An experimental and numerical study on nonlinear impact responses of steel-plated structures in an Arctic environment
Introduction
An era of North Pole routes, which have been said to be ‘dream waterways’, is becoming a reality due to the effects of global warming. With the opening of the North Pole passages, the market for shipbuilding and offshore industries is expected to become more active with economical transportation of cargo and the development of natural resources in association with the Arctic Ocean.
When the Arctic passages actually open, ships that use those waterways and the related offshore structures may be exposed to risks associated with accidents such as collisions with icebergs. Safety studies regarding such accidents are thus required to meet health, safety and environmental requirements. As far as collisions are concerned, structural safety is evaluated on the basis of the collision energy absorption capability of the structure until the accidental limit state is reached. Because the energy absorption capability can be obtained by integrating the area below the reaction forces versus the indentation curve of the structure, structural crashworthiness involving crushing, yielding and fracture forces must be characterised by obtaining the resulting force-indentation curve of the structure in the event of a collision or grounding accident [1], [2], [3], [4], [5], [6]. In this process, the effects of the environmental conditions associated with the low temperatures in Arctic regions should, of course, be taken into account.
An extensive review has been conducted in the literature in terms of collision [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], and most of the previous studies mainly focused on the performance of damaged ships after collision and grounding events. Recently, Youssef et al. [18] proposed a method for assessing the risk of ship hull collapse following a collision. A set of credible collision scenarios which represent the entire range of possible collision accidents was selected using a sampling technique based on probability density distributions of influencing parameters. Kim et al. [19] also investigated the environmental consequences of the involvement of oil tankers in collision using probabilistic approaches. Ehlers et al. [20] examined the numerical and experimental investigation on collision resistance of the X-core structures. The analysis included a detailed investigation of the non-linear plate and laser weld material behaviour using optical, full-field strain measurements. The resulting material relationships were implemented into the finite element model.
Some recent developments in the dynamic inelastic behaviour of structures were extensively reviewed by Jones [21], while a number of useful studies [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [33], [34] associated with nonlinear structural responses due to impact loads have been undertaken in recent years in the literature. Jones [35], [36], [37] developed an analytical model to predict the maximum plastic deformation of rectangular plates under simply supported and fully clamped boundary conditions. The model was validated with experimental results at room temperature (RT) obtained for plates that underwent impact from blunt, conical and hemispherical projectiles. Cho and Lee [38] investigated the responses of stiffened steel plates subjected to impact loads (approximately 1.6–6.2 m/s) at RT and developed design formulas for the prediction of the extent of the resulting damage to the stiffened plates. Liu et al. [39] studied the impact response and failure mode of thin aluminium plates under impact loads (4.5 m/s) and validated the experimental results with numerical studies at RT. Mohotti et al. [40] examined the impact resistance of aluminium plates subjected to low-velocity impact (5–15 m/s) and developed an analytical model to predict the out-of-plane deflection of the aluminium plates. Paik and Won [41] developed a new empirical formula as a function of the impact velocity, the properties of the target plate and the striker for the impact perforation energy on steel-plated structures. Haris and Amdahl [42] proposed a new analytical formula that can be used to calculate the axial force of steel-plated structures under impact loads. Most recently, Samuelides [43] discussed the methods that have been developed and used for the determination of the damage of ship structures subjected to impact loads. It was mainly focused in association with realistic modelling of the material behaviour. To the best of our knowledge, however, the above-mentioned studies were all performed at RT rather than at a low temperature.
When designing steel-plated structures for low-temperature applications, it is important to realise that the influence of low-temperature on the material properties, especially from the point of view of yield and tensile strength, should be considered. In general, yield and tensile strengths of materials tend to increase at low temperature. However, the performance of structures tends to decrease at low-temperatures in association with the reduction of tensile toughness which is a measure of a material's brittleness or ductility; it is often estimated by calculating the area below the stress–strain curve.
Experimental studies conducted in low-temperature conditions but in a quasi-static loading condition can be found in the literature. Paik et al. [44] investigated the effects of low temperature (−40 °C and −60 °C) on the crushing response of steel-plated structures. Dipaolo and Tom [45] examined the same topic [44] at −45 °C. McGregor et al. [46] studied the crushing characteristics of aluminium-plated structures and found that the average crushing force of hexagonal aluminium box sections increased as the temperature decreased (from RT to −40 °C). With respect to impact loads at low temperatures, Min et al. [47] conducted an experiment associated with the plastic deformation of steel-plated structures subjected to impact loads (approximately 5–5.5 m/s) and performed comparative studies through numerical analysis. The experiment was conducted at −30 °C and −50 °C using DH36. Manjunath and Surendran [48] studied dynamic fracture toughness of aluminium 6063 with multilayer composite patching at lower temperatures.
At present, studies on the nonlinear impact responses of steel or aluminium structures at low temperatures are lacking, and more research regarding Arctic environments is necessary. The objective of this study was therefore to provide useful contributions and insights associated with the nonlinear impact responses of steel-plated structures at low temperatures.
Section snippets
Test set-up for the quasi-static test
Quasi-static (0.05 mm/s) tensile tests were conducted at RT (room temperature) and at −60 °C to determine the mechanical properties of DH36, which indicates polar-class high-tensile steel. The dropped-object experiment described later was performed on steel-plated structures made of DH36. The specimen size and shape are shown in Fig. 1a in accordance with the requirements of the American Society for Testing and Materials E8 [49]. The specimens were extracted on the basis of the rolling
Test models and scenarios
Two types of test models were used for the dropped-object tests in small-scale, as shown in Fig. 5. The type I model was an unstiffened plate, while the type II model was a stiffened panel with cross-shaped flat bar stiffeners welded onto it. The edges of the test models were also welded to the surrounding rigid jig, which was fully clamped by bolts. Both types of plates were 1200 mm × 1200 mm × 6 mm. The drop height of the striker was 3 m at RT and 5 m at −60 °C for type I and type II models,
Nonlinear finite element analysis
The nonlinear impact responses obtained in the dropped-object tests were compared by nonlinear finite element (FE) analysis. In this study, LS-DYNA 3D, a general-purpose FE analysis code that is appropriate for nonlinear explicit dynamic simulations was used for the analysis of the structural responses of the test models.
Influence of low-temperature
When the results for the type II model at RT are compared with those at a low temperature, it can be seen that the relation between force and indentation at the initial stage was almost identical. It was also of a similar level of structural stiffness compared to that in RT conditions and showed a good degree of resistance against deformation. It was found that the initial stiffness of the type II model was maintained at −60 °C. Also, the presence of stiffeners increased the stiffness of the
Conclusions
The aim of the present study has been to investigate the nonlinear impact responses of steel-plated structures in an Arctic environment through an experimental and numerical technique. In the experiment, tensile tests on material and small-scale dropped-object tests on unstiffened and stiffened plate panels were undertaken. In the computation, LS-DYNA FE simulations were performed.
Based on the study, the following findings and insights were obtained.
- 1.
From the material tensile test, the
Acknowledgments
This research was supported by the Leading Foreign Research Institute Recruitment Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & future Planning (MSIP) (Grant no.: 2014040731). This work was part of the JDP titled ‘Limit states design of type B independent LNG cargo tanks’, which was funded by Class NK and STX Offshore & Shipbuilding Co., Ltd. The study was undertaken at the Lloyd's Register Foundation Research Centre of Excellence at
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