Contact between entities in this world is basic concept in social and humanity as well as science in engineering. In marine and ocean engineering filed, contact can be used to perform something useful such as marine steel plate roll and treatment. In other hand, contact also can become something remarkable with immense loss, i.e. grounding and collision. This contact type is called impact which occurs in short-time period and usually happens during accident phenomenon. Impact in accident especially in this field is very wide subject that need to be observed. The objectives of this observation are indeed diverse, including to improve the structure safety, develop appended material etc. The endless possibilities and causes are directly influencing the results mode which can be in term of energy, load and even damage extent. This situation makes this impact phenomenon in ocean engineering and marine structures is continuously studied. Various researchers in the past had performed studies in impact phenomenon including ship collision by several methods. The researches in analytical theory had been introduced by Minorsky  with his empirical formula to estimate the collision energy in term of high-energy collision. As the rapid improvement on technology, virtual experiment can be deployed to solve various structure problems such as collision between ships with ease in these days as it was used by Bae et al.  to perform rapid prediction of structural response accounting for collision. The inner effect of ship structures in collision phenomenon can be divided into two major classifications, namely structure and material. These parameters are certainly producing different output during and after collision processes.
This paper presents the study on ship collision based on various impact scenarios models. The scenario models are built based on two classifications of inner effect in collision event such as structure and material. Preference of structure component accounting for the striking ship direction namely deck structure as longitudinal component and side hull shell as transverse component will represent analyses in term of structure. The various material effect such as mechanical strength, hardening and failure strain are used as representative of material aspect. Virtual experiment will be performed in order to acquire results of impact scenario models.
2 Overview on impact characteristic and topology
Impact phenomenon had been observed since more than half century ago and due to of its complexity and scope, this field become interesting to be observed accounting for various point of views. Several known research on impact science and engineering are including impact assessment by Oterkus et al. , pulse pressure observation by Schleyer et al.  and response subjected to blast by Panciroli and Abrate .
Impact phenomenon of ship collision is a complex process with involvement of large contact force, crushing of hull structure and rupture of side plating. The consequences may be severe as well remarkable and the process itself is highly nonlinear. The nonlinearities of impact phenomenon are also influenced by the material characteristic. Isotropic, kinematic, or a combination of isotropic and kinematic hardening may be obtained by varying a parameter, called β between 0 and 1. Krieg and Key  formulated this model and the implementation is based on their paper. In isotropic hardening, the center of the yield surface is fixed but the radius is a function of the plastic strain. In kinematic hardening, the radius of the yield surface is fixed but the center translates in the direction of the plastic strain. The yield stress of mild steel is well known very sensitive to the strain rate as introduced by Jones . It can be concluded from his work that the yield stress of mild steel increases with increasing strain rates. Jones on other hand mentioned that aluminum is essentially insensitive to strain rates normally encountered in practice. In event of contact between two structure objects, when a structure has been deformed enough, it will rupture and undergo a failure. Predicting the rupture on structure accurately is a complex problem. Different load conditions will give different failure modes . Rupture criteria of ductile metal beams subjected to large dynamic loads was discussed by Jones and Wierzbicki . Three main failure criteria were discussed. The first mode is tensile tearing failure mode. This failure mode occur when the maximum strain equals the critical rupture strain of the material and beam rupture. The second is the transverse shear failure mode which develops in a beam when large transverse shear deformations occur within a very short region of the plastic beam. The third failure is the energy density failure mode. This mode is assumed that rupture occurs in a rigid-plastic structure when the absorption of plastic work per unit volume reaches the critical value.
