Creep of the Austenitic Steel AISI 316 L(N)

Transcription

1 Forchungzentrum Karlruhe in der HelmholtzGemeinchaft Wienchaftliche Berichte FZKA 7065 Creep of the Autenitic Steel AISI 316 L(N) Experiment and Model M. Rieth, A. Falkentein, P. Graf, S. Heger, U. Jäntch, M. Klimiankou, E. MaternaMorri, H. Zimmermann Intitut für Materialforchung Programm Kernfuion November 2004

2 Forchungzentrum Karlruhe in der HelmholtzGemeinchaft Wienchaftliche Berichte FZKA 7065 Creep of the autenitic teel AISI 316 L(N) Experiment and Model M. Rieth, A. Falkentein, P. Graf, S. Heger, U. Jäntch, M. Klimiankou, E. MaternaMorri, H. Zimmermann Intitut für Materialforchung Programm Kernfuion Forchungzentrum Karlruhe GmbH, Karlruhe 2004

3 Impreum der PrintAugabe: Al Manukript gedruckt Für dieen Bericht behalten wir un alle Rechte vor Forchungzentrum Karlruhe GmbH Potfach 3640, Karlruhe Mitglied der Hermann von HelmholtzGemeinchaft Deutcher Forchungzentren (HGF) ISSN urn:nbn:de:

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5 ABSTRACT Thi report provide a general review on deformation mechanim relevant for metallic material. Different mechanim are decribed by rate equation which are derived and dicued in detail. For the example of an autenitic 17Cr12Ni2Mo teel (AISI 316 L(N) or DIN ) thee equation are applied to experimental creep data from own invetigation at IMFI (epecially longterm creep tet with creep time of up to 10 year) and from NRIM, Japan. Stepbytep a teadytate creep model i et up that i able to predict creep behaviour in a wide temperature and tre range. Due to the mall number of adjutable parameter it may alo be eaily adapted to other material. Since autenitic tainle teel are well known for their problematic aging behaviour at elevated temperature, microtructure and precipitation formation a well a their impact on creep are outlined above all. i

6 Kriechverhalten de autenitichen Stahl AISI 316 L(N) Experimente und Modelle ZUSAMMENFASSUNG Der vorliegende Bericht beinhaltet eine allgemeine Übericht über Verformungmechanimen, die bei metallichen Werktoffen auftreten können. Dabei werden Gleichungen für die unterchiedlichen Mechanimen hergeleitet und auführlich dikutiert. Am Beipiel eine autenitichen 17Cr12Ni2MoStahl (AISI 316 L(N) oder DIN ) findet dann die Anwendung dieer Gleichungen auf experimentelle Kriechdaten au eigenen Unteruchungen im IMFI (inbeondere Langzeitkriechunteruchungen mit Veruchzeiten von bi zu 10 Jahren) und von NRIM, Japan tatt. Dadurch wird chrittweie ein Modell für da tationäre Kriechen aufgetellt, da da Kriechverhalten in einem weiten Temperatur und Spannungbereich vorheragen kann. Auf Grund der wenigen anzupaenden Parameter kann e auch leicht auf andere Werktoffe angewandt werden. Da autenitiche rotfreie Edeltähle für ihr problematiche Alterungverhalten bei höheren Temperaturen bekannt ind, wird vor allem auch die Mikrotruktur, die Bildung von Aucheidungen und deren Einflu auf da Kriechen dargetellt. ii

7 CONTENTS 1 Introduction Experimental Material Equipment, Specimen, Tet Procedure, and Evaluation Creep Tet Reult Microtructure Deformation Mechanim Overview Diffuional Flow (Diffuion Creep) NabarroHerring Creep Coble Creep Alternative Decription Powerlaw Creep (Dilocation Creep) Powerlaw Creep by Climb (plu Glide) Powerlaw Breakdown Mechanical Twinning Dilocation Glide (Low Temperature Platicity) Platicity Limited by Dicrete Obtacle Platicity Limited by Lattice Friction Elatic Collape Summary SteadyState Creep Model Diffuion Creep Platicity (Dilocation Glide) Power Law Creep (Dilocation Climb) Tranition from Creep by Climb to Creep by Glide Aement and Dicuion of the Stationary Creep Model...39 iii

8 5 Concluion Literature Appendix/Table Contant and Parameter Experimental Data Metallographic Examination Tet No. ZSV1921: 750 C, 2650 h Tet No. ZSV1913: 750 C, h AISI 316 L(N) KSW heat (imilar to preent CRM heat): 750 C, 1404 h AISI 316 L(N) KSW heat (imilar to preent CRM heat): 750 C, h...72 iv

9 Introduction 1 Introduction Among many other application the autenitic 17/12/2 CrNiMo teel 316 L(N) (DIN ) i ued or enviaged for both conventional and nuclear power plant contruction a well a in the International Nuclear Fuion Project. Worldwide a huge number of experimental invetigation have already been carried out to determine the material propertie (including creep behavior) of thi teel type in the conventional tre and temperature range. Our previou creep tudie, for example, focued on three batche in the temperature range of C for period of up to h [16]. In the deign relevant lowtre range at 550 C and 600 C, however, creep data allowing tatement to be made about the tre dependence of the minimum creep rate or about the technically relevant creep train limit are almot unavailable. Thi i not only due to reaon of time, but to technical reaon, too. In thi tretemperature range, the expected creep or train rate are o mall that they can hardly be meaured by conventional creep tet. Therefore, a pecial longterm creep teting program at 550 C and 600 C, repectively, wa tarted in 1991 [7]. After an experimental period of about 10 year the creep tet have been aborted and evaluated. Now, thi lowtre creep data not only allow for a much better longterm prediction of the reliability of 316 L(N) application but alo enable deformation modeling for a broader tre range. The preent report focue mainly on the etup of a teadytate creep model for the 316 L(N) teel. Therefore, after an overview of experimental procedure and material propertie, a hort review on deformation mechanim and their decription by rate equation i given. In the final ection thee equation are applied to the experimental creep data and the reulting model i critically dicued in detail. 1

10 Experimental 2 Experimental 2.1 Material A part of the AISI 316 teel family alo known a V4ASerie or a trademark NIROSTA i hown in Fig.1. AISI 316L(N) NIROSTA 4429 Fe 17.3% Cr 12.5% Ni 2.4% Mo 1.8% Mn 0.02% C 0.08% N 0.32% Si CrNiMo Steel: V4ASerie AISI 316LN 4429 X2CrNiMo17133 AISI 316L 4404 X2CrNiMo17122 AISI X5CrNiMo Ni, Mo, N C Fig. 1: The AISI 316 autenitic teel family. Mot data ued in the current report reult from experiment performed with the heat no from CreuotMarell (CRM). Thi heat had been delivered a 40 mm hot rolled plate with a final heat treatment at 1100 C followed by water quenching. Quality inurance reported thi batch a nearly free of δferrite (< 1 %). In addition to that, ome ingle data point have been taken from NRIM data heet [6, 811] for comparable alloy (for chemical compoition ee Table 1). Thee had been produced a 50 mm, a 60 mm bar, a tube (wall thickne 8.8 mm) and a 24 mm plate. Their final heat treatment wa 1050 C, 1080 C, 1130 C, and 1100 C, alo water quenched. 2

11 Experimental Table 1: Chemical compoition of different AISI 316 L(N) teel in wt. per cent. Alloy C Si Mn P S Cr Ni Mo Cu N Al B CRM SUS 316B ADA SUS 316H TB AAL Equipment, Specimen, Tet Procedure, and Evaluation All creep pecimen were produced out of the centre of the 40 mm plate (CRM 11477) tranvere to rolling direction. For the pecimen crew head of 5 mm and 8 mm in diameter with 30 mm, and 200 mm gauge length were elected. The increaed length of 200 mm enure that the meaurement of the creep behaviour i much more accurate than for tandard pecimen (Ø8 x 50 mm, ee Fig. 2). The tet temperature wa controlled by mean of three PtRhPt thermocouple and kept contant at ±2 K by mean of three PID control unit. For creep meaurement, the pecimen were equipped with a doublecoil extenometer and the creep behaviour wa regitered continuouly. The reolution wa about mm (1:1250). Loading took place in normal atmophere (air) via lever arm (1:15) uing weight. A picture of the creep facilitie i given in Fig. 2. Creep Tet Facilitie Creep Specimen Low Stre Regime creep rate of 10 9 to 10 7 /h, that i: gauge length 30 mm µm/year gauge length 200 mm 2200 µm/year Fig. 2: Creep tet facilitie and pecimen. To improve reolution and enitivity of creep tet, an increaed pecimen length ha been ued for longterm tet. 3

12 Experimental The continuouly regitered train curve have been digitalized (ee Fig. 3, blue dot). Then the creep rate ha been obtained by numerical differentiation (Fig.3, red dot). teadytate creep range Fig. 3: Determination of characteritic creep data from the regitered train curve. Due to fluctuation it i ometime rather difficult to determine the range of teadytate creep. However, in all cae we defined the teadytate creep rate a minimum value while onet and end of the teadytate creep range ha been defined by a catter band of ±20 % of the minimum value. 2.3 Creep Tet Reult A number of different tet have been performed with tandard pecimen (Ø5 x 30 mm) in the uual tre range at temperature between 550 and 750 C. To examine longterm creep even experiment were performed at 550 C in the tre range of MPa and another ix tet were run at 600 C in the range of MPa. Of coure, a certain cattering occur at creep rate of ε& 10 7 h 1 which correpond to a train rate of 0.1 mm / 5000 h even for a gauge length of L o = 200 mm. Thi cattering may be due either to meaurement technology or to the material ued. 4

