The dynamic response of clamped rectangular Y-frame and corrugated core sandwich plates

Transcription

1 The dynamic resonse of clamed rectangular Y-frame and corrugated core sandwich lates V. Rubino, V. S. Deshande 1 and N.A. Fleck Cambridge University, Engineering Deartment, Trumington Street, Cambridge, CB2 1PZ, U.K. Abstract The dynamic resonse of fully clamed, monolithic and sandwich lates of equal areal mass has been measured by loading rectangular lates over a central atch with metal foam rojectiles. All lates are made from AISI 34 stainless steel, and the sandwich toologies comrise two identical face-sheets and either Y-frame or corrugated cores. The resistance to shock loading is quantified by the ermanent transverse deflection at mid-san of the lates as a function of rojectile momentum. At low levels of rojectile momentum both tyes of sandwich late deflect less than monolithic lates of equal areal mass. However, at higher levels of rojectile momentum, the sandwich lates tear while the monolithic lates remain intact. Three-dimensional finite element (FE) calculations adequately redict the measured resonses, rior to the onset of tearing. These calculations reveal that the accumulated lastic strains in the front face of the sandwich lates exceed those in the monolithic lates. These high lastic strains lead to failure of the front face sheets of the sandwich lates at lower values of rojectile momentum than for the equivalent monolithic lates. Keywords: Sandwich lates, dynamic resonse, FE simulations, lattice materials. 1 Author to whom all corresondence should be addressed. Fax: ; vsd@eng.cam.ac.uk. 1

2 1... Introduction Clamed lates are reresentative of the structures used in the design of commercial and military vehicles. For examle, the hull of a shi comrises lates welded to an array of stiffeners. Over the ast decade there have been substantial changes in shi design, see for examle the review by Paik et al. (23). One such innovation has been the Schelde Shibuilding 2 sandwich design of shi hulls with a Y-frame core, see Fig. 1a. Full-scale shi collision trials reveal that the Y-frame design is more resistant to tearing than conventional monolithic designs, see Wevers and Vredeveldt (1999) and Ludolhy (21). Likewise, the finite element simulations by Konter et al. (24) suggest that the Y-frame confers imroved erforation resistance. Naar et al. (22) have argued in broad terms that the ability of the bending-governed Y- frame toology to sread the imact load over a wide area, combined with the high inlane stretching resistance of the Y-frame, gives the enhanced erformance of the Y- frame sandwich construction over conventional single and double hull designs. The corrugated sandwich core (Fig. 1b) is a cometing rismatic toology to that of the Y- frame. Pedersen et al. (26) and Rubino et al. (27b) have investigated the quasi-static structural resonse of Y-frame sandwich beams while Côté et al. (26) studied the resonse of sandwich beams with a corrugated core. These studies reveal that geometrical imerfections and/or non-uniform loading (such as indentation loading) induce bending within the struts of the corrugated core and reduce the comressive strength of the corrugated core to aroximately that of the Y-frame core. Tilbrook et al. (27) have erformed a combined exerimental and numerical investigation into the dynamic comressive resonse of these cores. They found that buckling of the webs is delayed at low imact velocities by inertial stabilization of the webs while lastic shock wave effects dominate the resonse at higher imact velocities. Radford et al. (25) have develoed an exerimental technique to subject structures to high intensity ressure ulses using metal foam rojectiles. The alied ressure versus time ulse mimics shock loading in air and in water, with eak ressures on the order of 1 MPa and loading times of aroximately 1 μs. This laboratory method has been emloyed in several investigations on the dynamic resonse of sandwich beams and lates, see for examle Radford et al. (26a) and Rathbun et al. (26). Rubino et al. (27a) have recently used this technique to demonstrate that sandwich beams with Y-frame and corrugated cores have a suerior dynamic erformance to monolithic beams of equal areal mass; in these tests, the rismatic axis of the cores was aligned with the longitudinal axis of the beams. However, clamed lates are more reresentative of marine structural comonents. The main aim of the current study is to determine the relative dynamic erformance of clamed 2 Royal Schelde, P.O. Box AA Vlissingen, The Netherlands. 2