Topology of impact phenomenon in ship collision is also diverse. Accounting for position as presented in Figure 1, impact can be divided into:
- (a)Side collision
- (b)Head-to-head collision
In term of striking object or indenter, various objects can be taken into consideration based on its involvement possibility in event of collision, namely:
- (c)Bridge pier
- (d)Offshore jacket
- (e)Port wall
In addition to collision type and indenter classification, friction properties also affect the structural response during and prior collision process. In impact of ocean engineering, typically, static coulomb friction coefficients in the range of 0.2-0.4 are adopted . However, based on friction investigation based on collision accident by Bae et al. , the implementation of friction coefficient between mild steel can be considered as other coefficient option in observation of impact behavior. In the simulation carried out in the following section, the steels friction coefficient has been implemented.
3 Development in calculations method and instrument
Demand to increase safety for ship and its crew and cargo makes numerous researchers from different fields expand their attention in accidental load phenomenon. In order to achieve satisfaction in calculation for collision and other impact incidents, methodology is improved continuously. The estimation of structural response is proposed by Minorsky  in his known energy estimation formula for high-energy collision. This method assumes that energy to destroy involved components in collision is equally perpendicular with volume of destroyed material. This formula is inviting researchers to refine it, such as done by Woisin  in his low-energy collision formula and Zhang  who divides the energy formula based on several deformation pattern. The proposed formula by mentioned researchers before is presented consecutively in Equations 1 to 5. Besides empirical formulas, the implementation of simplified expressions in prediction structure behaviour under various loadings is also performed in impact engineering such by Haris and Amdahl  at NTNU who assumed that the complex structural arrangement of ship is presented in simplification models of several basic elements, such as cruciform, T-section, girder, and plating. The total resistance of this method for side and bow structures respectively is presented in Equations 6 and 7. The both of discussed methodology are built based on actual experiment, survey, and also assumption. In history of ship collision, several full-scale experiments are recorded, for example in the Netherlands 1998. Before that, joint cooperation between Japan, the Netherlands, and Germany also conducted similar experiment using two inland waterway tankers . In other hand, a research based on real accident was also conducted by several parties such as by joint cooperation between Indonesia and South Korea in predicting recent collision in Sunda strait. Several surveys are conducted to shipyard where the target ship is repaired to measure damage extent and also take material specimen for laboratory experiment . The accuracy of calculations with this method is believed good enough to be a reference for empirical and simplified methods. However, constraint in time and cost make full-scale experiment and survey cannot be conducted comfortably by wide parties. Empirical formula and simplified expression are also need continuous update in order to seek sustainable precision. The process to develop formula is considered costly which is expected consume more time of main analysis and calculation.
As exceptional high improvement in computational technology, finite element method rises as reliable calculation instrument to predict various phenomenon in science and technology. This method is judged powerful enough to predict nonlinear phenomenon which is complicated, such as collision [15–18] and grounding . By this method all design of involved objects’ components can be defined in both structural and material levels. Computational code which is used by this method is flexible and can be implemented for various analyses. An algorithm for collision analysis is presented in Equations 8 to 10. Time computation of this method can be adapted according to time and cost allocation which longer time space for calculation and related data of actual experiment in material for example, will boost up the reality and reliability aspects of performed works.
4 Impact scenario and experiment preparation
This section presents the model of impact scenario in collision simulation. The preparation for virtual simulation is given together with illustration of coordinate system and ship model.
4.1 Involved vessel model
A series of collision analysis is performed for various impact models with the explicit FE code ANSYS LS-DYNA. The considered struck ship is an 85 m passenger ship with a double hull structure configuration as presented in Figure 2. The larger ship is taken into analyses by cargo vessel with 144 m in length. The width of the striking ship is 19.8 m, design the draft is 5.6 m and the height is 10.2 m.
4.2 Proposed impact scenario
The scenario of collision impact is built based on side collision type with two major parameters, namely structure and material. In term of structure, the component preferences of hull structure is defined based on coming direction of the striking ship, i.e. side shell for transversal component and deck as longitudinal component are used as given in Figure 3.
