Experimental and numerical investigations on laser-welded corrugated-core sandwich panels subjected to air blast loading

Marine Structures 40 (2015) 225e246

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Experimental and numerical investigations on laser-welded corrugated-core sandwich panels subjected to air blast loading Pan Zhang a, Yuansheng Cheng a, Jun Liu a, *, Chunming Wang b, Hailiang Hou c, Yong Li a a

School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China b School of Materials Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, China c Department of Naval Architecture Engineering, Naval University of Engineering, Wuhan 430033, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 29 July 2014 Received in revised form 4 November 2014 Accepted 21 November 2014 Available online

Experimental investigations on the laser-welded triangular corrugated core sandwich panels and equivalent solid plates subjected to air blast loading are presented. The experiments were conducted in an explosion tank considering three levels of blast loading. Results show that the maximum deflection, core web buckling and core compaction increased as the decrease of standoff distance. Back face deflections of sandwich panels were found to be nearly half that of equivalent solid plates at the stand-off distances of 100 mm and 150 mm. At the closest stand-off distance of 50 mm, the panel was found to fracture and fail catastrophically. Autodyn-based numerical simulations were conducted to investigate the dynamic response of sandwich panels. A good agreement was observed between the numerical calculations and experimental results. The model captured most of the deformation/failure modes of panels. Finally, the effects of face sheet thickness and core web thickness on the dynamic response of sandwich panel were discussed. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Metallic sandwich panel Triangular corrugated core Air blast loading Deformation mode Laser welding

* Corresponding author. Tel.: þ86 27 87543258; fax: þ86 27 87542146. E-mail addresses: [email protected] (P. Zhang), [email protected] (J. Liu).

http://dx.doi.org/10.1016/j.marstruc.2014.11.007 0951-8339/© 2014 Elsevier Ltd. All rights reserved.

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1. Introduction Sandwich structures, which are composed of two stiff face sheets separated by a low density core, are considered to be an excellent solution in shipbuilding for structural decks, walls, bulkheads, and ramps et al. [1e5]. Practical applications of laser welded sandwich structures in shipbuilding were realized from the mid 1990's onwards. After some very limited prototype applications in the US Navy the focus shifted to Europe. The famous European research project SANDWICH [6] enlarged the field of applications of sandwich structures in various surface transport sectors. Main reasons for the applications were due to their unique and unbeatable combination of properties, such as low specific weight, efficient capacity of energy dissipation, superior bending strength and high impact resistance [7e13]. Many researchers have focused on the dynamic mechanical behavior of sandwich structures, particularly in the last decade. A variety of such structures of different metallic cores including stochastic foams, honeycombs, prismatic topologies, and lattice topologies have been investigated experimentally and numerically, in particularly to improve their blast/impact resistance. Tilbrook et al. [14] investigated the dynamic out-of-plane compressive response of V-type and Y-type corrugated core sandwich panels using a Kolsky bar. They found that buckling of core webs is delayed at low impact velocities by inertial stabilization of the core webs while plastic shock wave effects dominate the response at higher impact velocities. Rubino et al. [15,16] examined the dynamic response of V-type and Y-type corrugated core sandwich beams and plates by firing metal foam projectiles at the central region. It is found that the sandwich constructions outperform equivalent monolithic counterparts at low levels of projectile momentum. However, these benefits will be compromised with the increase of projectile momentum. Ehlers et al. [17] performed a combined experimental and numerical investigation into the collision resistance of laser-welded X-type corrugated core sandwich panel. The influences of the laser weld properties and ship motions on the response of X-core structure were evaluated. Fleck and Deshpande [18], and Qiu et al. [19] developed an analytical methodology for analyzing the blast resistance of clamped sandwich beams and plates. In their theory, the deformation history is split into three sequential stages: fluid-structure interaction, core compression and overall structural response. Pioneering studies by Xue and Hutchinson [20,21], and Hutchinson and Xue [22] showed the superior performances of sandwich plates relative to solid plates with same mass under shock loading in water and air. Zhu et al. [23], Chi et al. [24], and Nurick et al. [25] conducted numerous experimental studies to test the structural response of aluminum alloy honeycomb sandwich panels subjected to blast load. The effects of face sheet configuration and core configuration were evaluated in detail. The failure modes of honeycomb sandwich panels were classified and analyzed systematically. Cui et al. [26] reported results from air blast experiments on tetrahedral lattice sandwich structures which were compared with honeycomb sandwich panels [23]. It was demonstrated that the tetrahedral lattice sandwich structures possess a better impulsive resistance than the honeycomb sandwich panels [26]. Dharmasena et al. [27,28] assessed the performance of sandwich panels with honeycomb cores and pyramidal lattice cores under air blast loading. Results revealed that the sandwich panels performed better than solid plates with identical mass by reducing the back face deflection and the load transmitted to supports. However, no failure criterion was included in their calculations. Corrugated core sandwich structures, a type of prismatic topology structures, are considered as ideal cores of sandwich panels applied in naval ships to replace the conventional stiffened plates due to their high longitudinal shearing and bending strength [1,14]. Therefore, the capacity of corrugated core sandwich panel to meet the demands of blast loading is of interest to researchers. Liang et al. [5] investigated the optimum design of metallic corrugated core sandwich panels subjected to blast loads by using the Feasible Direction Method coupled with the Backtrack Program Method. Rimoli et al. [29] and Wadley et al. [30] tested the dynamic response of corrugated sandwich panels subjected to wet sand blast loading, and utilized a discrete particle-based method to investigate the dynamic deformation and fracture processes. The simulation results rationalized the existence of strong coupling between the wet-sand and the dynamically evolving shapes of tested panels, which resulted in local deformation between the core webs at panel center. Li et al. [31] performed the air blast experiment of corrugated core sandwich panels which were made of aluminum with face sheets and

