tm (K) | m | (s−1) | ηk |
0.01366 | 0.00116 | 293 | 1673 | 0.921 | 1.379 | 0.9 |
Cp (J/kg K) | ρ (ton/m3) | E (GPa) | a | b0 | c | γ |
420 | 7.85 | 201 | 1.785 | 0.946 | 0.045 | 0.025 |
A (MPa) | ε0 | n | k0 (MPa) | Q (MPa) | β | α |
---|---|---|---|---|---|---|
1058 | 0.007986 | 0.1794 | 444.7 | 293.1 | 21.89 | 0.55 |
C | (s−1) | Tr (K) | Tm (K) | m | (s−1) | ηk |
0.01366 | 0.00116 | 293 | 1673 | 0.921 | 1.379 | 0.9 |
Cp (J/kg K) | ρ (ton/m3) | E (GPa) | a | b0 | c | γ |
420 | 7.85 | 201 | 1.785 | 0.946 | 0.045 | 0.025 |
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |
© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Cerik, B.C.; Choung, J. Fracture Estimation in Ship Collision Analysis—Strain Rate and Thermal Softening Effects. Metals 2021, 11, 1402. https://doi.org/10.3390/met11091402
Cerik BC, Choung J. Fracture Estimation in Ship Collision Analysis—Strain Rate and Thermal Softening Effects. Metals. 2021; 11(9):1402. https://doi.org/10.3390/met11091402
Chicago/Turabian StyleCerik, Burak Can, and Joonmo Choung. 2021. "Fracture Estimation in Ship Collision Analysis—Strain Rate and Thermal Softening Effects" Metals 11, no. 9: 1402. https://doi.org/10.3390/met11091402