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1 Hyde, Christopher J. nd Sun, W. nd Leen, Sen B. (21) Cyclic thermo-mechnicl mteril modelling nd testing of 316 stinless steel. Interntionl Journl of Pressure Vessels nd Piping, 87 (6). pp ISSN Access from the University of Nottinghm repository: %221%2%282%29.pdf Copyright nd reuse: The Nottinghm eprints service mkes this work y reserchers of the University of Nottinghm ville open ccess under the following conditions. This rticle is mde ville under the Cretive Commons Attriution Non-commercil No Derivtives licence nd my e reused ccording to the conditions of the licence. For more detils see: A note on versions: The version presented here my differ from the pulished version or from the version of record. If you wish to cite this item you re dvised to consult the pulisher s version. Plese see the repository url ove for detils on ccessing the pulished version nd note tht ccess my require suscription. For more informtion, plese contct eprints@nottinghm.c.uk

2 Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e372 Contents lists ville t ScienceDirect Interntionl Journl of Pressure Vessels nd Piping journl homepge: Cyclic thermo-mechnicl mteril modelling nd testing of 316 stinless steel C.J. Hyde, *,W.Sun, S.B. Leen Deprtment of Mechnicl, Mterils nd Mnufcturing Engineering, University of Nottinghm, University Prk, Nottinghm NG7 2RD, UK Deprtment of Mechnicl nd Biomedicl Engineering, Nun s Islnd, Ntionl University of Irelnd, Glwy, Repulic of Irelnd rticle info strct Article history: Received 3 Novemer 28 Accepted 3 Jnury 21 Keywords: Thermo-mechnicl ftigue Creep Plsticity Choche unified viscoplsticity model 316 Stinless steel A progrmme of cyclic mechnicl testing of 316 stinless steel, t tempertures of up to 6 C under isotherml conditions, for the identifiction of mteril constitutive constnts, hs een crried out using thermo-mechnicl ftigue test mchine (with induction coil heting). The constitutive model dopted is modified Choche unified viscoplsticity model, which cn del with oth cyclic effects, such s comined isotropic nd kinemtic hrdening, nd rte-dependent effects, ssocited with viscoplsticity. The chrcteristion of 316 stinless steel is presented nd compred with results from tests consisting of cyclic isotherml, s well s in-phse nd out-of-phse thermo-mechnicl ftigue conditions, using interpoltion etween the isotherml mteril constnts to predict the mteril ehviour under nisotherml conditions. Ó 21 Elsevier Ltd. All rights reserved. 1. Introduction Thermo-mechnicl ftigue, or TMF, hs received n incresing mount of ttention over the lst thirty yers. The two most common experimentl TMF wveforms re in-phse (IP) nd outof-phse (OP) s shown in Fig. 1, where 4 represents the phse ngle etween the strin nd temperture wveforms. Some of the res of prticulr interest hve included the effect of phse ngle on the life nd filure of mterils undergoing TMF s shown y Phlvnyli et l. [1], TMF ehviour of superlloys, e.g. Evns et l. [2], TMF of specific components, e.g. Hrrison et l. [3], nd crck growth under TMF conditions, e.g. Di et l. [4]. Unified mteril models re considered s roust wy of modelling the ehviour of mterils where oth rte-independent nd rte-dependent effects occur simultneously, e.g. for hightemperture cyclic loding. The Choche unified viscoplsticity model, for exmple, includes oth non-liner isotropic hrdening nd kinemtic hrdening, for cyclic phenomen such s hrdening nd the Buschinger effect [5], s well s creep effects. This model ws first pulished y Choche nd Rousselier in 1983 [6,7] nd is discussed further y LeMitre nd Choche [8]. Since then the model hs een widely used, for exmple, Tong nd Zhn et l. [9e14]. * Corresponding uthor E-mil ddress: exch@nottinghm.c.uk (C.J. Hyde). The present pper is prticulrly concerned with the ppliction of the Choche model to nisotherml conditions. In order to chieve this, isotherml tests hve een performed to otin the mteril constnts t rnge of tempertures. At ech temperture, the