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Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
Studies on geometrical featured metallic shell structures for inward inversion
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Studies on geometrical featured metallic shell structures for inward inversion

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  • 1. INTERNATIONAL JOURNAL OF CIVIL ENGINEERING AND International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME TECHNOLOGY (IJCIET)ISSN 0976 – 6308 (Print)ISSN 0976 – 6316(Online)Volume 3, Issue 2, July- December (2012), pp. 251-264 IJCIET© IAEME: www.iaeme.com/ijciet.htmlJournal Impact Factor (2012): 3.1861 (Calculated by GISI) IAEMEwww.jifactor.com STUDIES ON GEOMETRICAL FEATURED METALLIC SHELL STRUCTURES FOR INWARD INVERSION Ram Ranjan Sahua, Dr. Pramod Kumar Guptab a PhD scholar, Civil Engineering Department, IIT Roorkee, India (Working as Assistant General Manager in Engineering Research Centre of TATA Motors- Pune, through Tata Technologies, Pune, India) A1-404, Kumar Prerana, Aundh, Pune (MH), Pin 411007 India Email: RamRanjan.Sahu@tatatechnologies.com b Associate Professor, Structural Engineering Department of Civil Engineering, IIT Roorkee, (Uttarakhand), Pin 247667 India Email: pkgupfce@iitr.ernet.in ABSTRACT The geometrical inward inversion studies were planned on the metallic shell geometries. These geometries are circular in shapes. They are closed at the top and open at the bottom. In between top and bottom faces, the geometrical features are changed from sample to sample. Feature changes are in shape, apical angle, steps, thickness etc. Studies were made to see how these features play role in inversion process of large deformation. Force stroke graphs were plotted for featured samples and discussed in details for deformation characteristics. Comparative analysis is done for samples in context to energy absorption. The analytical simulations were also done for experiments. Good correlations were found with experimental results. The parameters which could not be obtained physically could be simulated analytically for parametric studies. This paper also gives a guide line on parameters to be taken for good energy absorption, in inward inversion process. Keywords: Large Deformations, Shell structures, Energy absorption, load-deflection, Finite Element analysis I. INTRODUCTION The geometrical inward inversion is of great interest for researcher in the field of energy absorption phenomenon. Alghamadi [1] paper reviews the common shapes of collapsible energy absorbers and their different modes of deformations. Also Alghamdi [2] introduced direct inversion method on frusta. Aljawi et al. [3] simulated the inversion collapse process 251
  • 2. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEof frusta, through finite element analysis using ABAQUS software. Good agreement wasobtained between experimental results and theoretical predictions. Further inversion studieswere done on frusta during axial crush, by Aljawi and Alghamdi [4]. Reid [5] reported one ofthe interesting energy absorber by tube inversion which basically involves the turning insideout of a thin circular tube made of ductile material. This deformation process gives constantinversion load for a uniform tube. Collapse studies on varying wall thickness of metallicfrusta subjected to axial compression was done by P. K. Gupta [6]. The mode of collapseforms by the development of one concertina fold followed by the plastic zone. During thedevelopment of mode of collapse some portions of the frusta move radially inward and someradially outward. Nia and Hamedani [7] studied the axial crushing on various section shapes(circular, square, rectangular, hexagonal, triangular, pyramidal and conical etc) made ofaluminium sheets of 1 and 1.5mm thickness. They investigated that in axial quasi-static tests,the larger the number of section edges, the greater the energy absorption capacity. This is dueto an increase of the number of folds and plastic hinges in sections with larger number ofedges. For their test the absorbed energy per unit mass was maximum for cylindrical tubes. NK Gupta et al. [8] Studied on collapse behavior of thin spherical shells under quasi-staticloading. Also three-dimensional numerical simulations were carried out for all the specimenstested under quasi-static loading using ANSYS. They found that the relatively thick shellsdeform axi symmetrically and major load is absorbed by the rolling plastic hinges. When thethickness is reduced considerably, the inward dimpling is followed by non symmetricmultiple number of lobes which are caused by the formation of stationary hinges. The shape, size, material, geometrical features could affect the inversion phenomenon alot. Few samples which were studied are shown in Figure 1, having different shapes andgeometrical features. Figure 1: Test samples shape II. EXPERIMENTS2.1. Experimental setupThe experiment setup consist of 1) Machine to apply load Samples were inverted at quasi-static condition by the use of a 4-ton Instron universaltesting machine (UTM), at a constant plunger crosshead speed of 15 mm/min. The plungercan go up down by 125mm from its mean position. Hence it may happen that the start of 252
  • 3. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEgraph can be from any +/- position depends on position of plunger, for that sample. Theschematic of test setup is shown in Figure 2. Figure 2: Schematic of Test set-upThe alignment of sample and its fixture is assured with machine axis. 2) Fixture to hold and position the sampleTop fixture is inversion rod whose one end is fixed to load cell of UTM and other end fixedto the top of model, through washers. The bottom fixture consists of cylindrical vessel andlocating ring. The locating ring rests on the top of the vessel through stoppers. Vessel is kepton moving ram of machine. The Photograph of test setup along with bottom fixture andlocating ring is shown in Figure 3. a) b) c) Figure 3: Photograph of a) test set-up b) bottom fixture and c) locating ring 253
