Identification of Ductile Damage Parameters for Austenitic Steel

Transcription

1 Identifiation of utile amage Parameters for Austeniti Steel J. zugan, M. Spaniel, P. Konopík, J. Ruzika, J. Kuzelka Abstrat The modeling of inelasti behavior of asti materials requires measurements providing information on material response to different multiaxial loading onditions. ifferent triaxiality onditions and values of Lode parameters have to be overed for omex desription of the material asti behavior. Sames geometries providing material asti behavoiur over the range of interest are proposed with the use of FEM analysis. Round sames with 3 different nothes and smooth surfae are used together with butterfly type of sames tested at angle ranging for to 9. Identifiation of dutile damage parameters is arried out on the basis of obtained experimental data for austeniti stainless steel. The obtained material asti damage parameters are subsequently apied to FEM simulation of nothed CT normally sames used for frature mehanis testing and results from the simulation are ompared with real tests. Keywords baqus, austeniti steel, omputer simulation, dutile damage, triaxiality. T I. INTROUCTION HE omputer simulations in the field of design and safety assessment represent very powerful tools, but are strongly limited by available material models and material input data. Most of the urrent alulations are performed on the basis of standard tensile tests, if not only on database data or data from literature. Suh a material desription is not suffiient for aurate design assessment. Standard tensile test is mainly based on uniaxial same loading and more omex loading appears after material neking, in ase of dutile materials. However, the state after neking is not properly evaluated by standard testing proedure using mehanial extensometer for strain measurement. The standard tensile test results are useful for elasti solutions or elasti-asti solution for small asti strains. If states near to frature are to be onsidered, more omex material desription is neessary, taking into aount multiaxial loading onditions [1]-[5]. Thus sames of various geometries and tested under various loading modes has to be used. On the basis of these tests a omex material behavior model overing elasti and asti material behavior for various triaxiality states an be obtained. This would allow a wide range of apiation from alulation of omponent limit loading onditions, over alulation of the properties, that ould not be diretly measured on available amount of the experimental material in ases when restrited amount of the materials is available, to material properties onversion for sames of different sizes. Current paper is dealing with dutile damage parameters determination for austeniti steel. There will be hosen appropriate sames geometries based on the FEM stress state analyses of sames at first. Subsequently testing of proposed sames is performed and material parameters are evaluated. The obtained material asti damage parameters are subsequently apied to FEM simulation of nothed CT sames used for frature mehanis testing and results from the simulation are ompared with real tests of the same simulated. II. AL SAMPLES PROPOSAL The modeling of inelasti behavior of asti materials requires measurements providing information on material response to different multiaxial loading onditions. This an be obtained by various sames geometries and loading modes resulting in different stress triaxialities and values of Lode parameter. On the basis of literature survey [1]-[9] there were proposed sames geometries that were subsequently analyzed with the use of FEM and triaxiality and Lode parameter were identified for these sames. Finally, following set of sames was proposed for dutile damage material parameters desription: smooth tensile sames, nothed tensile sames with noth radius 1, and mm and butterfly type of speimens used in [7]. Tensile sames were in all ases of minimal diameter 1mm. Butterfly sames were proposed to be used at angles, 3, 5, 7, and 9 in tension. This set of sames was supposed to over neessary range of triaxialities and values of Lode parameter. Sames geometries are shown in Figs. 1. J. zugan is with the COMTES FHT In., obrany, 33 1, The Czeh Republi (phone: ; fax: ; jan.dzugan@omtesfht.z). M. Spaniel is with Czeh Tehnial University, Prague, The Czeh Republi. ( miroslav.spaniel@fs.vut.z). P. Konopík is with the COMTES FHT In., obrany, 33 1, The Czeh Republi ( pavel.konopik@omtesfht.z). J. Ruzika is with Czeh Tehnial University, Prague, The Czeh Republi. ( jan.ruzika@fs.vut.z) J. Kuzelka is with Czeh Tehnial University, Prague, The Czeh Republi. ( jiri.kuzelka@fs.vut.z) Fig. 1 Quarter of nothed tensile same 1mm noth radius 3