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core joined together with hot melt adhesive membranes, and analyzed energy absorption characteristics of corrugated core sandwich panels using numerical approach. In the present study, the method of making triangular corrugated core sandwich panel in laboratory using the laser welding technology was firstly described. The influence of laser welding on the material properties of base material was evaluated by analyzing the morphology and micro-hardness profile of laser welds. The dynamic responses of triangular corrugated core sandwich panels and equivalent solid plates subjected to three levels of air blast loading were investigated experimentally. Finite element simulations were performed to reveal the response process and failure mechanisms of panels, and to explore the effects of face sheet thickness and core web thickness on the dynamic response of panels. 2. Experiment 2.1. Specimens The triangular corrugated cores used in experiments were fabricated using a folding technique, as illustrated in Fig. 1. For all of the stainless corrugations, sheets were folded to an angle of 45 relative to the horizontal plane, and were subsequently cut by electro-discharge machining (EDM) to the dimensions of 300 mm (length, out-of-plane direction in Fig. 1)  288 mm (width). All corrugated cores are of a 0.7 mm web thickness, a 28 mm cell size and a 14 mm core thickness, as shown in Fig. 1. Then, the relative density of cores is about 6.6%. Stainless face sheets with a thickness of 1.4 mm were laser cut to the dimensions of 452 mm  440 mm. The calculated equivalent solid plate thickness was 3.72 mm. A 3.75 mm thick solid plate was actually used in experiments. The material of the face sheets and cores of sandwich panels and the equivalent solid plates was the commercially available 304 stainless steel (Fee18Cre8Ni). The desirable mechanical performances (i.e. high ductility, significant strain, and strain-rate hardening) of 304 stainless steel make it well-suited for dynamic loading application, and thus it was chosen as the base material of test panels. The steel was supplied by TISCO company (Shanxi Taigang Stainless Steel CO., China). To characterize the mechanical properties of the steel, quasi-static tensile tests were performed using 100 KN servo-hydraulic universal testing machine (WDW-100 E III) at room temperature. The cross-head velocity of the actuator was 2.4 mm/min in tests, giving a strain rate of 1  103 s1 in the gage area of specimens. According to Ref. [32], a good approximation of the true stress may be obtained from the fact that the volume of the specimen remains nearly constant as necking occurs. Then, the measured engineering stress-engineering strain curve was transformed into the true stressestrain curve, as shown in Fig. 2. The stressestain curve revealed that the sheet specimens exhibited diffuse necking rather early (around the strain value of 0.10 ~ 0.15). From the features of sheet specimens shown in Fig. 2, it is found that the specimens finally fractured due to localised necking. The stainless steel has an elastic modulus of ~200 GPa, a 0.2% offset yield strength of 310 MPa, a tensile strength of 740 MPa, a density of 7900 kg/m3 and a ductility up to ~42% (failure strain).

Fig. 1. Illustration of the bending process used to manufacture the triangular corrugated cores.

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Fig. 2. Static true stressestrain curve for the 304 stainless steel. The specimens failed in shear after some necking.

The experimental laser, which is an Ytterbium Fiber laser (YLR-4000, IPG Photonics), was used to join the face sheets and core. The laser welding head (YW50, Precitec Group) was mounted on the welding robot (IRB 4400, ABB), which is used to push the laser welding head over the welding components at desired welding speed. Before laser welding, any leftover grease/oil was removed by cleaning with acetone. A series of preliminary experiments were conducted on two lap configurations existing in this study (i.e. from 0.7 mm to 1.4 mm, and from 1.4 mm to 1.4 mm) to ascertain the appropriate welding parameters, including laser power, welding speed, shielding gas flow rate and focal point position. Based on the measurements of the laser weld properties, the promising welding parameters to join the face sheets and core were determined, as listed in Table 1. For triangular corrugated core with thin web thickness, the welding line is an approximate face-line joint. Therefore, the accuracy of positions starting and ending welding process is crucial to the quality of the core-to-facing joints. To overcome this tough problem, a thin rectangular strip with 300 mm in length, 5 mm in width and 1.4 mm in thickness was introduced to enlarge the tolerance of each welding position. The whole laser welding process adopted in this study consists of four steps, as illustrated in Fig. 3. Step one (Fig. 3(a)): The thin rectangular strips were firmly bonded parallel to each other upon the working platform using the No. 502 glue. The interval distances between the adjacent strips are set to the cell size of corrugated core. Step two (Fig. 3(b)): Corrugated core was placed on the strips with the folded line lying in the symmetry plane of strips, and then was clamped by a well-designed fixture, as shown in Fig. 4. After finding the moving locus of the laser welding head, the welding procedure of this step was executed using the welding parameters of the lap configuration of 0.7 mme1.4 mm (Table 1). Step three (Fig. 3(c)): The front face sheet was placed upon the working plate. The assembly made in previous step was clamped on the front face sheet. Then, the core and front face were welded together using the same welding parameters as those used in step two. The final step (Fig. 3(c)) was to join the back face sheet and strips. The welding condition of this step corresponds to the configuration of 1.4 mme1.4 mm (Table 1). In order to evaluate the influence of laser welding on the material properties of base metal, one specimen used to analyze the morphology and micro-hardness profile of laser welds, was cut from an

Table 1 Welding parameters applied to join the face sheets and cores. Weld condition

0.7 mme1.4 mm

1.4 mme1.4 mm

Laser power (kW) Welding speed (m/min) Shielding gas flow (l/min) Focal point position (mm)

3.5 9.0 16.7 0

3.5 7.0 20.0 0

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Fig. 3. Schematic illustration of the laser welding process used to fabricate triangular corrugated core sandwich panels. (a) Thin strips were firmly bonded to the working platform. (b) Corrugated core and thin strips were welded together using laser welding. (c) The assembly made by step two was inverted on the front face sheet which had been fixed on the working platform. Laser beam walked along the folded line to join the front face and core. (d) Back face sheet was welded to strips.