13 Experimental However, the minimum creep rate wa reached for the higher tree. For lower tree, ometime the value could only be etimated. The reult for the teadytate creep rate are hown in Fig. 4. Fig. 4: Steadytate creep rate depending on tre for different temperature interpreted in term of powerlaw creep. It can be noticed that the dependence of the teady tate creep rate at 550 and 600 C on the tre i changed coniderably in the lowtre range a compared to the hightre range. Thi mean that the creep rate are much higher than the value that would have been extrapolated from the uual tre range. At firt glance, a plauible explanation could be the fact that all experiment performed at 550 C and 600 C with σ >210 MPa are found to be in tre range with initial platic train of more than 5 % at the tart of the experiment, which are due to the low yield tre at thee temperature. Thi mean that the creep behavior at tree of le than 210 MPa actually refer to the pecified olutiontreated tate, wherea the material i found to be in the olutiontreated deformed tate at tree of more than 210 MPa (up to 25 % at 380 MPa). 5

14 Experimental It wa already demontrated by everal experiment with the Mofree teel X6CrNi 1811 (correponding to AISI 304) that thi platic deformation at the tart of the tet act like a preceding cold deformation [12]. Cold deformation of pecimen by 12 % prior to the tet or deformation by 12 % at the tet temperature reulted in creep and trength value which were imilar to thoe obtained for olutiontreated pecimen with initial train of more than 10% at the tart of the experiment. Therefore, it might be aumed that the oberved change of the teadytate creep rate at lower tree could reult from thi experimentally buildin cold work. However, in Section 3 another explanation will be favored. 2.4 Microtructure Quite another but alo reaonable decription could be the change of the microtructure with time ince autenitic tainle teel are well known for their thermal intability at higher temperature. a b 100 x 500 x c rolling texture d 100 x 500 x rolling texture Fig. 5: Microtructure of the material a delivered (a, b). Thi i the uual tructure of autenitic tainle teel with ome twin and a light texture along the rolling direction. The microtructure change coniderably after aging of h at 600 C (c, d). 6

15 Experimental Figure 5 a, b how the microtructure of the 316 L(N) teel in the condition a delivered. In general there i nothing unuual. Typical twin formation are recognizable a well a a light texture along the rolling direction combined with a few rather mall incluion. Other invetigation have alo hown mall part of delta ferrite. After aging at 600 C for h the microtructure ha changed coniderably (Fig. 5 c, d). Precipitation have formed mainly at grain boundarie and along the rolling texture. A imilar formation can be oberved in SEM obervation after 2650 h at 750 C (Fig. 6). a Sequence and type of precipitation in AISI 316 autenitic tainle teel are well known and invetigated (ee, for example, [13, 14] and reference therein, ee alo Sec. 7): M 23 C 6 carbide are the firt phae that form during aging where M repreent Cr, Fe, Mo, and Ni. Initially thee b carbide conit of a higher amount of Fe that uually i replaced by Cr and/or Mo during aging. A typical compoition for AISI 316 teel i (Cr 16 Fe 5 Mo 2 )C 6. For the preent material the carbon content i 200 ppm at room temperature while at 600 C the carbon olubility in equilibrium Fig. 6: a) SEM image of precipitation within and at grain with the M 23 C 6 carbide i boundarie after 2650 h at 750 C. b) Magnification of inner grain precipitation after h at 750 C. about 4 ppm. That i, at 600 C almot all of the carbon i removed from the matrix by precipitating a M 23 C 6 carbide. The mot favorable precipitation ite are grain boundarie followed by twin and dilocation where cold deformation enhance precipitation within grain. The preence of nitrogen inhibit or delay formation of M 23 C 6 carbide. Therefore, at 600 C with the preent material M 23 C 6 precipitation at 7

16 Experimental grain boundarie tart after only a few hundred hour and the formation of carbide within grain take even 1000 hour and more. Due to the mall amount of carbon only a minor part of the precipitation hown in Fig. 5 and 6 can be explained by M 23 C 6 carbide. Beide carbide precipitation, during longterm aging (epecially at higher temperature) AISI 316 teel are prone to formation of intermetallic phae. Below 800 C uually M 23 C 6 precipitation i followed by precipitation of Lave phae. grain boundary a b grain boundary Fig. 7: TEM image of grain/twin boundarie before (a) and after aging at 600 C for h (b). The reult of the line can on the left ide how the relative change of Fe, Cr, Ni, and Mo concentration. The canning path are indicated in the TEM image. 8

17 Experimental In the cae of the AISI 316 L(N) autenitic teel Lave phae coniting of Fe 2 Mo tart to form after aging at 600 C for about h firt at grain boundarie and finally within grain. An example i given in Fig. 7 where the intenity drop of the Fe ignal and the rie of the Mo ignal lead to a Fe/Mo ratio of about 1:1 after analyzing the TEM ignal. The lat phae to appear i the igma phae. It ha a very low kinetic when forming from autenite and, therefore, take aging of about h at 600 C. But formation from ferrite i about 100 time fater. Thi i another reaon why δferrite i undeirable in autenitic teel. However, the compoition of igma phae in AISI 316 L(N) teel can be approximated by (Fe, Ni) 3 (Cr, Mo) 2 or in wt%: 55Fe29Cr11Mo5Ni. Sigma phae precipitate mainly on grain boundarie (epecially on triple junction) and on intragranular incluion. Fig. 8: SEM image of remaining grain boundarie (mainly igma phae precipitation during aging at 600 C for h) after etching. Since igma phae precipitation are enriched in Cr and Mo they are more reitant againt acid and can be een quite clearly after etching. An example i given in Fig. 8 where the former grain boundarie are till viible after urface etching due to the high amount of igma phae formation. Even wall of igma phae are ticking out of the urface for a few micro meter. 9

18 Experimental The large amount of igma phae precipitation after hour at 600 C finally lead to dendritic formation at and in ome cae even within grain (Fig. 9). Further example are given in Sect. 7. a A conequence of the formation of intermetallic phae i the depletion of the adjacent σphae matrix in chromium and molybdenum. Thi in turn increae the olubility of carbon in the matrix which lead to at leat partial diolution of the σphae (Fe,Ni) 3 (Cr,Mo) 2 SEM b SEM Fig. 9: Dendritic formation of igma phae precipitation in AISI 316 L(N) autenitic tainle teel after aging at 600 C for hour. prior formed carbide. That i, after longterm aging carbide like M 23 C 6 are nearly vanihed. For an evaluation of the influence of the timedependent microtructural compoition on the creep behavior a precipitation diagram i neceary. At NIMS, Japan extenive aging experiment have been performed followed by TEM examination to generate a timetemperatureprecipitation diagram for a 18Cr12NiMo teel that i comparable to the AISI 316 L(N) [15]. In Fig. 10 thi precipitation map i hown together with the reult of the 316 L(N) igma phae obervation. A can be een, the reult for both material are in good agreement. Now the quetion i: Can the dependency change of the teady tate creep rate on the tre in the lowtre range (ee Fig. 4) be correlated with the aging (precipitation) behavior? For thi purpoe the creep tet have been divided into low and high tre range. For the tet at 550 C and 600 C medium tre range (i.e., the range where the change in creep 10

19 Experimental behavior occur) have been additionally conidered. Then all particular time of the minimum creep rate have been determined and illutrated for each temperature a bar in the timetemperatureprecipitation diagram (ee Fig. 11). Fig. 10: Timetemperatureprecipitation diagram by NIMS [15] for an autenitic tainle teel comparable to the AISI 316 L(N). The reult of the AISI 316 L(N) igma phae detection are hown a red dot to demontrate the agreement. At a glance, there i no correlation at all. Looking at the high tre range, for example, how only that, depending on temperature, there are none, ome or even more carbide precipitation. But thee do not reflect in the creep behavior. In the mot intereting medium tre range there are either carbide (at 550 C) or Lave phae precipitation (at 600 C). The ame can be oberved in the low tre range at C. That i, neither M 23 C 6 nor Lave phae precipitation can be the reaon for a different creep rate behavior. A we have een in Fig. 8 and 9, only the evere igma phae formation could have had a ignificant influence on the creep propertie. To check whether thi i the cae here, we have to correlate the teadytate period with the time of igma phae formation. Thi ha been illutrated in Fig. 11. From each curve in Fig.4 the two upper and the lower mot experiment ha been ued determine the period of contant train rate (teadytate). Thee period are drawn over the timetemperature precipitation map a bar with lined and 11

20 Experimental quared end (one ha to keep in mind that the teadytate time are ignificantly lower than the overall creep rupture time or experimental time). Further, for the cae of 550 C and 600 C the teadytate time have been determined from the experiment directly at and around the kink of the trecreep rate curve (ee Fig. 4). Thoe time have been plotted with circle ended line in Fig. 11. A can be clearly een in, at time when igma phae precipitation tart the creep tet are already far away from minimum creep rate even in the lowet tre range. Fig. 11: A correlation attempt of the minimum creep rate time with precipitation area. The oberved minimum creep time are diplayed a bar correponding to the low (line ended), medium (circle ended), and high (quare ended) tre range. In ummary, during teadytate creep of all tet ( C) in the medium and low tre range only carbide and Lave phae precipitate at the grain boundarie and within the grain. But only the creep tet at 550 C and 600 C how a change of the teadytate creep rate. Therefore, the change of microtructure with time can not be the reaon for the oberved creep behavior hown in Fig.4. In fact, a will be demontrated in the following ection, the teadytate creep rate depend trongly on the underlying deformation mechanim which in turn depend on the applied tre. 12