model hs een used to simulte isotherml cyclic conditions nd the predictions compred to the experimentl dt. Ech mteril constnt ws then represented s function of temperture for simultion of the nisotherml IP nd OP TMF conditions. The results from these simultions re compred with experimentl TMF dt. Exmples of previous work on TMF of stinless steel include tht of Sntcreu et l. [15] concerned with utomotive exhust pplictions nd Ru et l. [16] in the explortion of more complex testing conditions, to understnd more relistic ehviours of mterils in industril use. 2. Experimentl progrmme All of the results presented hve een otined using 316 stinless steel specimens. Tle 1 shows the chemicl composition of the 316 stinless steel otined s n verge of three sprk emission tests performed on mteril from the sme tch s the specimens TMF mchine nd therml clirtion The TMF mchine used in this work is n Instron 8862 thermomechnicl ftigue system which utilises rdio-frequency (RF) /$ e see front mtter Ó 21 Elsevier Ltd. All rights reserved. doi:1.116/j.ijpvp

3 366 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e372 Strin ε, T ε, T Strin Temperture t t Temperture Fig. 1. Schemtic representtions of n: () in-phse TMF wveform, 4 ¼ nd () out-of-phse TMF wveform, 4 ¼ 18. Tle 1 Chemicl compositions of the 316 stinless steel (wt%). Fe Cr Ni Mo Mn Si Cu V Co S C N P W Ti Al < induction heting nd forced ir cooling through the centre of the specimen in order to chieve rpid heting nd cooling, respectively. The mximum chievle lod from the mchine is 35 kn (limited y the grips) nd the mximum llowle temperture is 11 C. The requirement for temperture uniformity in the guge section of the specimen during testing ws tht the entire guge section ws within 1 C of the trget temperture. Therefore initil experimentl work ws concerned with chieving this. Thermocouples were plced long the guge section of the specimen in order to monitor the xil, s well s the circumferentil temperture grdients within the specimen guge section during series of rmp nd hold, s well s cyclic therml testing. Initilly the results were not within this tolernce, with xil devitions of up to 3 C from the trget temperture. Therefore new coil designs were investigted. A key prolem fced ws chieving the temperture uniformity required whilst leving enough spce etween the turns of the coil for the ttchment of the extensometer to the guge section of the specimen. Fig. 2 shows the finl coil design which gives temperture uniformity throughout the guge section to within the tolernce required for trget tempertures rnging from 2 C to 1 C. Fig. 3 shows the temperture uniformity results otined using this coil nd 316 stinless steel specimen for trget temperture of 8 C Isotherml cyclic testing Isotherml cyclic tests were crried out t tempertures of 3 C, 5 C, 55 Cnd6 C. Fig. 4 shows the specimen geometry used in these tests. At ech temperture, the test ws performed for fifty loops t four strin rnges, i.e. stepped strin-rnge testing (2 loops in totl), using one specimen for ech temperture. Exmple results t 6 C from these tests re shown in Fig. 5. It cn e seen tht the mjority of the mteril hrdening occurred t the first nd lowest strin rnge (.3%). Therefore these test results t strin rnge of.3% were used to otin the mteril constnts for the Choche unified viscoplsticity model (see Sections 3 nd 4) for ech temperture TMF Fig. 2. Photogrph of the heted specimen, induction coil nd extensometer setup on the TMF mchine. The results of two TMF tests, crried out under IP nd OP conditions re presented. The IP TMF test ws crried out using strin rnge, D3, of.5% nd temperture rnge, DT, of3 C with minimum temperture, T min,of3 C nd mximum temperture, T mx,of6 C. A sw-tooth wveform ws used s shown in Fig. 1 nd the results for this test re shown in Fig. 6. The OP TMF test ws crried out using strin rnge, D3, of.6% nd the sme temperture wve s the IP TMF test, the sw-tooth wveform ws is shown in Fig. 1 nd the results for this test re shown in Fig. 6.

