Dose Dependence of Strength After Low-TemperatureIrradiation in Metallic Materials

THAK SANG BYUN, MEIMEI LI, and KENNETH FARRELL

This study intends to review and characterize the low-temperature (<473 K [200 �C]) irradiation-hardening behaviors in metallic materials and to propose new interpretations on the dosedependence of strength, particularly in the prehardening and saturation regimes. The analysis ofresults of yield stress-dose curves indicate that four dose-dependence regimes exist: the pre-hardening, main hardening, saturation, and embrittlement regimes. The semilog plots of yieldstress vs dose data revealed that the prehardening regime displaying zero hardening or softeningwas common at least for the alloys with low-dose data available. It was observed that the doserange of the prehardening regime increased with the strength of material, which indicates thatslower initiation in irradiation hardening is expected when strength is higher. For the majorityof the metallic materials analyzed, it was reconfirmed that the exponent of the power-lawhardening function was evaluated to be about 0.5 in the main hardening regime and about 0.1 inthe saturation regime. In these positive hardening regimes, the low strength pure metals such asFe, Ta, Cu, and Zr displayed lower hardening exponents. The minimum dose to the saturationof irradiation hardening was in the range of 0.003 to 0.08 dpa, depending on the category ofmaterials. It was also reaffirmed that there exists a strong relationship between the saturation inirradiation hardening and the occurrence of plastic instability at yield.

DOI: 10.1007/s11661-012-1309-z� The Minerals, Metals & Materials Society and ASM International (outside the USA) 2012

I. INTRODUCTION

A low-temperature irradiation can significantly hardenmetallic materials by accumulating numerous tiny defectclusters without significant influence from the thermallyactivated annihilation of defects.[1–4] The majority ofpast studies on mechanical properties in irradiatedmaterials have focused on the irradiation-hardeningphenomenon because it is almost always accompaniedby degradation of critical mechanical properties such asthe loss of ductility and embrittlement.[3–11] In mostmetallic materials, irradiated at low temperatures(£473 K [200 �C]), the change from main hardening tosaturation regime occurs at doses <0.1 dpa, and thehardening exponent decreases from about 0.5 to about0.1.[3,10,11] Some experimental results, however, showedlittle irradiation hardening or even radiation softening inlow-dose region before hardening initiated.[12–17] Thisirradiation-softening phenomenon is obvious in high-strength metals, notably in refractory metals,[13–15] but itis not known if such a softening-then-hardening behav-ior is a common phenomenon in the relatively softmetallic materials.

Most of the strength data produced in the past do nothave enough dose resolution in the low-dose region, andtherefore, the phenomena in the early irradiations were

largely ignored, and the question of irradiation softeningas a common phenomenon in metallic materials has notbeen answered. As advanced nuclear power systemsrequire more high-strength materials that tend to showobvious irradiation softening or delay in irradiationeffects, however, it is worth understanding phenomenaoccurring in early irradiation. Finding a controllingparameter for the hardening and softening phenomenaneeds to be emphasized since the regime of nonharden-ing can be extended to a significant dose in advancedhigh-strength materials.This study aims at characterizing the regimes in the

strength–dose response of metallic materials to low-temperature (£473 K [200 �C]) irradiation. It was alsoattempted to generalize various phenomena such as theirradiation softening (or prehardening regime) andsaturation of irradiation hardening. In this study, thelow-temperature irradiation-hardening database pro-duced by the authors in the past decade was extendedand reanalyzed to achieve these goals. The dose depen-dence of strength is characterized focusing on thesimilarities among material groups: Four distinguish-able hardening regimes in DYS-dose curves wereidentified and described as a common behavior inhigh-strength metallic materials after low-temperatureirradiation. Note that DYS is defined as the irradiation-induced change of the 0.2 pct offset yield stress or theupper yield stress with obvious yield drop. Examples ofirradiation softening were displayed and it was sug-gested that the existence of a prehardening regime iscommon for many alloys. It was also found that thedose range of the prehardening regime was proportionalto the strength of the material. Finally, an attempt was

THAK SANG BYUN and KENNETH FARRELL (Retiree),Research Scientists, are with Oak Ridge National Laboratory, OakRidge, TN 37831. Contact e-mail: byunts@ornl.gov MEIMEI LI,Research Scientist, formerly with Oak Ridge National Laboratory, isnow with Argonne National Laboratory, Argonne, IL 60439.

Manuscript submitted February 19, 2012.Article published online July 20, 2012

S84—VOLUME 44A, JANUARY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

made to find a relationship between irradiation harden-ing and plastic instability (necking).

II. STRENGTH DATA FORLOW-TEMPERATURE IRRADIATION

For this study, we used the tensile property databasefor low temperature (£473 K [200 �C]) irradiations thathave been accumulated at ORNL for the past decade, ofwhich the latest version includes several high dose-resolution data sets for ferritic carbon steels, Fe-based

model alloys, Ta and Ta-1W alloy, and the new data setsfor Mo metals.[15,18,19] The majority of these data havebeen published in earlier publications but not targeted atthe early irradiation phenomena.[9–11,14,15,18–23] Of theaccumulated data sets, 47 sets of yield stress vs dose datawere selected and used for the current analysis: Table Ilists those cases divided into three groups of materials:the body-centered cubic (bcc), face-centered cubic (fcc),and hexagonal close-packed (hcp) materials. Details forthe materials like chemical compositions, heat treat-ments, and specimen types are described in the earlierpublications.[9–11,18,19] Note that some figures presented

Table I. Irradiation and Test Conditions for BCC, FCC, and HCP Metals

CrystalType Material Category

IrradiationFacility

DoseRange (dpa)

IrradiationTemperature [K (�C)]

TestTemperature [K (�C)]

BCC (35 sets)Fe-a pure metal HFIR 0 to 0.79 333 to 373 (60 to 100) 298 (25)Fe-b (high purity) pure metal HFIR 0 to 1.07 333 to 373 (60 to 100) 298 (25)Fe-c pure metal HFIR 0 to 1.07 333 to 373 (60 to 100) 298 (25)Fe-0.01Cu* model alloy HFIR 0 to 0.057 333 to 373 (60 to 100) 298 (25)Fe-0.25Cu* model alloy HFIR 0 to 0.057 333 to 373 (60 to 100) 298 (25)Fe-0.7Ni* model alloy HFIR 0 to 1.07 333 to 373 (60 to 100) 298 (25)Fe-0.7Ni (0.025P)*model alloy HFIR 0 to 0.057 333 to 373 (60 to 100) 298 (25)Ta (Aesar Ta1)* pure metal HFIR 0 to 0.14 333 to 373 (60 to 100) 298 (25)Ta (Aesar Ta1)* pure metal HFIR 0 to 0.14 333 to 373 (60 to 100) 523 (250)Ta (Aesar Ta2)* pure metal HFIR 0 to 0.14 333 to 373 (60 to 100) 298 (25)Ta (Aesar Ta2)* pure metal HFIR 0 to 0.14 333 to 373 (60 to 100) 523 (250)Ta (ISIS Ta)* pure metal HFIR 0 to 0.14 333 to 373 (60 to 100) 298 (25)Ta (ISIS Ta)* pure metal HFIR 0 to 0.14 333 to 373 (60 to 100) 523 (250)Mo (LCAC)* pure metal HFIR 0 to 0.28 333 to 373 (60 to 100) 373 (100)Mo (LCAC)* pure metal HFIR 0 to 0.28 333 to 373 (60 to 100) 298 (25)Mo (LCAC)* pure metal HFIR 0 to 0.072 333 to 373 (60 to 100) 248 (�25)Mo (LCAC)* pure metal HFIR 0 to 0.072 333 to 373 (60 to 100) 223 (�50)Nb pure metal HFIR 0 to 0.37 333 to 373 (60 to 100) 298 (25)V pure metal HFIR 0 to 0.69 333 to 373 (60 to 100) 298 (25)3Cr-3WV ferritic/martensitic steel HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)9Cr-1MoVNb ferritic/martensitic steel HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)9Cr-1MoVNb-2Ni ferritic/martensitic steel HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)9Cr-2VWTa ferritic/martensitic steel HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)9Cr-2VWTa ferritic/martensitic steel LANSCE 0 to 10.2 323 to 433 (50 to 160) 298 (25)9Cr-2WV ferritic/martensitic steel HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)9Cr-1MoVNb ferritic/martensitic steel LANSCE 0 to 10.2 323 to 433 (50 to 160) 298 (25)A212B* carbon steel HFIR 0 to 1.07 333 to 373 (60 to 100) 298 (25)A350* carbon steel HFIR 0 to 0.057 333 to 373 (60 to 100) 298 (25)A36* carbon steel HFIR 0 to 1.07 333 to 373 (60 to 100) 298 (25)A533B-a pressure vessel steel HFIR 0 to 0.89 333 to 373 (60 to 100) 298 (25)A533B-b pressure vessel steel HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)A533B-c pressure vessel steel HFIR 0 to 0.057 333 to 373 (60 to 100) 298 (25)A588B* low alloy steel HFIR 0 to 0.057 333 to 373 (60 to 100) 298 (25)Ta-1W* Ta-W alloy HFIR 0 to 0.14 333 to 373 (60 to 100) 298 (25)Ta-1W* Ta-W alloy HFIR 0 to 0.14 333 to 373 (60 to 100) 523 (250)

FCC (9 sets) Cu pure metal HFIR 0 to 0.92 333 to 373 (60 to 100) 298 (25)Ni pure metal HFIR 0 to 0.6 333 to 373 (60 to 100) 298 (25)316-a austenitic SS HFIR 0 to 0.78 333 to 373 (60 to 100) 298 (25)316-b austenitic SS HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)316LN austenitic SS HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)IN718-SA super alloy HFIR 0 to 1.2 333 to 373 (60 to 100) 298 (25)EC316LN austenitic SS LANSCE 0 to 10.7 323 to 433 (50 to 160) 298 (25)HTUPS316 austenitic SS (ppt-hardened)LANSCE 0 to 10.7 323 to 433 (50 to 160) 298 (25)AL6XN austenitic super SS LANSCE 0 to 10.7 323 to 433 (50 to 160) 298 (25)

HCP (3 sets) Zr pure metal HFIR 0 to 0.63 333 to 373 (60 to 100) 298 (25)Zr-4-a Zr alloy (fuel cladding) HFIR 0 to 0.8 333 to 373 (60 to 100) 298 (25)Zr-4-b Zr alloy (fuel cladding) LANSCE 0 to 24.6 323 to 433 (50 to 160) 298 (25)

*Not analyzed in the earlier study.[9]

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JANUARY 2013—S85

in this article have been revised from earlier versions toreflect the updates in the database.

Irradiation experiments were performed at two facil-ities using three types of tensile specimens: the HydraulicTube facility of the High Flux Isotope Reactor (HFIR)at ORNL and the target area of the Los Alamos NeutronScattering Center (LANSCE) accelerator.[14,20,21] In theHFIR irradiation facility, the tensile specimens wereexposed to fast neutrons (E > 0.1 MeV) for differentperiods to achieve target damage levels. The irradiationtemperature in the HFIR irradiation facility was in therange 333 K to 373 K (60 �C to 100 �C). In the LAN-SCE accelerator, on the other hand, the tensile specimenswere irradiated at different target-area locations fordifferent irradiation exposures to protons and spallationneutrons. The kinetic energy of the incident protons (p)was 800 MeV and spallation reactions by the protonsproduced neutrons (n) with a wide range of kineticenergy (<800 MeV).[21–23] The protons produced themost displacement damage in those specimens atthe front positions of the target (p>n area), where thespecimens in the list were irradiated, while the spallationneutrons made more or similar amount of contributionsto the damage at the back positions of target (n>p area).The specimens were water cooled during irradiation, andthe maximum temperatures measured by thermocoupleswere in the range 333 K to 373 K (50 �C to 160 �C). Theeffect of high helium production on the strength in theLANSCE-irradiated stainless and ferritic/martensiticsteels was not significant,[21–23] and therefore, the effectwas not considered in the current analysis.

Three types of miniature tensile specimens, SS-3, S-1,and BES/NERI types, were used for the irradiationexperiments.[9–12,20–23] All tensile tests were conducted atlow temperatures of 223 K to 523 K (–50 �C to 250 �C)in screw-driven machines at a nominal strain rate ofabout 10–3 s–1. The load-displacement curves wererecorded and used to calculate the strength and ductilityparameters, among which only the yield stress (YS) datawere used for this study.

III. LOW-DOSE REGIME

In high-strength refractory metals, irradiation soften-ing is often profound after low-dose irradiation. Inparticular, some pure molybdenum showed a significantirradiation softening at room temperature and lower.[13–15] In the single-crystal high-purity Fe, such irradiationsoftening or nonhardening behavior was quite signifi-cant in the low-temperature (£183 K [–90 �C]) tensiletests, where the strength of the pure Fe is relativelyhigh.[12] Some ferritic steels have a short constant-strength region before the hardening stress becomesmeasurable.[16,24] Lately, the low-carbon arc-cast puremolybdenum (LCAC Mo) has been tested after neutronirradiation to explore the temperature or strengthdependence of irradiation softening.[14] The results haveshown a significant decrease of yield stress with dose,along with prompt plastic instability or failure atrelatively high doses.[14,15] In this paper, the DYS vsdpa data are displayed in a semilog plot (Figure 1) to

reveal the change from radiation softening to hardeningin the same material. It clearly shows that at lowertemperatures, the irradiation softening is more profoundand the initiation of hardening is delayed to higherdoses: At a higher temperature, 373 K (100 �C), or whenstrength is lower, the softening stress (~30 MPa) is muchlower than the value at a lower temperature of 223 K(–50 �C) (~220 MPa). At the highest temperature, how-ever, the delay in irradiation hardening is minimal(~0.0007 dpa) or within error range.These results led to a speculation that the delay period

in irradiation hardening is dependent on the strength ofthe material, and the irradiation softening or delay inhardening is a common phenomenon in metallic mate-rials. Most of the strength data sets presented in the pastdo not have enough dose resolution in the low-doseregion, and therefore, the phenomena in the earlyirradiation were largely ignored. This has been almosta common practice in the relatively soft materials wherethe irradiation softening or delay in hardening isnegligible. In this study, such an early response ofmaterials to irradiation is named as the nonhardeningregime. To answer the question if irradiation softening isa common phenomenon in metallic materials, the datasets for commercial alloys with medium strength,including all bcc, fcc, and hcp structures, are plottedtogether in the semilog coordinate (Figure 2). It isevident that these materials have a delay in hardening, ifnot softening, before the irradiation hardening becomesmeasurable. The doses when the DYS values start toincrease above the horizontal line are below 0.001 dpa forthe six alloys. Since this softening or delayed hardeningoccurs at such a low dose in most of the commercialstructural alloys, the phenomenon has been previouslyinterpreted as a phenomenon unique to refractory mate-rials or highly hardened materials only.[14,15]

It is now postulated from the semilog plots inFigure 2 that the negative or delayed hardening can bea common phenomenon at least for many of at least

Fig. 1—Temperature dependence of irradiation hardening (DYS) inLCAC molybdenum.

S86—VOLUME 44A, JANUARY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

medium- and high-strength metallic materials. To quan-tify such delay in hardening, a dose parameter is definedin Figure 3, where the dose to initiation of irradiationhardening (DI) is newly defined here as the dose whenthe YS extrapolated from the main hardening regimemeets the horizontal line or the YS for the nonirradiatedspecimen. Figure 4 displays the DI values for materialsgroups, and those for individual cases are listed inTable II, along with the other two dose parametersdiscussed in the last section. A notable finding from thesemilog plot is that DI depends on yield stress. Some softmetals, such as Cu, Ta, and IN718-SA, have very low DI

values below 10–5 dpa (0.01 mdpa), at which any changein mechanical property is unnoticeable in most irradi-ation experiments. Among the test materials, the longestdelay of hardening occurred in the two molybdenumcases where the test temperatures were 248 K and 223 K(–25 �C and –50 �C), as shown in Figure 1. Thisstrength dependence of delayed irradiation hardeningconfirms the observation in the past that the high-strengthmaterials are more prone to irradiation softening.

As implied by the labeled cases in Figure 4, thestrength dependence seems to rule the early hardeningbehavior of a material. The first example is the puremolybdenum: The difference in yield stress over a 423 K(150 �C) range affected the prehardening behaviorsignificantly. The DI value in the 223 K (�50 �C) caseis about two orders of magnitude higher than in the373 K (100 �C) case. The second example is the pureiron, whose purity levels, and thus their strengths (104and 213 MPa), are different. The strength dependence isobvious in DI although the difference is only threefold(3.7 9 10–5 dpa vs 1.1 9 10–4 dpa). These lead to aconclusion that a lower purity (in Fe) delays irradiationhardening due to solid-solution hardening.

Although the overall linearity inDI vs yield stress plot iswell demonstrated in Figure 4, the authors recognize thata smallDI value (<10–4 dpa), if obtained by extrapolationfrom correspondingly small strength changes, cannot be

statistically meaningful. The lowest dpa we could achievein experiment was 2 9 10–5 dpa (0.02 mdpa) and theminimum dose was about 10–4 dpa or higher for themajority of data sets inTable I. In the process described inFigure 3, therefore, the extrapolations made into the verylow dose range (<10–4 dpa) should be considered as‘‘nonvalidated.’’ Therefore, the existence of the prehar-dening regime may not be claimed in such cases.Furthermore, while the strength dependence is obvi-

ous in the DI vs dose data, no significant differences inthe dose dependences are observed among differentcrystal types. However, there are two data points foundoutstanding: the Ni-doped FM steel (modified 9Cr steel)and the solution-annealed IN718 alloy. The authors’speculation for the reason is that the high Ni content inthose alloys prompts irradiation hardening by theproduction of tiny helium bubbles due to (n, a) nuclearreactions.[25,26] Once the helium bubbles are accumu-lated, the strengthening mechanism can be changedbecause those cannot be removed by gliding disloca-tions, while most of the other types of irradiationinduced defect clusters can be removed by glide ofdislocations.[27–33] If those bubbles can continue to serveas obstacles to dislocation glide, then any softeningmechanism, which determines the degree of delay in theirradiation hardening, will not be effective.

IV. MAIN HARDENING AND SATURATIONREGIMES

This main hardening regime has been a focus of manystudies in the past. The strength parameter that has beenused in such studies to describe irradiation-hardeningbehaviors was the yield stress change DYS.[6–9,23] TheDYS data have been often plotted against dpa on thelog-log scale because such plots can effectively displayhardening regimes as almost linear lines with differentslopes. The log-log plots for the irradiated steels aregiven in Figure 5. Additional log-log plots for fcc and

Fig. 2—Delay in irradiation hardening in selected materials. (Tirr �353 K [80 �C]; Ttest = RT).

Fig. 3—Definition of the dose to initiation of irradiation hardening(DI). Displayed are two cases for the nonhardening regime withnear-zero hardening or softening.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JANUARY 2013—S87

hcp have been published,[9] and duplication is avoidedhere. These log-log plots show two distinctive regimes:the main hardening regime where the majority ofhardening occurs for each material and the saturationregime presenting considerably reduced slope or littlehardening. One setback of these log-log plots is that theycannot display the negative hardening phenomenon,which is often observed in the very low-dose region inrelatively high-strength materials. This type of plot is,therefore, not appropriate to describe the prehardeningregime described above. In some metals (3Cr and A212Bsteels, for example), very small yield stress changes areobserved at low doses, so the data points are positionedwell below the trend lines for their main hardeningregime.

In the past, a few irradiation-hardening models havebeen proposed, focusing on obtaining expressions forthe dose dependence of DYS.[6–9,34] Although thebarrier-hardening models were widely used to drawthe theoretical formula of irradiation hardening,[7,8,35]

the simplest and most widely used form to describe theDYS vs dose curves is the empirical form given as apower-law function: DYS ¼ h dpað Þn; where h and n arethe regression coefficients.[9,34–38] As indicated in the log-log plots in Figure 5, where the linear lines change theirslopes, at least two different hardening regimes appear inthe positive-hardening process. Figure 6 compares then1 and n2 values. Taking all bcc, fcc, and hcp cases intoaccount, the mean values for n were about 0.49 for themain hardening regime (n1) and about 0.11 for thesaturation regime (n2).[9] While this low exponenthardening behavior in the saturation regime has notbeen well explained, the average exponent for the mainhardening regime, 0.49, agrees reasonably well with thebarrier-hardening models.[7,8,36] It is also observed thatrelatively strong steels (ferritic and ferritic martensiticsteels) and refractory metals (Zr-4, niobium, and vana-dium) exhibited higher n1 values (>0.5), while some softmetals, such as Fe, Ta, Cu, type 316 steels, and Zr,displayed lower values (<0.4).

While the n1 values represent the major irradiation-hardening characteristics of the materials, the n2 valuesdisplay no strong dependence on material properties. Allthe n2 values obtained were in the range 0.11 ± 0.1. Thedoses to reach this saturation regime with a reducedirradiation-hardening rate, which was defined as DS,were in the range 0.003 to 0.08 dpa.[9] Above thissaturation dose, the material will still experience furtherhardening, but at a much lower rate, throughout thesaturation regime. The yield stress will eventually startto decline as any embrittlement mechanism commencesusually at a high dose and becomes identical to thefracture stress of the material.[10,11]

Another way of showing the division of main hard-ening and saturation regimes might be the irradiation-hardening rate (DYS/Ddpa) vs dpa plots. In Figure 7,the trend lines in the log-log plots clearly displaydeflection points in the middle dose range 0.001 to0.1 dpa. Most ductile metals showed similar irradiation-hardening rates that fall within a narrow band, irre-spective of crystal type. Over a wide dose range (0 to25 dpa) the irradiation-hardening rate decreased withdose: The irradiation-hardening rates were in the range100 to 1000 GPa/dpa at the lowest dose of ~0.1 mdpadpa and a few tens of MPa/dpa or less at a few dpa. Ineach material, the deflection point clearly divided theirradiation-hardening behavior into the main and satu-ration dose regimes.

V. IRRADIATION-HARDENING REGIMES

In most previous studies for irradiation hardening,two hardening regimes, the main hardening and satura-tion regimes, have been studied, focusing particularly onthe main hardening regime. The discussion in previoussections confirms the prehardening regime to be the firstregime that appears in many metallic materials. Thisregime many be observed experimentally in many softmaterials at low temperatures. However, this newlyrecognized regime might become increasingly importantas the advanced nuclear systems such as fusion and fastreactors need higher strength materials, and as indicatedin the case of the nanostructured ferritic steels, moreextremely high strength materials emerge as primaryfuture nuclear materials.[39,40] Therefore, delaying theonset of irradiation hardening is useful, although caremust be taken to not decrease ductility to achieve highstrength.Another regime that will be surely observed for all

metallic materials at high doses may be the embrittle-ment regime. In the saturation regime, the fracture stressstarts to decrease at some point, sometimes abruptly,while the increase of yield stress is slowed.[10] Once thefracture stress decreases to be identical to the yieldstress, the material will exhibit brittle failure. Theembrittlement regime usually starts at high doses(>1 dpa) with some exceptions like the molybdenumproduced by powder metallurgy, which show embrittle-ment at a low dose (<0.1 dpa). The fourth regime is notexplored in detail in this study, although all existingmetallic materials should end up with this regime as

0.0000001

0.000001

0.00001

0.0001

0.001

0.01

0.1

0 200 400 600 800

YS-nonirradiated, MPa

DI,

dp

a

bcc-Pure Metalsfcc-Pure Metalshcp-Pure Metalsbcc-Annealed Alloysfcc-Annealed Alloyshcp-Annealed Alloysbcc-Q&T Steels

Tirr < 200 °C; –50 °C ≤ Ttest ≤ 250 °C

Fe

IN718-SA

F/M-2 pct Ni

Mo Mo

Mo

MoFe

Fe

Fig. 4—Strength dependence of DI. The trend indicates that the ini-tiation of irradiation hardening is delayed more in harder materials.

S88—VOLUME 44A, JANUARY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

irradiation continues.[10] Thus far, therefore, four dis-tinct regimes in irradiation-hardening behavior havebeen identified:

A. Prehardening Regime

In this early hardening regime, the irradiation hard-ening is minimal or sometimes irradiation softeningoccurs. This regime can be called the very low-doseregime for most metallic materials; however, the discus-sion in previous sections predicts this regime can beprolonged to a high dose (>1 dpa) in very high strengthmaterials or at low temperatures as the reduction of

yield stress by irradiation can be profound in suchcircumstances.

B. Main Hardening Regime

The majority of hardening occurs in this regime formany metallic materials, and the irradiation hardeningis presented by the hardening exponent of about 0.5 inpower-law regression. So far, no metallic material testedat room temperature after low-temperature irradiationhas shown this regime after reaching 0.1 dpa. Theirradiation-hardening behavior for the materialswith extended prehardening regime above 0.1 dpa (for

Table II. Yield Stress and Dose Parameters

MaterialIrradiation

Temperature [K (�C)]Test

Temperature [K (�C)]YS-Nonirradiated

(MPa) DI (mdpa) DC (dpa) DS (dpa)

Fe-a 333 to 373 (60 to 100) 298 (25) 213 0.11 0.2 0.05Fe-b (high purity) 333 to 373 (60 to 100) 298 (25) 104 0.037 6 0.05Fe-c 333 to 373 (60 to 100) 298 (25) 168 0.055 0.03 0.04Fe-0.01Cu 333 to 373 (60 to 100) 298 (25) 168 0.1 0.1Fe-0.25Cu 333 to 373 (60 to 100) 298 (25) 176 0.12 0.02 0.025Fe-0.7Ni 333 to 373 (60 to 100) 298 (25) 193 0.12 0.031 0.02Fe-0.7Ni-0.025P 333 to 373 (60 to 100) 298 (25) 201 0.03Aesar Ta1 333 to 373 (60 to 100) 298 (25) 203 0.024 0.004 0.004Aesar Ta1 333 to 373 (60 to 100) 523 (250) 118 0.005Aesar Ta2 333 to 373 (60 to 100) 298 (25) 216 0.032 0.004 0.004Aesar Ta2 333 to 373 (60 to 100) 523 (250) 123 0.005ISIS Ta 333 to 373 (60 to 100) 298 (25) 191 0.061 0.004LCAC-Mo 333 to 373 (60 to 100) 373 (100) 260 0.074 0.072 0.072LCAC-Mo 333 to 373 (60 to 100) 298 (25) 473 0.52 0.072LCAC-Mo 333 to 373 (60 to 100) 248 (–25) 633 6.38 0.072LCAC-Mo 333 to 373 (60 to 100) 223 (–50) 740 4.91 0.0072Nb 333 to 373(60 to 100) 298 (25) 240 0.026 0.007 0.003V 333 to 373 (60 to 100) 298 (25) 304 0.065 0.0017 0.0033Cr-3WV 333 to 373 (60 to 100) 298 (25) 546 0.56 0.025 0.059Cr-1MoVNb 333 to 373 (60 to 100) 298 (25) 570 0.58 0.034 0.039Cr-1MoVNb 323 to 433 (50 to 160) 298 (25) 562 0.09 0.049Cr-1MoVNb-2Ni 333 to 373 (60 to 100) 298 (25) 754 0.52 0.054 0.049Cr-2VWTa 333 to 373 (60 to 100) 298 (25) 545 0.054 0.049Cr-2VWTa 50 to 160 298 (25) 552 0.12 0.049Cr-2WV 333 to 373 (60 to 100) 298 (25) 541 0.054 0.035A212B 333 to 373 (60 to 100) 298 (25) 332 0.37 0.03 0.02A350 333 to 373 (60 to 100) 298 (25) 368 0.36 0.015 0.015A36 333 to 373 (60 to 100) 298 (25) 260 0.24 0.05 0.015A533B-a 333 to 373 (60 to 100) 298 (25) 497 0.77 0.02 0.05A533B-b 333 to 373 (60 to 100) 298 (25) 444 0.35 0.015 0.03A533B-c 333 to 373 (60 to 100) 298 (25) 449 0.64 0.02 0.025A588B 333 to 373 (60 to 100) 298 (25) 334 0.52 0.03 0.015Ta-1W 333 to 373 (60 to 100) 298 (25) 299 0.091 0.004 0.008Ta-1W 333 to 373 (60 to 100) 523 (250) 227 0.038 0.04Cu 333 to 373 (60 to 100) 298 (25) 39 0.002 0.12 0.05Ni 333 to 373 (60 to 100) 298 (25) 63 0.036 0.15 0.04316-a 333 to 373 (60 to 100) 298 (25) 234 0.06 27 0.04316-b 333 to 373 (60 to 100) 298 (25) 223 0.15 35 0.04316LN 333 to 373 (60 to 100) 298 (25) 277 0.703 40 0.04IN718-SA 333 to 373 (60 to 100) 298 (25) 325 0.008 120EC316LN 323 to 433 (50 to 160) 298 (25) 290 22 0.04HTUPS316 323 to 433 (50 to 160) 298 (25) 179 5 0.04AL6XN 323 to 433 (50 to 160) 298 (25) 279 17 0.04Zr 333 to 373 (60 to 100) 298 (25) 44 0.015 0.09 0.07Zr-4-a 333 to 373 (60 to 100) 298 (25) 396 0.26 0.009 0.01Zr-4-b 323 to 433 (50 to 160) 298 (25) 386 0.004 0.01

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JANUARY 2013—S89

example, the nanostructured ferritic steels[39]) is not wellknown.

C. Saturation Regime

The hardening rate is slowed by saturation of defectcluster density or by the plastic instability at yield.[9] Fortypical materials, the hardening exponent in this regimeis about 0.1, but with a large percentage variation.

D. Embrittlement Regime

This regime starts when the yield stress becomesidentical to the fracture stress of the material. The yieldstress can be defined in stress–strain curve but actuallyat fracture. In this regime, the fracture stress usually

decreases with dose. Since the fracture stress is afunction of stress constraint or specimen geometry, thecritical dose for this regime may vary with thesenonmaterial factors.It is worth mentioning that there can be influences

between these regimes. It is obvious that an earlyinitiation of the embrittlement regime in the powdermetallurgy molybdenum, for example, can lead to adecreased or eliminated main hardening and saturationregimes.[10,11] It is also believed that the saturationregime is independent of prehardening regime, althoughthe extension of the prehardening regime seems toshorten the main hardening regime (Figure 3).

VI. DISCUSSION ON THE PHENOMENARELATED TO SATURATION OF HARDENING

A. Saturation of Irradiation Hardening

It is presented in Figures 5 and 7 that in the metallicmaterials the main hardening regime was not observed toextend to above 0.1 dpa. The low-rate hardening in thesaturation regime has been explained by the saturation ofdefect cluster density, which has been shown for variousmetallic materials by transmission electron microscopystudies.[22,33,38,41–43] Furthermore, computer simulationresults showedmore cascade overlaps occurring at higherdoses because of closer spacing between defect clusters.The point defects in the next cascade are more likely toreact with existing clusters at the expense of new clusters,or the next cascade can occur more likely on the top ofexisting defects and can erase them.[41,42] Such overlapof events in a given space should result in a reduced rate ofnet cluster production and, consequently, result in a lowerirradiation-hardening rate.Comparing the dose dependences of defect cluster

density, it is noticed that the saturation behavior is notthe same for different materials. In pure Cu, the densityof defect clusters saturated in the dose range 0.01 to 0.1dpa at low temperatures (<~573 K [300 �C]).[4] A similarsaturation dose (~0.1 dpa) was observed for pure Ni,although the visible defect density was 5 to 10 timeslower than in Cu.[44,45] Figures 5 and 7 confirm thatthese doses are in line with the saturation doses forirradiation hardening (DS). These results from micro-structural studies indicate that a dose within 0.01 to0.1 dpa should be an upper limit for rapid accumulationof defect clusters in most of the metallic materials. Thebarrier-hardening models indicate that the strength of amaterial depends directly on the accumulation of defectclusters. In the majority of the metallic materials,therefore, the transition from the main hardening regimeto the saturation regime should occur at about 0.1 dpaor lower, but not lower than 0.01 dpa. In some bccmetals, however, the DS values (the doses to saturationin irradiation hardening) are well below the dose range:The saturation doses in the range 0.003 to 0.008 dpawere measured for V, Nb, Ta, and Ta-1 pct W.[10,11,46,47]

These discrepancies imply that the saturation in hard-ening can occur not only by the saturation of defectcluster density but also by a nonmicrostructural factor.

Fig. 5—Examples of irradiation-hardening data in main and satura-tion regimes in ferritic steels (Tirr < 473 K [200 �C]; Ttest = RT).Note that the majority of data in this figure and more DYS-dpa datafor fcc and hcp pure metals and alloys and for pure bcc metals arefound in Ref. [9]

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

3Cr-

3WV

9Cr-

1Mo

VN

b9C

r-1M

oV

Nb

-2N

i9C

r-2V

WT

a9C

r-2W

VA

212B

A35

0A

36A

533B

-aA

533B

-bA

533B

-cA

588B

Aes

ar T

a1A

esar

Ta2

Fe-

0.01

Cu

Fe-

0.25

Cu

Fe-

0.7N

iF

e-b

Fe-

cN

bT

a-1W

VC

u Ni

316a

316b

316L

N Zr

Zr-

4

Har

den

ing

exp

on

ent

n1 n2 Tirr ≈ 80 oC; Ttest = RT

Fig. 6—Comparison of irradiation-hardening exponents. A similardata set can be found in a tabulated form.[9]

S90—VOLUME 44A, JANUARY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

B. Relationship to Plastic Instability at Yield

It was proposed that the plastic instability (diffusenecking) accounted for the reduced irradiation-harden-ing rate after the main hardening regime.[9] This statesthat once the irradiation dose reaches a critical levelwhere tensile curve starts to show necking at yield, theyield stress cannot increase with dose at a high rate, andthe main hardening regime ends there. In this study, thatargument is reaffirmed by the extended database. Theplastic instability stress (PIS) was defined as the truestress at the ultimate tensile strength,[10,11,46,47] and itwas shown that the engineering tensile curves afterirradiation experienced necking at yield when the YSbecame higher than the dose-independent PIS. Thecritical dose DC, obtained when YS = PIS, was definedas the dose to plastic instability (or prompt necking) at

yield.[10,11,46] This PIS criterion for plastic instability wasalso applied to the cold-worked stainless steels hardenedby dislocation tangles.[48] This dose parameter can beregarded as a lifetime for mechanical stability since thematerials will show unstable plastic deformation abovedose DC. In bcc materials, the DC values ranged from~0.001 to 0.2 dpa except for one high purity Fe, whichhas an outstanding value of 6 dpa for the critical dosebecause of its low yield strength.[46] The ferritic steels(annealed) and bainitic or ferritic/martensitic steels(quenched and tempered) have DC values in the rangeof 0.015 to 0.12. The irradiation responses of the hcpmetals, zirconium, and its alloys, are similar to those ofbcc metals: 0.004 and 0.009 dpa were obtained forZircaloy-4 cases and 0.09 dpa for pure zirconium case.The austenitic steels show very high critical doses of at

bcc Metals-I

0.1

10

1000

100,000

10,000,000

dpa

Irr.

har

den

ing

rat

e, M

Pa/

dp

a

TaTa-1WLCAC-MoNbVFeFe-0.01CuFe-0.25CuFe-0.7NiA588BA212BA350A36

(a)

bcc Metals-II (Quenched & Tempered Steels)

1

100

10,000

10,00,000

dpa

Irr.

har

den

ing

rat

e, M

Pa/

dp

a

A533BFe-9Cr-1MoVNbFe-9Cr-1MoVNb-2NiFe-9Cr-2WVTaFe-9Cr-2WVFe-3Cr-3WV

(b)

fcc & hcp Metals

1

100

10,000

10,00,000

0.00001 0.0001 0.001 0.01 0.1 1 10 0.00001 0.0001 0.001 0.01 0.1 1 10

0.00001 0.0001 0.001 0.01 0.1 1 10

dpa

Irr.

har

den

ing

rat

e, M

Pa/

dp

a

316SS316LNHTUPS316AL6XNIN718-SACuNiZr-4Zr

(c)

Fig. 7—Irradiation-hardening rate for the positive hardening regimes in (a) bcc metals, (b) ferritic steels, and (c) fcc and hcp metals. (Note: Datasets for Fe, Ta, A533B, 316SS, and Zr-4 include all sub–data sets listed in Table I. Tirr < 473 K [200 �C]; Ttest = RT).

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JANUARY 2013—S91

least 5 dpa, while the fcc pure metals, Cu and Ni, havemuch smaller DC values: 0.12 to 0.15 dpa, respectively.

We have asserted previously that the plastic instabilityat yield affects the irradiation hardening by concentrat-ing dislocation glides in narrow slip bands.[9] Althoughthe details of the gliding dislocation-defect clusterinteractions are not well known, the effect, if any,should be reflected in irradiation-hardening parameters.To examine this aspect, the DC values were graphicallydetermined using the YS vs dose curves and PIS vs dosecurves and compared with the doses for the saturationof hardening values DS in Figure 8. This figure displaysthat the DS vs DC plot has approximately a one-to-onelinearity for most of the metallic materials or when bothof those are less than about 0.1 dpa. This indicates thatthe saturation of irradiation hardening can be directlyrelated to the plastic instability at yield. Considering theaforementioned discrepancy between the observed dosesfor saturation in irradiation hardening and defectaccumulation, the plastic instability at yield is believedto reduce the rate of irradiation hardening.[9] With theplastic instability occurring at yield, the dislocation glideand slip bands should tend to concentrate at the neckedarea. This may lead to an easier removal of defectclusters and, consequently, to a lower irradiation hard-ening. A conclusion drawn from this result is, therefore,that the irradiation-hardening behavior changes fromthe main irradiation-hardening regime to the saturationregime whenever dose reaches the DC value and thenplastic instability occurs at yield.

In the DS vs DC plot (Figure 8), a plateau band existsin the DS range of 0.04 to 0.08 dpa. As mentionedabove, the irradiation hardening of the materials in this~0.04-dpa-wide band is believed to be limited bysaturation of defect cluster number density. In additionto the austenitic stainless steels and high-purity iron (Fe-b), many pure metals and nonaustenitic steels, Mo, Zr,

Cu, Ni, Fe-a, and most of the quenched and temperedsteels (9Cr, 3Cr, and A533B steels), also may belong tothis materials group. In Figure 8, we can easily see thatfor these pure metals and steels, the saturation inhardening can be explained either by saturation in defectaccumulation or by plastic instability at yield. It can beconcluded, therefore, that the macroscopic phenomenon,the plastic instability at yield, is considered as one of themain causes for saturation in irradiation hardening.It is worth mentioning again that only two materials,

austenitic stainless steels and high purity iron (Fe-b),exhibit significant uniform deformation after the satu-ration of irradiation hardening. It is believed that thehigh deformability of the stainless steels originates fromthe low yield point of their pristine materials and lowstacking-fault energy that promotes deformation twin-ning and, at least, linear planar slip of dislocations:First, the yield stress of annealed austenitic stainlesssteels is relatively low (~200 MPa), but their truefracture stress is as high as those of much strongerquenched and tempered steels (~1500 MPa).[10,11] Evenafter irradiation to a high dose, therefore, there can be awide stress span available for deformation between theyield and the final fracture. The true fracture stress isknown to be not changed by irradiation up to high dosesbefore an embrittlement mechanism is enacted. Second,the irradiation hardening, or any sorts of hardening,promotes more planar slips and then deformationtwins.[49] Deformation twinning occurs gradually asstrain increases and steadily adds more obstacles in thedeforming material. This can induce a high strain-hardening rate and extend uniform deformation. Irra-diation enhances twinning, which helps to retain a highstrain-hardening rate at high strains. Third, the strongtendency of planar slip due to their low stacking-faultenergy provides another cause for the high deformabi-lity.[49] The planar slip, even with channeling at highdoses, creates a strong back stress hardening becausedislocations tend to form large pileups at obstacles likegrain boundaries. Also, the high DC found in the ironFe-b can be explained for the first reason suggestedabove. It is a high purity (>99.999 pct) and fullyannealed material and its yield stress in pristine state isjust above 100 MPa, which is less than 50 pct of theyield stress of Fe-a (213 MPa). Their true stresses at theonset of plastic instability were at ~300 MPa, whichleaves a larger window of uniform deformation in Fe-b.

VII. SUMMARY AND CONCLUSIONS

The dose dependence of yield stress has been charac-terized for almost four dozen data sets for bcc, fcc, andhcp materials after low-temperature (<473 K [200 �C])neutron or neutron plus proton irradiation. New find-ings and conclusions are summarized as follows:

1. In the DYS vs dpa curves at least four distinctregimes can be recognized: (1) the prehardeningregime where irradiation hardening is negligible oreven irradiation softening occurs, (2) the main hard-ening regime where the majority of hardening

Fig. 8—Comparison of the dose parameters, DS and DC, to revealthe relationship between the saturation of irradiation hardening andthe plastic instability. (Note: Irradiation hardening in the materialsbelonging to the band with 1-to-1 slope is saturated by plastic insta-bility. As implied in Table I, this plot was revised from the Fig. 6 ofRef. [9] with additional data for Ta, low alloy (A2&3-series) steels,model Fe alloys, and Mo).

S92—VOLUME 44A, JANUARY 2013 METALLURGICAL AND MATERIALS TRANSACTIONS A

occurs, (3) the saturation regime where the irradia-tion-hardening rate is reduced either by saturationof defects or occurrence of plastic instability atyield, and (4) the embrittlement regime where theyield stress and fracture stress become identical andboth of those decrease with dose.

2. Most part of the yield stress change (DYS) occurredin the main hardening regime. The regressionanalyses for DYS-dose curves indicated that in themajority of metallic materials the exponent of thepower-law hardening function was about 0.5 inthe main hardening regime and about 0.1 in the satu-ration regime. For both positive hardening regimes,the low-strength pure metals such as Fe, Ta, Cu, andZr displayed lower hardening exponent values.

3. The prehardening regime, which is represented byirradiation softening or nil hardening in early irra-diation, is commonly found for many metallicmaterials with middle or high strength. The dose tothe initiation of hardening increases with thestrength of the material, which indicates thatstrengthening materials by some means may delayirradiation effects.

4. The doses to saturation in irradiation hardeningwere in the range 0.003 to 0.08 dpa, and were com-pared with the doses to plastic instability at yield.The transition from main hardening to saturationregime occurs either by plastic instability at yield orby saturation of defect cluster density.

ACKNOWLEDGMENT

This research was sponsored by U.S. Department ofEnergy, Offices of Nuclear Energy and Basic EnergyScience, under Contract DE-AC05-00OR22725 withUT-Battelle, LLC. The authors express special thanksto Drs. J. T. Busby and C.S. Shin for their thoroughreviews and thoughtful comments.

REFERENCES1. R.E. Stoller: J. Nucl. Mater., 1996, vol. 233, pp. 999–1003.2. S.J. Zinkle, P.J. Maziasz, and R.E. Stoller: J. Nucl. Mater., 1993,

vol. 206, pp. 266–86.3. M. Eldrup, B.N. Singh, S.J. Zinkle, T.S. Byun, and K. Farrell: J.

Nucl. Mater., 2002, vols. 307–311, pp. 912–17.4. B.N. Singh, A.J.E. Foreman, and H. Trinkaus: J. Nucl. Mater.,

1997, vol. 249, pp. 103–15.5. M. Rieth, B. Dafferner, and H.D. Rohrig: J. Nucl. Mater., 1998,

vol. 258, pp. 1147–52.6. M.J. Makin and F.J. Minter: Acta Metall., 1960, vol. 8, pp. 691–

99.7. A.H. Cottrell and R.J. Stokes: Proc. Roy. Soc., 1955, vol. A233,

pp. 17–33.8. A.K. Seeger: Proc. of the 2nd Intern. Conf. on Peaceful Uses of

Atomic Energy, 1958, vol. 6. pp. 250–73.9. T.S. Byun and K. Farrell: J. Nucl. Mater., 2004, vol. 326, pp. 86–

96.10. T.S. Byun, K. Farrell, and M. Li: Acta Mater., 2008, vol. 56,

pp. 1044–55.11. T.S. Byun, K. Farrell, and M. Li: Acta Mater., 2008, vol. 56,

pp. 1056–64.

12. D. Brunner and J. Diehl: Phys. Stat. Solidi A-App. Res., 1997,vol. 160, pp. 355–72.

13. A. Seeger: J. de Phys. IV, 1995, vol. 5, pp. 45–65.14. M. Li, T.S. Byun, L.L. Snead, and S.J. Zinkle: J. Nucl. Mater.,

2008, vol. 377, pp. 409–14.15. M. Li, M. Eldrup, T.S. Byun, N. Hashimoto, L.L. Snead, and S.J.

Zinkle: J. Nucl. Mater., 2008, vol. 376, pp. 11–28.16. A. Sato and M. Meshii: Scripta Mater., 1974, vol. 9, pp. 851–59.17. A. Sato, T. Mifune, and M. Meshii: Phys. Stat. Solidi A-App. Res.,

1973, vol. 18, pp. 699–709.18. K. Farrell, S.T. Mahmood, R.E. Stoller, and L.K. Mansur: J.

Nucl. Mater., 1994, vol. 210, pp. 268–81.19. T.S. Byun, M. Li, and K. Farrell: J. Nucl. Mater., 2008, vol. 377,

pp. 72–79.20. K. Farrell, T.S. Byun, and N. Hashimoto: Mapping Flow Locali-

zation Processes in Deformation of Irradiated Reactor StructuralAlloys, ORNL/TM-2003/63, Oak Ridge National Laboratory,Oak Ridge, TN, 2003.

21. S.A. Maloy, M.R. James, G. Willcutt, W.F. Sommer, M. Sokolov,L.L. Snead, M.L. Hamilton, and F. Garner: J. Nucl. Mater., 2001,vol. 296, pp. 119–28.

22. K. Farrell and T.S. Byun: Tensile Properties of Candidate SNSMaterials after Irradiation in Two Neutron Areas in the LANSCEAccelerator, SNS/TR-211, Oak Ridge National Laboratory, OakRidge, TN, 2001.

23. K. Farrell and T.S. Byun: J. Nucl. Mater., 2003, vol. 318, pp. 274–82.

24. I. Remec, J.A. Wang, F.B.K. Kam, and K. Farrell: J. Nucl. Ma-ter., 1994, vol. 217, pp. 258–68.

25. E. Wakai, S. Jitsukawa, H. Tomita, K. Furuya, M. Sato, K. Oka,T. Tanaka, F. Takada, T. Yamamoto, Y. Kato, Y. Tayama, K.Shiba, and S. Ohnuki: J. Nucl. Mater., 2005, vol. 343, pp. 285–96.

26. J.D. Hunn, E.H. Lee, T.S. Byun, and L.K. Mansur: J. Nucl.Mater., 2000, vol. 282, pp. 131–36.

27. F.A. Smidt, Jr.: Dislocation Channeling in Irradiated Metals, NRLReport 7078, Naval Res. Laboratory, Washington DC, 1970.

28. M.S. Wechsler: Dislocation Channeling in Irradiated and QuenchedMetals, in: The Inhomogeneity of Plastic Deformation, ASM,Materials Park, OH, 1971.

29. M.J. Makin and J.V. Sharp: Phys. Stat. Solidi, 1965, vol. 9,pp. 109–18.

30. J.V. Sharp: Phil. Mag., 1967, vol. 16, pp. 77–96.31. J.V. Sharp: Acta Metall., 1974, vol. 22, pp. 449–57.32. A. Okada, K. Kanao, T. Yoshiie, and S. Kojima: Mater. Trans.

JIM, 1989, vol. 30, pp. 265–72.33. K. Farrell, T.S. Byun, and N. Hashimoto: J. Nucl. Mater., 2004,

vol. 335, pp. 471–86.34. P.M. Kelly: Int. Metal. Rev., 1973, vol. 18, pp. 31–36.35. S.J. Zinkle: Rad. Effects Sol., 1999, vol. 148, pp. 447–77.36. T.H. Blewitt, R.R. Coltman, R.E. Jamison, and J.K. Redman: J.

Nucl. Mater., 1960, vol. 2, pp. 277–98.37. A. Okada, T. Yoshiie, S. Kojima, and M. Kiritani: J. Nucl. Mater.,

1986, vols. 141–143, pp. 907–10.38. S.J. Zinkle: J. Nucl. Mater., 1987, vol. 150, pp. 140–58.39. D.A. McClintock, D.T. Hoelzer, M.A. Sokolov, and R.K. Nans-

tad: J. Nucl. Mater., 2009, vols. 368–388, pp. 307–11.40. G.R. Odette, M.J. Alinger, and B.D. Wirth: Ann. Rev. Mater.

Res., 2008, vol. 38, pp. 471–503.41. H.L. Heinisch and B.H. Singh: J. Nucl. Mater., 1999, vols. 271–

272, pp. 46–51.42. Y. Satoh, I. Ishida, T. Yoshiie, and M. Kiritani: J. Nucl. Mater.,

1988, vols. 155–157, pp. 443–48.43. N. Hashimoto, T.S. Byun, K. Farrell, and S.J. Zinkle: J. Nucl.

Mater., 2005, vol. 336, pp. 225–32.44. S.J. Zinkle and L.L. Snead: J. Nucl. Mater., 1995, vol. 225,

pp. 123–31.45. B.N. Singh, J.H. Evans, A. Horsewell, P. Toft, and G.V. Muller: J.

Nucl. Mater., 1998, vols. 258–263, pp. 865–72.46. T.S. Byun and K. Farrell: Acta Mater., 2004, vol. 52, pp. 1597–

1608.47. T.S. Byun, K. Farrell, and N. Hashimoto: J. Nucl. Mater., 2004,

vols. 329–333, pp. 998–1002.48. T.S. Byun, N. Hashimoto, and K. Farrell: Acta Mater., 2004,

vol. 52, pp. 3889–99.49. T.S. Byun: Acta Mater., 2003, vol. 51, pp. 3063–71.

METALLURGICAL AND MATERIALS TRANSACTIONS A VOLUME 44A, JANUARY 2013—S93