2 R R1 R R Fig. Butterfly same III. TESTING There are tensile tests and tests of butterfly type of sames to be exeuted. In the ase of tensile sames, standard proedure and fixtures an be emoyed. While in the ase of butterfly type of sames, testing fixture had to be designed at first and subsequently manufatured prior to tests exeution. The fixture preparation was suessfully ometed and fixture was suessfully tested in the testing system. All urrent tests were done under quasi-stati loading onditions at room temperature on servohydrauli testing system MTS. In order to obtain maximum information from the tests, next to standard mehanial extensometer also high speed amera was used for all tests. The reordings enable later evaluation of strains at ertain points and evaluation of neking during tensile tests. In the ase of butterfly sames disaements at six points diretly on the same were determined. Testing set up for butterfly sames is shown in Fig. 3. Fig. 3 Testing set up for butterfly sames Reords obtained for round sames and butterfly type of sames is shown in Figs. and Fig. Reords of tensile tests Butterfly Buttefly 3 Butterfly 5 Butterfly 7 Butterfly Butterfly 9 Fig. 5 Reords of tests of Butterfly type of sames tested at different angles It appears to be useful to have for the first guess of the astiity urve determination a true stress - true strain diagram, thus there was additionally measured smooth tensile same with video reording for this purposes. This test was exeuted with partial unloadings that were aimed to be used for damage evaluation, but this evaluation was not performed so far. Evaluated true stress-true strain diagram is shown in Fig.. True Stress [MPa] 1 1 1,,,, 1 True Strain [1] Fig. Measured True stress true strain diagram 35

3 IV. UCTILE AMAGE PARAMETERS IENTIFICATION In the urrent investigations standard simified model of metal astiity is used, based on the seond deviatori stress invariant. The model is using von Misses astiity ane with assoiated law of asti flow with isotropi hardening. This simified model shall yield satisfatory results for onsidered monotoni loading. The simulations are done in ABAQUS. Continuum damage onept is assuming that response of damaged material is based on the response of the original material. Geometri and physial damage parameters are not desribed on the miro sale, but are using a fitive salar damage parameter ω, that an be expressed by aumulation of asti deformation, Eq. 1. parameters that, if used for FEM simulation, provide as lose results to real tests as possible. The measure of alibration auray is area between measured and alulated urve fore versus disaement as shown in Fig. 7. The smaller area, the better is the alibration. = & (1) ( ) ω f p, q, ξ, T,, d where is: p hydrostati pressure q Von Misses stress invariant ξ Lode parameter T temperature strain & strain rate Failure riterion is usually expressed in normalized form ω =1. In the ases where damage had feedbak to material elasti-asti behavior, oued model is onsidered for ontinuum damage, otherwise there is unoued model. The experimental findings in the field of metals dutile damage have shown that the seond deviatori stress invariant has influene on the failure as well as hydrostati pressure and Lode parameter [1]-[5], [7]. The hydrostati pressure is overed by triaxiality whih is expressed in following form: η p q Thus the Eq. 1 an be rewritten into: = () = & (3) ( T ) ω f η, ξ,,, d If damage proess in the ourse of deformation is evenly distributed, the funtion f is independent of strain level, it is possible to desribe damage by: where ω d η ξ = & (,, T, ) () is aumulated asti deformation intensity at whih failure takes ae if onstant values of η, ξ, Τ and. are used for hypothetial alibration experiment. Calibration parameters of astiity and damage are searhed on the basis of real tests results and their FEM simulations. The aim of the alibration is to find material Fig. 7 Area between experimental and FEM urve Plastiity and dutile damage alibration is done with the use of open optimization sripts in Python, that an minimize the funtion by hange of the variables. The alibration sripts are based on simex algorithm of loal optimization. This algorithm allows simultaneous multie parameters optimization. The optimization unertainty and demand on omputing apaity is strongly inreasing with inreasing number of variable parameters. Therefore, there is always a tendeny to use model with minimum of parameters for optimization. isadvantage of the loal optimization is a high demand on the auray of the initial estimate of parameters. Simex algorithm assures loal minimum of target funtion only. The investigations here are performed with the use of ABAQUS FEM pakage. It has imemented fenomenologi model of ontinuum damage as an add-in to lassi metal astiity models. These models are not oued, thus there are higher requirements on the astiity models, but in the urrent ase of the monotoni loading, this obstale doesn t ay a signifiant role. The main problem is that there is not imemented Lode-parameter. In the urrent work Von Misses astiity model with isotropi hardening is used together with unoued dutile damage model. Taking into aount slow monotoni loading at room temperature, one an rewrite Eq. into following form: ω = d (, =, & ) η T C The above mentioned astiity model requires alibration of the atual yield stress in relation to aumulated asti energy intensity, whih an be expressed as: σ σ ( ) True True Y Y ln (5) = () 3

