Finite Elements Method in Split Hopkinson Pressure Bar developing process

Transcription

1 6th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING, Venice, Italy, November 1-3, Finite Element Method in Split Hopkinon Preure Bar developing proce ROTARIU ADRIAN *, BUGARU MIHAI **, CHERECHEŞ TUDOR * * Department of Mechanic, ** Department of Mechanic * Military Technical Academy, ** Politehnica Univerity of Bucharet * George Cobuc Avenue 81-83, Bucharet, ** Splaiul Independenţei 313, Bucharet ROMANIA arotariu99@yahoo.com, bugarum@yahoo.com, chereche@mta.ro Abtract: - A erie of FEM imulation of SHPB tet were ued in deigning of Split Hopkinon Preure Bar equipment and it dedicated oftware, developed in Impact Laboratory, a facility of Military Technical Academy. In thi paper are analyzed and evaluated by the imulation mean three major topic: quality of acquired data mathematical proce, practical SHPB tet iue (projectile impact, additional pecimen load and impact) and pule haping technique. The ued model in imulation were axial ymmetric. Key-Word: - FEM, imulation, SHPB, impact, validation algorithm, SPH 1 Introduction An important tep in deigning of tructure capable to upport high train rate load i numerical imulation of tructure behavior in actual working condition [1]. Knowledge about tructure material behavior i neceary to accomplih thi tep. One of the mot utilized laboratory method in material behavior analyi for high train rate procee i Split Hopkinon Preure Bar, SHPB. In lat two year a SHPB intallation and it dedicated oftware were developed in Impact Laboratory, a Military Technical Academy facility, Fig. 1. The developing proce contain a erie of validation and analyi tep, preented in paper, where we ued FEM imulation. The principle of SHPB i induction of a dynamic uniaxial tre tate in a material pecimen by two rod impact, Fig.. The impact create an elatic wave which travel the incident bar, reache the pecimen tranmitting a part of energy in tranmiion bar and reflect the ret. The train rate hitory and alo tre hitory of pecimen are obtained by meauring elatic deformation of input and output bar with train gage mounted on both bar. A oftware application wa developed in order to proce thee hitogram. Thi application wa tood to a validation algorithm, which implied a erie of SHPB imulation. Alo, during trial tet wa tudied if projectile i coaxial with incident bar at impact moment. A new method to verify impact quality wa et. A thin film of oil wa applied to terminal urface implied in impact proce. A uniform radial ejection of oil indicate a correct impact. A imulation of impact in preence of oil film wa created. The oil film wa modeled by SPH technique. In early tet of developed SHPB intallation were oberved, by video mean, multiple dynamic load of pecimen. In abence of other invetigation mean wa neceary to imulate the abovementioned tet in order to evaluate the multiple load effect on final pecimen dimenion. In order to prepare SHPB uing in ceramic material analyi, a pule haping technique baed on pule haper cruh wa imulated. Fig. 1. SHPB developed in Impact Laboratory Fig.. Schematic of Split Hopkinon Preure Bar

2 6th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING, Venice, Italy, November 1-3, Software application and it validation algorithm Accuracy of data acquired by train gage uffer motly becaue of the wave diperion and noie preence. Hence, before uing SHPB data in material model calibration, ome mathematical treatment i impoed in order to bring acquired data cloer to true pecimen deformation hitory. One of our goal wa to integrate mentioned above data proceing, together with material model calibration algorithm in an SHPB dedicated oftware application. Firt tep in data proceing i removal of undeired noie. The filtration i baed on Savitzky- Golay algorithm. From filtered ignal three fragment (incident, ε I, reflected, ε R, and tranmitted, ε T, wave) are iolated, repreenting the effect of pecimen preence on elatic wave propagation, fragment which give train rate and tre hitorie [], [ubcript indicate pecimen propertie and b mean bar propertie]: Ab σ = Eb ε T (1) A C ε () ε 0 = L t R C0 ε = ε Rdt (3) L 0 Approach ued to fitting a nonlinear material model (e.g. Simplified Johnon-Cook Model) to SHPB data i the minimum chi-quared method [6]. It i aumed that the model choued i able to predict the value of the meaured data. For each meaured datum x i,, the model provide a value y i in term of the SHPB experiment and a parameter vector a, repreenting the material model. The parameter that bet fit the data are typically taken thoe that minimizeχ [ xi ( )] = yi a χ (4) σ i i where σ i i the expected rm deviation of the meaurement d i. The vector which minimize the value of relation (4) i etablihed following the Levenberg-Marquardt algorithm. In thi way the model material parameter are determined, Fig. 4. Software application ued in cientific reearch area impoe a critical aement of their capacity to extract true material model coefficient. In our cae the aement follow an application validation algorithm developed by author and hown in thi paper. The algorithm conit in extraction of material model parameter from a erie of SHPB tet imulation reult, run under LSDYNA, and comparion with initial value inputted in imulation. Each one of them i proceed in order to eliminate the effect of diperion on wave hape, a pecific phenomenon to wave propagation in bar [3,4], following Gorham algorithm [5] baed on Fat Fourier Tranform analyi. Uing corected reflected and tranmitted wave in equation (1) (3) are obtained tet pecific hitogram, Fig 3. Fig. 4 Material model parameter identification window Input model Simulation 1 Simulation Axial tre hitorie 1 Axial tre hitorie Software application Simulation 3 Axial tre hitorie 3 Output model Fig. 3 Main window of SHPB tet data proceing Fig. 5. Application validation algorithm