21 Deformation Mechanim 3 Deformation Mechanim 3.1 Overview Crytalline olid deform platically by a number of different and ometime competing mechanim. Although it i often convenient to decribe a polycrytalline olid by a well defined yield trength, below which it doen t flow and above which flow i rapid, thi i only true at zero temperature. But platic flow i a kinetic proce and in general, the trength of olid depend on both train and train rate, a well a on temperature. It i determined by all the atomic procee that occur on the atomic cale like, for example, the glide motion of dilocation line, the combined climb and glide of dilocation, the diffuive flow of individual atom, the relative diplacement of grain by grain boundary liding including diffuion and defect motion in the boundarie, mechanical twinning by the motion of twinning dilocation, and o on [16]. But it i more convenient to decribe the platicity of polycrytalline olid in term of the mechanim to which the atomitic procee contribute. Often the deformation mechanim are divided into five group [16]: Diffuional Flow (Diffuion Creep) baed on either (a) lattice diffuion (Nabarro Herring creep) or (b) grain boundary diffuion (Coble creep). Powerlaw Creep (Dilocation Creep) diffuion controlled climbpluglide procee: (a) baed on lattice diffuion controlled dilocation climb (high temperature creep), (b) baed on core diffuion controlled dilocation climb (low temperature creep), (c) tranition from climbpluglide to glide alone (powerlaw breakdown). Mechanical Twinning low temperature platicity by the motion of twinning dilocation. Dilocation Glide low temperature platicity baed on dilocation glide, limited by (a) dicrete obtacle or (b) by lattice reitance. Elatic Collape flow for tree above the ideal hear trength. Some mechanim which are not important for the preent material (e.g. HarperDorn creep or creep baed on recrytallization) have been left out. 13

22 Deformation Mechanim Platic flow of fully dene olid i caued by the hear tre σ (deviatoric part of the tre field). In term of the principal tree σ 1, σ 2 and σ 3 : [( σ σ ) + ( σ σ ) + ( σ σ ) ] 1 σ = (1) 6 It exert force on defect (dilocation, vacancie, etc.) in the olid and caue them to move. The defect are the carrier of deformation and, therefore, the hear train rate γ& depend on denity and velocity of thee deformation carrier. In term of the principal train rate ε& 1, ε& 2 and ε& 3 it i given by: 2 [ ] 3 = (2) & γ (& ε & ε ) + (& ε & ε ) + (& ε & ε ) For imple tenion, σ and γ& are related to the tenile tre σ 1 and train rate ε& 1 by: σ 1 = σ 1, γ 3ε 1. (3) 3 & = & Macrocopic variable of platic deformation are tre σ, temperature T, train rate γ&, train γ and time t. During creep or creep rupture tet the tre and temperature are precribed. Typically form of train and train rate are hown in Fig. 12. At low temperature of about 0.1 T M (melting point T M ) the material undergoe work hardening until the flow trength equal the applied tre. During thi proce it tructure change: the dilocation denity increae, therefore, further dilocation motion i blocked, the train rate decreae to zero, and the train tend aymptotically to a fixed value. During tenile tet the train rate and temperature are precribed. At low temperature the tre rie a the dilocation denity rie (Fig. 12). That i, for a given et of tate variable S i (dilocation denity, dilocation arrangement, cell ize, grain ize, precipitate ize, precipitate ditribution, and o on) the trength i determined by γ& and T, or the train rate i determined by σ and T. At higher temperature (about 0.5 T M ) polycrytalline material creep (ee Fig. 12). After a tranient during which the tate variable change, a teady tate may be reached. During the teady tate the olid continue to deform with no further (ignificant) change in S i. Here the tate variable S i depend on tre, temperature, and train rate and a relationhip between thee three macrocopic variable may be given. 14

23 Deformation Mechanim At very high temperature, or very low tree, or very low train rate the tate variable may ocillate intead of tending to teady value. But often it i poible to define a quai teady tate anyway in which tre, temperature and train rate are related. Fig. 12: Typical curve of train, train rate, and tre obtained by creep and tenile tet on metal or alloy at low and high temperature. A ha been hown, either tre or train rate can be ued a independent variable. For the current work we will chooe the train rate γ& a independent variable ince mot experimental reult are received from creep and creep rupture tet. In thi cae each deformation proce can be decribed by a rate equation which relate γ& to the tre σ, temperature T, and to the tructure of the material at that intant: ( σ, T, S P ) & γ = f,. (4) i j 15

24 Deformation Mechanim A already mentioned, the et of i quantitie S i are the tate variable which decribe the current microtructural tate of the olid. The et of j quantitie P j are material propertie like lattice parameter, atomic volume, bond energie, moduli, diffuion contant, and o on. Mot often thee can be conidered a contant. But the tate variable S i generally change during the deformation procee (except in teady tate). So a econd et of equation i needed to decribe their rate of change: ds dt i i ( σ, T, S, P ) = g. (5) i j The coupled et of equation (4) and (5) are the contitutive law for a deformation mechanim. They can be olved with repect to time to give the train after any loading hitory. But while there are atifactory model for the rate equation (4), there i till lack of undertanding the tructural evolution with train or time. Therefore a ufficient decription of the equation et (5) i not poible at preent. However, to proceed further, implifying aumption about the tructure have to be made. Here are two poible alternative. A very imple aumption i that of contant tructure: 0 S i = S i. (6) Then the rate equation for γ& completely decribe platicity. The econd aumption i that of teady tate: ds i = 0. (7) dt In thi cae the internal variable no longer appear explicitly in the rate equation. They are determined by the external variable of tre and temperature. Either implification reduce the contitutive law to a ingle equation: ( σ ) & γ = f,t, (8) ince, for a given material the propertie P j are contant and the tate variable are either contant or determined by σ and T. In the following ection rate equation in the form of Eq. (8) are aembled for each of the deformation mechanim (i.e., we conider only teady tate creep). 16

25 Deformation Mechanim 3.2 Diffuional Flow (Diffuion Creep) NabarroHerring Creep Nabarro and Herring developed a model that decribe vicou creep by treinduced diffuion of vacancie [17, 18]. Thi mechanim applie to polycrytalline metal at high temperature where all dilocation are aumed to be pinned and grain boundarie are conidered a ditinguihed ource or ink for vacancie. By a tre σ normal to a boundary, vacancy formation i promoted, becaue the work neceary to form a vacancy i reduced by the amount σ Ω, where Ω i the volume of the vacancy (Ω b³) and b i the magnitude of Burger vector). The equilibrium probability of finding a vacancy near a grain boundary (e.g. urface A and B in Fig. 13) i given by [19]: Fig. 13: Vacancy flow (red) and oppoed atom flow (blue) in a grain under tenile and compreive tre (chematic drawing). N N V S σ F f σ Ω = exp exp. kt kt (9) Here N V i the number of vacancie for N S lattice ite and F f i the free energy for vacancy formation. If a grain i loaded by normal tree σ (ee Fig. 13), then the vicinity of face A and B how vacancy concentration ~exp(σ Ω/kT) while the immediate urrounding of face C and D have concentration ~exp(σ Ω/kT). Therefore a concentration gradient i etablihed which caue a vacancy flow from A and B to C and D [19] a indicated in Fig. 13. Simultaneouly the vacancy flow i accompanied by a matching flow of atom in the oppoite direction (ee Fig. 13). The mechanim for thee combined flow are well known (ee for example [20]): The poibilitie for diffuive atomic movement are by direct interchange of 17

26 Deformation Mechanim pair of adjacent atom, by ring mechanim, by movement a intertitial atom, or by crowdion formation. Additionally, in alloy the atomic flow can be coniderably enhanced by the Kirkendall effect. Together thi lead to grain elongation or creep in the longitudinal direction and tranveral contraction. Under the aumption that vacancy generation and annihilation are very rapid the concentration difference between neighboring grain face (like A and C in Fig. 13) become α σ Ω σ Ω F f C = exp exp exp Ω kt kt kt, (10) where α i a contant jut le than unity, ince the vacancy concentration at the boundarie differ lightly from the equilibrium value [19]. Obviouly σ i not contant along the grain face, and therefore the diffuion path are horter near the grain corner. Due to tre relaxation one can aume that σ = β σ at ditance d/4 from the boundarie (d i the grain ize, σ i the macrocopic hear tre. and β i nearly unit). The length of a diffuion path through thi point i l = π/2 (d/4) and the atomic flux acro one atom area i then given by: J = v b D v C l = v b D v 8 C π d, (11) where D v i the diffuivity of vacancie. Further, the hear train for each tranferred atom i γ = 2b/d and with Eq. (10) the teadytate creep rate become: 32α βσ Ω & γ = D inh. (12) 2 π d kt Since the argument of the hyperbolic ine in Eq. (12) i mall for low tree the teadytate creep rate can be approximated by [19]: 32αβ D σ Ω & γ =, (13) 2 π d kt where D i the elfdiffuion coefficient. Thi rate equation i widely known a Nabarro Herring creep. The equation (13) agree well with experimental reult at very high temperature, like for example on Ag [21], on Au [22], on Cu [23] or on δfe [24]. Other analye of thi diffuional flow at high temperature have been hown by [2527]. The reulting relation are imilar to Eq. (13) but with different contant. 18