3 monolithic lates and clamed sandwich lates with Y-frame and corrugated cores. In order to enable a fair comarison with the beam results in Rubino et al. (27a) we shall emloy the same methodology to load the sandwich lates investigated here. The outline of the aer is as follows. First, the manufacturing route of the sandwich lates is detailed and the exerimental rotocol is described for dynamic loading the lates over a central atch by metal foam rojectiles. The exerimental results are then comared with the corresonding observations for beams with two orientations of the core and also for monolithic lates of equal areal mass. Finally, finite element redictions are used to estimate the onset of failure in the lates Exerimental investigation Clamed rectangular sandwich lates, made from AISI 34 stainless steel and comrising two identical face-sheets and either a Y-frame or corrugated core, were loaded dynamically with metal foam rojectiles as sketched in Fig. 2a. The main aims of this exerimental study were: (i) To measure the shock resistance of rectangular sandwich lates with Y-frame and corrugated cores, and of monolithic lates. All lates have an equal areal mass. (ii) To comare the dynamic erformance of clamed rectangular sandwich lates and of end-clamed beams. (iii) To investigate the fidelity of three-dimensional finite element calculations in redicting the observed dynamic resonses. 2.1 Secimen configuration and manufacture The core and face sheets of the sandwich lates were made from AISI tye 34-3 stainless steel of thickness t.3 mm and of density 79 kgm. The Y- frame and corrugated cores had an effective density c 2 kgm (corresonding to a relative density 2.5 % ) and a core deth c = 22 mm. All sandwich lates had an areal mass m 2t c 1 kgm. f c f -3 A co-ordinate system ( X1, X2, X 3) is introduced in Fig. 2a in order to clarify the orientations of the cores in the sandwich lates. The longitudinal and transverse axes of the Y-frame and corrugated core are aligned with the X 1 and X 2 directions, resectively, while the through thickness direction of the core is along the X 3 axis. The short edge of the late between the clamed edges is labelled b along the X 2 direction while the long edge is labelled 2L along the X 1 direction; the chosen asect ratio b / 2L =.52 matches that of Royal Schelde s hull anels. The total deth of the sandwich lates is denoted c 2t. The cross-sectional dimensions of the Y- 3

4 frame and corrugated core are given in Figs. 2b and 2c, resectively. Note that the Y- frames and corrugated cores are close-acked along the X 2 direction such that adjacent cores touch as sketched in Fig. 2. The manufacturing sequence for the Y-frame sandwich lates is outlined in Fig. 3. The Y-frame webs were comuter-numerical-control (CNC) folded to roduce a continuous corrugated rofile with flat tos. Slots were then CNC-cut along the tos of the corrugations as seen in Fig. 3a. Each corrugated sheet contained five Y-frame webs. The legs of the Y-frame were CNC folded and then teeth were CNC-cut into the bottom of these legs to mate with the slots of the corrugations (Fig. 3a). The assembly was then laser welded together (Fig. 3b). This core assembly was of length 375 mm and of width 13 mm. Next, the Y-frame was sot welded to 375 mm 25 mm stainless steel face sheets (Figs. 3c and d). The face sheets were then continuous laser welded to the core using CNC laser welding. In order to ensure intimate contact between the face sheet and the core during the laser welding, an aluminium insert temorarily suorted the core (Fig. 3d). The corrugated core, comrising ten struts (five corrugations) inclined at 6 (Fig 2c), was also manufactured by CNC folding. The core was then laser welded to two identical face sheets using the same rocedure as that described above for the Y- frame sandwich lates. In order to minimize rotations and deflections of the sandwich lates along the clamed erihery, the claming rocedure as sketched in Fig. 4 was emloyed. Along the sides of the sandwich anel, two steel inserts of dimension 375 mm 6 mm 22 mm were glued between the face sheets. The ends of the sandwich core were then died in eoxy resin to a deth of 62.5 mm, as sketched in Fig. 4a. The erihery of the sandwich lates was then clamed between two steel frames using M8 bolts, as shown in Fig. 4b. The inner dimensions of the claming frame were 25 mm 13 mm and thus the effective dimensions of the Y-frame and corrugated core sandwich lates (i.e. sans of the late between the clamed edges) were 2L 25 mm and b 13 mm. Monolithic rectangular lates of thickness h 1.2 mm were also made from the AISI 34 stainless steel; they ossessed the same areal mass as the sandwich lates, m 1 kgm, and were of overall dimension 375mm x 25mm. As for the sandwich case, the monolithic lates were clamed between the steel frame of Fig. 4b, giving an effective san between the clamed edges of 2L 25 mm and b 13 mm. 4