as-manufactured sandwich panel, as shown in Fig. 5(a). The morphology of laser welds was observed under a stereo microscope (LWD300LCS). The macrostructure of the laser welded joint depicting the front face sheet and corrugated core attachment is shown in Fig. 5(b), while Fig. 5(c) demonstrates the macrostructure of the laser welds among core, narrow strip and back face. It can be seen that the laser power and welding speed adopted in this study yielded incomplete penetration. The profiles of the joints are acceptable. No cracking and porosity were observed in welds. The width and depth of fusion for the joint between the front face and core were similar to that for the joint between the core and narrow strip. The measured fusion width and depth are about 0.81 mm and 1.49 mm, respectively. For the joint between the narrow strip and back face sheet, the width and depth of fusion are about 0.48 mm and 2.57 mm, separately. Fig. 5(d) displays the optic micrograph near the weld junction of the joint between the front face and core. It is found that the parent material and fusion zone could be discriminated easily. The microstructure of joint revealed that the transition zone and HAZ near the fusion boundary were not apparent. It is considered that the effect of HAZ on the performance of sandwich panels is negligible. The micro-hardness of the laser weld region of the joint between the front face and core was measured, as illustrated in Fig. 6. The measurements were performed using SCTMC Digital Microhardness Tester DHV-1000, which can measure microscale Vickers hardness. In the present experiments, constant load of 200 gf (1.96 N) and dwell time of 15 s were applied. Each measuring point and

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Fig. 4. Photograph of the fixture system used for clamping the welding parts and exerting pretightening loads to minimize the gap between the welding parts.

its Vickers hardness value are shown in Fig. 6(a). It is observed that the average micro-hardness of parent material is higher than that of the laser welding zone (about 200 HV). Fig. 6(b) shows the microhardness profile (converted to tensile strength) across the welded region. It is found that the laser welding process resulted in an indistinct softening of the steel from 700 to 650 MPa. Based on the measurements that the fusion width is small, the HAZ seems to be absent, and the softening effect is not remarkable, it is considered that the influence of laser welding on the material properties is limited. 2.2. Set-up The experiments were conducted in an explosion tank with an inner diameter of 5 m and a height of 7.5 m. The detailed experimental set-up used to study the deformation and rupture of test structures is depicted in Fig. 7(a). The set-up consists of explosion tank body, ventilation system, drainage system, vibration isolation system, sound isolation system, illuminating system, and the fixture system used for clamping the test sandwich panels. The test panels were mounted horizontally and bolted onto a 30 mm thick plate resting on I-beam supports along all four edges. The I-beam supports were restrained from movement by stiff concrete bricks. The 30 mm thick support plate had a 288 mm  300 mm square hole cut out at the center to allow open space for the test panels to deform. A 10 mm thick picture frame arranged upon the sandwich panel was used for edge clamping, and provided a 288  300 mm2 exposure area to shock wave, as shown in Fig. 7(b). To ensure adequate edge restraint on face sheets, the rest part of core was filled with solid metal blocks. The blast wave was created by the detonation of a 55 g cylindrical TNT explosive with a radius of 17.5 mm and a height of 37.2 mm. The charge was detonated with an electric detonator slightly buried in the surface of the explosive furthest from the test sandwich panel. The side wall and the top of tank remained at about 2.5 m and 7.0 m, respectively, away from the explosion. The scaled distance for the position of 2.5 m is 2.5/0.0551/3 m ¼ 6.574 m. The correlated overpressure of the incident shock wave is very low, about 0.18 bar [33]. Hence, it is believed that the influence of edge reflections on structural response is negligible. The experiments were performed to investigate the effect of stand-off distance on the deformation and failure modes of the sandwich panels and their equivalent solid plates. In this study, three stand-off distances of 50 mm, 100 mm and 150 mm from the center of explosive to the top surface of the target test structures were adopted. The same process of test panel assembly, explosive charge placement and detonation were followed for each sandwich panel and solid plate.

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Fig. 5. (a) Corrugated core unit cell cut from an as-manufactured sandwich panel. (b) Macrostructure of the joint between the front face and core. (c) Macrostructure of the joints among core, narrow strip and back face. (d) Microstructure of the joint between the front face and core.

2.3. Experimental results and discussions The measured center deflections of the sandwich panel's front and back face sheets and that of the equivalent monolithic plates are summarized in Table 2 and Table 3, respectively. Fig. 8 shows the top view of a localized face sheets failure of the triangular corrugated core sandwich panel tested at the stand-off distance of 50 mm. It is evident that the panel fractured and failed catastrophically, especially for the front face sheet. A part of center region of the front face sheet was eroded by the high intensity shock wave. A crack with dimension of about 50 mm  60 mm was formed, as shown in Fig. 8(a). The rest part of center region of front face sheet underwent a large

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Fig. 6. (a) Measured microscale Vickers hardness values (in Vickers hardness units) at various locations of the joint between the front face and core. (b) Local material tensile strength (deduced from microscale Vickers hardness values) in the weld region.

bending deflection. Careful examination of Fig. 8(c) shows that several macroscopic cracks emerged on the front face. In order to clearly descript the propagation of the cracks, the lap welds near the cracks and the path of crack propagation have been marked with white dash lines in Fig. 8(c). The crack originated in the panel center, and grew along the direction toward the lap welds. After propagating along the left side of the laser welds with a distance of about 8 mm, the crack walked across the weld line. Finally, the crack was arrested with a crack opening angle of about 45 . Under the impact loading from front face and core webs, the panel back face underwent localized plastic deformation accompanied by a visible crack with length of about 57 mm, as shown in Fig. 8(b) and (d). From the evidence of the discontinuity in inclination of the panel at the supports, it is revealed from Fig. 8(a) and (b) that the stationary plastic hinges (marked as red dash lines) were formed at four clamped edges of tested panel.