The structure configurations of double hull with difference on distance between outer and inner shell as given in Figure 2 are also taken as impact model. In material side, the mechanical properties of material especially strength characteristic as introduced by Callister  are adopted for scenario model. Four material types are used with several failure strain values. The material definition in term of kinematic hardening, isotropic hardening and kinematic-isotropic hardening are included in impact models. The detail of each impact scenario models are presented in Table 1 and 2.
|AISI/SAE or ASTM Number||Composition (wt %)||Strength (MPa)||Ductility (% Elongation)|
Detail of proposed scenario models.
|Impact Type||Parameters||Impact Scenario Model|
|Side collision||Structure||Component preference||Transversal component|
|Double hull configuration||Distance of inner-outer shell||3.5 m|
|Material||Strength characteristic||Material type||1010|
|Failure characteristic||Failure strain||0.1|
|Material definition||Hardening model||kinematic|
4.3 Virtual experiment
In virtual experiment process, the struck ship will be considered as a deformable structure and the striking ship as a rigid body. In present analysis, the plastic-kinematics material is applied into numerical models and the yield function of this material model is given in Equation 11 and 12.
The element choice for present research is Belytschko–Tsay element. Tornqvist and Simonsen  suggested that the element-length-to-thickness (ELT) ratio should be within the range of 5-10 so that the local stress and strain fields can be captured well. Fine mesh with size 80 mm is applied on the core area of the struck ship and fine mesh with size 90 mm and 100 mm are applied on the transition and the outside area respectively. The element-length-to-thickness (ELT) ratio for this area in range 8-10. The area of the striking ship model is divided into two parts: the first area will experience direct contact with the struck ship. A fine mesh with size 340 mm is applied. The second is the rest area, where fine mesh of size 680 mm is applied.
During collision process, the striking ship will move with velocity 12 knots or 6.17 m/s to proposed target point while the struck ship is set to be fixed in centerline while the ends of the model will be clamped. The fixation is applied on all frames in the end of model. In the simulation which involved the struck ship as a deformable structure and the striking ship as a rigid body, the virtual experiment model consists of more than 70,000 elements and the total computation time are varies between 9 – 21 hours on a high performance computer (4th Generation Intel Core i7-4790 Processor 4.00 GHz, 16 GB RAM).
5 Finite element simulation results
The analysis results of various impact scenario models are presented in this section. The global results of 14 analyses are given in Table 3. Several remarkable results can be observed on these data. First, in term of component preference, the longitudinal structure was proofed provided better resistance subjected to impact load as presented in Figure 4 and 5.
Structural results of ship structure according applied parameters.
|No.||Observed Subject||Subject Details||Energy||Damage Extent|
|Collision||Kinetic||Type||Outer Shell||Type||Inner Shell|
|1||Component preference||Side shell||7550620||932015||Tearing||3.9550||Tearing||1.6940|
|2||Main deck||11293200||1086650||Tearing||2.2726||Plastic Def.*||0.5913|
|3||Double hull||3.5 m||10445800||939360||Tearing||3.4140||Plastic Def.*||0.3498|
The cross-section based on coming direction of the striking ship was much smaller than side shell which was transversal component. During collision happened to the side shell, large area was more easily deformed due to centralized load on wide cross-section if it was compared with collision on main deck. As a consequences, the collision energy of collision on transversal component was lower but the tearing on side zone was bigger than collision on longitudinal component.
Still in structure parameter, the width of the double hull was evidenced affect the collision energy as well as damage extent on both of outer and inner shell. The effect of wide distance between two shells is indeed providing much better defence subjected to side collision. However, amount of carried the carried cargo may be drastically reduced as well as the efficiency of ship itself will be going down. The illustration of damage between two double hull sizes is presented in Figure 6.
