Dynamic response mechanism of thin-walled metallic defensive structure from explosion in transportation

: Defensive structure is important in transportation field for kinds of intentional or unintentional explosion. Structures subjected to unconfined and confined explosion will bear different blast loads and their dynamic responses are different. The present work focus on the dynamic response mechanism of steel plate under unconfined and confined blast loads through both numerical and experimental studies. In the experiment, Digital Image Correlation (DIC) technique was applied to record and analyze the dynamic response process of large-scale field blast test. The DIC measured curve and the numerical calculated curves agrees well in both the trends and the peak values. Then, the dynamic response mechanism of steel plate under unconfined blast (UB) load and confined blast (CB) load were compared and discussed. Results show that the dynamic response of plate can be divided into three phases under both UB and CB loads, while with different mechanism. In phase I, plastic hinge starts from the center and moves to the boundary in UB condition, while in case of CB, plastic hinge occurs close to the boundary and moves in the opposite direction. In phase II, two plastic hinge lines propagates towards each other, and a platform exists between the boundary and the central area remains undeformed in UB condition, while in CB condition, larger deformation in peripheral region rather than central area produces.


Introduction
Safety is the eternal theme of transportation. In recent years, frequently serious disasters related to explosion happened around the world in kinds of transportation equipment such as buses, trains and infrastructures. Some are caused by deflagration content unintentionally carried by passengers; some even caused by terrorist activities.
To shield such attacks, defense technology or infrastructures (see Fig.1), particularly with light-weight efficient defensive structures should be developed. In addition, some particular reinforcement design should also be considered for ship cabins and railway vehicles. For this purpose, the vulnerability of the structures needs to be adequately investigated firstly. As the existing finding's shown, structures subjected to unconfined and confined explosion bears different blast loads and their dynamic responses are different [1]. Under unconfined blast, the structure performs different dynamic response which hugely depends on the explosive source distance (i.e., close-in airblast [2], and faraway airblast), shield materials (i.e. thin aluminium, steel plates [3]) as well as the structure patterns. More studies were focused on the failure of the shield plates and effect of stand-off distance, as done by Nurick et al. [4][5], Bonorchis et al. [6][7], Chung et al. [8][9], Jacob et al. [10], respectively. As found that in these studies, the whole process can be categorized into three distinct phases, including, a) Phase "i" , the expansion of explosion, from time of detonation to its interaction with the structure; b) Phase "ii" , explosive plate interaction; and c) Phase "iii", expansion of the explosion from time of separation from plate to expansion of the plate equilibrium [11]. In addition, to further explain the dynamic mechanical behavriours, further effectively predict response modes, some theoretical analyses were also developed [13], analytical solution were obtained in good agreement with numerical and experimental observation.
These constructive methodologies were also extended to analyze underwater shock wave loading [14]. As aforementioned, the flexural waves emanate from the plate boundary and propagates towards the plate center [15]. Thanks for the development of innovative material technologies, kinds of composited light-weight structures were also investigated [16][17][18][19][20] under impact loads.
Unlike the previous unconfined blast situation, a Confined blast (CB) means that explosion occurs within a structure, which limits the propagation of blast wave.
Existing researches have shown that CB waves are more complicated and more destructive than that of unconfined blast (UB) with equivalent explosive charge [21][22][23]. Whilst the dynamic response mechanism of structures under CB loads and the differences between CB and UB loads are less investigated.
In order to investigate the dynamic response mechanism, effectively measuring the dynamic response process is necessary. However, traditional measurement methods are difficult in measuring the 3D dynamic response and obtain full-field data of blast loaded plate [24][25][26]. Fortunately, an advanced method using Digital Image Correlation (DIC) technique [27][28] is adept in measuring the 3D dynamic response of structures under impact loading, and it has been turned out to be a reliable tool for full-field transient plate deformation measurements during blast loading, with high accuracy and efficiency [29]. Rigby et al. [30] studied the transient deformation of plates subjected to near-field explosive blasts by using DIC technique, the flexural waves were observed.
Spranghers et al. [31] and Kumar et al. [32] employed the DIC technique in the study of the dynamic response on aluminum panels. While, the application of the 3D-DIC technique in the large-scale field test of confined blast is inadequate.
The present work aims at investigating on the dynamic response mechanisms of steel plate under both CB and UB loads, field blast test is conducted and 3D-DIC technique is employed together with elaborate numerical simulations, which paves a way on crashworthiness designing of the kinds of defensive structures.