  • 4. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME 3) Test Samples The aluminum test samples of different shapes, having different geometrical features in it,were picked up from market, where these were readily available. They have 11 categoriesbased on shape and features, as shown row wise and in increasing order towards right side, inFigure 4. Figure 4: Test Samples 254
  • 5. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME2.2. Material properties The tensile test pieces were cut directly from the sample and shaped with dimensions asper ASTM E8 [9] specifications. These test pieces were tensile tested with standard tensiletesting machine at room temperature. The typical stress strain graph is shown in Figure 5. Figure 5: Stress-strain graphs for the sampleFrom the graph, the material tensile strength is 55 N/mm2 @ 4% elongation and 0.2% proofstress is 45 N/mm2.Since top and bottom fixture were made of steel, these were supposed to very rigid ascompared to model.2.3. Experimental results The typical force-displacement (F-H) graph is shown in Figure 6 for the sample category7. Forces are measured in kN and displacement (machine stroke) in mm, hence here afterthese units only are referred. Figure 6: Typical F-H graphThe shapes of the graphs are similar for other category of samples. The deformation stages ofsample are also depicted in figure for easy understanding. The load quasi statically rises frompoint 1 to 2 as shown in Figure 6, to a maximum value to point 2. This is the force required to 255
  • 6. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEgenerate the plastic zone at the top cap end. Afterwards it decreases, which is the indicationof start of the inversion process. This is shown from point 2 to 3. On further load application,the graph nature depends on the geometrical features. It may go up and down depending onrolling hinges volume, as well can be shaky in shape, based on wavy nature of geometry. Therepresentation of each samples category while testing are shown in Figure 7 a to c. In thisfigure, the photographs of the samples are shown on its initial, mid and final stages ofdeformations. Also corresponding load displacement (F-H) graph are shown in extreme rightside. Prefix S suffix, prefix=sample category, S=sample, suffix=sample no Figure 7a: Sample category 1 to 3 256
  • 7. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME 7s1 Prefix S suffix, prefix=sample category, S=sample, suffix=sample no Figure 7b: Sample category 4 to 9 257
  • 8. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Prefix S suffix, prefix=sample category, S=sample, suffix=sample no Figure 7c: Sample category 10 to 11The samples test results are enlisted in Table 1. In this table the samples stroke, theirinversion length, specific energy and average force of the process is tabulated. Table 1: Test results The sample category 1 has shape of frusta with apical angle of 6 to 7 degree. On loadapplication it gives typical and smooth F-H graph (refer Figure 7a). Also from Table 1, this 258
  • 9. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEMEgeometry gave highest energy absorption as compared to other samples. The samples 9s1,9s2, 8s4 having step features (figure 4), gave very less specific energy as compared to othersamples. Refereeing sample category 3 of figure 7a, the local crushing took place. Since noinversion process could be started, rather local crushing yielded a quite shaky graph. Thoughits specific energy content is high, it cannot be used as energy absorber, whose basicrequirement is smoothness in F-H graph.III. FINITE ELEMENT SIMULATION Finite element simulation was used to simulate the models inward inversion process. Itwas also used for weight calculation up to deformed portion of the samples. FE simulationscould be used to study in details, about the model deformation phenomenon, to extract salientfeatures during experiments like deformation, its effort, energy associated, correlation to testdata like F-H graph etc. HyperMesh [10] is used for FE model building. Aluminum modelswere represented with 4 node shell elements at mid plane surface. The locating ring andfixtures were represented with rigid elements representation. The LsDyna [11] explicit solverwas used to solve the problem. The material models *MAT_RIGID was used for fixtures and*MAT_PIECEWISE_LINEAR_PLASTICITY was used for samples. The contact type*CONTACT_AUTOMATIC_SURFACE_TO_SURFACE was used to define contactsbetween disjoint parts. Also for self contact*CONTACT_AUTOMATIC_SINGLE_SURFACE was used. Coulomb friction type wasused to define the coefficient of friction between samples and fixtures. Fig. 8 shows the FEshell model and its deformed cut section is compared with actual sample cut section. Shellelement formulation choosen was Belytschko-Tsay because of its less computation cost withgood accuracy. FE model fully represent the sample and simulate the experimental process.Result interpretation was done through LS-PREPOST. Figure 8: FE model and cut section comparison3.1. Simulation results The energy balance graph of FE simulation for sample 7s1 is shown in Figure 9. From thegraph it is evident that the unwanted energies like kinetic energy, Hourglass energy, slidingenergy are minimum in the simulation. Hence the total energy is contributed only throughsample internal energy, which is caused by deformation. This graph represent perfect energybalace of FE simulation and hence ensure the correctness of simulation 259
  • 10. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Figure 9: Energy balance of FE simulationThe FE simulated F-H graph and vonMises stress contour at different deformation stages isshown in Figure 10 for sample 7s1. The F-H graph resembles to experimental graph. The redcolored stress indicates the formation of plastic zone. The drift of hinges which rolls from topto bottom can be clearly seen in this figure. Figure 10: FE simulated F-H graph and Stress contourIV. DISCUSION Referring Figure 7b, the sample category 4 wherein at the top, a wavy geometricalfeatures (curvature radius=3 mm, height=5 mm, numbers=3) exists, its F-H graph also havewave, having 3 peaks. This waviness is attributed to the change in hinges volume due towavy geometry. Sample category 9 have step of 2 mm at the height of 55 mm from base. On loadapplication it buckles at this step location. Hence the corresponding graph also have suddendeep gradient from point 2 to 3. Similar behavior is also noticed in sample 8s5. The sample 9s4 buckled at mid featured location, yielding very wavy graphs due to localcrushing as shown in Figure 11. 260
  • 11. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Figure 11: Buckling at feature The effect of apical angle change, on F-H graph is shown in Figure 12. The up gradient innoticed in graph for 5 degree (sample 2s2) while it is down gradient for sample 11s1, whoseapical angle is 8 degree. Figure 12: Effect of apical angle change on F-H graph A plateau is noticed on F-H graph at point 2, for samples (8s1, 8s2) having straightportion at the top end as shown in figure 13. This plateau is due to good resistance offered bystraight portion after onset of plastic zone (point 2). 261
  • 12. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Figure 13: Effect of top straight portion on F-H graph Thickness of sample play important role in energy absorption. Its effect on F-H graph canbe seen in Figure 14. More the thickness more is the energy absorption. The energy absorbedby sample 2s2 (thickness=0.95 mm) is 4.22kJ/kg, while it has increased to 6.23kJ/kg forsample 2s3 whose average thickness is 1.3 mm. Figure 14: Thickness effect on F-H graph The energy absorption in different stages of deformations (sample 7s1) was compared forexperimental and numerical simulation. Results matched well as shown in Fig. 15. Thisshows that the numerical simulations where material properties are taken from the test,geometrical representations and boundary conditions assumptions are perfectly all right. 262
  • 13. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME Figure 15: Energy absorption comparisonCONCLUSION Experimental and computational studies of inward inversion on featured geometries weredone. It was found that all geometry has undergone the inward inversion process properly,except those who had features like step and wave patterns. Step feature invited a localbuckling while wave feature yielded waviness in F-H graph or started local crushing. Also itis noticed that the less the apical angle of geometry, more is the energy absorption capacity.A Finite Element computational model of the development of inward inversion mode is alsopresented. The FE deformation and actual deformation shape matched well. Also FE could befor weight calculation of deformed portion of samples.ACKNOWLEDGEMENTS The authors gratefully acknowledge the support of engineering research centre of TATAMotors at Pune, for the supporting experimental works. Also thanks to the proto shop forfabrication of fixtures and material testing group for getting the material non linear propertiesthrough test.REFERENCES[1] Alghamdi AAA (2001), “Collapsible impact energy absorbers: an overview”. Thin-Walled Structures, Vol.3, No.2, pp. 189–213.[2] Alghamdi AAA (1991), “Design of simple collapsible energy absorber, Master of ScienceThesis", Jeddah, Saudi Arabia: College of Engineering, King Abdulaziz University[3] Aljawi AAN, Alghamdi AAA (1999), “Investigation of axially compressed frusta asimpact energy absorbers, In: Gaul L, Brebbia AA, editors. Computational methods in contactmechanics IV. Southampton: WIT Press, pp. 431–43.[4] Aljawi AAN, Alghamdi AAA (2000), “Inversion of frusta as impact energy absorbers”,In: Hassan MF, Megahed SM, editors. Current advances in mechanical design and productionVII. New York: Pergamon Press, pp.511–9.[5] Reid SR (1993), “Plastic deformation mechanisms in axially compressed metal tubes usedas impact energy absorbers”, Int J Mech Science, Vol. 35. No. 12, pp. 1035–52.[6] P.K. Gupta (2008), “A study on mode of collapse of varying wall thickness metallic frustasubjected to axial compression”. Thin-Walled Structures, Vol.46, pp. 561–571. 263
  • 14. International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print),ISSN 0976 – 6316(Online) Volume 3, Issue 2, July- December (2012), © IAEME[7] Nia and Hamedani (2010), “Comparative analysis of energy absorption and deformationsof thin walled tubes with various section geometries”, Thin-Walled Structures, Vol.48,No.12, pp. 946-954.[8] N.K. Gupta, N. Mohamed Sheriffb, R. Velmurugan (2008), “Experimental and theoreticalstudies on buckling of thin spherical shells under axial loads”. International Journal ofMechanical Sciences, Vol.50, pp.422–432.[9] ASTM International: ASTM E8 / E8M - 09 Standard Test Methods for Tension Testing ofMetallic Materials[10] HyperMesh11. A product of Altair Engineering HyperWorks[11] LsDyna software and its user manuals. Livermore Software Technology Corporation,Livermore, California 94550-1740. 264

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