In terms of material, mechanical properties are clearly affect the results on energy and load as presented in Figure 7. The small difference was spotted between material 1010 and 1020 since these materials were coming from same class, plain low-carbon steel. In other hand, during comparison that was performed using 1040 and 1080, the significant result in term of damage extent had clearly happened after collision process. As presented in Appendix A, during collision on structure with material 1080, the tearing on inner shell was very small and from Table 3, the tearing length was below 1 meter. In deployment of double hull structure with the width between inner and outer walls 1.5 m, this material type can be considered as good option to be applied in structural arrangement in order to reduce the damage due to side impact. This work also successfully verified that carbon composition is the most suitable indicator in assessing material strength. The highest strength material contains highest carbon composition which after simulation, it is found that this material produces the best resistance among of all proposed materials in this work.
The effect failure strain to collision energy can be considered significant. With the change 0.1, the product of energy can differ by almost 5 MJ. During the observation on effect of this parameter, the higher failure strain, the less difference in collision energy occurred. It can be seen in the results of Table 3 and Figure 8, the difference in term of energy between 0.2 and 0.3 is below 3.5 MJ which is smaller than difference between 0.1 and 0.2. The higher failure strain also affected the damage extent on both of hulls. The damage from failure strain value 0.1 to 0.3 gradually went down.
In hardening parameter, no significant results were found in terms of collision energy as presented in Appendix B. However, if the damage illustration in Appendix B is observed carefully, the more wrinkling was found during structure was defined as isotropic hardening. This phenomenon occurred because during isotropic hardening was applied on structure, the yield surface expands uniformly in all directions with plastic flow which made the intersection structure between deck and shell experienced more folding than when kinematic hardening was applied onto the structure. Characteristic of structure after rupture is also described together with illustration for different material assumptions in this appendix.
6 Final remarks
This paper presents the study of the behavior in structure and material levels considering for various side impact scenario models. The scenario models were successfully solved in virtual experiment and the results were successfully delivering important information regarding effect of several parameters in impact phenomenon. In terms of ship material, the resistance capability of ship was highly influenced by specific chemical composition. For the same target structure, higher Carbon composition would provide advantage during accidental load occurred. Failure strain in analysis affected produced energy for destroying involved structure which for the same size of double hull, occurred deformation pattern was also triggered by hardening type. In case of different width between inner and outer walls, a wider space was considered provide more safe distance in event of side collision. Alternative options to increase safety and resistance against side collision can be considered based on present work. The design of construction configuration especially accounting for accidental load should be given serious attention while the efficiency of the ship has to be in reasonable level. The material from medium and high-carbon steel could be taken as consideration to be applied on side hull and other area which susceptible suffer big loss due to impact load. The chosen material also could be judged from its chemical as well as mechanical properties to provide balance between cost and safety. The impact simulation which involves very high nonlinearities, the given parameter namely failure strain and hardening rules could significantly affect the results. The tendency of implementation of these parameters are presented in this work which could be guideline and reference for further impact analyses.
The gratitude is offered to colleagues of the authors, Mr. Irfan Taufiqurrahman and Mr. Teguh Fajar Basuki who both of them from PT Samudra Marine Indonesia (SMI) Cilegon Branch, West Java, Republic of Indonesia for guiding the chance to perform survey on repair process of ship which experienced collision accident and providing ship design plan for present work. The special thanks is given especially by corresponding author to Mr. Teguh Putranto from Institute Technology of Sepuluh Nopember for providing guidance in performing the virtual experiments.