Fig. 7. (a) Sketch of the configuration of explosion tank used for blast experiments. (b) Photograph of the fixture system used for clamping the test structure.

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Table 2 Comparison of measured and predicted sandwich panel center deflections. Stand-off distance (mm)

50 100 150

Sandwich front deflection (mm)

Sandwich back deflection (mm)

Experimental

Numerical

Experimental

Numerical

Failure 22.71 12.91

Failure 26.31 15.01

31.70 10.31 5.18

34.83 11.85 7.08

To clarify the blast performance of the sandwich panels and equivalent solid plates tested at each stand-off distance, the post-mortem analysis basing on the section profiles of specimens was conducted, as shown in Figs. 9 and 10. As the decrease of stand-off distance, the corresponding impulse intensity was increased and exhibited more evident spatial localization. Therefore, it can be seen in Figs. 9 and 10 that the deformation/damage level of the sandwich panels and equivalent solid plates increased as the decrease of stand-off distance. The three solid plates underwent remarkable plastic deformation but they were intact after tested. However, it is evident that the sandwich panel tested at the stand-off distance of 50 mm failed severely (see Fig. 9(a)), and a small crack was observed at the center of panel front face tested at stand-off distance of 100 mm, as shown in Fig. 9(b). Only the panel tested at the stand-off distance of 150 mm preserved its integrity. The measured permanent deflections revealed that the sandwich panels suffered smaller back face deflections than the equivalent solid plates at the stand-off distances of 100 mm and 150 mm. However, it should be noted that the sandwich panels were more susceptible to fracture in the most severely loaded scenarios. Similar phenomenon occurred at other accident loadings, such as the metal foam projectile loading [16] and wet sand blast loading [30]. Under the three different levels of blast loading, both the sandwich panels and solid plates exhibited different deformation modes. The features of face sheet deformation of the panel tested at stand-off distance of 50 mm were described clearly in the above paragraph. The section profile of this panel shows that the welds between the strips and back face failed under this high intensity loading. Fig. 9(a) and (d) shows the occurrence of core debonding symmetrically located to the central fractured field due to the failure of welds. The extent of weld separations was measured and marked in Fig. 8(b) with green lines. It is found that the weld separations have spread over almost half panel length. At the same blast loading, the deformation of equivalent solid plate resembled a large global dome superimposed with an inner dome, as shown in Fig. 10(a). At the stand-off distance of 100 mm, the core of sandwich panel crushed completely at the center, resulting in the occurrence of a small inner dome at the center of back face, as shown in Fig. 9(b). Increasing the stand-off distance to 150 mm, the sandwich panel suffered a significant deformation but the core was not completely crushed (see Fig. 9(c)), while the solid plate profile resembled a global dome, without the inner dome at the center (see Fig. 10(c)). The enlarged views of sectional images of tested panels were shown in Fig. 11, providing a detailed insight into the failure modes of cores. Fig. 11(a) indicates that the core crushing at the panel center occurred by plastic buckling of core webs. A part of core web material was eroded by blast loading. The incompatible deformation of front and back face sheets resulted in the core debonding at panel center. At the stand-off distance of 100 mm, the core in the center remained in contact with front face, Fig. 11(b). The core web had begun to fold at the center. The core web folding is an efficient manner to dissipate kinetic energy of panel. Due to the stretching deformation of front face, some core webs were

Table 3 Comparison of measured and predicted monolithic plate center deflections. Stand-off distance (mm)

Monolithic plate deflection (mm) Experimental

Numerical

50 100 150

33.24 18.53 11.34

33.00 17.02 10.16

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Fig. 8. Photograph showing tearing of (a) front and (b) back face sheets of the sandwich panel tested at stand-off distance of 50 mm. (c) and (d) are higher magnification views of the fractured regions of front and back face sheets, respectively.

in tension. A plastic buckling failure can also be found at the core webs of the panel tested at the standoff distance of 150 mm, as shown in Fig. 11(c). But, the folding mode varied and the fold wavelength was larger relative to that of the panel tested at the stand-off distance of 100 mm. It should be explained that the reproducibility tests were not conducted in this study, due to the expensive cost of experiments, especially of the laser welding. It is known that the most expected influence on the reproducibility includes the base material properties and fabrication technology. The base material properties used to make panels have been checked by conducting uniaxial tensile tests, and the cell size of those fabricated cores has carefully examined to monitor spring back effect during the folding process. Meanwhile, a series of preliminary experiments were conducted on all lap configurations existing in this study to ascertain the appropriate welding parameters. All those work was to ensure good repeatability in the manufacturing process and experiments. 3. Numerical simulations ANSYS/Autodyn software V12.1.0, which is a versatile explicit analysis code, was used for modeling the numerical models of the experiments. All numerical simulations were performed on a desktop computer which uses four processors Intel Core i7-3770, 16 GB RAM system.

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Fig. 9. Deformed experimental sandwich panel shapes for each stand-off distance. (a) stand-off distance ¼ 50 mm, (b) stand-off distance ¼ 100 mm, (c) stand-off distance ¼ 150 mm.