27 Deformation Mechanim Coble Creep Selfdiffuion in poly crytal comprie two mechanim: lattice and grain boundary diffuion. While lattice diffuion dominate at very high temperature, grain boundary diffuion take over mainly at lower temperature (ee for example [28, 20]). Coble decribed the diffuional flow at lower temperature and tree with the following rate equation (Coble creep [29]): 42π δ σ Ω = d 3 kt γ& DB. (14) Here D B i the boundary diffuion coefficient and δ the effective thickne of the grain boundary Alternative Decription In mot model for diffuion creep both mechanim (Eq. (13) and (14)) are combined in one rate equation (ee, for example, [16]): 42σ Ω = d 2 kt γ& Deff, (15) with D eff πδ D + B D 1. (16) d D = L L Here D L i the lattice diffuion coefficient. At high temperature a poly crytal may glide along it grain boundarie. Since face of neighboring grain boundarie are uually randomly ditributed, there are tre peak at the grain edge. To get train larger than about 10 6 cm along a boundary the tre peak have to be reduced by atomic flux, i.e. by diffuion. For thi Raj and Ahby developed a reaonable model (ee [30] or [31]): The arrangement of grain boundarie i implified by a twodimenional hexagonal network (Fig. 14) and the profile of the diplacement face (e.g. for mode 1) i developed in a Fourier erie. The firt component of thi erie i decribed by it wave length λ and amplitude d/2. Grain diplacement by a hear tre σ i then accompanied by normal tree σ n a hown in Fig. 15, where the normal tree are given by: 19

28 Deformation Mechanim σ n σ λ 2π y = 4 in (17) π d λ Fig. 14: Ideal poly crytal with a hexagonal network of grain boundarie which enable gliding on two orthogonal mode (blue and red). The vacancy flux i indicated with dotted arrow. Fig. 15: Grain boundary gliding lead to cavitie which are compenated by according flow of vacancie from expanion (red) to compreion (blue) zone (indicated by arrow). 20

29 Deformation Mechanim Thee normal tree produce an additional chemical potential for the vacancy generation µ = σ n Ω which force the vacancie to flow from the expanion to the compreion zone at the boundary (ee Fig. 15). Thi proce define the train rate at the grain boundary [30, 31]: 64σ Ωλ πδ D = + B & γ DL 1. (18) 3 π d kt λ DL It i a imilar reult like that from Nabarro, Herring, and Coble (Eq. (15) and (16)). But here the lattice diffuion creep rate depend on λ/d 3 intead of 1/d 2 while the grain boundary creep rate depend on δ/d 3 in both decription. That i, in Eq. (18) lattice diffuion i decribed not only by grain ize but by the grain hape (with a hape factor d/λ). 3.3 Powerlaw Creep (Dilocation Creep) At high temperature material how rate dependent platicity, or creep. Above 0.3 T M for pure metal and about 0.4 T M for alloy thi dependence on train rate become rather trong. It may be expreed by an equation of the form: n σ &, (19) γ ~ µ where µ i the hear modulu and where n ha a value between 3 and 10 in the high temperature regime. Therefore thi deformation mechanim i called powerlaw creep Powerlaw Creep by Climb (plu Glide) At high temperature dilocation acquire two degree of freedom: they can climb a well a glide. If a gliding dilocation i blocked by dicrete obtacle, a little climb may releae it, and, therefore, enable it to glide to the next obtacle where the whole proce i repeated. The glide tep i reponible for almot all of the train, while the average dilocation velocity i determined by the climb tep. Mechanim which are baed on uch a climbpluglide equence are referred to a climbcontrolled creep [3234]. There i an important difference between powerlaw creep and the deformation mechanim of the following ection like, for example, dilocation glide (low temperature platicity, ee Section 4.5): the ratecontrolling proce i the diffuive motion of ingle ion or va 21

30 Deformation Mechanim cancie to or from the climbing dilocation, rather than the activated glide of the dilocation itelf. That i, the dominant proce take place at an atomic level. A teadytate dilocation theory baed on the climb of edge dilocation ha been propoed by Weertman [35]. In hi propoal it wa aumed that work hardening occur when dilocation are arreted and piled up againt exiting barrier uch a grain boundarie or precipitate. The tre field at the tip of the piledup dilocation induce multiple lip and the formation of LomerCottrell eile dilocation anywhere along the original piledup dilocation. At thi point dilocation beyond the LomerCottrell barrier may eaily ecape by climb. But climb behind the LomerCottrell barrier would lead to the generation of new dilocation loop and to a teadytate creep rate. Thi model can be applied very well to fcc and bcc metal. In a further propoal Weertman [36] uggeted that edge dilocation of oppoite ign gliding on parallel lip plane would interact and pile up whenever a critical ditance between lip plane i not exceeded. Like in the firt model, dilocation may ecape from the piledup array by climb. Dilocation pileup lead to work hardening while climb i a recovery proce. Therefore, a teadytate condition i reached when the hardening and recovery rate are equal. The creep rate will then be controlled by the rate at which dilocation can climb. On the other hand, the climb mechanim require that vacancie be created or detroyed at dilocation with ufficient eae and that in the vicinity of the dilocation an equilibrium concentration of vacancie be maintained at a level ufficient to atify the climb rate. At the tip of a pileup of dilocation a nonvanihing hydrotatic tre may exit which exert a force on a dilocation in a direction normal to the lip plane and favor up or down climb. Vacancie are aborbed where the tre i compreive and they are created where the tre i tenile (compare previou ection and Fig. 1315). Thi reult in a change in the vacancy concentration near a dilocation line. Therefore, a vacancy flux i etablihed between egment of dilocation which act a ource and egment acting a ink. The vacancy concentration C e in equilibrium with the lead dilocation in a pileup i given by: C e = C 0 ± 2Lσ 2 b 2 exp, (20) µ kt 22

31 Deformation Mechanim where 2L i the length of the dilocation pileup and C 0 i the equilibrium concentration of vacancie in a dilocation free crytal. The vacancy concentration at a ditance r from each pileup i aumed to be equal to C 0. Thu the rate of climb X & i approximated by [19]: 2 4 C Dv σ Lb X& 2 0 =, (21) µ kt where D v i the coefficient for vacancy diffuion and with 2Lb 2 σ ²/µkT < 1. Thi relation ha been obtained under the aumption that vacancie are eaily detroyed or created and that an equilibrium concentration exit between pileup in the vicinity of dilocation. The diffuion problem for the flux of vacancie, however, may be different for pecific climbing procee. Further, if vacancie are only created or detroyed at jog, the energy of jog formation ha to be taken into account in the cae that they are formed by thermal fluctuation. On the other hand, if thee are formed mechanically by interection, then the rate of climb may till depend primarily on elfdiffuion. Thi i certainly the cae if it i accepted that vacancie will diffue rapidly along a dilocation line toward or away from a jog. For the econd model by Weertman the rate of dilocation climb i given alo by Eq. (21). The teadytate creep model in thi cae become: X& & γ = NAb, (22) 2r where N i the denity of dilocation participating in the climb proce or for thi model the denity of ource, A i the area wept out by a loop in the pileup, and 2r i the eparation between pileup. The tre neceary to force two group of dilocation loop to pa each other on parallel lip plane ha to be greater than µb/4πσ. Thu an etimate of r may be ued with: µ b r =. (23) 4πσ Further, the probability p of blocking the dilocation loop generated from one ource by loop emanating from three other loop i given by: 2 2NL µ b p =. (24) 3σ 23

32 Deformation Mechanim Now the creep rate can be obtained from Eq. (21)(24) by etting p=1, A=4πL², and by the aumption that elfdiffuion occur by vacancy migration. The creep rate at low tree become [19]: cπ σ D & γ =, (25) 7 bnµ kt where c i a numerical contant of about ¼ and D i the coefficient for elfdiffuion. Equation (25) ha been proofed experimentally for pure metal at low tree to a greater extent than any other theoretical creep relation [19]. Although exception exit to the exponent of 4.5 on the tre, thi value i remarkably cloe to oberved value. There i general agreement that high temperature creep i diffuioncontrolled and that it depend on D. It wa hown for many metal teted at variou temperature [37, 38] that a plot of ln[γ& /D ] againt ln[σ /µ] reduce the experimental reult into a ingle band, further ubtantiating Eq. (25). On the other hand, there are ome point and obervation which don t fit to thi theory. It i quetionable whether pileup can reult from the interaction between edge dilocation of oppoite ign gliding on parallel lip plane. Calculation have hown that the interaction between uch dilocation doe not impede their motion. They can cro over each other and form dipole which in turn are mobile (ee, for example, [39]). Further, in thi theory the number of dilocation in a pileup i given by 2σ L/µb which predict extenive pileup at high tree but not necearily at low tre level. Another deduction of powerlaw creep baed on climbpluglide i given in [16] which i briefly outlined in the following: Above about 0.6 T M climb i generally latticediffuion controlled. The velocity v c at which an edge dilocation climb under a local normal tre σ n acting parallel to it Burger vector can be approximated by [40]: v c DL σ n Ω bkt, (26) where D L i the lattice diffuion coefficient and Ω the atomic volume. The baic climbcontrolled creep equation may then be obtained under the aumption that σ n i proportional to the applied tre σ and that the average velocity of the dilocation i proportional to the 24

33 Deformation Mechanim rate at which it climb. With Eq. (26), the Orowan theory [41], and an etimate of the denity of mobile dilocation [42] the creep equation become: 3 DLµ b σ & γ = c1, (27) kt µ with the approximation Ω b³. All contant are incorporated in c 1 which i of order unity. Some material but they are exception obey thi equation with a power of 3 and a contant c 1 of about 1 [43]. It appear that the local normal tre i not necearily proportional to σ implying that dilocation may be moving in a cooperative manner which concentrate tre. Or the denity of mobile dilocation varie in more complicated manner than aumed by [42]. Over a limited range of tre up to about 10 3 µ experiment are well decribed by a modification of Eq. (27) [44]: n DLµ b σ & γ = c2, (28) kt µ where the exponent n varie between 3 and about 10. However, preent theoretical model for thi behavior are unatifactory. None can convincingly explain the oberved value of n. And further, the very large value of the dimenionle contant c 2 trongly ugget that ome important phyical quantity i till miing from the equation (ee, for example, [45, 43]). However, it provide a good decription of experimental data and a generalization of Eq. (27) it ha ome bai a a phyical model. But Eq. (28) cannot decribe the increae of the exponent n and the drop of the activation energy for creep at lower temperature which are experimental fact. To incorporate thee obervation one ha to aume that the tranport of matter via dilocation core diffuion contribute ignificantly to the overall diffuive tranport of matter. And under certain condition thi mechanim hould become dominant [46]. A poibility to include the contribution of core diffuion i the definition of an effective diffuion coefficient (ee [47] and [46]): D = D f + D f, (29) eff L L C C where D C i the core diffuion coefficient, and f C and f L are the fraction of atom ite aociated with each type of diffuion. The value of f L i nearly unity while the value of f C i determined by the dilocation denity ρ: f C = a c ρ, (30) 25

34 Deformation Mechanim where a c i the croection area of the dilocation core in which fat diffuion i taking place. Meaurement of the quantity a c D C can be found in [48]: the diffuion enhancement depend on the dilocation orientation (it i probably 10 time larger for edge than for crew dilocation) and on the degree of diociation (and therefore on the arrangement of the dilocation). Even the activation energy i not contant. But in general, D C i about approximately equal to the grain boundary diffuion contant D B, if a c i taken to be 2δ ² (δ i the effective grain boundary thickne). A common experimental obervation for the dilocation denity i (ee, for example, [42] or [59] for the cae of tungten in the creep regime): 10 σ ρ 2 b µ 2, (31) Then the rate equation for powerlaw creep with an effective diffuion coefficient become: n 2 µ b σ 10 ac σ DC γ& = c2 DL 1 +, (32) 2 kt µ b µ DL Equation (32) i a combination of two rate equation. At high temperature and low tree lattice diffuion i dominant ( γ& ~σ n ) while at higher tree (or low temperature) core diffuion i the dominant proce ( γ& ~σ n+2 ) Powerlaw Breakdown At high tree above about 10 3 µ the imple powerlaw break down. The meaured train rate are ignificantly greater than predicted by Eq. (32). Thi proce i evidently a tranition from climbcontrolled to glidecontrolled flow, that i, it i a tranition from diffuioncontrolled to thermally activated mechanim. There have been numerou attempt to decribe it empirically and mot decription lead to the generalized form ([60, 61, 19]): [ ( n Q )] cr γ& ~ inh c σ exp, (33) RT which reduce to a imple powerlaw at low tree (c σ < 0.8) and which become an exponential at high tree (c σ > 1.2). Meaurement of the activation energy Q cr in the powerlaw breakdown regime often give value which exceed that of elfdiffuion. Thi might indicate that the recovery proce dif 26

35 Deformation Mechanim fer from that of climbcontrolled creep. Some of the difference, however, may imply reult from the temperature dependence of the hear modulu which ha a greater effect when the tre dependence i in the exponential region. Then a better fit to experiment may be found by [16]: n a σ Q cr γ& = A inh exp, (34) µ RT The equation may be rewritten for an exact correpondence with the powerlaw equation (32). Then the rateequation for both powerlaw creep and powerlaw breakdown read a follow [16]: n 2 µ b σ = 10 ac σ DC γ& A inh a DL 1 +. (35) 2 kt µ b µ DL 3.4 Mechanical Twinning Twinning i an important deformation mechanim at low temperature in hcp and bcc metal (and ome ceramic). In fcc metal (like the autenitic teel AISI 316 conidered in thi work) it i le important and occur only at very low temperature. The tendency of fcc metal to twin increae with decreaing tacking fault energy being greatet for ilver and completely abent in aluminium. Therefore, and becaue exiting decription are rather uncertain, it i jut mentioned briefly in the following. Twinning i a variety of dilocation glide involving the motion of partial intead of complete dilocation. The kinetic of the proce, however, often indicate that nucleation and not propagation determine the rate flow. Anyway, it may till be poible to decribe the train rate by a rate equation for twinning by [16]: F N σ & γ = & γ t exp 1. (36) kt σ t Here F N i the activation free energy to nucleate a twin without the help of external tre, γ& t i a contant which include the denity of available nucleation ite and the train produced for a ucceful nucleation, and σ t i the tre required to nucleate twinning in the 27

36 Deformation Mechanim abence of thermal activation. Further the temperature dependence of F N mut be included to explain the obervation that the twinning tre may decreae with decreaing temperature (ee [49]). 3.5 Dilocation Glide (Low Temperature Platicity) Below the ideal hear trength flow by the conervative or glide motion of dilocation i poible, provided a ufficient number of independent lip ytem i available. Thi motion i almot alway obtaclelimited, i.e., it i limited by the interaction of potentially mobile dilocation with other dilocation, with olute or precipitate, with grain boundarie, or with the periodic friction of the lattice. Thee interaction determine the rate of flow and at a given rate the yield trength. Dilocation glide i a kinetic proce while dilocation climb (plu glide) i a diffuioncontrolled proce, a outlined in Section 4.3. Thi kinetic proce wa firt decribed by Orowan [41]: Mobile dilocation with a denity ρ m move through a field of obtacle with an average velocity v ; the velocity i almot entirely determined by their waiting time at the obtacle; the train rate they produce due to their movement i then given by: & γ = b v, (37) ρ m where b i the magnitude of the Burger vector of a dilocation. At teady tate the denity of mobile dilocation ρ m i a function of tre and temperature only. The implet function conitent with both theory and experiment i given by [42]: 2 σ ρ m = α, (38) µ b where α i a contant of order unity. The velocity v depend on the force F acting on the dilocation by: F = σ b, (39) and on it mobility M: v = M F. (40) Now the problem i to calculate M, and therefore v. In the mot intereting range of tre M i determined by the rate at which dilocation egment are thermally activated through or round obtacle. The next difficulty encounter by the fact that the velocity i alway an ex 28

37 Deformation Mechanim ponential function of tre, but the detail of the exponent depend on the hape and nature of the obtacle. So at firt ight there are a many rate equation a there are type of obtacle. But on cloer examination obtacle can be divided in two broad clae: dicrete obtacle and extended, diffue barrier to dilocation motion. Example of the firt type are trong diperoid or precipitate which can be bypaed individually by a moving dilocation. Other example of dicrete obtacle are foret dilocation or weak precipitate which may be cut by dilocation movement. Obtacle of the econd cla are concentrated olution or the lattice itelf which lead to latticefriction Platicity Limited by Dicrete Obtacle The velocity of dilocation in a polycrytal i frequently determined by the trength and denity of the dicrete obtacle it contain. If the free energy of activation for cutting or bypaing an obtacle i G(σ ), the mean velocity i given by the kinetic equation (ee [5052, 16]): v ( ) σ G = β bν exp, (41) kt where β i a dimenionle contant and ν i a frequency. The quantity G(σ ) depend on the ditribution of obtacle and on the pattern of internal tre which characterize one of them. A regular array of boxhaped obtacle each one viewed a a circular patch of contant, advere, internal tre lead to the imple reult [16]: σ ( ) = G σ F 1, (42) ˆ τ where F i total free energy the activation energy required to overcome the obtacle without aid from external tree. The material property τˆ i the tre which reduce to zero, forcing the dilocation through the obtacle without help from thermal energy. It can be though of a the flow trength of the olid at 0 K. But obtacle are eldom boxhaped and regularly paced. Therefore, to decribe other obtacle hape a well a random ditribution, the equation may be rewritten in the following way [51]: G 29

38 Deformation Mechanim G ( σ ) = F p q σ 1. (43) ˆ τ The value of p, q, and F are bounded, i.e., all model lead to value of [16]: 0 p 1. (44) 1 q 2 The importance of p and q depend on the magnitude of F. When F i large, their influence i mall and their choice i unimportant. Therefore, for dicrete obtacle p = q = 1 i a good choice. But when F i mall, the choice become more critical. In thi cae (e.g. for diffue obtacle) p and q have to be fitted to the experimental data (ee alo Section 4.5.2). The train rate enitivity of the trength i determined by F (it characterize the trength of a ingle obtacle). It i helpful to categorize obtacle by their trength a hown in Table 2; example for typical value of F are 2 µb³ for large or trong precipitate, and 0.5 µb³ for pure metal in the workhardened tate. The quantity τˆ i the hear trength in the abence of thermal energy. It reflect not only the trength but alo the denity and arrangement of the obtacle. For widely paced, dicrete obtacle τˆ i proportional to µb/l, where l i the obtacle pacing. The actual value of τˆ depend on obtacle trength and ditribution (ee Table 2). For pure metal trengthened by workhardening it can be imply aumed that τˆ = µb/l. At thi point a combination of all the above lited equation lead to the rate equation for dicrete obtacle controlled platicity: 2 σ F σ & γ = αβν exp 1. (45) µ kt ˆ τ When F i large (a i normally the cae), the tre dependence of the exponential i o large compared to the preexponential γ& 0 that it may be et contant for a reaonable fit to experimental data: 2 σ 1 γ& = αβν. (46) µ 30

39 Deformation Mechanim Table 2: Characteritic of obtacle, where F i the activation energy for a dilocation to overcome an obtacle, τˆ i the hear trength at 0 K, and l i the obtacle pacing [16]. Obtacle Strength Strong Medium Weak F τˆ Example 3 2 µ b µ b < 0.2 µ b 3 3 µ b > l µ b l µ b l diperion; large or trong precipitate foret dilocation; radiation damage; mall or weak precipitate << lattice reitance; olution hardening Platicity Limited by Lattice Friction The velocity of dilocation in mot polycrytalline olid i limited by an additional ort of barrier the interaction with the atomic tructure itelf. Thi Peierl force or lattice reitance reflect the fact that the energy of the dilocation fluctuate with poition. The amplitude and wavelength of the fluctuation are determined by the trength and eparation of the interatomic bond. The crytal lattice preent an array of long, traight barrier to the motion of the dilocation. It advance by throwing forward kink pair (with help from the applied tre and thermal energy) which ubequently pread apart (ee [53, 51, 39]). It i uually the nucleation rate of kink pair which limit the dilocation velocity. The free energy of activation for thi event depend on the detailed way in which the dilocation energy fluctuate with ditance and on the applied tre a well a on temperature. Like thoe for dicrete obtacle, the activation energie for all reaonable hape of lattice reitance form a family which can be decribed a before (Eq. (43)). Together with a choice of p and q adapted to experiment (ee [16] or [54]) the final rate equation for platicity limited by lattice reitance read: σ F p σ & γ = & γ p exp 1, (47) µ kt ˆ τ p where F p i the free energy of an iolated pair of kink and τˆ p i (approximately) the flow tre at 0 K. The σ ² term in the preexponential ha to be retained in thi cae, becaue F p i relatively mall. For bcc metal and ceramic γ& p may be et to / [16]. 31

40 Deformation Mechanim 3.6 Elatic Collape The ideal hear trength define a tre level above which deformation of a perfect crytal or of one in which all defect are pinned ceae to be elatic and become catatrophic. Then the crytal tructure become mechanically untable. The intability condition and hence the ideal hear trength at 0 K can be calculated from the crytal tructure and an interatomic force law by imple tatic, provided the interatomic potential i known for the material of interet (ee, for example, [55, 56]). But above 0 K the problem become a kinetic one: The frequencie at which dilocation loop nucleate and expand in an initially defectfree crytal have to be calculated. Since the focu in the preent work lie on creep behavior, a imple decription of the elatic collape eem to be ufficient: & γ & γ = = 0 for for σ αµ. (48) σ < αµ Mot often it i aumed that the temperature dependence of the ideal hear trength i the ame a for the hear modulu µ. For fcc metal the contant α take value of about 0.06, for bcc metal it i about 0.1 [16]. However, for a creep model thi tre range i not of interet and will be neglected in the further conideration. 32

41 Deformation Mechanim 3.7 Summary The preent ection provide an overview of the main deformation mechanim and their decription that will be ued in the following Section for modeling the creep behavior of the 316L(N) teel. Fig. 16: Diffuion creep i dominated by two procee. At high temperature lattice diffuion control the rate (NabarroHerring creep). Grain boundary diffuion (Coble creep) take over at lower temperature. With uual creep tet diffuion creep become detectable only for temperature well above 0.6 T m. At the ame time, the applied tenile tree have to be maller than the yield limit. In thi range, boundary diffuion control the train rate which i alo called Coble creep. At even higher temperature (about 0.8 T m for autenitic tainle teel), lattice diffuion (NabarroHerring creep) take over (ee Fig. 16). For the combined decription of thee two diffuion mechanim we ue equation (15) and (16). For tenile tree above the yield limit dilocation tart to glide and pile up at obtacle. They may be releaed by climb motion. Dilocation climbing i a rather low proce which i mainly controlled by diffuion. Therefore, climbcontrolled powerlaw creep ha to be decribed by lattice diffuion and core diffuion (ee Fig. 17) Fig. 17: Powerlaw creep i mainly baed on diffuion controlled dilocation climb procee. Diffuion may occur along dilocation cell or through the lattice. Both mechanim are included in the rate equation (32). At high temperature and low tree lattice diffuion i dominant ( γ& ~σ n ) while at higher tree (or low temperature) core diffuion i the domi 33

42 Deformation Mechanim nant proce ( γ& ~σ n+2 ). At tree higher than about 0.1 % of the hear modulu a tranition take place. With increaing tre the glidecontrolled flow dominate over the diffuioncontrolled dilocation climb (ee Fig. 18). The generalized form of empirical decription for thi tranition range i given by Eq. (33). Fig. 18: For tree about higher than 10 3 µ the powerlaw break down. A tranition from climbcontrolled to glidecontrolled flow take place. Fig. 19: Below the ideal hear trength flow by the conervative or glide motion of dilocation i poible, provided a ufficient number of independent lip ytem i available. Thi motion i almot alway obtaclelimited. At even higher tree but below the ideal hear trength pure conervative motion of dilocation dominate (platicity). Thi kinetic proce (dilocation glide) i mot often obtaclelimited (ee Fig. 19) and may be decribed bet by the Orowan formalim [41]. Depending on the type of obtacle thi lead to different rate equation for the deformation decription. In the preent cae a retriction to dicrete obtacle i ufficient. The according decription i given by Eq. (45). A combination of all deformation decription combined with experimental reult allow for compiling illutrative ocalled deformation map [57, 16]. Thee diagram ummarize deformation procee depending on tre and temperature. The preent work, however, i retricted to deformation rate which are typical for creep tudie. 34

43 SteadyState Creep Model 4 SteadyState Creep Model 4.1 Diffuion Creep For the decription of diffuion creep we ue Eq. (15) and (16), that i 1 σ πδ & C = 42 Ω DL + DB, (49) d kt d γ 2 where D L and D B are lattice and boundary diffuion coefficient, repectively, with D L L QL RT Q RT = D 0 e and D = D 0 e. (50) B B B Fig. 20: Contribution of boundary diffuion creep to the train rate according to the model given by Eq. (49). (Symbol repreent experimental reult). In thi model mot contant are well known, like the atomic volume Ω, grain ize d, and grain boundary thickne δ (ee Appendix 6.1). Value for the lattice diffuion coefficient D 0L and activation energy Q L are taken from [16]. Since boundary diffuion data are not readily available for the preent material the according value have to be adjuted to the experiment and reaonable aumption. In our cae the boundary diffuion activation energy Q B ha been choen to be 200 kj/mol which i about 20 % higher than the value reported for 316 teel [16]. With thi, the aumption that the contribution of lattice and boundary diffuion are equal at about 0.6 T M lead to a value for D 0B of m²/. A can be een in Fig. 20, only the longterm creep tet performed at 600 C are near the range dominated by boundary diffuion creep. According to our model, all other tet have not been influenced by diffuion creep. 35

44 SteadyState Creep Model Figure 21 how both boundary and lattice diffuion a predicted by the model given by Eq. (49). It can be clearly een that lattice diffuion certainly play no role for the given temperature range. It contribution to the train rate become only relevant at much higher temperature (> 0.6 T M ) where it dominate over the contribution of grain boundary creep. Fig. 21: Contribution of boundary diffuion creep (continuou line) and lattice diffuion creep (dahed line) to the train rate according to the model given by Eq. (49). (Symbol repreent experimental reult). 4.2 Platicity (Dilocation Glide) Low temperature platicity i a high tre deformation mechanim. Therefore it play only a minor role for creep. However, to cover the whole tre range in our model we ue the implified decription for platicity (Eq. (45) and (46)) which read then F σ Q & γ = & P γ 0 exp 1 or = kt ˆ P σ & γ & P γ 0 exp 1. (51) τ RT ˆ τ For the preent material τˆ can be approximated a µb τˆ, (52) l where b i the magnitude of Burger vector, l i the obtacle pacing, and µ i the temperature dependent hear modulu given by T 300K µ = µ ( T ) = µ (53) T M 36

45 SteadyState Creep Model Due to the large amount of precipitate the obtacle pacing take a relatively mall value of about 40 nm. The activation energy F ha been etimated to be about 0.75 µ 0 b 3 which correpond to Q P = 460 kj/mol (all contant are given in Appendix 6.1). A ha already been mentioned and a can be clearly een from Fig. 22, the train rate of creep tet are uually too mall to approach the regime of platicity. According to the model only the tet reult for 550 C are cloe to thi region. Fig. 22: Contribution of low temperature platicity to the train rate according to the model given by Eq. (51). The black triangle repreent an additional creep tet reult at 500 C. The grey dahed line correpond alo to 500 C. (Symbol repreent experimental reult, line are from model). For verification there i added an additional value of a creep tet at 500 C to the diagram in Fig. 22 which wa deformed only platically and which fit nicely to the model. 4.3 Power Law Creep (Dilocation Climb) A ha already been outlined in connection with Eq. (28) the current decription of dilocation creep include ome degree of freedom. Therefore the model ha to be fitted to the experimental data. For thi we ue the experimental reult from jut three tet temperature in the following model etup. Then the reulting model can be verified with help of the data from the other two tet temperature. Equation (32) decribe the whole powerlaw creep including dilocation climb, activated by lattice and core diffuion. But a ha been demontrated with the diffuion creep model (Section 4.1, Fig. 21) lattice diffuion can be completely neglected within the preent temperature range. Therefore the expreion for powerlaw creep reduce to 37

46 SteadyState Creep Model n+ 2 µ b σ γ& PL = c3 DC, (54) kt µ where D C i the core diffuion coefficient with D C C QC RT = D 0 e. (55) D C i of the ame order of magnitude a the grain boundary diffuion contant D B and ha therefore been choen to be 10 5 m²/. Again, the hear modulu µ depend on temperature a given in Eq. (53). Thi leave three remaining parameter the exponent n, the activation energy Q C, and the contant c 3 which have to be fitted to the experimental data. In loglogrepreentation the lope i defined by n, the vertically ditance by Q c, and the offet by c 3. Fig. 23: Contribution of powerlaw creep to the train rate according to the model given by Eq. (54) and (55). For the adjutment of the three free parameter only reult gained at 600 C, 650 C, and /00 C are conidered. (Symbol repreent experimental reult, line are from model). The according reult i hown in Fig. 23. Here the parameter have been choen a follow: Q C = 520 kj/mol, n = 5, and c 3 = Tranition from Creep by Climb to Creep by Glide At tree above about 10 3 µ the powerlaw break down. That i, tarting from thi point (for the preent material the onet i at 86 MPa) the model ha to decribe a tranition from creep by climb (powerlaw) to creep by glide (platicity). Adapting Eq. (35) to the preent model lead to 38