4 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e Guge section Hole through centre of specimen TC 1 TC 2 - Control TC 3 TC 1 ( C) Temperture TC 3 TC 2 - Control Time (s) Fig. 3. Thermocouple positions nd therml uniformity results using the finl coil. Fig. 4. Specimen geometry used on the TMF mchine. 3. Definition of the mteril ehviour model The Choche unified viscoplsticity model hs een chosen to represent the unixil cyclic mteril ehviour of 316 stinless steel. The unixil form of the model is s follows: f n _3 p ¼ sgnðs cþ Z ( ( 1 x > (1) where, sgnðxþ ¼ x ¼ ndhxi ¼ 1 x < xx x < nd f ¼ js cj R k (2) Eqution (1), the viscoplstic flow rule, is the governing eqution within the model. As cn e seen from equtions (2) to (8), ll of the other model vriles, such s those used for clculting oth types of hrdening (isotropic, R nd kinemtic, c) nd viscous stress, s v, re dependent on the vlue of plstic strin, 3 p, clculted from this viscoplstic flow rule. Eqution (2) is the yield criterion for the model. As previously mentioned, this model tkes ccount of oth kinemtic hrdening nd isotropic hrdening. Fig. 7 shows the physicl mening of oth types of hrdening nd the effect they hve on the yield surfce, oth types of hrdening re shown in three-dimensionl (principle) stress spce. When the stress stte within the mteril cuses the edge of the yield surfce to e reched, kinemtic hrdening, implemented y equtions (3) nd where the elstic domin is defined y f nd the inelstic domin y f > _c i ¼ C i i _3 p c i _p (3) where i ¼ 1, 2 c ¼ c 1 þ c 2 (4) _R ¼ ðq RÞ _p (5) s v ¼ Z _p 1. n (6) _p ¼ _3 p (7) s ¼ c þðr þ k þ s v Þsgnðs cþ ¼E 3 3 p (8) Fig. 5. Isotherml cyclic test results t 6 C.

5 368 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e372 Fig. 6. Experimentl TMF dt: () in-phse nd () out-of-phse. (4), is represented s the movement of the yield surfce, s shown in Fig. 7. Isotropic hrdening, implemented y eqution (5), represents the growth of the yield surfce, s shown in Fig. 7. Eqution (6) defines the viscous stress, which tkes the form of the widely used Norton creep lw. Eqution (7) shows tht the vrile, p, used in the clcultion of mny of the other vriles is the ccumulted plstic strin, 3 p. The ove model hs een implemented in Mtl which is top level progrmming lnguge. 4. Identifiction of the mteril constnts In totl, the mteril model requires the identifiction of 1 mteril constnts. Within this section re rief descriptions of the methodologies used in clculting these constnts, following the developments detiled in [11] Initil yield stress, k nd Young s modulus, E From the initil experimentl tensile curve, Young s modulus, E, is tken s the grdient of the initil liner region. The initil yield stress, k, cn e estimted s the stress vlue t the point t which the dt egins to devite from this initil liner region Isotropic hrdening prmeters, Q nd Eqution (5) for the rte of isotropic hrdening cn e integrted with respect to time to give the following eqution: R ¼ Q 1 e p (9) Eqution (9) shows tht s the ccumulted plstic strin, p, increses, R exponentilly pproches sturtion to vlue of Q. σ 1 σ σ 3 σ 3 σ 2 σ 2 Fig. 7. Schemtic representtions of hrdening ehviour: () kinemtic nd () isotropic. 2 1 Therefore, ssuming tht the mteril hrdening is entirely due to isotropic hrdening nd plotting R ginst the ccumulted plstic strin, the sturted vlue of R is identified s Q, s shown in Fig. 8. Then choosing point roughly hlf wy into the trnsient region of the hrdening ehviour, shown circled in Fig. 8, the corresponding vlues of R nd p re identified. These vlues (long with the clculted vlue of Q) re then put into the following eqution, which is simply rerrnged version of eqution (9) for. By choosing this point roughly hlf wy into the trnsient region of the hrdening ehviour, the vlue of clculted forces the model to go through this point nd with the model sturting t the vlue of Q, the result is close model fit to the experimentl dt s shown in Fig. 8. lnð1 R=QÞ ¼ (1) p 4.3. Kinemtic hrdening prmeters, 1,C 1, 2 nd C 2 Eqution (3) for the rte of kinemtic hrdening cn e integrted, with respect to time, to give the following equtions: c 1 ¼ 1 1 e C1 3 p (11) c 2 ¼ 2 1 e C2 3 p (12) Sustituting equtions (11) nd (12) into eqution (8) gives: s ¼ 1 1 e C1 3 p þ 2 1 e C2 3 p þ R þ k þ s v (13) R (MP) p (s) Q Experimentl dt Isotropic hrdening model Fig. 8. Isotropic hrdening vrile R versus p for 316 stinless steel t 6 C.