3.1. Final model particulars The simulations were performed to give insight into the deformation mechanism and fluidestructure interaction (FSI) effects, which were not measured directly during the experiments. Considering the symmetry of panels and loads, only one quarter model was established to reduce the computation time, as shown in Fig. 12(c). The perimeter of the panel face was modeled as fully clamped. It is assumed that the back face and core were firmly “welded” together by strips. The narrow strips used in test panels were not considered in calculations in order to reduce the complexity of simulations. Generally, structures can be defined in a Lagrangian reference frame where the mesh follows the material movement, and the Eulerian reference is a more preferable method to describe the gas flow from detonating explosives. In the present study, the face sheets and cores of sandwich panels and monolithic plates were modeled with Belytschko-Tsay shell elements based upon Mindlin theory [34], while the surrounding air and explosive were modeled with multi-material Euler elements which is an extension of Eulerian approach. A fully coupling algorithm was used to connect the shell solver and Eulerian solver. During the process of coupling, the Euler elements intersected by the Lagrange interface define a stress profile for the Lagrange boundary vertices. In return, the Lagrange interface defines a geometric constraint to the flow of material in the Euler grids. The parameter named “cover

Fig. 10. Deformed experimental solid plate shapes for each stand-off distance. (a) stand-off distance ¼ 50 mm, (b) stand-off distance ¼ 100 mm, (c) stand-off distance ¼ 150 mm.

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Fig. 11. Photograph of center section profile of tested panels. (a) stand-off distance ¼ 50 mm, (b) stand-off distance ¼ 100 mm, (c) stand-off distance ¼ 150 mm.

fraction limit” is used to determine when a partially covered Euler cell is blended to a neighbor cell. The value of cover fraction limit was set to 0.5. In order to function the coupling properly, shell parts should be artificially thickened. It is stated in the theory manual of ANSYS/Autodyn that the artificial shell thickness should be at least twice the largest cell size in the surrounding Euler grid [34]. Effects of the contact between the core cell wall and the face sheets due to the plastic buckling, as well as the selfcontact of the core wall due to cell wall folding, were taken into account in simulations by defining contact among these shell parts. The contact algorithm adopted in this study was formulated using a penalty method, and the contact state was taken to be frictionless. For blast simulations, it is crucial to start the ignition and detonation process of explosive with a very fine mesh to guarantee an acceptable error of initial energy of shock wave. The computational cost

Fig. 12. Remapping the pressure distribution from 2D model to 3D model. (a) Initial state of 2D model. (b) Pressure contour of 2D model before remapping. (c) Pressure contour of 3D model after remapping.

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for a highly resolved 3D model is very expensive. Alternatively, the remapping technique available in ANSYS/Autodyn is a perfect method to be employed to overcome this problem [35]. Using the remapping technique, the results from a fine meshed 2D model can be mapped into a coarser mesh 3D model. Then, the purposes to save computational time and increase the accuracy of simulations can be achieved [36]. The whole work flow for the application of remapping mainly consists of three steps. Firstly, a 2D axisymmetric model was set up for simulating the detonation and initial expansion of cylindrical explosive, as shown in Fig. 12(a). The detonation was initiated at the center of the furthest face of explosive from panel. In order to reduce the influence of high orthotropic property of sandwich panel on the flow of shock wave, the 2D model was run until the shock front is close to the panel front face, where the symmetry condition would be violated thus the flow becomes multi-dimensional, as shown in Fig. 12(b). Secondly, a binary remap file (which contains the final state of variables of 2D simulations) should be created, and then was used to fill the 3D Eulerian domain as initial condition, as shown in Fig. 12(c). Lastly, the 3D calculation could then proceed from that point. The air block used in 3D simulations allowed the explosive to further expand and interact with structures. According to Ref. [37], the air block was only applied over the center part of panel model because of the localization of blast wave. A typical air block with the dimensions of 70 mm  70 mm  200 mm is shown in Fig. 12(c). Flow out boundary conditions were set at the outer boundaries of the air block. The loading phase in 3D simulation is completed once the midpoint of the plate has begun to oscillate about its final deflection and the maximum pressure in the Eulerian mesh is below 300 kPa [38]. After these criteria are met, the Eulerian mesh is deactivated and the sandwich panels continue to deform under its own inertia. It should be noted that it is impossible to conserve both momentum and kinetic energy during remapping. The remapping algorithm adopted by ANSYS/Autodyn is based on the assumption of momentum conservation [35]. A conservative result will be obtained. However, a reasonable mesh length ratio between the 2D model and 3D model can reduce the energy error. The suitable ratio recommended by Lapoujade et al. [39] should not exceed 10 during remapping. The element sizes for 2D model were fixed at 0.1 mm  0.1 mm, while the side length of the cubic elements in 3D model was 1 mm. The shell elements had mesh size of 1 mm  1 mm. Additional studies indicated that the current meshing scheme yielded convergent simulation results. The CPU times for the 2D Euler simulations used to create the initial map files to fill the 3D domain for three different stand-off distances (50 mm, 100 mm, and 150 mm) are 16 min, 32 min and 43 min, respectively. Most of 3D simulations in present study ran CPU time between 20 and 25 h. 3.2. Material formulation The JohnsoneCook material model was used to describe the von Mises flow stress of used steel as expressed in Eq. (1) and (2). The dynamic flow stress is the function of strain, strain rate, and temperature. The model assumes that the strength of the material is isotropic and independent of mean stress.

!# " eq h  m i  eq n i ε_ p 1  T* ; sy ¼ A þ B εp 1 þ c ln ε_ 0 h

T* ¼

T  Tr ; Tm  Tr

(1)

(2)

eq eq where sy is the dynamic flow stress, εp is the equivalent plastic strain, ε_ p is the equivalent plastic strain rate, T is the material temperature, Tm is the melting temperature of the material and Tr is the room temperature. The constants A, B, n, c, ε_ 0 , and m are material parameters and can be determined from an empirical fit of flow stress data. The measured true stressestrain curve (Fig. 2) agrees very well with the constitutive behavior of annealed 304 stainless steel as reported in the literature [40]. Therefore, the JohnsoneCook parameters for 304 stainless steel are determined from Ref. [40], as listed in Table 4.