47 SteadyState Creep Model n+2 inh σ 3 α γ& PLBD = c DC (56) µ which leave only one free parameter (α ) to fit to experiment. For thi we have only ued data from the 600 C creep tet to verify the reult later on with the other data. Figure 24 how the tranition curve according to α = 800. Fig. 24: Tranition from powerlaw creep (long dahed gray line) to platicity (hort dahed gray line) according to the model given by Eq. (56). For the adjutment of the free parameter α only reult gained at 600 C are conidered. (Symbol repreent experimental reult, line are from model). 4.5 Aement and Dicuion of the Stationary Creep Model To obtain the complete model all contribution have to be ummed up accordingly: & γ PL for σ 86 MPa & γ = & γ C + & γ P + (57) & γ PLBD for σ > 86 MPa where the ingle contribution are given by the Eq. (49), (51), (54), and (56). A comparion between the model and the experimental data i given in Fig. 25. A can be een, the tranition from powerlaw creep to platicity (which ha been fitted to the 600 C reult) fit alo nicely to the reult gained at 550 C and 650 C. At higher temperature the experiment have been performed at tree below the tranition range. 39

48 SteadyState Creep Model The powerlaw creep range which ha been fitted to the 600 C, 650 C, and 700 C experimental reult, applie alo for the 750 C tet reult. But the experiment at 550 C, however, are well above the prediction from the model. Fig. 25: The tationary creep model (line) a defined by Eq. (57) compared to the experimental reult (ymbol). A already mentioned, only the creep tet performed at 600 C reach down to the range of diffuion creep. Therefore, it i not poible to verify the model for the other temperature. But at leat for 600 C the model prediction fit perfectly to the experiment. With the exception of the lowtre longterm creep tet reult at 550 C there i a good agreement between experimental data and model prediction. Now the quetion i why the model doen t reemble the lowtre 550 C value, or vice vera. From a phyically point of view it i rather unlikely that an additional deformation mechanim hould occur only at lower temperature. And ince thi tre range i dominated excluively by diffuion baed procee, it i even more quetionable, that the train rate hould increae with lower temperature compared to the applied powerlaw. 40

49 SteadyState Creep Model Error Analyi 180 MPa 550 C Fig. 26: After hour the creep rate uddenly drop from one tationary level down to another. If the tet had been aborted at hour, everybody would have accepted the higher tationary creep rate a abolute minimum. Now even a further drop can be imagined. Error Analyi 150 MPa 550 C Fig. 27: The tet wa aborted after about hour becaue it wa thought that tationary creep had already been reached. But now it can not be excluded that there could have been a drop in train rate during a further continuation of thi creep tet imilar to the obervation in Fig. 26. Thee conideration have neceitated a cloer look on the experimental data (low tre reult at 550 C) and their evaluation. It revealed the ituation depicted exemplarily in Fig. 26 and 27. In the cae of 550 C and 180 MPa (Fig. 26) there ha been a udden drop after 41

50 SteadyState Creep Model hour from one tationary creep range to another. Thi creep tet wa aborted after hour with a pecified minimum creep rate of about /h. But if thi tet had already been aborted after hour, nobody would have doubted the reulting value of /h. And now it ha to be expected that there might have been further drop in train rate, if the tet had been continued. The other example in Fig. 27 (150 MPa, 550 C) how no uch drop in the train rate curve. But obviouly the given value for the minimum creep rate i now rather doubtful. It i eay to imagine that a continuation of the creep tet could have led to much lower value. The other creep tet at 550 C in the lowtre range are imilar to thoe of Fig. 26 and 27. That i, actually the according data had to be corrected toward lower value. Since quantitative tatement are not poible, the only thing known i that the real value are lower than the already publihed reult. Thi i indicated in Fig. 28 and give even more reaon to acknowledge the tationary creep model.? Fig. 28: The 550 C lowtre data have to be corrected toward lower value ince the according creep tet were aborted too early. 42

51 Concluion 5 Concluion The preent invetigation have been mainly baed on reult from creep experiment performed at IMFI, FZK with the autenitic tainle teel AISI 316 L(N) (heat no from CreuotMarell). Epecially longterm creep tet have hown that there i a coniderable change in the teadytate creep behavior at low tree: the creep rate are much higher than the value that would have been expected by an extrapolation from the uual (higher) tre range. For component deign thi i a bad ituation, becaue the real lifetime would be ignificantly horter compared to etimate baed on the uually available creep data. Since AISI 316 type teel i a very common material for all kind of application alo for ITER component it would be highly helpful, if it eemingly odd teadytate creep behavior could be decribed by a far reaching model. The etup of uch a model wa the motivation of the current paper. At firt glance, there are three poible reaon for the kink in the creep rate v. tre curve: (I) At very low tree the initial train i within the elatic range while at higher tree pecimen are deformed platically at the tart of the creep tet. Thi platic deformation could act like cold working the material and, therefore, lead to higher creep trength. (II) Autenitic tainle teel are known for their thermal intability, that i, they are prone to aging. Hence, more or le evere formation of precipitation could change the microtructure ignificantly and caue higher creep rate, dependent on creep time which in turn i correlated to the applied tree. (III) Creep rate depend on different tredependent deformation procee. If the tre dependency of thee procee differ coniderably let aume σ in one cae and σ 7 in another, an according change of the teadytate creep rate would be obviou. Reaon (I) can be ruled out, becaue the decreae in initial train take place continuouly with decreaing tree. Cold work and accompanied hardening certainly play a role in creep behavior, but thi i not an explanation for the current dramatic change in creep rate at low tree. Alo precipitation formation can not be the reaon for the oberved creep behavior, ince there i no correlation between the different precipitation type, the time of formation and the period of teadytate creep. Of coure, precipitation may alo influence creep propertie, but again, not in uch a ditinctive way a oberved. 43

52 Concluion For a reaonable explanation thi leave only the interaction of different deformation mechanim which have been reviewed in detail: diffuional flow, powerlaw creep, mechanical twinning, dilocation glide, and the elatic collape. It ha been demontrated that for a decription of the teadytate creep behavior only grain boundary diffuion, powerlaw creep, and the tranition from dilocation climb to dilocation glide are relevant, where the latter i jut a limit that i barely reached with contant load creep tet. Thi lead to a model coniting of three main deformation mechanim and two tranition: At very low tree only grain boundary diffuion contribute to the train rate which i proportional to the tre (~ σ). Thi regime can only be reached by performing extremely longterm tet. In the preent cae diffuion creep occurred alluively after 10 year at 600 C. Then there i a relatively harp tranition to creep triggered by dilocation climb. In the preent cae dilocation climb depend on core diffuion and lead to creep rate proportional to the 7 th power of tre (~ σ 7 ) thu the name Powerlaw Creep. Starting from medium tree there i a continuou tranition from creep by dilocation climb to platicity which depend olely on dilocation glide. The platicity regime i uually not reached with creep tet. Here the train rate depend exponentially on tre (~ e σ ). To adapt the model to creep experiment with the AISI 316 L(N) teel it need only a few parameter: grain boundary diffuion coefficient and activation energy to decribe diffuion creep, a generic contant, the core diffuion coefficient and activation energy, and the power exponent to decribe powerlaw creep, and jut a generic contant for the decription of the tranition from powerlaw creep to platicity. For completene of the model, platicity may be decribed by four additional parameter. To determine all parameter from experimental data, it need creep tet at three different temperature in the uual tre range and at leat ome longterm experiment which reach down into the diffuion creep regime. In the preent cae the latter wa not quite fulfilled. Therefore, diffuion creep might be decribed omewhat too conervative. However, all data (with the exception of the 550 C longterm experiment) fit nicely to the model prediction. 44

53 Concluion But it ha been hown that thee experiment were aborted too oon, that i, it wa not poible to extract reliable minimum creep rate. In ummary, the preented teadytate creep model for the autenitic tainle teel AISI 316 L(N) i baed on well known deformation mechanim and can predict creep rate in the whole temperature range relevant for application deign. Due to the mall number of parameter it hould be no problem to apply the rate equation to other material. 45

54 Literature 6 Literature 1. T. Nakazawa, Mat. Sci. Eng. A 148, (1988). 2. M. D. Mathew, International Conference on High Nitrogen Steel, HNS 88, Lille, France, 1820 May, M. Schirra, Nucl. Eng. Deign 147, 6378 (1993) 4. M. Schirra, Nucl. Eng. Deign 188, (1999). 5. M. Schirra, KfKReport 4767, 4861, and 6699, Forchungzentrum Karlruhe, Germany, September 1990, Augut 1991, and February NRIMCreep Data Sheet No , National Reearch Intitute for Metal, Tokyo, Japan. 7. M. Schirra, Annual Meeting on Nuclear Technology, Aachen, Germany, May NRIMCreep Data Sheet No. 14A1982, National Reearch Intitute for Metal, Tokyo, Japan. 9. NRIMCreep Data Sheet No. 15A1982, National Reearch Intitute for Metal, Tokyo, Japan. 10. NRIMCreep Data Sheet No , National Reearch Intitute for Metal, Tokyo, Japan. 11. NRIMCreep Data Sheet No. 6B2000, National Reearch Intitute for Metal, Tokyo, Japan. 12. M. Schirra, KfKReport 4273, Forchungzentrum Karlruhe, Germany, February A. F. Padilha and P. R. Rio, ISIJ International 42, (2002). 14. P. R. Rio and A. F. Padilha, Encyclopedia of Material: Science and Technology, K. H. Buchow et al. (Ed.), , Elevier, Amterdam, NRIMMetallographic Atla of Longterm Crept Material No. M2, National Reearch Intitute for Metal, Tokyo, Japan, H. J. Frot, and M. F. Ahby, Deformationmechanim Map, Pergamon Pre, Oxford, F. R. N. Nabarro, in: Report on Conference on Strength of Solid, Phy. Soc. of London, 75, C. Herring, J. Appl. Phy. 21, 437 (1950). 19. F. Garofalo, Fundamental of Creep and CreepRupture in Metal, MacMillan, New York, B. Chalmer, Phyical Metallurgy, John Wiley, New York, A. P. Greenough, Phil. Mag. 43, 1075 (1953). 22. B. H. Alexander, M. H. Dawon, and H. P. Kling, J. Appl. Phy. 22, 439 (1951). 23. A. L. Pranati, and G. M. Pound, Tran. AIME 203, 664 (1955). 24. A. T. Price, H. A. Hall, and A. P. Greenough, Acta Met. 12, 49 (1964). 25. E. Orowan, J. Wet Scot. Iron and Steel Int. 54, 45 (194647). 26. W. Kauzman, Tran. AIME 143, 57 (1941). 46