6 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e Fig. 9. Plot used in the clcultion of the kinemtic hrdening mteril constnts 2 nd C 2 for 316 stinless steel t 6 C. Fig. 1. Plot of log (E3 T s) vs. used in determining the constnts used in the RmergeOsgood eqution. If the lter stges of hrdening re considered, it cn e ssumed tht c 1 (nd therefore 1 nd C 1 ) hs negligile effect on the hrdening nd therefore the kinemtic hrdening is dominted y c 2 ( 2 nd C 2 ). Therefore, eqution (13) cn e simplified to: s ¼ 2 1 e C2 3 p þ R þ k þ s v (14) Differentiting eqution (14) with respect to 3 p, rerrnging nd tking nturl logs of oth sides gives the following eqution (ssuming yield stress, k, nd viscous stress, s v, to e constnts): vs ln vr ¼ C v3 p v3 2 3 p þ lnð 2 C 2 Þ (15) p Therefore plotting lnðvs=v3 p vr=v3 p Þ vs. 3 p s shown in Fig. 9 llows the identifiction of C 2 from the grdient nd 2 from the y-xis intercept. Similrly, 1 nd C 1 cn e found, for the lower strin region, from eqution (13), hving lredy identified 2 nd C 2 [11]. In order to perform this fit to the dt, it is necessry to otin expressions for vs=v3 p nd vr=v3 p, s functions of 3 p, to use in eqution (15). For the initil tensile curve (the first qurter cycle), p ¼ 3 p, which cn e sustituted into eqution (9). This expression cn then e differentited with respect to 3 p, to give the following: vr v3 p ¼ Qe 3 p (16) The clcultion of vs=v3 p is more complicted. Tking ds=d3 p, multiplying y dt=dt nd d3 T =d3 T, then rerrnging gives the following: Tle 2 RmergeOsgood constnts for 316 stinless steel t multiple tempertures. T( C) 3 (%) s (MP) n ds d3 p ¼ ds d3 T $ 1 _3 p $_3 T (17) Hence, expressions for ds=d3 T nd _3 p re required. The vlue of _3 T is controlled during testing s hence is known. To otin _3 p, Hooke slw,3 e ¼ s=e, is sustituted into the following eqution for totl strin: 3 T ¼ 3 e þ 3 p (18) Rerrnging eqution (18) nd differentiting it with respect to time gives the following: d3 p ¼ d3 T ds dt dt dt $1 E Multiplying the finl term in eqution (19) y d3 T =d3 T rerrnging gives the following: _3 p ¼ _3 T 1 1 E $ ds d3 T (19) nd (2) In order to otin n expression for ds=d3 T, smoothing function is needed to eliminte complictions cused y sctter in the Fig. 11. Comprison of model predictions of cyclic s 3 ehviour to isotherml experimentl dt t 55 C. () Monotonic tensile curve nd 1st loop nd () sturted loop.

7 37 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e Δ σ /2 (MP ) Δ σ /2 (MP ) Cycle no Cycle no. Fig. 12. Comprison of model predictions of hrdening ehviour to isotherml experimentl dt t 55 C. Fig. 14. Comprison of model predictions of hrdening ehviour to isotherml experimentl dt t 6 C. experimentl dt, which could cuse negtive vlues of ds=d3 T to e otined t some strin vlues. The smoothing function used in this cse is the RmergeOsgood eqution, i.e.: 3 T ¼ s s n þ (21) 3 s s 3 ¼ s (22) E Eqution (22) cn e sustituted into eqution (21) to give: E3 T ¼ s s n þ (23) s s s which cn then e differentited with respect to 3 T to give: ds d3 T ¼ s 3 1 þ n ss n 1 (24) The RmergeOsgood constnts, nmely 3, s nd n, cn e found y rerrnging nd tking logs of oth sides of eqution (23) to give the following: logðe3 T sþ ¼n logs þð1 n Þlogs (25) Therefore, plotting logðe3 T sþ vs. logs llows the identifiction of n (grdient) nd s (from the y-xis intercept). An exmple of this plot for temperture of 6 C is shown y Fig. 1. Eqution (22) cn then e used to determine 3. Tle 2 shows the RmergeOsgood constnts clculted for the four tempertures Creep constnts, Z nd n Typicl vlues of Z nd n hve een tken from literture, such s Ryu [17] nd Hyde [18e2]. The Mtl computer progrm for the model ws run vrying these constnts round the typicl vlues in order to otin good fits to the model; this resulted in the constnts presented in Tle Mteril constnts Tle 2 summrises the mteril constnts identified from the isotherml test dt for the four tempertures (Fig. 13). 5. predictions 5.1. Comprison of model predictions to isotherml experimentl results Figs. 11e14 show comprisons of the experimentl nd model results for the isotherml cses of 55 C nd 6 C for strin rnge of.3%. The figures show the monotonic tensile curve nd first cycle, sturted cycle nd hrdening ehviour of the mteril. Fig. 15 shows the complete predicted history (fifty loops) from the Fig. 13. Comprison of model predictions of cyclic s 3 ehviour to isotherml experimentl dt t 6 C. () Monotonic tensile curve nd 1st loop nd () sturted loop.