4 As an initial estimate of the relation of the atual yield stress on aumulated asti deformation, the true stress-true strain tensile urve of the smooth tensile same was used. There were apied two parametrization tehniques: 1. The urve is desribed by analytial funtion with parameters A, B and n. True n σy = A + B( ln ) (7). The urve is desribed by initial sequene of points True ( σ, ) Y σ ln i with variable parameters A, A 1, B: = A + A, ln, i B ln, i True True Y, i 1 σ Y, i = () Considering dependeny of material damage on triaxiality and Lode parameter, it is neessary to perform alibration experiments on sames with various pre-mentioned parameters. Plastiity parameters identifiation is done on the same sames population in order to assure the best average agreement of the asti response for varying material loading onditions. The alibration proedure is shematially desribed in Fig.. Fig. Calibration proedure It is lear from the Eq. 5, that failure desription has to be done on the basis of alibration of the aumulated intensity of the asti deformation in relation to triaxiality = ( η). Parametrization of this relation an be done for exame aording to Johnson-Cook model in following form: 1 e 3 = + η (9) Parameters 1, and 3 an be alibrated by target funtion minimization. * i d i, j F = 1 ωi, ωi = max j i ( ηi, j ) () where index i represents types of the experimental sames and j finite elements in target area of sames. With the use of above mentioned proedure dutile damage parameters were determined. A omparison of urves for seleted sames obtained with optimized set of parameters based on whole population of the experimental sames with experimental urves an be found in Figs. 9 to 15. j R CALIBRATE / Fig. 9 Comparison of the experimental urve with alibrated urve smooth same R1 CALIBRATE 1/ Fig. Comparison of the experimental urve with alibrated urve R R CALIBRATE / Fig. 11Comparison of the experimental urve with alibrated urve R R CALIBRATE,5 1 1,5,5 3 3,5 1/ Fig. 1 Comparison of the experimental urve with alibrated urve R 37

5 Comparison of the experimental and the alulated urves shows differene in disaement. This differene is originating from the fat that measured extension is taken from the rosshead and thus the whole testing system omianes are inluded in the reord. The optimization itself was done for asti part of the urve in oordinates fore versus asti deformation and there an be found signifiantly better agreement. A urve desribing astiity in relation to triaxiality was onstruted on the basis of the experimental tests and omputer simulation. The obtained urve is shown in Fig. 1. 1, 1, 1 Butterfly Calibrated,,,, 1 1, 1, Fig. 13 Comparison of the experimental urve with alibrated urve Butterfly 1 Butterfly 5 Calibrated,5 1 1,5,5 Fig. 1 Comparison of the experimental urve with alibrated urve Butterfly Butterfly 9 Plasti def. [1] 1,,,, _Round sames COMBINATION _Butterfly -,33 -,13,7,7,7,7,7 Triaxility [1] Fig. 1 Relation of asti deformation to triaxiality V. VERIFICATION The verifiation of the apiability of the identified dutile damage parameters for the investigated steel was done by omparison of experimental test of omex same with FEM simulation of the same same. As a verifiation same, Central Tension (CT) frature mehanis same of thikness 5,mm was used. The CT sames for the urrent purposes were nothed only without pre-rak. In this way large asti deformation at the noth tip were attained. Testing was performed with the apiation of the unloading omiane tehnique enabling rak length monitoring in the ourse of stable rak growth during the test. Reord of the test is shown in Fig. 17 together with results of FEM simulation. FEM alulation of the CT same was exeuted with identified dutile damage parameters. There an be seen very good agreement between measured and simulated urves. In the ourse of the test although large asti deformation, rak tip blunting appeared only. CT same after test together with FEM model at the same state are disayed in Fig. 1. CT same broken after test at liquid nitrogen temperature an be seen in Fig. 19. There is not visible any stable rak extension. 5 3 CALIBRATE 1 Calibrated Fig. 15 Comparison of the experimental urve with alibrated urve Butterfly / CO [mm] Fig. 17 Comparison experimental test of CT same and FEM simulation 3