3 6th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING, Venice, Italy, November 1-3, In a erie of three SHPB tet imulation, run under LS-DYNA, wa input a pecimen material a JC-S model repreenting 1006 teel propertie [7]. The moving element of SHPB intallation are coaxial. Thi permitted to ue a D axial model with hell element. The finite element model were created for the ame SHPB tet only one parameter being modified, impact velocity, from 10 m/ to 15 and 0 m/. The bar radiu wa taken at 10 mm, projectile length at 50 mm and incident and tranmitted bar length at 000 mm. The maximum meh ize inide the bar wa etablihed at 1 mm, fallowing the Zenker obervation [8]. The bar material i a high-trength teel (yield point GPa) with Poion ratio v 0 = 0.30 and ma denity ρ 0 = 808 kg/m 3. The pecimen dimenion utilized in imulation were 5 mm for radiu and 5 mm for diameter, with a meh ize of 0.5 mm. At the pecimen-bar interface i no friction contraint. Geometric detail of model are preented in Fig.. The imulation erie reult covered train rate interval from 10 3 to 3*10 3-1, maximum platic train value achieved being around In Fig. 6 the imulation reult for 15 m/ impact velocity are preented. Fig. 6. Simulation reult repreenting true tre, true train rate and true train hitogram for 15 m/ impact velocity Model Known parameter parameter Fitted parameter A [MPa] B [MPa] n [none] C [none] Input model Output model Table 1 Input and Output model The reulted hitogram of axial elatic train in incident and tranmiion bar [ee (a) and (c) in Fig. ] were input in oftware application a pecific ASCII file. The material parameter fitted repreent output model. Thee two model, input and output were compared in Table 1. The difference found are very mall except B coefficient were the difference i around 9%, tolerance accepted in high train rate load area. Axial tre hitogram in center of pecimen [ee (b) in Fig. ] wa ued a intermediate check point. Both imulation hitogram and application reulted hitogram, for 15 m/ impact velocity imulated cae, are preented in Fig. 7. Graphic comparion how good agreement between thee two hitogram. 3 Analyi of impact in oil film preence An iue tudied during trial tet wa projectile poition at impact moment. A condition for correct tet et-up i that the projectile to be coaxial with incident bar at impact moment. In order to verify impact quality a thin oil film wa applied to terminal urface implied in impact proce. A uniform radial ejection of oil indicate a correct impact, Fig. 8. In order to evaluate in a qualitative way the ejection proce a imulation of impact in preence of oil film wa created. The oil film wa modeled by SPH technique. The film thickne wa etablihed at 0.1 mm and SPH dimenion at 0.01 mm. To imulate oil vicoity wa ue a vicoelatic model with tatic hear elatic modulu G 0 = 0 MPa. The vicoity wa et to 0.1 Pa. The hydro tenile limit value wa et to 0 MPa. In Fig. 9-1 are preented detail of the ejection proce imulation for 10 m/ impact velocity. Fig. 7. Comparion of pecimen tre rezulted from imulation and computed from application Fig. 8 Uniform radial oil film ejection at impact

4 6th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING, Venice, Italy, November 1-3, Fig. 9 Detail of initial SPH configuration Fig. 10 Detail of modified SPH configuration Fig. 13 VISION XS camera recorded image Fig. 11 Oil ejection in early tage of impact proce Fig. 1 Oil ejection at final tage 4 Additional load and impact Trial tet on copper pecimen, recorded with high VISION XS, a high peed camera, how that pecimen uffer a erie of additional impact, Fig. 13 (3000 frame/econd, from right to left). At that moment of tet evolution the acquired data by train gage mean ha no relevance in etimation of the effect of additional impact on pecimen deformation tate. The wave diperion and wave uperpoition make impoible a correct data interpretation. Intead to ue train gage data the tet were imulated (D, axial ymmetric) and platic train evolution in pecimen wa analyzed. The bar were modeled in the ame way a for validation algorithm with a ingle modification. The projectile length wa 400 mm, dimenion which correpond to real projectile. The teted cooper pecimen had 10 mm length and 10 mm diameter. The pecimen geometry ued in imulation take in to conideration thee data. At the pecimen-bar interface Coulomb friction i aumed at 0.05 a