8 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e Fig. 15. Full s 3 model predictions for 5 loops under isotherml conditions t 6 C. () Full loops nd () zoomed for mximum strin hrdening ehviour. Tle 3 Mteril constnts for 316 stinless steel t multiple tempertures. T( C) k (MP) E (GP) Q (MP) 1 (MP) C 1 2 (MP) C 2 Z (MP s 1/n ) n Fig. 16. Comprison of model predictions of cyclic s 3 ehviour with in-phse TMF experimentl dt t high strin rnge. () Monotonic tensile curve nd 1st loop nd () sturted loop Fig. 17. Comprison of model predictions of cyclic s 3 ehviour with out-of-phse TMF experimentl dt t high strin rnge. () Monotonic tensile curve nd 1st loop nd () sturted loop.

9 372 C.J. Hyde et l. / Interntionl Journl of Pressure Vessels nd Piping 87 (21) 365e372 model for temperture of 6 C, illustrting the predicted cyclic hrdening phenomenon (Fig. 12) Comprison of model predictions to nisotherml experimentl results Tle 3 shows tht the mteril constnts used in the Choche unified viscoplsticity model re generlly temperture dependent. Therefore, one wy of implementing the nisotherml condition within the model is to identify expressions for the constnts s functions of temperture nd inputting these expressions to the model rther thn single vlues. This llows ech of the constnts to e clculted t the eginning of ech time increment depending on the vlue of temperture t the eginning of tht time increment. These vlues re then used in the clcultion of the susequent vlues of plstic strin, stress, etc., hence creting temperture-dependent (TMF) mteril model. Figs. 16 nd 17 show the experimentl/model comprisons for the two TMF test conditions. 6. Conclusion A unified mteril model, which includes oth (non-liner) isotropic nd kinemtic hrdening ehviour s well s viscoplsticity phenomen, such s rte-dependency, hs een successfully implemented in Mtl. A progrmme of isotherml nd nisotherml thermo-mechnicl tests hs een conducted using induction coil heting, with the temperture uniformity controlled to within 1 C up to tempertures of 6 C. The isotherml tests hve een employed to identify the mteril constnts for the mteril model t different tempertures etween 3 C nd 6 C. The experimentl dt hs lso een employed to vlidte the Mtl implementtion of the unified viscoplsticity model, showing excellent model to test correltion for the isotherml tests considered. Interpoltion of the temperture-dependency of the mteril constnts, for ppliction to the nisotherml simultions, hs lso shown resonly good correltion, lthough the model ppers to slightly under-predict the pek tensile stresses during forwrd plstic deformtion nd overpredict the intermedite to high compressive stresses during reverse plstic deformtion. It is lso worth noting tht the mteril constnts were otined only from the.3% strin rnge (isotherml) dt, due to the use of the stepped strin-rnge technique to minimise specimen usge, wheres the TMF experimentl dt ws otined t strin rnges of.5% nd.6%, the model predictions therefore represent n extrpoltion in terms of the strin rnge used. Further testing to chrcterise TMF ehviour of the mteril t the strin rnge t which the mteril constnts were otined is expected to improve the nisotherml predictions. A prllel project is concerned with the development of optimistion techniques for utomting nd refining the process of mteril constnt identifiction. Acknowledgements The uthor would like to thnk the EPSRC for the funding of this project otined from the Doctorl Trining Progrmme, nd lso Steve Willims, Nin Bnerjee nd Gemm