5 2.2 Uniaxial resonse of the constituent materials Tensile tests were erformed on dog-bone secimens machined from the as-received AISI 34 stainless steel material. The true stress versus logarithmic strain curve ( ) of the AISI 34 stainless steel measured at an alied nominal strain-rate of 3 1 s -1 is reorted in Fig. 5a. The resonse is linear elastic with a Young s modulus E 21 GPa, followed by linear hardening above a yield strength of Y 21 MPa. The finite element model requires a descrition of the high strain rate resonse of the 34 stainless steel. The strain-rate sensitivity of the AISI 34 stainless steel was documented by Stout and Follansbee (1986) in the range 1 s & 1 s. Following their aroach, we define a dynamic strength enhancement ratio R as the ratio of the strength d (at a lastic strain 1. ) at an alied strain-rate & to the strength (. 1) 3-1 at an alied & 1 s. Stout and Follansbee (1986) found that the ratio R is reasonably indeendent on the choice of lastic strain at which R is calculated. We make use their measured values for R( & ) and write the dynamic strength d versus lastic strain resonse in the decouled form: = R( & ) ( ). (1) d This rescrition for the strain rate sensitivity of the stainless steel is used in the finite element calculations described in Section 4; ( ) is the measured quasi-static stress versus strain history (Fig. 5a). For illustration, the estimated true tensile stress versus logarithmic lastic strain behaviour of the AISI 34 stainless steel is sketched in Fig 5a at four selected values of alied strain-rate using the R values given by Stout and Follansbee (1986). The rojectiles used to imact the lates are made from Aloras aluminium alloy foam of relative density. 11. The comressive resonse of the foam is required in order to calibrate the constitutive arameters of the finite element model. The 3 quasi-static comressive resonse of the foam was measured at a strain-rate of 1 s - 1 using a cylindrical secimen similar to that of the rojectile in the dynamic exeriments (diameter 5.8 mm and length 51 mm). The nominal comressive resonse is shown in Fig. 5: the foam has a lateau strength of aroximately 2.5 MPa and a nominal densification strain of D Protocol for the dynamic tests The clamed rectangular monolithic and sandwich lates were imacted by Aloras aluminium foam rojectiles over a central circular atch of diameter d, as shown in Fig. 2a. Radford et al. (25) have recently demonstrated that foam rojectiles can be used to rovide well-characterised ressure versus time loading ulses. This method 5

6 has been used to measure the dynamic resonse of sandwich beams with lattice cores (Radford et al. 26a) and circular sandwich lates with metal foam cores (Radford et al. 26b) and lattice cores (McShane et al. 26). The imact site of the Y-frame and corrugated core sandwich lates is marked in Fig. 2: in keeing with the Y-frame structures used in shis constructed by Schelde Shibuilding, the web of the Y-frame was adjacent to the imacted face of the late while the Y-frame leg was attached to the non-imacted face of the sandwich late. Projectiles of length l 51 mm and diameter d 5. 8 mm were electro-discharge machined into a circular cylindrical shae from Aloras foam blocks of density kgm. The rojectiles were fired at a velocity v in the range 94 ms to ms using a gas gun with circular barrel of diameter 5.8 mm and length 4.5 m. Results are given in terms of the rojectile momentum er unit area I lv, as listed in Table 1. The lates were insected after each exeriment in order to measure the ermanent central deflection and to detect any visible signs of failure Exerimental results At least four levels of momentum I were imarted to the monolithic and sandwich lates by varying the metal foam rojectile imact velocity. A summary of the measured deflections, core comression and observed failure modes is rovided in Table Effect of rojectile momentum uon the deformation of monolithic and sandwich lates The dynamic resonse of the sandwich and monolithic lates is summarised in a lot of ermanent back face deflections w b at the centre of the lates versus the initial momentum of the foam rojectile I, see Fig. 6a. Both tyes of sandwich late have a similar erformance over the rojectile momentum range 2kNsm I 5kNsm and are erforated by the rojectile at higher values of I. In contrast, the monolithic lates have higher deflections w b than the sandwich lates but remain intact over the entire range of I investigated. Define the ermanent core comressive strain as c c / c, where c is the reduction in core thickness at the centre of the late due to imact. The measured deendence of c uon I is lotted in Fig. 6b for the two sandwich late configurations. Both sandwich lates undergo similar levels of core comression over the range of I values investigated. Photograhs showing the imacted face of the as-tested lates ( I 5kNsm ) within the claming frame are shown in Fig. 7. Tears running arallel to the X1 -axis are 6

7 observed on the imacted face sheets of both the Y-frame and corrugated core sandwich lates. In contrast, the monolithic late remained intact at this value of I. Partial ull-out of the monolithic late from the clamed suorts is evident in Fig. 7a: a en-line was traced along the inner clamed boundaries of the lates rior to each test, and the line moved inwards during the test. In order to gain insight into the dynamic deformation mechanisms, the monolithic and sandwich lates tested at I 3kNs m were sectioned along their mid-san X1. Photograhs of the sectioned secimens are shown in Fig. 8a for the monolithic late, in Fig. 8b for the sandwich late with the Y-frame core and in Fig. 8c for the sandwich late with the corrugated cores. The sectioned rofiles show that significant lastic deformation occurs in the vicinity of the foam imact site and that the lates are continuously curved. It is deduced that the dynamic deformation of lates involves the formation of travelling hinges, similar to the observed behaviour of monolithic and sandwich beams and lates reorted by numerous investigators, for examle Radford et al. (26b); McShane et al. (26) and Rubino et al. (27a). For both tyes of sandwich late, the core has sheared and comressed. 3.2 Comarison of the erformance of rectangular sandwich lates and beams Rubino et al. (27a) investigated the resonse of clamed Y-frame and corrugated core sandwich beams imacted by metal foam rojectiles. Beams with both transverse and longitudinal core orientations were investigated in that study and constituent materials used to manufacture the sandwich beams, the core and face sheet thicknesses and core relative density were identical to those emloyed in the resent investigation. Moreover, the sans of the beams in Rubino et al. (27a) were 25 mm, that is equal to the length of the longer side of the rectangular lates studied here. Given these similarities between the two studies it is instructive to comare the resonses of the Y-frame and corrugated core sandwich beams and lates. In qualitative terms, the deformed shae on the X1 lane of the late secimens (Fig. 8a) is in good agreement with that observed by Rubino et al. (27a) for corrugated and Y-frame sandwich beams in the transverse configuration. The ermanent back face deflections w b at mid-sans of the Y-frame and corrugated core sandwich beams and lates are comared in Fig. 9a and 9b, resectively. Recall that the sandwich lates have the longitudinal axis of the rismatic cores along the X 1 axis while the transverse core direction is aligned along the X 2 axis. However, the measured sandwich late deflections are not intermediate to the sandwich beams with transverse and longitudinal core arrangements. Rather, the sandwich lates outerform the sandwich beams (in terms of w ) with the longitudinal core orientation over the entire range of rojectile velocities investigated here. This is resumably due to the enhanced stretch resistance of the face sheets in the clamed late configuration. However, the enhanced stretching of the face-sheets results in tearing of the front face sheet at lower values of I comared to the sandwich beams b 7