Setup and DIC technique
To create a confined blast loading condition, a steel box chamber was designed and manufactured, as shown in Fig.2 And the TNT explosive is suspended in the inside center of the chamber (see Fig.2). DIC technique can record the full-field and 3-D surface deformation with high spatial resolutions and excellent accuracy [29][30]. In this experiment, 3D-DIC technique is applied to record the dynamic response process of the target steel plate.
Before the test, two high-speed digital cameras are placed in the front of the target plate arranged at a specific angle to record synchronized images (see Fig. 3).

Experimental results
The dynamic deformation processes of fully confined blast obtained through DIC technique are shown in Fig. 5, in which the value is a absolute result considering the bending displacement (the orginal value is negative according to location in Fig.2).
With the detonation of the TNT explosive, deformation occurs within a very short time at the central area. The plate center deflection increases to 7 mm at = 0.52 ms (see

Finite element model
Finite element (FE) models of steel plate under UB and CB load were built by using ANSYS software®. The model for UB load is showed in Fig. 6(a), in which the plate is fixed in both directions with a thickness of 4 mm, and the explosive is placed above the plate center with a distance of 300 mm. The model for CB load is showed in   result displacement of the plate center.

Material and propeties
Numerical method, using finite element method (FEM) programs, has become a common tool in the investigation of structural impact [7,26]. LS-DYNA has been widely applied for its ability to solve problems with large plastic deformation and can consider the strain rate effect [33]. In the numerical models, air is assumed to ideal gas that modeled by linear-polynomial EOS and linear in internal energy [34][35]. The explosive is viewed as a high explosive burning material and the Jones-Wilkins-Lee (JWL) equation of state (EOS) is selected to simulate the pressure of the explosive explosion. It can be expressed as follows: where , are linear blast parameters; , 1 and 2 are nonlinear parameters; is relative volume and is specific internal energy. TNT is selected for explosive charge in the current tests, the parameters of material model and EOS can be referred in Refs. [34][35].
The steel material is modeled by Johnson and Cook (J-C) model [35] which has been shown of accurate predictions of steel structures subjected to blast loads. The general equation of J-C model is presented as Eq. (4). The parameters for steel are listed in The Gruneisen equation of state for steel as compressed materials is presented as follows: and for expanded materials as: where 1 , 2 , and 3 are the coefficients of the slope of the − curve; 0 is the Gruneisen gamma; is the first order volume correction to 0 ; = / 0 − 1 .     for plate center is about 0.0045 (see P1 curves in Fig. 10). The strain of P3 is much larger than that of P1 and P2. In conclusion, the numerical model built in the present study is capable of simulating the dynamic response of plate under blast loads well and shows adequate accuracy.

Results and correlation
The dynamic response of steel plate under UB load and CB load (the models were shown in Fig. 6) were calculated based on the previous introduced numerical method.
The pressure-time curves of UB model and CB model at the target plate center were given in the Fig. 11. There was only one impulse load in UB model with a peak value of 5.4 MPa. While, in the CB model, several smaller peaks followed the first impulse were observed due to the reflection of shock waves in the confined model. The plate center deflection-time curves of the two finite element models were campared in Fig.   9. The maximun deflection of UB model (the black curve) was much smaller than that of CB model (the blue and red curves), and springback response occurring after maximum deflection in the UB loading. The springback phenominon is called "counterintuitive behaviour" which are studied by several scholars [37][38][39], their works show that the plates or shells can even reach a final deflection in a direction opposite to the direction of the pulsive loads in specific loading conditions. The results in Fig. 9 and     The dynamic response process of plate under confined blast load was showed in

Discussions
From the studies of the dynamic response process of both FEM and DIC results, the dynamic response of the plate under UB load is very different from the CB load.
The response mechanisms of plate under UB load and CB load are shown in Fig. 17.
The dynamic response of plate under UB load can be divided into three phases as shown in Fig. 17(a). In phase I, the central region deforms, a plastic hinge circle forms around the deformed region, and the deformed region increases with the plastic hinge circle propagates radially. In phase II, new plastic hinge line occurs around the boundaries and propagates in the opposite direction to the central plastic hinge, and a platform remain undeformed between the boundary and the center. In phase III, the whole plate deformed, and deformation in the central area increased to the maximum value. The dynamic response of plate under CB load can be also divided into three phases as shown in Fig. 17(b). In phase I, the plastic hinge line happens in the boundaries, and propagates towards the plate center. A larger deformation in peripheral region than central area occurs in phase II. Same as the UB, maximum deformation happens in the central area at last, that's phase III.

Conclusions
According to the analyses mentioned above, some major conclusions can be drawn as below: