Modeling microstructural evolution in fusion reactor environments

Journal

of Nuclear

Materials

127

1338~134 (1985) 127-133

MODELING MICROSTRUCTURAL EVOLUTION IN FUSION REACTOR ENVIRONMENTS

interactions between dislocation. cavity and precipitate evolution in austentic stainless steels irradiated in fission reactors are analyzed, Cavity evolution is modeled using the critical bubble concept: helium bubbles grow stably with the incremental addition of helium up to a critical size. thereafter they grow rapidly as voids. Dislocations and precipitates are preferred sites for bubbles and influence the critical size, hence. incubation period. The models predict broad trends in the swelling data base. as well as many detailed observations. The calibrated models predict a nonmonotic swelling response to increases m helium, with a peak at intermediate values; this suggests that fusion environments will generally have lower incubation times and higher swelling than found for fission reactor irradiations. The mechanisms controlling swelling in Ti-modified steels are also examined: partitioning of helium to a fine distribution of stable MC phases is found to be the key factor in retarding swelling.

1. Introduction

The evolution of the microstructure and microchemistry of structural alloys subject to large neutron exposures at elevated temperatures involves subtle interactions between a large number of complex solid state reaction [l]. Hence. attempts to develop rigorous ab initio models of microstructural evolution are unlikely to succeed. However. simple semiempirical models can be derived to help interpret data and guide the design of experiments. This requires a combination of: analysis of broad data trends: results of single variable experiments; detailed microstructural observations; specific submodels of important mechanisms; and integrated models which can be related to important observables. The emphasis here is on analysing the large data base on void swelling in the 300 series austenitic stainless steels from fission reactor irradiations. ~icrostructural changes in fusion environments are expected to be governed by the same basic physical process.

2. Key concepts and observations Three simultaneous evolutions ing dislocations (both loops and and alloy matrix chemistry. and and voids). Interactions between critical in determining the path dence of the individual processes.

are important, includnetwork), precipitates cavities (both bubbles these evolutions are and exposure depen-

The evolution of the dislocation structure has been modeled [2.3] in terms of production (loops nucleate and grow, network is formed from loop unfaulting and climb sources) and loss (loop unfaulting and network climb to annihilation) terms. After a transient period, a quasi-steady-state (production = loss) condition is achieved. Both the network and. particularly, loop denOU22-3115/85/$03.30 c’ Elsevier Science Publishers (hearth-H(~lland Physics Publishing Division)

B.V.

sities are dependent on temperature. This substructure is critical to cavity evolution since dislocations are [4]: (1) normally the dominant point defect sink for fast reactor irradiations; (2) the primary source of interstitial bias; (3) an important site for the formation of helium bubbles. Sink densities can be directly measured and used with simple models [5] to calculate sink strengths. Even in the rapid swelling regime the dislocation to void sink strength ratio is typically 5 to 10. and is relatively independent of temperature 141. Calculation of dislocation bias involves many complications, assumptions and uncertainties. However, the post-incubation swelling rates can be used to estimate empirical bias factors, which are found to be in excess of 0.2 (41, consistent with simple theory. Obstacles cause dislocations to bow as they climb due to excess interstitial capture in parallel to swelling. Bowing lowers significantly the excess flux of vacancies to other sinks at small bowing radii (high strength) and high temperatures. This can be modeled as a compressive stress. If dislocations sources do not operate. flow of vacancies from the grain boundaries would control swelling, in a form of irradiation driven Herring-Nabarro creep [6]. 2. .?.

Preciprtutes

and

matrix

chemistq’

Austenic stainless steels undergo decomposition reactions dependent on temperature. time. and prior thermal mechanical history [7,8,9]. The effects of irradiation fall in three categories: perturbed on where a phase forms at shorter times and/or lower temperatures and with different number densities and slightly varied composition; modified - where there is a major change in the composition or morphology; and induced or prevented - where a phase which does not form thermally occurs under irradiation or vice versa. The primary effect of irradiation appears to be perturbations or modifications of thermal phases. Three basic processes

are important: radiation enhanced diffusion (RED): radiation induced segregation (RIS); and formation of defect-solute sinks. The phases are enriched in particular alloy ~onstjtu~ilts, hence pr~~jpitatiol~ also influences the matrix chemistry, which is also changed by RIS to sinks even absent discrete second-phase particles. Estimates of RED for typical fast reactor conditions are equivalent to temperature increases ranging from about 40 to 100°C at irradiation temperatures of 650 to 450°C. The accelerated precipitation will be amplified by a higher density of precipitates formed at lower temperatures. Lee et al. [7] and Williams [S] have shown that a number of thermal phases are inherently nickel and silicon rich, and that some of these can be further enriched in these solutes due to RIS by factors of up to two or more. Phases which are not naturally silicon and nickel rich tend to be destabilized by excess local concentrations of these solutes. The RIS around sinks forms a local microalloy region, and. if the sink density is not too high (i.e. RIS is nor diluted), can also lead to radiation induced phases such as y’ [9]. Application of mass balance principles allows approximate evaluation of changes in the matrix chemistry. The alloy composition dictates the volume fraction of the important radiation perturbed and modified phases which can form due to competition for critical elements. limiting them to several percent. Observed enrichment levels and the volume fractions of the various phases. show that matrix depletion of solutes due to precipitation will not exceed a few percent: hence. the relative changes are small for nickel, but large for elements such as silicon and carbon. Solute depletion decreases with increasing temperature. Hence. nickel depletion by precjpitation is not a likely trigger for the onset of rapid swelling. The apparent correlation between matrix nickel depletion and rapid swelling is largely due to segregation OF the voids themselves. Further, rapid nickel enrichment of certain phases observed to coincide with rapid swelling can be readily related to transfer of segregated nickel to precipitates from associated voids.

Theoretical considerations [IO-121 and direct experimental observations [1,9,12,13] demonstrate the sequence of events for cavity evolution. Cavities first form as small, possibly overpressurized, gas bubbles. Beyond a relatively modes size they grow with the addition of helium atoms as near-equilibrium bubbles. The bubbles have a distribution of sizes dictated both by continuing nucleation into the smallest size classes, and helium absorption and resolutioning/re-emission. Bubbles grow up to a maximum size where they become unstable and continue to grow, without the necessity of addition of helium. as voids. A varying fraction of the bubble population converts to voids, leading to bimodal size

distributions in some cases. Two limiting modes of cavity evolution are a predominantly bubble path and a predominantly void path: a switch in the basic path induced by changes in mi~r~3stru~tural variables ha\ been termed a bifurcation. Dislocations and precipitate interfaces are preferred sites for bubble formation and act as collectors to promote growth. Theory would suggest that dislocation nodes are particularly favorable bubble locations. Hence. it is notable to observe that cavity densittes in fast reactor irradiations are roughly proportional to the Jislocation node density 141. Boundaries between the matrix and ceramic particles which are good traps for helium have inherently IOU diffusion coefficients which depend on the type of intcrface 1141. The interface helium mobility would also be influenced by precipitate misfit strains: compressive strains would result in vacancy subsaturations. hence. low diffusion rates; tensile strains would induce local vacancy supersaturations. hence, increase interfact helium diffusivity. This suggests that positive misfit strain (PMS) precipitates would tend to have a stable population of small bubbles, while negative misfit strain (NMS) phases would be more likely to have lower densities of bubbles which would tend to coarsen. This behavior is clearly observed in comparing bubble distributions on MC particles (PMS) to those on Labrs precipitates (NMS) [9.15]. General scaling laws to predict bubble densities and site distributions as a function of the irradiation and microstructural variables are under development [ 161. but are not currently available. Bubble-to-void conversion (BVC) takes place at :I critical number of helium atoms in a bubble ( m) [5. I I ]. The value of nr is a function of the net vacancy influx. and the emission rate which is determined by the properties of the bubble. Neglecting recombination. the vacancy influx is proportional to the defect production rate divided by the total sink strength and self-diffusron coefficient. Hence. ,>r is sensitive to both the irradiation induced mi~r[?stru~ture and altered matrix microchemistry, since the diffusion coefficient is dependent on both the major alloy elements (i.e. Fe-NipCr) and minor additions such as silicon. Elements which have positive vacancy binding energies are believed to be particularly important since they tend to increase the diffusi~~n rates at temperatures in the swelling regime [17]. Silicon appears to fall in this category [l&19]. Hence. commercial steels would he expected to have larger m and larger incubation exposures than high purity model alloys. Other effects of alloying elements and impurities may be increases in strength. reductions in bias factors, increased recomhination rates due to vacancy trapping, alteration of surface energies, and enhancement of the production rate and thermal stability of transient cascade vacancy clusters.

similar suggestion based on their observation that swelling 304 (0.24% MO) is lower than in 316 (2.5% MO) stainless steels irradiated at 590°C. Such behavior is contrary to the effects on swelling attributed to lower nickel (9.6 vs 13.4%) and higher chromium (18.4 vs 16.5%) in the 304. The reversed role of higher carbon leading to shorter incubation times at higher temperatures [25] can be similarly interpreted.

Precipitation can have an indirect influence on the exposure required for the onset of rapid swelling. by removal of important elements. such as silicon from the matrix. However, at higher temperatures precipitates appear to have a direct effect on the BVC process. through a number of mechanisms. The m of bubble located on a precipitate is lower due to the balance of surface-interface energies [4]. Misfit strains would result in precipitates acting as biased sinks, perturbing both matrix supersaturations and local flows of nearby defects. Precipitates with NMS would be biased for interstitials. and would divert interstitial fluxes away from attached cavities: further, such precipitates would generate stresses on boundary sources, resulting in an additional vacancy flux to interface cavities. The potentially powerful effect of such precipitate sites on the bubble conversion process is evident if the total misfit volume of about 31~6 is the misfit strain and ~1~ the precipitate volume, is compared to the much smaller volume change associated with a permanent BVC. Conversely, precipitates with positive misfit strain would increase the critical helium number needed for BVC by the inverse of many of these mechanisms. Precipitate assistance is probably required for void formation in commercial alloys at high temperatures. Fig. 1 shows trend bands for swelling in commercial 316 SS [20-221 and Fe-Ni-Cr ternaries [23] with a similar base composition at three temperatures; limited data on a pure 316 containing 2.5% MO [24] and a low carbon commercial steel [25] are also included. At a temperature of 520°C the purer alloys clearly swell considerably sooner than their commercial couterparts: at 590°C there is an essential overlap of the trend curves; while at 650°C there is an indication that the incubation period is slightly longer in the pure ternaries. Presumably precipitates in commercial alloys assist BVC more than the matrix impurities retard it. The lower incubation time of the pure 316 at 590°C relative to ternaries may be in part due to the formation of Laves phase (FeMo,). Weiner and Boltax [26] have made a

3. Critical bubble models Quantitative applications of the concepts outlined above have been incorporated in critical bubble models (CBM). The critical helium content for BVC is calculated as a function of the effective vacancy supersaturation I$, irradiation temperature T, surface energy y. and the precipitate interface energy factor F,, as [4,27]. m=R(~)~,(y/kT)i(l/ln~)2 where the effective

supersaturation

+ = ( D,C, - D,C,)/D,C,v

(1) is defined

as (2)

Here the DC parameters are the diffusivity concentration products for vacancies (v) and interstitials (i). and DC;l is the thermal self-diffusion coefficient. The function g( +) is a derived analytic expression which corrects for deviations from ideal gas behavior [27]. Rate theory is used to calculate $J as a function of the evolving microstructure and microchemistry [4]. The rate theory calculations can incorporate vacancy trapping, solute enhanced diffusion. various biased sinks, cascade clusters, external or internal stress fields, etc. The helium is partitioned to an initial distribution of small bubbles and other trapping sites based on sink-strength ratios [4,11]. Dislocations act as collectors for matrix bubbles and precipitates are assigned time-dependent sink strengths and numbers of associated bubbles. Bubbles grow to m where they convert to voids. Void growth is modeled using rate theory [4,11].

30

I 6

10 01 (n/m*)

20 x 10:

01 (n/m*)

Fig. 1. Comparison of swelling trends for ternary Fe-Ni (12-16R)-Cr with those for commercial 316 alloys at three temperatures.

dt (n/m*)

(16%). low carbon and pure stainless steel (2.5% Mo) alloys

The microstructural parameters are empirical and observed incubation fluences and swelling rates are used to fit a minimum number of model parameters: the dislocation bias has been used as the primary fit parameter. It is notable that a bias consistent with both theory and experimental swjelling rates also yields reasonable \alues of incubation times for nominal choices of other Important model parameters. The effects of statistlcal nucleation are neglected in CBM. Calculations show that for most circumstances of interest void formation on bubbles i.\ much more rapid than for homogeneous gas free nucleation. Clearly. nucleation on bubbles would be expected at sizes approaching the critical radius. However. because of the rapid dropoff in the nucleation rate with decreasing helium content. actual deviations from a void formation path through the critical bubble \ize do not have a significant effect on either void formation times or number densities. It is further noted that nucleation (because it is a highly nonlinear process) ia particularly sensitive to defect concentration fluctuations induced by the stochastic cascade defect productlon mechanism. In contrast. the BVC is insensitive to such fluctuations. As a corollary, BVC is also relatively insensitive to external pulsing effects. The CBM has been applied to swelling of 316 in fast reactors yielding predictions of incubation times and transition and rapid post-incubation swelling rates which arc in good agreement with observations over a wide range of temperatures [4]. Predicted reductions in swelling at low temperatures are due to the consequence of including cascade vacancy clusters. which become an important sink in this regime. However, data for aged steels [2X] and for Fe-NipCr ternary alloys [23] suggests that rapid swelling at temperatures as low as 400°C is possible. This may suggest that impurities enhance the formation or thermal stability of cascade cluster sinks. The CBM has been used to evaluate the effect of the helium-to-displacement [He(appm)/dpa] ratio on swelling of a 20% CW heat of 316 (DO heat) irradiated in both the HFIR and EBR-II with He/dpa ratios ranging from about 70 to 0.5 respectively. The model, calibrated to the EBR-II data. predicted the higher cavity density in HFIR would lead to extended incubation exposure and lower swelling in the temperature range from 450 to 650°C‘ up to exposures of 100 dpa [29] consistent with observation (up to about 70 dpa). The model also predicted the observed microstructural differences ~ large precipitate associated voids in EBR-II and small matrix bubbles in HFIR. A subsequent CBM calibration to a much larger set of fast reactor data for 20% CW first core stainless steels was used to explore the effect of He/dpa variations (41. The cavity density (N,) was treated parametrically as. N, a (He/dpa) p. The model predicted a nonmonotonic dependence of swelling on the He/dpa ratio. depending on temperature and p. Low swelling is predicted for high values of p. He/dpa ratios and tempera-

ture due to the bifurcation effect noted above: at very high cavity densities matrix bubbles become the dominant sink for both helium and point defects. thereby retarding the formation of precipitate associated voids. The effect of high cavity densities is greater at higher temperatures due to larger critical bubble helium content, M. However. at lower values of p and temperature, increases in the He/dpa ratio are predicted to increase swelling. because the effect of higher total helium is larger than the influence of a more modest increase in partitioning sites and m. For conditions and parameters believed to be most relevant to fusion reactors (e.g. He/dpa - 10 and temperatures below 600°C) accelerated swelling (relative to fast reactor irradiations) is predicted by the model. Recently. the CBM has been used to examined the individual effects of important microstructural and material parameters on jrz and bifurcations [30]. The model predicts that the strongest effects on m are due to the diffusion coefficient, dislocation density, damage rate. and strongly vacancy biased sinks; higher sensitivity is generally found with increasing temperature. More recent results are shown in fig. 2 [31]. Fig. 2(a) shows the predicted ratio of the incubation exposure at

c tlGARNER ET AL 600 700 TEMPERATURE (“C)

500

10 . -

0 50

DATA MODEL

I - BATES

1 (JNM

98, 1981)

TRENDS

I

/

100

150

Ti - T, (“C)

Fig. 2. C’omparison of calibrated C‘BM predictions with (a) stress. and (b) temperature history effects data for (‘W 316 \1CClh.

G. R. Odette / Modeling evolution MIfwon

an applied stress level of 100 MPa to the stress free value for a range of temperatures; the agreement with experimentally derived ratios [32] is excellent. Little effect of applied stress on the steady-state swelling is predicted, also consistent with observation [32]. Fig. 2 shows model predictions for the excess swelling (actual minus isothermal) at 50 dpa for gradual temperature decreases from an initial temperature T, to a final temperature T,. Excellent agreement with experiment [33] is found for the 525°C starting temperature and the predicted trends and reasonable consistency is found for the 585°C starting temperature. The model predicted little effect of temperature variations on post-incubation swelling rates as found experimentally [34]; and comparisons for gradual temperature increases were also found to be in semiquantitative agreement with experiment [34]. Fig. 3a shows the predicted temperature variation in incubation exposures, compared to the data [23] for ternary alloys containing 12 to 16% nickel and 16% chromium. In this calculation the nominal microstructural parameters for total cavity and dislocation density used in the previous study of stainless steel were assumed; slight adjustments in the surface energy and diffusion coefficient result in the excellent fit achieved.

1

0 -

1

TERNARY

INCUBATION

EXPOSURE’

MODEL BUBBLE-VOID CONVERSION EXPOSURE

12-15%

Ni. 16% Cr

*DATA

COMPILATION

- GARNER

(a)

500

450

550

600

TEMPERATURE

650

700

(“C)

125 0 650°C

-MODEL

Fig. 3. Comparison of experimental incubation times (7) data with CBM predictions: (a) for 12-16s nickel, 16% chromium ternary alloys as a function of temperature; and (b) as a function of nickel content at 500°C and 650°C for 16% chromium ternary alloys.

reactor environments

131

Fig. 3(b) shows the effect of nickel variations over the range from 10 to 30% on the incubation exposure at several temperatures. This has been modeled by assuming a diffusion coefficient dependence on nickel in the form, D,,(Ni) = Dsd(O.l)(l + A(Ni - 0.1)). A value of A = 4.2 yielded the model predictions shown as solid lines at 500 and 65O”C, consistent with the data trends. This parameter gives a ratio of the diffusion coefficient D,,(0.3)/Db,(0.1) of about 1.9. Published composition dependent values of D,d in the literature can be extrapolated to 575°C over this nickel range for comparison: for Fe-Ni binary alloys, Million’s [35] results gives a ratio of about 1.0, while for Zensiy the ratio is about 20 [36]; for Fe-Ni-Cr ternary alloys the results of Rothman suggest a ratio of about 3. The effect of silicon enhanced diffusion on swelling incubation is also consistent with the CBM. Compositional effects submodels can be readily incorporated into the integrated swelling model. For example, increasing silicon depletion from the matrix due to precipitation could be treated as an exposure-dependent diffusion coefficient. The effect of nickel depletion on swelling incubation in 316 stainless steel can be further assessed based on these observations and concepts. Fig. 3(b) shows that such variations would be expected to be important only at higher temperatures, and then in a very modest way. Indeed, the potential importance of precipitation induced nickel depletion is further reduced. if it is recognized that the magnitude of the nickel depletion decreases at higher irradiation temperatures. precisely in the regime where the decrease in incubation time with decreasing nickel becomes more important, The CBM has been most recently applied to analyse the swelling resistance of titanium modified stainless steels which where subject to various heat treatments before irradiation to about 45 dpa at 600°C in HFIR [31]. Based on nominal 316 stainless steel parameters. the CBM predicts a bifurcation to a low swelling bubble microstructure out to 50 dpa. beyond a cavity density of 3 X IOZ2/m’. This is consistent with the experimental observations. The 25% CW alloy has little void swelling and high density of small bubbles of about 5 x lO”/m’; the SA and SA-aged alloys have cavity densities of about 1 X 10”/m3. and are rapidly swelling by 45 dpa. A CW-aged alloy shows intermediate cavity densities and swelling. There is a corresponding variation in the phases, with a predominance of fine MC in the low swelling CW condition and void associated laves and G-phase in the high swelling SA condition. The major effect of the heat treatment appears to be on early helium partitioning and phase development.

4. Discussion These physical models and concepts important experimental observations:

rationalize many the sequence of

132

ti. R. Odette / Modeling evolution in fusron reactor envwonment.r

events leading to rapid void swelling; bimodal cavity distributions; precipitate association of large voids; evolution of the dislocation microstructure; the temperature dependence and magnitudes of the swelling incubation exposures; the relative temperature insensitivity of the rapid swelling regime. Swelling models based on the critical bubble concept also predict the observed effects of applied stress, some compositional variations. and the helium-to-displacement ratio. Further, such models predict observed microstructurally mediated bifurcations between void and bubble dominated cavity microstructures. Application of the models to predict swelling behavior of CW 316 stainless steel alloys in fusion environments generally suggests shorter incubation exposures and corresponding higher swelling levels relative to behavior in fast reactor environments, A key aspect of these models is the explicit treatment of interactions between the various evolutions. including the critical role of dislocations and precipitates in controlling the early formation of a bubble distribution, and the direct and indirect effects of various precipitates on bubble-to-void conversion. The important characteristics of the precipitates are misfit strains and interface diffusivity; this separates good from bad second phases. The major factor in the swelling resistance of titanium modified steels involves helium partitioning to a high density of MC particle traps. which are able to maintain a fine distribution of bubbles due to their interface properties. The duration of the incubation period is thus directly controlled by the stability of the helium bubble-MC particle complexes: instabilities which form void associated precipitates, such as G-phase. will lead to the rapid onset of swelling. These semiempirical models will require continued updating based on new data and refined theories. Important unresolved issues include: the low temperature dependence of swelling as governed by mechanisms such as cascade clusters; cavity density scaling laws which account for variations in microstructure, and helium mobility and displacement generation rates and ratios: the effects of elements such as phosphorus and boron which appear to retard both high temperature thermal creep and swelling; and solute partitioning and thermodynamic factors which control the stability and balance of phases under irradiation.

Acknowledgements

Helpful discussions with P. Maziasz of ORNL, H. Trinkhaus of KFA-Julich, and G. Lucas of UCSB are gratefully acknowledged. Special thanks are given to Roger Staller formally at UCSB, and now at ORNL. as a key collaborator in much of the work described in this paper. The research was supported by the US Department of Energy, Office of Fusion Energy, under contract DE-AM03-76SF0034.

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