Minorsky V.U., An analysis of ship collision with reference to protection of nuclear power ships, Journal of Ship Research, 1959, 3, 1-4
Bae D.M., Prabowo A.R., Cao B., Zakki A.F., Haryadi G.D., Study on collision between two ships using selected parameter in collision simulation, Journal of Marine Science and Application, 2016, 15, 63-72
Ortekus E., Guven I., Madenci E., Impact damage assessment by using peridynamic theory, Central European Journal of Engineering, 2012, 2, 523-531
Schleyer G.K., Underwood N.J., Do H.M., Paik J.K., Kim B.J., On pulse pressure loading of plates with holes, Central European Journal of Engineering, 2012, 2, 496-508
Panciroli R., Abrate S., Dynamic response of sandwich shells to underwater blasts, Central European Journal of Engineering, 2012, 2, 509-522
Krieg R.D., Key S.W., Implementation of a time dependent plasticity theory into structural computer programs, constitutive equations in viscoplasticity: computational and engineering aspects, American Society of Mechanical Engineers, 1976, 20, 125-137
Jones N., Structural impact, Cambridge University Press, 1989
Prabowo A.R., Bae D.M., Sohn J.M., Zakki A.F., Evaluating the parameter influence in the event of a ship collision based on the finite element method approach, International Journal of Technology, 2016, 7, 592-602
Jones N., Wierzbicki T., Structural crashworthiness and failure, Elsevier Applied Science, 1993
Prabowo A.R., Bae D.M., Cao B., Zakki A.F., Haryadi G.D., The study of selected parameters on ship collision based on finite element approach method, Proceedings of 6th International Symposium on Advanced Engineering (22-24 October 2015, Busan, South Korea), Pukyong National University, 2015, 56-59
Zhang S., The mechanics of ship collisions, PhD Thesis, Technical University of Denmark, Lyngby, Denmark, 1999
Alsos H.S., Amdahl J., On the resistance of tanker bottom structures during stranding, Journal of Marine Structures, 2007, 20, 218-237
Woisin G., Design against collision, Schiff & Hafen, 1979, 31, 1059-1069
Haris S., Amdahl J., Analysis of ship-ship collision damage accounting for bow and side deformation interaction, Marine Structures, 2013, 32, 18-48
Prabowo A.R., Bae D.M., Sohn J.M., Cao B., Energy behavior on side structure in event of ship collision subjected to external load, Heliyon, 2016, 2(11):e00192
Bae D.M., Prabowo A.R., Cao B., Sohn J.M., Zakki A.F., Wang Q., Numerical simulation for the collision between side structure and level ice in event of side impact scenario, Latin American Journal of Solids and Structures, 2016, 13, 2991-3004
Prabowo A.R., Bae D.M., Sohn J.M., Zakki A.F., Cao B., Cho J.H., Effects of the rebounding of a striking ship on a structural crashworthiness during ship-ship collision, Thin-Walled Structures, 2017, 115, 225-239
Prabowo A.R., Bae D.M., Sohn J.M., Zakki A.F., Cao B., Wang Q., Analysis of structural behavior during collision event accounting for bow and side structure interaction, Theoretical and Applied Mechanics Letters, 2017, 7, 6-12
AbuBakar A., Dow R.S., Simulation of ship grounding damage using the finite element method, International Journal of Solids and Structures, 2013, 623-636
Callister Jr., W.D., Material science and engineering; an introduction, seventh ed., John Wiley & Sons (Publisher), Inc., 2007
Bauccio M., ASM metal reference book, third ed., ASM International, Material Park, OH, 1993
Davis J.R., Davis and Associates, ASM speciality handbook – carbon and alloy steels, ASM International, Material Park, OH, 1996
Harvey P.D. (editor), Engineering properties of steels, American Society for Metals, Material Park, OH, 1982
ASM International, Metal handbook, Volume 1 – Properties and selection: irons, steels, and high-performance alloys, tenth ed., ASM International, Material Park, OH, 1990
Boyer H.E., Gall T.L., Metals handbook, American Society for Metals, Material Park, OH, 1985
Giancoli D.C., Physics for scientists and engineers with modern physics, second ed., Prentice Hall Publishers, Englewood Cliffs, NJ, 1989
Society of Automotive Engineers, SAE ferrous materials standards manual, 1999 ed., Society of Automotive Engineers, Inc., Warrendale, PA, 1999
Tornqvist R., Simonsen B.C., Safety and structural crashworthiness of ship structures; modelling tools and application in design, International Conference on Collision and Grounding of Ships, Izu, Japan, 2004