6 ACKNOWLEGMENT This work was done within the work on the projet utile damage parameters identifiation for nulear power ants - FR-TI/79 sponsored by Ministry of Industry and Trade of The Czeh Republi. Fig. 1 Real same and FEM model at the end of test Fig. 19 CT same after test without stable rak growth VI. CONCLUSION The paper deals with dutile damage parameters determination for austeniti steel. There were proposed sames geometries with various states of stress triaxialities and values of Lode parameter at first. These various onditions are neessary if a broad range of asti behavior is to be overed. Round sames with nothes of radius 1, and mm and smooth ones were tested together with butterfly type of sames tested at different angles. The experimental results served as a input data for dutile damage parameters identifiation. Plastiity and dutile damage parameters identifiation was done with the use of open optimization sripts in Python, that an minimize the funtion by hange of the variables. A simex based algorithm was used for loal optimization. The optimization was done on the basis of minimization of the area between measured and alulated urves that was arried out for whole sets of the sames investigated simultaneously. The identified dutile damage parameters were subsequently apied to simulation of 1in thik CT frature mehanis same. There were performed also experimental tests on CT sames. Very good agreement between experimentally measured urve and simulated one was found. Current results are one of the first steps of the projet. Further investigations will be arried out on material exhibiting stable rak growth at onsidered onditions. Also investigation of the materials dutile behavior will be arried out at inreased temperature and dynami loading onditions. A hallenge is proedures development for dutile damage parameters identifiation based on measurements on miniature sames available in ases e.g. when remnant servie evaluation of in servie strutures an be established is established. REFERENCES [1] N. Bonora,. Gentile, A. Pirondi, G. Nowaz, utile damage evolution under triaxial state of stress: theory and experiments, International Journal of Plastiity 1 (5), pp [] Y. Bai, T. Wierzbiki, Apiation of extended Mohr Coulomb riterion to dutile frature, Int J Frat () 11, pp.1. [3] Y. Bai, T. Wierzbiki, A new model of metal astiity and fraturewith pressure and Lode dependene, International Journal of Plastiity (), pp [] T. Wierzbiki et al., Calibration and evaluation of seven frature models, International Journal of Mehanial Sienes 7 (5), pp [5] Y. Bao, T. Wierzbiki, A Comparative Study on Various utile Crak Formation Criteria, Transations of the ASME, Vol. 1, JULY, pp [] Y. Li, T. Wierzbiki, Mesh-size Effet Study of utile Frature by Non-loal Approah, Proeedings of the SEM Annual Conferene June 1-, 9 Albuquerque New Mexio USA, [7] J.. Seidt, Plasti eformation and utile Frature of -T351 Aluminum under Various Loading Conditions, issertation, Graduate Program in Mehanial Engineering, The Ohio State University,. [] M. Brunig, O. Chyra,. Albregt, L. reimeier, M. Alves, A dutile damage riterion at various stress triaxialities, International Journal of Plastiity (), pp [9]. Celentano, P. Tapia, J. Chabohe, AL AN NUMERICAL CHARACTERIZATION OF AMAGE EVOLUTION IN STEELS, Meania Computaional Vol. XXIII, G.Busaglia, E.ari, O.Zamonsky (Eds.), Barilohe, Argentina, November, pp