55 Literature 27. A. H. Cottrell, and M. A. Lawon, Proc. Roy. Soc. A 19, 104 (1949). 28. P. G. Shewmon, in: Phyical Metallurgy, ed. by R. W. Cahn, NorthHolland Publihing Company, Amterdam, R. L. Coble, J. Appl. Phy. 34, 1679, (1963). 30. R. Raj, and M. F. Ahby, Tran. AIME 2, 1113 (1971). 31. P. Haaen, Phyikaliche Metallkunde, SpringerVerlag, Berlin, J. Weertman, J. Mech. Phy. Solid 4, 230 (1956). 33. J. Weertman, Tran. AIME 218, 207 (1960). 34. J. Weertman, Tran. AIME 227, 1475 (1963). 35. J. Weertman, J. Appl. Phy. 26, 1213 (1955). 36. J. Weertman, J. Appl. Phy. 28, 196 and 1185 (1957). 37. O. D. Sherby, Acta Met. 10, 135 (1962). 38. D. McLean, Metallurgiacal Review 7, 481 (1962). 39. D. Hull, Introduction to Dilocation, 2 nd Edition, Pergamon Pre, Oxford, J. P. Hirth, and J. Lothe, Theory of Dilocation, McGraw Hill, E. Orowan, Proc. Phy. Soc. 52, 8 (1940). 42. A. S. Argon, Scripta Met. 4, 1001 (1970). 43. A. M. Brown, and M. F. Ahby, Scripta Met. 14, 1297 (1980). 44. A. K. Mukherjee, J. E. Bird, and J. E. Dorn, Tran. ASM 62, 155 (1969). 45. R. L. Stocker, and M. F. Ahby, Scripta Met. 7, 115 (1973). 46. S. L. Robinon, and O. D. Sherby, Acta Met. 17,109 (1969). 47. E. W. Hart, Acta Met. 5, 597 (1957). 48. R. W. Balluffi, Phy. Stat. Sol. 42, 11 (1970). 49. G. F. Bolling, and R. H. Richman, Acta Met. 13, 709 and 723 (1965). 50. A. G. Evan, and R. D. Rawling, Phy. Stat. Sol. 34, 9 (1969). 51. U. F. Kock, A. S. Argon, and M. F. Ahby, Prog. Mat. Sci. 19 (1975). 52. B. de Meeter, C. Yin, M. Doner, and H. Conrad, in: Rate Procee in Platic Deformation, ed. by J. M. C. Li and A. K. Mukherjee, A.S.M., P. Guyot, and J. E. Dorn, Can. J. Phy. 45, 983 (1967). 54. P. L. Raffo, J. LeCommon Metal 17, 133 (1969). 55. W. R. Tyon, Phil. Mag. 14, 925 (1966). 56. A. Kelly, Strong Solid, Oxford Univerity Pre, M. F. Ahby, Acta Met. 20, 887 (1972). 58. L. D. Blackburn, The Generation of Iochronou StreStrain Curve, ASME Winter Annual Meeting, New York, R. R. Vandervoort, Met. Tran. 1, 857 (1970). 60. C. M. Sellar and W. J. McG. Tegart, Mem. Sci. Rev. Met 63, 731 (1966). 61. W. A. Wong and J. J. Jona, Tran. AIME 242, 2271 (1968). 47

56 Appendix/Table 7 Appendix/Table 7.1 Contant and Parameter The baic material contant for the preent AISI 316 L(N) tainle teel a well a ome phyical contant are given in Table 3. All parameter ued for the creep model are lited in Table 46. Table 3: Phyical and material contant for the AISI 316 L(N) tainle teel. Contant Value Ref. Boltzmann contant, k x J/K Ga contant, R J/(mol K) Melting temperature, T M 1810 K [16] Grain ize, d 100 µm meaured Thickne of grain boundary, δ 20 x 10 9 m meaured Atomic volume, Ω 1.21 x m 3 [16] Lattice contant, L x m [16] Burger vector (magnitude), b 2.58 x m [16] Shear modulu at 300 K, µ MN/m 2 [58] Temperature dependence of hear T d modulu, M µ 0.85 [58] µ 0 dt Table 4: Diffuion creep parameter ued for the AISI 316 L(N) tainle teel. Parameter Lattice diffuion coefficient, D 0L Latt. diff. activation energy, Q L Boundary diffuion coefficient, D 0B Bound. diff. activation energy, Q B Value 37.5 x 10 6 m²/ 280 kj/mol 6 x 10 6 m²/ 200 kj/mol 48

57 Appendix/Table Table 5: Platicity parameter ued for the AISI 316 L(N) tainle teel. Parameter Activation energy, Q P Activation energy, F Obtacle pacing, l Value 460 kj/mol 1.04 x J 40 nm Preexponential, γ& / Table 6: Powerlaw and powerlaw breakdown parameter ued for the AISI 316 L(N) tainle teel. Parameter Value Pre contant, c 3 2 x Core diffuion coefficient, D 0C 10 x 10 6 m²/ Core diff. activation energy, Q C 520 kj/mol Creep exponent, n 5 Contant, α

58 Appendix/Table 7.2 Experimental Data Table 7: Creep tet reult for the AISI 316 L(N) tainle teel. Specimen dimenion have been M5 x 30 mm. Z u : reduction of area, A u : total elongation, ε o : initial train, t m : time to rupture. Tet No. T C σ MPa t m h ε o % A u % Z u % ε& min 10 6 /h ZSV ZSV ZSV ZSV ZSV ZSV ZSV ZSV ZSV aborted ZSV ZSV ZSV ZSV

59 Appendix/Table Table 8: Lowtre longterm creep tet reult for the AISI 316 L(N) tainle teel. Specimen dimenion have been M8 x 200 mm. Tet No. T C σ MPa aborted after h ε o % ε& min 10 6 /h Table 9: Creep tet reult from NRIM (ee Ref. 11) of the 18Cr12NiMo teel AAL. Only data from the medium tre range i conidered ince thi material omewhat i different from the AISI 316 L(N) a well a the ued tet equipment. Z u : reduction of area, A u : total elongation, ε o : initial train, t m : time to rupture. NRIM ref. code T C σ MPa t m h ε o % A u % Z u % ε& min 10 6 /h AAL AAL AAL AAL

60 Appendix/Table Table 10: Lowtre longterm creep tet reult for the AISI 316 L(N) tainle teel at 550 C (TimeStrain value). Specimen dimenion have been M8 x 200 mm. Creep Time [h] ε 0 = 7.50 % σ = 250 MPa Strain [mm] ε 0 = 4.83 % σ = 210 MPa Strain [mm] ε 0 = 2.85 % σ = 180 MPa Strain [mm] ε 0 = 1.18 % σ = 150 MPa Strain [mm] ε 0 = 0.34 % σ = 135 MPa Strain [mm] ε 0 = 0.16 % σ = 120 MPa Strain [mm] ε 0 = 0.09 % σ = 100 MPa Strain [mm] aborted

61 Appendix/Table after h aborted

62 Appendix/Table after h after h aborted after h aborted after h aborted after h aborted Table 11: Lowtre longterm creep tet reult for the AISI 316 L(N) tainle teel at 600 C (TimeStrain value). Specimen dimenion have been M8 x 200 mm. ε 0 = 3.03 % ε 0 = 0.32 % ε 0 = 0.07 % ε 0 = 0.06 % ε 0 = % ε 0 = 0.04 % σ = 170 MPa σ = 120 MPa σ = 100 MPa σ = 80 MPa σ = 70 MPa σ = 60 MPa Creep Time [h] Strain [mm] Strain [mm] Strain [mm] Strain [mm] Strain [mm] Strain [mm]

63 Appendix/Table aborted after 7500 h aborted after h

64 Appendix/Table aborted after h aborted after h aborted after h aborted after h

65 Appendix/Table 7.3 Metallographic Examination Tet No. ZSV1921: 750 C, 2650 h 57

66 Appendix/Table 58

67 Appendix/Table 59

68 Appendix/Table 60

69 Appendix/Table Tet No. ZSV1913: 750 C, h 61

70 Appendix/Table 62

71 Appendix/Table 63

72 Appendix/Table 64

73 Appendix/Table 65

74 Appendix/Table AISI 316 L(N) KSW heat (imilar to preent CRM heat): 750 C, 1404 h 66

75 Appendix/Table 67

76 Appendix/Table 68

77 Appendix/Table 69

78 Appendix/Table 70

79 Appendix/Table 71

80 Appendix/Table AISI 316 L(N) KSW heat (imilar to preent CRM heat): 750 C, h 72

81 Appendix/Table 73

82 Appendix/Table 74

83 Appendix/Table 75

84 Appendix/Table 76