8 with the longitudinal core orientation as indicated in Fig. 9. Moreover, erforation of 2 the sandwich lates occurs at I 5.4 knsm which is about 15% lower than that for sandwich beams with a longitudinal core orientation. It is instructive to make a direct comarison of the deflections of the sandwich beams and lates with their monolithic counterarts. To address this, the ratio of measured ermanent back face deflection at the centre of the sandwich lates to that of monolithic lates (of same mass) w sandwich w monolithic is lotted as a function of rojectile momentum I in Fig. 1. The data for sandwich and monolithic beams from Rubino et al. (27a) are included in the figure. There is only a minor effect of core toology uon the mid-san deflection for the beams and lates. However, the sandwich lates and the beams with a longitudinal core orientation outerform the monolithic lates articularly at low imulse levels; in contrast, the sandwich beams with the transverse core orientation show negligible benefit over monolithic beams of equal mass Finite element simulations Finite element (FE) redictions for the monolithic and sandwich lates are resented in this section. All comutations were erformed using the exlicit time integration version of the commercially available finite element code ABAQUS 3 (version 6.5). We first briefly describe the details of these FE calculations. Three-dimensional simulations of half models of the rectangular sandwich and monolithic lates were erformed. Linear hexahedral elements (C3D8R in ABAQUS notation) were used to model the cylindrical foam rojectiles of diameter d 5.8 mm and length l 51 mm, with the elements swet about the cylindrical axis of the foam rojectile. The rojectiles had 51 elements in the axial direction and 25 elements along the radius. The sandwich and monolithic lates were modelled using four-noded shell elements (S4R in ABAQUS notation) for both the face-sheets and the core. Perfect bonding between the core and face sheets was assumed. All dimensions (face sheet thickness and core dimensions) were chosen to match the exerimental values and an element size of 1. mm was emloyed for all calculations reorted subsequently. Symmetry boundary conditions were secified at mid-san ( X1 ) and clamed boundary conditions were alied at X 1 L and at X 2 b 2 by constraining all rotations and dislacements to zero; see Fig. 2a. The loading was simulated by imact of a metal foam rojectile: at the start of the simulation the rojectile with an initial velocity v o was brought into contact with the front face sheet at the centre of 3 Hibbit, Karlsson and Sorensen Inc. 8

9 the rectangular lates. The general contact otion in ABAQUS was emloyed to simulate contact between all adjacent surfaces. The general contact algorithm in ABAQUS enforced hard, no-friction contact interaction using a enalty algorithm. 4.1 Material roerties The AISI 34 stainless steel was treated as a J2-flow theory rate deendent solid of -3 density 79 kgm, Young s modulus E 21 GPa and Poisson ratio 3.. f The uniaxial tensile true stress versus equivalent lastic strain curves at lastic strainrates 1 s 1 s were tabulated in ABAQUS using the rescrition described in Section 2.2 and emloying the data of Fig. 5a. The metal foam rojectile was modelled as a comressible continuum using the constitutive model of Deshande and Fleck (2). An isotroic yield surface is defined by: ˆ Y. (2) where Y is the current yield strength. The equivalent stress ˆ has the following form: ˆ 2 e m,... 1 / (3) where the arameter defines the shae of the yield surface, m kk / 3 is the mean stress and e 3sij sij / 2 is the von-mises effective stress in terms of the deviatoric stress s ij. The yield strength Y is assumed to be given by an over-stress tye relation Y ˆ c, (4) where is the foam viscosity, ˆ is the work conjugate lastic strain rate to ˆ and ˆ c is the uniaxial stress versus lastic strain relation at a negligible strain rate. In 3 the simulations, the Aloras foam is ascribed a density of 313 kgm, Young s modulus E c 1. GPa, an elastic Poisson s ratio 3.. Consistent with observations reorted by Deshande and Fleck (2) we assumed 3/ 2 which imlies that the "lastic Poisson's ratio". The yield strength c versus equivalent lastic strain ˆ history is calibrated using the comressive stress versus strain resonse resented in Fig. 5b. The assumed over-stress model smears the lastic shock wave in the foam rojectile over a width (Radford et al., 25): D w v, (5) where D is the nominal densification strain and v is the velocity jum across the shock. For the uroses of this discussion, v is aroximately equal to the rojectile velocity v o. The values of the viscosity were chosen so that w l /1 5 mm, which is aroximately equal to that observed in the exeriments 9