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Table 4 The JohnsoneCook material model parameters used for 304 stainless steel [40]. A (MPa) 310

B (MPa)

n

c

ε_ 0 (s1)

m

Tm (K)

Tr (K)

1000

0.65

0.07

1.00

1.00

1673

293

In order to capture the rupture of test panels, the failure criterion based on equivalent plastic strain was adopted. This criterion has gained popularity due to its simple and effective formulation, and has been proven to give results with satisfying accuracy [41e44]. It is well known that the equivalent plastic strain at failure is a function of the stress state. However, the study by Dey et al. [45] concluded that for ductile metals, the failure strain becomes largely independent of triaxiality when the stress triaxiality values are greater than a threshold. According to the work conducted by Rodríguez-Martínez et al. [44], a constant value of equivalent plastic strain can be used to predict the failure of 304 stainless steel thin sheets under projectile loading. It is known that both the projectile loading and the near-field air blast loading (in present study) yield localized deformation, and the tearing failure dominates the deformation of thin sheets. Therefore, the material failure is defined by a constant value of the equivalent plastic strain in present study. The value of failure strain of is 0.42, which was estimated from the natural logarithm of the ratio of the initial effective specimen (in tension test) cross-sectional area divided by the cross sectional area after fracture. It should be noted that this simplified estimation of the failure strain produces numerical results in agreement with experiments (as will be shown later). The air and post-burning explosive gas product media are assumed to behave as ideal gas. The ideal gas equation of state (EOS) is shown in Eq. (3).

p ¼ rg Cv T

  Cp 1 ; Cv

(3)

where rg is the air density, Cp and Cv are the specific heat at constant pressure and volume respectively, and T is the gas temperature. The standard constants of air model, as determined from ANSYS/Autodyn material library, are shown in Table 5. The air is assigned an initial internal energy of 206.8 kJ/kg for keeping the atmospheric pressure. The default model in ANSYS/Autodyn material library for TNT explosive is used to numerically model the TNT explosive from the experiments. The pressure of the expanding gas of the TNT is determined by the Jones-Wilkins-Lee (JWL) model as shown in Eq. (4).

    urp R1 rre urp R2 rre p þ B 1  p þ ur E e e p¼A 1 p m0 : R1 re R2 re

(4)

The parameters A, B, R1, R2 and u are all empirically derived values. re and rp are the densities of the explosive and the explosive products respectively. Em0 is the specific internal energy of the explosive. The default values from ANSYS/Autodyn material library for TNT are shown in Table 6. The state (velocity, internal energy and pressure) of detonation wave in explosive can be determined using Chapman-Jouquet condition. CJ point refers to the state of the detonation wave. The values of CJ point (CJ detonation velocity Vdet, CJ energy to volume fraction Evol and CJ pressure pcJ ) for TNT are also included in Table 6. Table 5 ANSYS/Autodyn material properties for ideal air [34]. rg (kg/m3) 1.225

T (K)

Cp (kJ/kg K)

Cv (kJ/kg K)

288.2

1.005

0.718

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Table 6 ANSYS/Autodyn material properties for TNT used to define the JWL model [34]. re (kg/m3)

A (GPa)

B (GPa)

R1

R2

u

Vdet (m/s)

Evol (kJ/m3)

pcJ (kPa)

1630

373.8

3.75

4.15

0.9

0.35

6930

6.0  106

2.1  107

3.3. Correlation with experiments To verify the material properties, boundary and contact condition in simulations, numerical results were compared to the experimental results for the corrugated core sandwich panel and monolithic plates. It is evident from Fig. 13 that the numerically predicted and experimentally measured midpoint deflections for panels and the equivalent solid plates were in good agreement. Meanwhile, two standard statistical parameters, viz. the Pearson's correlation coefficient (R2 ) and average relative error (D), were employed to quantify the predictability of the numerical model used to predict the dynamic plastic response of panels and monolithic plates. Correlation coefficient can provide information on the strength of linear relationship between predicted and measured values. R2 and D are mathematically expressed as:

  Pi¼N  i dexp  dexp dip  dp i¼1 R2 ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 P  2 ; Pi¼N  i i¼N i d d  d  d exp p exp p i¼1 i¼1

(5)

i i¼N di 1 X exp  dp D¼  100%; N i¼1 diexp

(6)

where dexp is the measured midpoint deflections, and dp is the predicted midpoint deflections. dexp and dp are the mean values of dexp and dp , respectively. The correlation coefficient R2 for sandwich panels and solid plates is 0.99, and the average relative error D is 5.25%. A good correlation was achieved, further indicating that the predictability of numerical model is reliable and excellent. 3.4. Numerical results The numerical midpoint deflections are listed in Tables 2 and 3 alongside the corresponding experimental values. Fig. 14 shows the deformed panels at the end of simulations for the stand-off

Fig. 13. Numerical versus experimental midpoint deflections.

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Fig. 14. Deformed sandwich panel shapes and the effective plastic strain distribution obtained from simulations for stand-off distances of (a) 50 mm, (b) 100 mm, and (c) 150 mm.

distances used in experiments. The simulations also show half sections of panels using a perspective similar to that of the tested panels (Fig. 9). It is encouraging to find that the simulations captured most of the deformation patterns observed in experiments, including the largest plastic deformation of the center region of panels, an increase in panel deflection with the decrease of stand-off distance, the appearance of an crevasse formed on the center of front face, the development of cracks on the front face and back face of panel tested at the stand-off distance of 50 mm, the undamaged features of panels tested at the stand-off distances of 100 mm and 150 mm. Careful inspection of the simulations reveals that the occurrence of cracks located to the side of laser welds on the front face should ascribe to the arrival of tension limit under stretching force. The high effective plastic strain regions were mainly distributed along the welding lines due to the stress concentration at the joints between the face sheets and core. Comparing the final deformation of cores obtained from simulations (Fig. 15) and experiments (Fig. 11), the results show that the simulations obtained a similar level of web buckling and core

Fig. 15. Detailed deformation of cores obtained from simulations for stand-off distances of (a) 50 mm, (b) 100 mm, and (c) 150 mm.