Drew of Rolls-Royce plc for their gretly vlued technicl support nd commitment to the project. Thnks re lso given to Tom Buss nd Brin Wester for their technicl support within the experimenttion. References [1] Phlvnyli S, Drew G, Ryment A, Re CMF. Thermo-mechnicl ftigue of polycrystlline superlloy: the effect of phse ngle on TMF life nd filure. Interntionl Journl of Ftigue 27;3:33e8. [2] Evns WJ, Screech JE, Willims SJ. Thermo-mechnicl ftigue nd frcture if INCO718. Interntionl Journl of Ftigue 27;3:257e67. [3] Hrrison GF, Trnter PH, Willims SJ. ling of thermomechnicl ftigue in eroengine turine ldes. In: AGARD conference on therml mechnicl ftigue of ircrft engine mterils 161 to 16-12, CP569; [4] Di Y, Mrchnd NJ, Hongoh M. Ftigue crck growth mesurements in TMF testing of titnium lloys using n ACPD technique. Specil Applictions nd Advnced Techniques for Crck Size Determintion; 1995:17e32. [5] Buschinger J. Ueer die Vernderungen der Elstizittsgrenze und der festigkeit des Eisens und Sthls durch Strecken, Quetschen, Erwrmen Akuhlen und durch oftmls wiederholte Belstung, vol. XIII. Munchen: Mitt. Mech- Tech L; [6] Choche JL, Rousselier G. On the plstic nd viscoplstic constitutive equtions e prt 1: rules developed with internl vrile concept. Journl of Pressure Vessel Technology 1983;15:153e8. [7] Choche JL, Rousselier G. On the plstic nd viscoplstic constitutive equtions e prt 2: ppliction of internl vrile concepts to the 316 stinless steel. Journl of Pressure Vessel Technology 1983;15:159e64. [8] Lemitre J, Choche JL. Mechnics of solid mterils. Cmridge University Press; [9] Tong J, Vermeulen B. The description of cyclic plsticity nd viscoplsticity of wsploy using unified constitutive equtions. Interntionl Journl of Ftigue 23;25(no. 5):413e2. [1] Tong J, Zhn ZL, Vermeulen B. ling of cyclic plsticity nd viscoplsticity of nickel-sed lloy using Choche constitutive equtions. Interntionl Journl of Ftigue 24;26(8):829e37. [11] Zhn Z. A study of creep-ftigue interction in new nickel-sed superlloy. Ph.D thesis, University of Portsmouth; 24. [12] Zhn ZL, Tong J. A study of cyclic plsticity nd viscoplsticity in new nickelsed superlloy using unified constitutive equtions. Prt I: evlution nd determintionofmterilprmeters. MechnicsofMterils 27;39(1):64e72. [13] Zhn ZL, Tong J. A study of cyclic plsticity nd viscoplsticity in new nickelsed superlloy using unified constitutive equtions. Prt II: simultion of cyclic stress relxtion. Mechnics of Mterils 27;39(1):73e8. [14] Zhn Z, Fernndo US, Tong J. Constitutive modelling of viscoplsticity in nickel-sed superlloy t high temperture. Interntionl Journl of Ftigue 28;3(7):1314e23. [15] Sntcreu P, Simon C, Colemn A. Thermomechnicl ftigue ehviour of stinless steel grdes for utomotive exhust mnifold pplictions. Thermomechnicl Ftigue Behviour of Mterils 22;4:227e39. [16] Ru K, Beck T, Lohe D. Two specimen complex therml-mechnicl ftigue tests on the Austenitic stinless steel AISI 316L. Thermomechnicl Ftigue Behviour of Mterils 22;4:297e311. [17] Ryu W-S, Kim WG, Lee KY, Yoon KB. Evlution of creep crck growth ehviour in type 316LN stinless steel. Mnuscript for SMiRT 17-NED Specil Issue, Kore. [18] Hyde TH. Creep crck growth in 316 stinless steel t 6 C. High Temperture Technology 1988;6(2):51e61. [19] Hyde TH. Anomlous creep ehviour of 316 stinless steel t 55 C. High Temperture Technology 1986;4(1):25e9. [2] Hyde TH. Creep of 316 stinless steel t 55 nd 6 C nd the effects of short durtion overlods on creep t 55 C. Mterils t High Tempertures 1997;14(1):27e35.