10 of Radford et al. (25). Large gradients in stress and strain occur over the shock width and thus the foam rojectile was discretized by a mesh size of 1 mm in order to resolve these gradients accurately. 4.2 Comarison of finite element redictions and measurements Reresentative FE calculations of the transient deflection of the centre oint of the sandwich and monolithic lates are lotted in Fig. 11 for I 3.2 knsm. The deflections of both the front and back face sheets of the sandwich lates are dislayed. In all cases only small elastic vibrations occur after the maximum deflections have been attained, so that the eak deflection is close to the ermanent deflection. The redicted ermanent deflections w b of the back face sheets of the sandwich lates and of the monolithic lates are included in Fig. 6a along with the corresonding measured values. The ermanent deflections in the FE calculations are estimated by averaging the dislacements over several cycles of elastic vibration (from trough to eak) immediately after the initial eak dislacement. We conclude that at least for the lower values of I where no tearing of the lates was observed, the FE simulations are able to redict the late deflections with reasonable accuracy. Some of the discreancies may be accounted for as follows: (i) At the high values of I the observed deflections of the monolithic lates are greater than the redictions as the lates start to ull out of the suorts, see Fig. 7a. (ii) The FE calculations overestimate w b for the Y-frame lates at intermediate values of I. We shall see subsequently that this is rimarily due to the fact that the FE calculations underestimate the degree of core comression in the Y-frame lates. The FE redictions for the final core comression c at the late centre are comared with measurements in Fig. 6b as a function of the alied momentum I. Good agreement between the measurements and redictions is achieved for the corrugated core, however the FE calculations under-redict the core comression in the Y-frame sandwich lates. The critical difference between the redictions and observations is that the FE calculations redict that the core comression remains constant at c.4 for I 3kNsm while in the exeriments core comression increases with increasing I over the entire range of rojectile velocities investigated here. We attribute this discreancy to the fact that tearing between the Y-frame leg and the back face sheet was observed in all secimens but was not modelled in the FE calculations. It is also worth noting that the slight kink in the FE redictions of the deflections of the back face of the Y-frame lates (Fig. 6a) corresonds to the I range over which the FE calculations redict that the core comression remains constant. 1

11 Comarisons between the measured and redicted ermanent deformation of the lates imacted at I 3kNsm are included in Fig. 8. In both the exeriments and the FE calculations the lates are sectioned along their mid-san X1 to reveal the core deformation in the sandwich lates. In general good agreement is obtained although there are some discreancies esecially for the Y-frame sandwich late as discussed above. 4.3 Estimation of the onset of front face tearing The final lastic strain distribution within the Y-frame and corrugated core sandwich lates was exlored in the FE simulations for the choice I 5.1 knsm. This imulse level was chosen as it gave front face tearing of both sandwich lates, but not comlete erforation. The location and direction of the maximum rincial strains in the sandwich lates are shown in Figs. 12a and 12b for the Y-frame and corrugated core lates, resectively. For the Y-frame late, the highest redicted strain occurs close to the joint between the Y-frame web and the front face sheet while for the corrugated core high values of final lastic strain occur both in the front face sheet and within the core itself. The lastic strain redictions of the FE calculations are generally consistent with the observation that failure always initiates in the front face sheet. The FE redictions of the maximum rincial lastic strains max in the face sheets of the Y-frame and corrugated core lates are comared with those in the corresonding sandwich beams (longitudinal core orientation) in Fig. 13a over a range of values of I. The FE redictions for the beams are obtained from the arallel study by Rubino et al. (27a). The FE calculations redict significantly higher values of max in the lates than in the beams, esecially for I 4kNsm ; this is consistent with the observation that the lates fail at lower values of I than the sandwich beams of longitudinal core orientation. Comarisons between the redicted values of max for the sandwich and monolithic lates are included Fig. 13b. Recall that failure of the front face sheet was observed at lower values of I in the Y-frame late than the corrugated core late. Also, no failure of the monolithic late was observed even at the highest value of I investigated here. Consistent with these observations, the FE calculations redict the lowest values of max in the monolithic lates followed by the corrugated core lates, and the largest strains occur in the Y-frame lates Concluding remarks 11