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compression to that seen in experiments. Careful examination of Fig. 13 reveals that the numerical models overpredicted the permanent deflections for all sandwich panels, presumably as a result of that the energy dissipated by the contact friction and the deformation of narrow strips was not considered in simulations. The displacement and velocity histories at the midpoint of both front and back faces of panel and equivalent solid plate at 100 mm stand-off distance are shown in Fig. 16. The velocity of front face instantly reached its maximum value in the early stage of response, and then decreased progressively due to the core crush and its own plastic deformation. After the core collapsing into a more stable configuration, the velocities of the front and back face sheets equalized in deformation response. Then, both the front and back faces underwent an oscillation until the kinetic energy was gradually dissipated by the introduced static damping. It can be seen that the front face of sandwich panel appeared to take off at a higher velocity than the back face, and the initial velocity of the equivalent solid plate lied between these limits. The low takeoff velocity of back face mainly resulted from the effect of communicating the movement of the front face through the dynamically crushing core. To better understand the deformation mechanism, the distributions of the in-plane strain were investigated both temporally and spatially by placing a series of gauge points. Points 1e5 were placed on the front face, and point 6e10 were placed on the back face. The in-plane strain results and exact locations of all points are shown in Fig. 17. In-plane strain 1 refers to the strain on the plane of face sheet along the direction perpendicular to the corrugations (viz. the X-axis), while the in-plane strain 2 is along the direction parallel to the corrugations (viz. the Y-axis). The maximum in-plane strains of front face and back face occurred at the panel center. Due to the high intensity loading at the center area, the stretching deformation has a significant contribution to the final deformation in this region. The final deformation patterns of both face sheets revealed that the front face underwent a larger deformation than the back face. Thus, the in-plane strains on the front face are relatively larger than those on the back face. Careful inspection of the strain results shows that the in-plane strains along the X-axis are larger than those along the Y-axis, owing to the lower bending stiffness along the X-axis. Due to the constraint on the panel edges, gauges 3 and 8 underwent large in-plane strain along the X-axis, while gauges 5 and 10 underwent large in-plane strain along the Y-axis. This verified the plastic hinge formation at the edges of panels tested in experiments. The reflected pressure and impulse intensity at the fluid structure interaction (FSI) interface decayed rapidly along the direction in width, showing spatial locality of shock wave, especially, for the closest stand-off distance, as shown in Fig. 18. The gas pressure interaction with the outskirts should be not significant. Therefore, the adopted size of air block is reasonable to simulate the dynamic response of tested panels. It is found that the pressure and impulse intensity of sandwich panel is significantly less than that of equivalent solid plate, due to a combination of beneficial FSI effects and a low core crushing stress. At the stand-off distance of 150 mm, several local peaks located between the corrugations and local valleys at the joints of core-to-facing were observed for reflected pressure and

Fig. 16. Center (a) displacement and (b) velocity histories of panel and equivalent solid plate at the stand-off distance of 100 mm.

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Fig. 17. In-plane strain time histories of different gauge points. (a) and (b) are for the in-plane strain.1 (along the X-axis) and for the in-plane strain.2 (along the Y-axis) of panel front face at the stand-off distance of 100 mm, respectively. (c) and (d) are the in-plane strain results of panel back face.

impulse of sandwich panel. A stronger reflected shock wave occurred due to the local bending of the front face between the corrugations, which increases the rigidity of the face sheet [30]. 4. Discussions Due to the good correlation, the validated numerical models were further used to investigate the effects of face sheet thickness and core web thickness on the blast performance of corrugated core sandwich panels. 4.1. The effects of face sheet thickness The panel tested at 100 mm stand-off distance in experiments was considered as the baseline to assess the influences of face sheet thickness on the back face deflection, the peak pressure and the impulse intensity of the midpoint of panel front face under same blast load. It is shown in Fig. 19 that the front face thickness can significantly affect the peak reflected pressure and impulse intensity while the effect of back face thickness is negligible. A beneficial FSI can be achieved by reducing the front face sheet thickness. On the other side, decreasing of face sheet thickness leads a weakening in stiffness of panel. Then, the permanent deflection of back face decreased with the increase of front face and back face thickness, as shown in Fig. 20. However, it is found that the change of front face thickness resulted in a more evident influence on the back face deflection than that of back face thickness. This indicates that a more efficient way to enhance the blast resistance of panel by adding weight expense is to increase the front face thickness. Moreover, a reasonable plan to retain the blast resistance of panel under weight saving scenario is to keep the front face thickness and decrease the back face thickness. A similar conclusion has been draw by Xue and Huchinson [20]. Due to that the blast load is a type of

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Fig. 18. Peak pressure and impulse intensity distributions at the fluidestructure interaction interface along the direction in width. (a) stand-off distance ¼ 50 mm, (b) stand-off distance ¼ 100 mm, (c) stand-off distance ¼ 150 mm.

accidental loading, the design of sandwich panel should be a function of the blast threat. If the statistical data of threat is given, an optimal design of sandwich panel under different blast loads is likely to be obtained. This is a subject to be investigated in future. 4.2. The effects of core web thickness The effect of core web thickness on the peak pressure and impulse intensity of the midpoint of front face is negligible, which is similar to the effect of back face thickness. However, the back face deflection

Fig. 19. The effects of face sheet thickness on the peak pressure and impulse intensity of the midpoint of front face. The stand-off distance was 100 mm.

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Fig. 20. The effects of face sheet thickness and core web thickness on the deflection of back face. The stand-off distance was 100 mm.

