A Novel Fluid Structure Interaction Experiment to Investigate Deformation of Structural Elements Subjected to Impulsive Loading

A Novel Fluid Structure Interaction Experiment to Investigate Deformation of Structural Elements Subjected to Impulsive Loading
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  See discussions, stats, and author profiles for this publication at: A Novel Fluid Structure Interaction Experimentto Investigate Deformation of StructuralElements Subjected to Impulsive Loading  ARTICLE   in  EXPERIMENTAL MECHANICS · JANUARY 2006 Impact Factor: 1.55 · DOI: 10.1007/s11340-006-0296-7 CITATIONS 61 READS 48 3 AUTHORS , INCLUDING:Horacio Dante EspinosaNorthwestern University 162   PUBLICATIONS   4,048   CITATIONS   SEE PROFILE Nicolaie MoldovanAdvanced Diamond Technologies 89   PUBLICATIONS   1,484   CITATIONS   SEE PROFILE Available from: Nicolaie MoldovanRetrieved on: 03 February 2016  A Novel Fluid Structure Interaction Experimentto Investigate Deformation of Structural ElementsSubjected to Impulsive Loading H.D. Espinosa  &  S. Lee  &  N. Moldovan Received: 20 June 2006 /Accepted: 31 August 2006 / Published online: 8 December 2006 # Society for Experimental Mechanics 2006 Abstract  This paper presents a novel experimentalmethodology for the study of dynamic deformation of structures under underwater impulsive loading. Theexperimental setup simulates fluid–structure interac-tions (FSI) encountered in various applications of interest. To generate impulsive loading similar to blast,a specially designed flyer plate impact experiment wasdesigned and implemented. The design is based onscaling analysis to achieve a laboratory scale apparatusthat can capture essential features in the deformationand failure of large scale naval structures. In the FSIsetup, a water chamber made of a steel tube isincorporated into a gas gun apparatus. A scaledstructure is fixed at one end of the steel tube and awater piston seals the other end. A flyer plate impactsthe water piston and produces an exponentially decay-ing pressure history in lieu of explosive detonation.The pressure induced by the flyer plate propagates andimposes an impulse to the structure (panel specimen),which response elicits bubble formation and watercavitations. Calibration experiments and numericalsimulations proved the experimental setup to befunctional. A 304 stainless steel monolithic plate wastested and analyzed to assess its dynamic deformationbehavior under impulsive loading. The experimentaldiagnostic included measurements of flyer impactvelocity, pressure wave history in the water, and fulldeformation fields by means of shadow moire´ and highspeed photography. Keywords  Fluid–structureinteraction.Underwaterimpulsiveloading.Dynamicstructuraldeformation Introduction Development of blast-resistant materials and struc-tures is a critical engineering problem in variousapplications, including plants which need provisionagainst emergency explosion such as in oil, chemistryor nuclear industries, and obviously military or civiltransportation vehicles in which the possibility of impulsive loading is always present. In this regard,sandwich structures having core materials between twoface sheets have been extensively investigated as ameans to increase strength and stiffness or reduceweight. Xue and Hutchinson [21, 22] and Hutchinson and Xue [6] performed detailed computational simu-lations to assess the performance of metal sandwichplates subjected to impulsive blast loads. To gaininsight into the efficiency of steel sandwich structures,these authors modeled the underwater structure byimposing an initial momentum to the face sheet incontact with the fluid, under the assumption that theblast pulse period is sufficiently short. Also, theydetermined the momentum impulse which needs tobe applied to the face sheet based on Taylor _ s work[18] neglecting the resistance offered by the core-bottom face sheet to the top face sheet. This prelim-inary work demonstrated that sandwich structures withvarious core topologies (honeycomb, folded beam,pyramidal truss) offer an advantage over solid plates,of equal mass per unit area, in the sense that they canabsorb a much larger impulse for a given maximumcentral displacement. Qui et al. [10–12], Fleck and Experimental Mechanics (2006) 46: 805–824DOI 10.1007/s11340-006-0296-7H.D. Espinosa ( * , SEM member)  I  S. Lee  I  N. MoldovanDepartment of Mechanical Engineering,Northwestern University, 2145 Sheridan Rd.,Evanston, IL 60208-3111, USAe-mail: SEM  Deshpande [4], and Deshpande and Fleck [2] also investigated sandwich panels with cellular cores. Theseauthors formulated an analytical model to describe theoverall deformation and strength of sandwich panelssubjected to impulse loading. Their model suggestedthat the response of such structures can be separatedinto three main stages: Stage I: impulse loading of front sheet; Stage II: core compression phase and loadtransferring to back sheet; and Stage III: platedeflection and stretching (overall structural response).The existence and limitation of this multistage defor-mation process was later analyzed in [9]. In this laterwork the relevance of the front sheet and core stiffnessin the context of fluid-structure interactions wasassessed. Through extensive numerical simulations,they showed that thin front sheets and low densitycores perform better.As an alternative to the development of sandwichstructures, researchers have pursued the design of metal alloys in which very high strength is achievedwhile reasonable levels of ductility are preserved. Forinstance, Vaynman et al. [19, 20] developed high performance hot-rolled and air-cooled low-carbonsteels, called NUCu steels, that show improvement intoughness, strength, weldability and weatherability.These material have low carbon content and thesatrengthening is mainly derived from copper-precip-itation on air-cooling from hot rolling; nickel, niobium,and titanium are added to improve the manufacturingprocess and control the grain size. For example,NUCu-100 steel can reach yield strength of 712 MPa,tensile strength of 780 MPa and elongation at break of 26.3%; this material shows also very high Charpyimpact energies at cryogenic temperatures [20]. Haoet al. [5] developed a multi-scale hierarchical constitu-tive model for the computational design of metalalloys. The approach was used to relate quantummechanical, micromechanical, and overall strength/toughness properties. This model, which can accountfor different kinds of alloy matrix inclusions, wasimplemented in a FEM code for the design of ultrahigh strength, high toughness steels. The afore-mentioned material multiscale model is particularlysuitable to the development of blast resistant alloys.The above theoretical, computational and experi-mental work points at the need for developing fluid–structure interaction (FSI) experiments without majoraprioristic assumptions, which can elucidate the mech-anisms of deformation and fracture of blast resistantstructures and materials. The experimental setupshould generate blast loadings in water and havedimensions representative of underwater explosion fullfield problems. In doing so, we expect to measurestructural rather than solely constitutive materialresponse under a realistic, although scaled, fluid–structure interaction event.In this paper the underwater explosion impinging ona naval hull structure problem is defined and anexperimental setup to reproduce it is proposed. Thenwe analyze the fundamental design steps that haveleaded to the development of the FSI apparatus, withparticular emphasis on its scaling. In addition, theexperimental procedure is described and details on thediagnostic tools implemented to monitor projectivevelocity, pressure history, and specimen panel out-of-plane full field displacements are given. Twocalibration experiments are then presented, and theexperimental data is compared with a finite elementmodel. The time-dependent behavior of the specimenand of the fluid is analyzed, with the finite elementmodel, focusing on the cavitation that takes place attheir interface. Experimental Configuration Problem DefinitionConsider the pressure wave generated by an underwa-ter explosion impingingon anaval hull structure, Fig. 1.Typically, a hull structural panel is clamped at theboundary and has a thickness of approximately 25.4mm and a span width of 2 m. The free-field incidentblast pulse in a fluid can be idealized as an exponentialpressure decay,  p  ¼  p 0 e  t  = t  0 , where  p 0  is the initial peakpressure and  t  0  is a characteristic decay time [16]. Thefree-field momentum (impulse/area) is given by  I  0  ¼ R  1 0  p dt   ¼  p 0 t  0 . For a typical blast  t  0 õ 10 j 4 s,  p 0 õ 100 MPa, and  I  0 õ 10 4 N s/m 2 , which correspondto the case of detonating 1 kg of TNT at 1 m distancefrom the structure or 1,000 kg of TNT at 10 m away inwater [16, 17]. Fundamental DesignThe proposed FSI experimental setup is depicted inFig. 2. To generate an impulsive load, similar to that of anexplosiveblast,aflyerplateofthickness h  s  is launchedagainst water confined in a pressure tube or anvil. For areview of plate impact testing, see [3]. Assuming onedimensional elastic wave propagation and a linearequation of state for the fluid, one can achieve thepressure profile as a piece-wise function, namely, P  N   ¼  sf  s  þ  f  V  0  s    f  s  þ  f    N  ; N   ¼  0 ; 1 ; ::::::; n  ð 1 Þ 806 Exp Mech (2006) 46: 805–824 SEM  where  f  =(  r c )  f   and  s =(  r c )  s  are the acoustic impedancesof the fluid and solid, respectively.  