12 Metal foam rojectiles have been used to imact clamed 34 stainless steel monolithic lates and sandwich lates with Y-frame or corrugated cores. The ermanent deflections and level of core comression of the sandwich lates have been measured as a function of rojectile momentum, and the measured resonses are comared with finite element simulations. The finite element (FE) simulations cature the observed deformation modes to reasonable accuracy. Failure of the joints between the core and the face sheets is not included in the FE redictions, and this leads to some discreancies esecially for the Y-frame lates. The sandwich lates outerform monolithic lates of equal mass at low values of the rojectile momentum I. Moreover, comarisons with the corresonding Y-frame and corrugated core sandwich beams revealed that the lates deflect less than the beams. However, the benefits of sandwich construction reduce with increasing I : (i) the ratio of the ermanent deflections of the sandwich lates to monolithic lates 2 increases with increasing I and aroaches unity for I 6kNsm ; (ii) stress concentrations at the attachment oints between the core and the face sheets result in failure of the sandwich lates at lower values of I than for the monolithic lates. We conclude that sandwich construction has otential for significantly enhancing the dynamic erformance of structures. However, sandwich construction must be used with caution in heavily loaded structures: the sandwich lates may fail at lower values of I than for monolithic lates of equal areal mass. Acknowledgments This work was suorted by the Netherlands Institute for Metal Research: roject number MC1.3163, The Otimal Design of Y-core sandwich structures. References Côté, F., Deshande V. S., Fleck N. A., Evans, A.G.,26. The comressive and shear resonses of corrugated and diamond lattice materials. International Journal of Solids and Structures 43, Deshande V. S., Fleck N. A., 2. Isotroic constitutive models for metallic foams. Journal of Mechanics and hysics of Solids 48, Konter, A., and Broekhuijsen, J., and Vredeveldt, A., 24. A quantitative assessment of the factors contributing to the accuracy of shi collision redictions with the finite element method. International Conference of Shi Collisions and Grounding, Tokyo, Jaan. Ludolhy, H., 21. The Unsinkable Shi -Develoment of the Y-Shae Suort Web. Proceedings of the 2 nd International Conference on Collision and Grounding of Shis, Coenhagen, Denmark. McShane G.J., Radford D.D., Deshande V.S. and Fleck N.A., 26 The resonse of clamed sandwich lates with lattice cores subjected to shock loading. Euroean Journal of Mechanics 25,

13 Naar, H., and Kujala, P., and Simonsen, B.C., and Ludolhy, H., 22. Comarison of the Crashworthiness of Various Bottom and Side Structures. Marine Structures 15, Paik, J.K., 23. Innovative Structural Designs of Tankers Against Shi Collisions and Grounding: A Recent State-of-the-Art Review. Marine Technology 4, Pedersen, C.B.W., and Deshande, V. S., and Fleck, N.A., 26. Comressive Resonse of the Y-Shaed Sandwich Core. Euroean Journal of Mechanics-A/Solids 25, Radford, D.D., Fleck N.A., Deshande V.S., 25. The use of metal foam rojectiles to simulate shock loading on a structure. International Journal of Imact Engineering 31, Radford, D.D., Fleck N.A., Deshande V.S., 26a. The resonse of clamed sandwich beams subjected to shock loading. International Journal of Imact Engineering 32, Radford D.D., McShane G.J., Deshande V.S. and Fleck N.A., 26b. The resonse of clamed sandwich lates with metallic foam cores to simulated blast loading. International Journal of Solids and Structures 43, Rathbun, H.J., Radford, D.D., Xue, Z., He, M.Y., Yang, J., Deshande, V.S., Fleck, N.A., Hutchinson, J.W., Zok, F.W., Evans, A.G., 26. Performance of metallic honeycomb-core sandwich beams under shock loading. International Journal of Solids and Structures 43, Rubino, V., Deshande V.S., Fleck N.A., 27a. The dynamic resonse of end-clamed sandwich beams with a Y-frame or corrugated core, submitted to International Journal of Imact Engineering. Rubino, V., Deshande V.S., Fleck N.A., 27b. The collase resonse of sandwich beams with a Y-frame core subjected to distributed and local loading, International Journal of Mechanical Sciences doi:1.116/j.ijmecsci Stout M. G., Follansbee P. S., Strain-rate sensitivity, strain hardening, and yield behaviour of 34L stainless steel. Trans. ASME: Journal of Engineering Materials Technology 18, Tilbrook, M.T., Radford D.D., Deshande V.S., Fleck N.A., 27. Dynamic crushing of sandwich anels with rismatic lattice cores. International Journal of Solids and Structures 44, Wevers, L. J., Vredeveldt, A. W., Full Scale Shi Collision Exeriments 1998, TNOreort 98-CMC-R1725, The Netherlands. 13