Fig. 21. Predicted section profiles of panels with different core web thicknesses. (a) 0.4 mm, (b) 0.7 mm, (c) 1.0 mm, (d) 1.4 mm. The stand-off distance was 100 mm.

of panels decreased linearly with the increase of core web thickness, as shown in Fig. 20. Examining the section profiles of panels with different core web thicknesses (Fig. 21), it is found that the crushing resistance of core is enhanced greatly with the increase of core web thickness. Then, the deformation mode of core webs changed. The buckling wavelength increased with the increase of core web thickness. The deformation mode of front face was affected by the variation of crushing resistance of core. For core web thickness of 0.4 mm, the front face deformed similarly to the deformation mode of a solid plate under blast loading. However, for core web thickness of 1.4 mm, a local deflection between two adjacent core webs was observed at the front face center. A thicker core web will lead to a larger load transferred to back face and supports. Therefore, using a core with appropriate characteristics is a way to keep balance between the energy absorption and the load transferred to the back face and supports. 5. Conclusions The triangular corrugated core sandwich panels were designed and fabricated through folding and laser welding technology. The dynamic responses of the triangular corrugated core sandwich panels

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and equivalent monolithic plates were investigated by performing air blast experiments in an explosion tank. The experiments revealed that the sandwich panels suffered smaller back face deflections than the equivalent solid plates at low impulses levels, but were more susceptible to fracture in the most severely loaded scenarios. This phenomenon also existed under metal foam projectile loading and wet sand blast loading for corrugated core sandwich panels. The cores behaved several different deformation/failure modes in experiments, including plastic buckling, stretching, debonding, and full compacted. Numerical calculations matched well with the experimental results. The in-plane strain distribution indicated that the stretching deformation is evident at the panel center. Investigation into the effects of face sheet thickness and core web thickness on the dynamic response revealed that the back face deflection reduced with the increase of both face sheet thickness and core web thickness. The front face thickness is critical to the reflected pressure and impulse intensity. An effective way to enhance the blast resistance of panel is to increase the thickness of front face. In order to obtain an optimal design of sandwich panel for shipbuilding, a further study is needed in future to investigate the mass allocation of panel under different blast loads. Likewise, an elaborate design of core is needed to balance the energy absorption and the load transferred to the back face and supports. Acknowledgments The reported research is supported by the National Natural Science Founding of P.R. China (under the contract number of 51209099) and the Supporting Technology Funding of Shipbuilding Industry. The financial contributions are hereby gratefully acknowledged. References [1] Wiernicki CJ, Liem F, Woods GD, Furio AJ. Structural analysis methods for lightweight metallic corrugated core sandwich panels subjected to blast loads. Nav Eng J 1991;103(3):192e202. [2] Lamb G. High-speed, small naval vessel technology development plan. 2003. DTIC Document. [3] Kujala P, Klanac A. Steel sandwich panels in marine applications. Brodogradnja 2005;56(4):305e14. [4] Ahuja G, Ulfvarson A. Sandwich construction-application on a superstructure. INMAT; 2005. [5] Liang C-C, Yang M-F, Wu P-W. Optimum design of metallic corrugated core sandwich panels subjected to blast loads. Ocean Eng 2001;28(7):825e61. [6] SANDWICH project. 2005. http://sandwich.balport.com/index1.html. [7] Gibson LJ, Ashby MF. Cellular solids: structure and properties. 2nd ed. Cambridge: Cambridge University Press; 1999. [8] Lu G, Yu TY. Energy absorption of structures and materials. Cambridge: Woodhead Publishing Ltd; 2003. [9] Banhart J. Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci 2001;46(6): 559e632. [10] Wadley HNG. Multifunctional periodic cellular metals. Philos Trans R Soc A-Math Phys Eng Sci 2006;364(1838):31e68. € m B. Manufacturing and applications of structural sandwich components. Compos Pt A-Appl Sci [11] Karlsson KF, Tomas Åstro Manuf 1997;28(2):97e111. [12] Romanoff J, Varsta P, Remes H. Laser-welded web-core sandwich plates under patch loading. Mar Struct 2007;20(1e2): 25e48. [13] Crupi V, Epasto G, Guglielmino E. Comparison of aluminium sandwiches for lightweight ship structures: honeycomb vs. foam. Mar Struct 2013;30:74e96. [14] Tilbrook MT, Radford DD, Deshpande VS, Fleck NA. Dynamic crushing of sandwich panels with prismatic lattice cores. Int J Solids Struct 2007;44(18e19):6101e23. [15] Rubino V, Deshpande VS, Fleck NA. The dynamic response of end-clamped sandwich beams with a Y-frame or corrugated core. Int J Impact Eng 2008;35(8):829e44. [16] Rubino V, Deshpande VS, Fleck NA. The dynamic response of clamped rectangular Y-frame and corrugated core sandwich plates. Eur J Mech A-Solids 2009;28(1):14e24. [17] Ehlers S, Tabri K, Romanoff J, Varsta P. Numerical and experimental investigation on the collision resistance of the X-core structure. Ships Offshore Struct 2010;7(1):21e9. [18] Fleck NA, Deshpande VS. The resistance of clamped Sandwich beams to shock loading. J Appl Mech-Trans ASME 2004; 71(3):386e401. [19] Qiu X, Deshpande VS, Fleck NA. Dynamic response of a clamped circular sandwich plate subject to shock loading. J Appl Mech-Trans ASME 2004;71(5):637e45. [20] Xue Z, Hutchinson JW. Preliminary assessment of sandwich plates subject to blast loads. Int J Mech Sci 2003;45(4): 687e705. [21] Xue Z, Hutchinson JW. A comparative study of impulse-resistant metal sandwich plates. Int J Impact Eng 2004;30(10): 1283e305. [22] Hutchinson JW, Xue Z. Metal sandwich plates optimized for pressure impulses. Int J Mech Sci 2005;47(4e5):545e69. [23] Zhu F, Zhao L, Lu G, Wang Z. Deformation and failure of blast-loaded metallic sandwich panelsdexperimental investigations. Int J Impact Eng 2008;35(8):937e51.

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