5 6th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING, Venice, Italy, November 1-3, contact urface were lubricated with mineral oil. For the pecimen material wa ued a Johnon-Cook model pecific to annealed cooper with platic limit et to 90 MPa. The additional load or impact are indicated by hift value of pecimen kinetic energy [e.g. Fig. 14]. The additional impact effect on pecimen are indicated by accumulated pecimen platic work. In imulation were recorded the effective platic train evolution in gage point (b), Fig.. In ome imulated cae the reult indicate major effect of additional impact on pecimen, the effective platic train evolution preent a econd hift after the hift which correpond to initial load. In Fig. 15 i preented evolution of effective platic train in gage point for 10 m/ velocity impact. The econd hift correpond to a econd load. For the ame gage the axial tre hitory i preented in Fig. 16. There are two time period when platic limit i exceeding, period which correpond to firt and econd load. After the econd load tre value are relatively mall, platic limit exceed no more. A platic train hift and repectively a pecimen platic work hift mean pecimen dimenion changing. Fig. 16 Axial tre (MPa) in gage point 5 Pule haping technique imulation The model of conventional SHPB wa modified by placing pule haper dik with different ize between projectile and incident bar. Thi modification make able tudy of the elatic and early yield behavior of pecimen by haping different elatic incident pule [9]. For the pule haper dik material wa ued a Johnon-Cook model pecific to annealed cooper with platic limit et to 90 MPa. In Fig. 17 i preented the model with the pule haper [green box] original thickne and diameter of mm and 6 mm, repectively. Hitory of axial tre recorded in incident bar at 400 mm from impact point, for 17 m/ impact velocity, i how in Fig. 18. Fig. 14 Kinetic energy (mj/rad) for 10 m/ impact velocity cae a) b) Fig. 17 Initial (a) and final (b) dik dimenion Fig. 15 Effective platic train at gage point Fig. 18 Incident bar haped axial tre

6 6th WSEAS International Conference on SYSTEM SCIENCE and SIMULATION in ENGINEERING, Venice, Italy, November 1-3, Concluding remark From validation algorithm reult wa found that oftware application developed enure a good confidence in aociated material parameter fitting proce. The SPH technique wa found to aure a good qualitative repreentation of oil ejection proce. The reult of additional load and impact imulation indicate to take precaution before uing final dimenion of pecimen in material behavior analyi. The impact imulation in preence of pule haper dik how that a wide variety of incident elatic pule can be produced by varying the geometry of the cooper dik and the length and triking velocity of projectile. Reference: [1] Rotariu A., Hazell P. J., Cernat M., A Numerical Study on The Effect Of Exploive Reactive Armour on a Lightweight Armoured Vehicle Hull, Journal of Battlefield Technology, Vol. 8, No., 005, pp. 1-5, [] Frew D. J., Forretal M. J. & Chen W., Pule haping technique for teting elatic-platic material with a Split Hopkinon Preure Bar, Experimental mechanic, Vol. 45, No., 005, pp [3] Tya A., Pope D. G., Full correction of firtmode Pochammer Chree diperion effect in experimental preure bar ignal, Meaurement cience and technology, Vol. 16, No. 3, 005, pp [4] Govender R. A., Cloete T. J., Nurick G. N., A numerical invetigation of diperion in Hopkinon Preure Bar experiment, Journal de Phyique IV, Vol. 134, 006, pp [5] Gorham D. A., A numerical method for the correction of diperion in preure bar ignal, Journal of Phyic E: Scientific Intrument, Vol. 16, No. 6, 1983, pp [6] Hanon K. M., Hemez F. M., Inference about the platic behavior of material from experimental data, Senitivity analyi of model output, Proceeding of the 4th International Conference on Senitivity Analyi of Model Output, 004, pp [7] ANSYS Inc., Any L-dyna uer guide, 005. [8] Zencker U., Clo R., Limiting condition for compreion teting of flat pecimen in the Split Hopkinon Preure Bar, Experimental mechanic, Vol. 39, No. 4, 1999, pp [9] Frew, D. J., Forretal, M. J., Chen W., Pule haping technique for teting brittle material with a Split Hopkinon Preure Bar, Experimental mechanic, Vol. 4, No. 1, 001, pp