14 Figure cations Fig. 1: Sketch of the (a) Y-frame and (b) corrugated sandwich cores as used in shi hull construction. The core is sandwiched between the outer and inner hull of the shi. Fig. 2: (a) Sketch of the clamed sandwich late geometry and the loading arrangement. Geometry of half sandwich late for (b) Y-frame and (c) corrugated sandwich cores investigated in this study. The cross-section is also shown for each toology. All dimensions are in mm. Fig. 3: The manufacturing sequence for the Y-frame sandwich lates. (a) The leg is inserted into the slots in the folded Y-frame web. (b) The leg is laser welded to the Y- frame web. (c) The Y-frame core is sot welded on to the front face sheet of the sandwich late. (d) An aluminium insert locates the core and face sheets and (e) the assembly is laser welded together. Fig. 4: The claming arrangement of the sandwich lates. (a) The steel inserts and eoxy filling of the core ends allow for high claming ressures. (b) The steel frame for claming of the lates. All dimensions are in mm. 1 Fig. 5: (a) The measured quasi-static ( 1 3 s ) tensile stress versus strain resonse of the AISI 34 stainless steel and the estimated resonses at three additional values of alied lastic strain rate, using the data of Stout and Follansbee (1986). (b) The quasi-static nominal comressive stress versus nominal strain resonse of the Aloras metal foam. Fig. 6: Measured and FE redictions of the ermanent (a) back face deflections and (b) core comression at the centre of the dynamically loaded sandwich lates, as a function of the foam rojectile momentum I. The data for the monolithic lates are included. Symbols denote measurements while the continuous lines are the FE redictions. Front face sheet failure is denoted by encircling the salient data oints of in (b). Fig. 7: Photograhs showing a view of the front face of the as-tested (a) monolithic (b) Y-frame and (c) corrugated core lates. I 5kNsm. Fig. 8: Photograhed sections of the mid-lane X1 of the as-tested (a) monolithic (b) Y-frame and (c) corrugated core lates. I 3kNsm. w b Fig. 9: Comarison of the measured ermanent deflections w b at the centre of the back face of the (a) Y-frame and (b) corrugated core sandwich lates and beams, as a function of the foam rojectile momentum I. The data are shown u to I values at which face sheet failure is first observed. The sandwich beam data are from Rubino et al. (27a) and are for the cases when the rismatic axis and transverse axis of the 14

15 core are along the length of the beam; these orientations are labelled longitudinal and transverse, resectively. Fig. 1: The ratio of measured back deflections of the sandwich lates to monolithic late versus rojectile momentum I. The data are shown u to I values at which face sheet failure is first observed. The sandwich beam data are from Rubino et al. (27a), with the rismatic and transverse axes of the core along the length of the beam; these two cases are labelled longitudinal and transverse, resectively. Fig. 11: Finite element rediction of the temoral variation of the deflection of the centre of the monolithic and sandwich lates loaded with a metal rojectile momentum of I 32kNsm.. Fig. 12: Sketch reresenting the FE redictions for the location and direction of the maximum rincial strain in the (a) Y-frame and (b) corrugated core sandwich lates. The beams were imacted by the foam rojectile of I 5.1 knsm. Fig. 13: FE redictions of the maximum rincial lastic strain in the front face sheet of the dynamically loaded sandwich lates. (a) Comarison of the Y-frame and corrugated core sandwich beams (longitudinal core orientation) and lates. (b) Comarison between the sandwich lates and monolithic lates. The FE redictions for the sandwich beams are taken from Rubino et al. (27a). List of Tables Table 1: The measured dynamic resonses of monolithic and sandwich lates. The symbol X denotes through-thickness tearing of the lates. 15

16 SPECIMEN PROJECTILE I = l v v w b (knsm ) (kgm -3 ) (ms -1 ) (mm) RESPONSE c Value of X 2 where tearing started (mm) Monolithic as-brazed Y-core (weld) X X Corrugated X X 26 (weld) Table 2: The measured dynamic resonse of monolithic and sandwich lates. The symbol X denotes through-thickness tearing of the lates. Tearing of the secimens started at X1 and at a value of X 2 given in the last column. See Fig. 2 for a definition of the coordinate system. 16

17 (a) (b) inner hull inner hull Fig. 1: Sketch of the (a) Y-frame and (b) corrugated sandwich cores as used in shi hull construction. The core is sandwiched between the inner and outer hulls of the shi. 17

18 (a) Longitudinal section d X 3 Metal Foam Projectile Cross section t v l X 3 c 2L X 1 t b X 2 (b) (c) Fig. 2: (a) Sketch of the clamed sandwich late geometry and the loading arrangement. Geometry of half sandwich late for (b) Y-frame and (c) corrugated sandwich cores investigated in this study. The cross-section is also shown for each toology. All dimensions are in mm. 18

19 (a) (b) Laser welding (c) Sot laser welding (d) (e) Aluminium insert Fig. 3: Manufacturing rocess for the laser welding of Y-frame sandwich lates. (a) The leg is inserted into the corresondent slots of the main frame and (b) is next manually welded on it along the 375 mm long side. (c) The Y-frame core is laser sot welded on the front face sheet with sots every 1 mm, (d) the back face sheet is added with laser sot welding. An aluminium tool (shown in the inset) is here used to ush together the two comonents to be sot welded. (e) A robot laser welds along the re-sot welded lines. 19