V  0  is the impactvelocity and  N   is the number of reverberations of thewave in the flyer. The time elapsed in each reverbera-tion is  t  N   ¼  2 h  s = c  s ð Þ N  . This pressure history can bemade equal to  p  ¼  p 0 e  t  = t  0 from which the impactvelocity can be related to the peak pressure and theflyer plate thickness to  t  0 : V  0  ¼  s  þ  f  sf  p 0  ð 2 Þ and e  t N   = t  0 ¼  s    f  s  þ  f    N  ;  2 h  s = c  s ð Þ ¼   1 t  0 ln  s   f  s þ  f     ð 3 Þ By selecting the fluid and the material for the flyerplate, one can determine the thickness of the flyerplate such that exponential pressure decay withcharacteristic time  t  0  is achieved. For example, the Fig. 2  Fluid–structure interaction ( FSI  ) experimental configuration Fig. 1  Underwater blastloading onto a naval hullstructure. Geometrical con-siderations ( left  ), and pres-sure history ( right  )Exp Mech (2006) 46: 805–824 807 SEM  pressure profile generated by the impact of an Al flyerplate, 5.3 mm-thick, against water is shown in Fig. 3.Selection of the initial pressure  p 0  determines theinitial impact velocity  V  0  according to equation (2).The above simple analysis shows that a flyer platelaunched by a gas gun against water contained in ananvil can be employed to generate an exponentiallydecaying pressure history in lieu of explosive loading.The FSI experimental setup is instrumented withseveral sensors to measure the pressure history andother variables of interest, Fig. 2. The impact velocityof the flyer plate is measured by a contact-pin typevelocity sensor [3]. The pressure history in the water isrecorded by dynamic high pressure transducers and adigital oscilloscope while the deflection history of thespecimen panel is measured optically by shadow moire´ using a Cordin Intensified CCD Camera 220-8 high-speed camera.Scaling IssuesThere are other design parameters to be determinedfor simulating the full scale phenomena with the abovelaboratory FSI setup: sample panel radius  R , samplepanel thickness  h , sample panel material propertiessuch as density,  r , yield stress,  s   y , and length of theanvil  L a . Note that the gas gun system utilized in thisinvestigation has the following dimensional limitations:(a) the inside diameter of the gas gun barrel is 3 ^  (76.2mm), which limits the size of the impacting flyer plateand the inside diameter of the anvil at the impact end;and (b) the inside dimension of the target chamber(approximately 900 mm in length) which limits thelength of the pressure tube. In full scale applications,panels of 2 m in width and 2.54 cm in thickness aretypically employed. Hence, scaling down is essential inthe development of FSI experiments.For simplicity, in the scaling analysis a solid plate isconsidered as a sample panel. The optimizationcriterion is based on the maximum deflection of thesystem normalized by the span of the structure.However, the analysis is valid also for sandwich beamsof various cores and other type of structures. Followingthe non-dimensional study by Xue and Hutchinson [21,22], key dimensionless parameters relevant to theproblem are:  M  .  r R ; t  .  R  ffiffiffiffiffiffiffiffiffiffi ffi  r  s   y q   ;  I  .  M   ffiffiffiffiffiffiffiffiffiffiffi s   y   r q   , which definedimensionless mass per unit area, dimensionless timeand dimensionless impulse, respectively. If we keepthese parameters the same between full scale applica-tion and the laboratory experimental setup, we have: M   ¼  r h ; M    r R  ¼  h = R  ð 4 Þ t R  ffiffiffiffiffiffiffiffiffiffi ffi  r  s   y q 0B@1CA E  ¼  t R  ffiffiffiffiffiffiffiffiffiffi ffi  r  s   y q 0B@1CA F  ð 5 Þ  I M   ffiffiffiffiffiffiffiffiffiffi ffi s   y   r q 0B@1CA E  ¼  I M   ffiffiffiffiffiffiffiffiffiffiffi s   y   r q 0B@1CA F  ð 6 Þ where the subscript  E   denotes  B experiment ^  and  F  B full scale. ^  If the material employed in the experi-ments is the same as the one employed in the full scaleapplication, the above conditions reduce to: hR   E  ¼  hR   F  ;  h E   ¼  1 K  h F  ;  t R   E  ¼  t R   F  ; t  E   ¼  l K  t  F  ;  I h   E  ¼  I h   F  ;  I  E   ¼  1 K  I  F  ; where  K  = R F  / R E   is the ratio of full scale and experimen-tal panel radii (half span). Hence, for a full fielddimension, the scaling factor  K   is determined by thepanel size employed in the laboratory experiments. If thediameter of the specimen is selected as 76.2 mm, which isthe maximum possible size of the flyer plate (limited bythe diameter of the gun barrel), the scaling ratio wouldbe 2,000/76.2=26.2. Therefore, a 25.4 mm thick solidplate is scaled down to 25.4 mm/26.2=0.97 mm, which isquite thin for accurate manufacturing and testing. Notethat a sandwich panel specimen with the same mass perunit area would have face sheets thinner than 0.32 mm,which is very difficult to manufacture and test.To obtain a more suitable scaling factor, the scalingof the plate diameter  D  (or 2 R ) should overcome thedimensional limitation imposed by the flyer plate size.A diffuser-type pressure tube allows the implementa- 10 20 30 40 50Time (  µ s)    N  o  r  m  a   l   i  z  e   d  p  r  e  s  s  u  r  e  p   /  p   o Fig. 3  Pressure profile at the water surface imposed by theimpact of a 5.3 mm-thick Al flyer plate808 Exp Mech (2006) 46: 805–824 SEM
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