20 (a) e b e 2L a Mild steel inserts Eoxy resin filler c S (b) 2L b Rigid frame Y-frame late Rigid frame Fig. 4: Sketches of the manufacturing technique used to clam the rectangular lates. (a) Mild steel inserts are glued between the face sheets of the long sides. A two art eoxy resin is oured in the two extremities of the lates. (b) The late is bolted between two rigid rectangular frames. 2

21 (a) 1.5 Y-frame n (MPa) 1.5 Corrugated core (b) 4 n 3 n (MPa) n Fig. 5: (a) Measured quasi-static comressive stress versus strain resonses of Y- frame and corrugated sandwich cores. (b) The quasi-static nominal comressive stress versus nominal strain resonse of the Aloras metal foam. 21

22 (a) (MPa) s 1 4 (b) R Fig. 6: (a) The measured quasi-static ( 1 3 s ) tensile stress versus strain resonse of the AISI 34 stainless steel and the estimated high strain rate resonse at three additional values of strain rate, using the data of Stout and Follansbee (1986). (b) The dynamic strength enhancement ratio R as a function of lastic strain-rate for the AISI 34 stainless steel at a lastic strain. 1. s 1 22

23 (a) Monolithic Y-frame Corrugated 3 Monolithic (FE) w b (mm) 2 1 Y-frame (FE) Corrugated-core (FE) failure of all sandwich lates (b) 1.9 I = l v (kns m ) front face tears front face tears c Corrugated core (FE) Y-core (FE) I = l v (kns m ) Fig. 7: Comarison of the measured and redicted ermanent (a) rear-face deflections and (b) core comression at mid-san of the dynamically loaded monolithic and sandwich lates, as a function of the foam rojectile momentum I. Symbols denote measurements and the continuous lines denote FE redictions. 23

24 (a) (b) (c) Fig. 8: Photograhs of the as-tested (a) monolithic, (b) Y-frame and (c) corrugated core sandwich lates at aroximately the same value of the foam rojectile initial momentum I 5kNsm. Front face tearing is observed in both the sandwich lates. 24

25 (a) Observation Prediction X 3 X 2 (b) (c) Fig. 9: Comarison between the observed and FE redicted deformed rofiles of the lates sectioned at mid-san. (a) Monolithic lates, (b) Y-frame and (c) corrugated core sandwich lates imacted by the foam rojectile at I 3kNsm. 25

26 (a) 5 w b (mm) Beam, transverse front face tears (at suort) front face tears (at mid-san) failure Beam, longitudinal 1 Plate I = l v (kns m ) (b) 5 w b (mm) Beam, transverse front face tears (at suort) front face tears (at mid-san) failure Beam, longitudinal 1 Plate I = l v (kns m ) Fig. 1: Comarison of the measured ermanent rear-face deflections at mid-san of the dynamically loaded (a) Y-frame and (b) corrugated core sandwich structures, as a function of the foam rojectile momentum I. The resonse of the sandwich lates (Fig. 7a) is comared to that of sandwich beams with either longitudinal or transverse cores (see Rubino et al., 27c). 26

27 1.8 Beam, transverse w sandwich w monolithic.6.4 Beam, longitudinal Plate.2 Y-frame Corrugated core I = l v (kns m ) Fig. 11: Comarison of the measured normalized ermanent rear-face deflections at mid-san of the dynamically loaded Y-frame and corrugated core sandwich structures, as a function of the foam rojectile momentum I. The rear-face deflection of the sandwich structure is normalized with the rear-face deflection of the corresonding monolithic structure of the same mass. 27

28 Mid-san deflection (mm) Front face Monolithic Rear face 5 Y-frame Corrugated-core time (ms) Fig. 12: Finite element rediction of the mid-san deflection versus time histories for monolithic and sandwich lates with Y-frame or corrugated core loaded with a metal rojectile momentum of I 32kNsm.. 28

29 (a) Clamed.6.6 (b) Clamed Fig. 13: Sketch showing the FE redictions for the location and direction of the maximum rincial strains of the (a) Y-frame and (b) corrugated core sandwich lates. The clamed lates were imacted with the foam rojectile momentum of I 51kNsm.. 29

30 (a).8.6 Plate failure of Y-frame lates max.4 Beam, longitudinal.2 (b).8 Beam, transverse I = l v (kns m ) max.6.4 Beam, longitudinal Plate failure of corrugated core lates.2 (c) Beam, transverse I = l v (kns m ).8.6 Y-frame Corrugated core max.4 Monolithic I = l v (kns m ) Fig. 14: Maximum rincial lastic strain of the front face at mid-san of the dynamically loaded (a) Y-frame and (b) corrugated core sandwich structures, as a function of the foam rojectile momentum I. The resonse of the lates is comared to beams with either longitudinal or transverse cores, see Rubino et al. (27c). (c) Comarison of the maximum rincial lastic strain in the front face of the sandwich lates and monolithic lates. 3