mechanical properties of irradiated materialscoupled with dislocation dynamic computer simulations...

International ConferenceNuclear Energy in Central Europe 2001Hoteli Bernardin, Portorož, Slovenia, September 10-13, 2001www: http://www.drustvo-js.si/port2001/ e-mail:[email protected].:+ 386 1 588 5247, + 386 1 588 5311 fax:+ 386 1 561 2335Nuclear Society of Slovenia, PORT2001, Jamova 39, SI-1000 Ljubljana, Slovenia

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MECHANICAL PROPERTIES OF IRRADIATED MATERIALS

I. M. Robertson, J. RobachDepartment of Materials Science and Engineering

University of Illinois1304 W. Green Street

Urbana, IL 61801 [email protected], [email protected]

B. WirthLawrence Livermore National Laboratory

7000 East Avenue, L-353, Livermore,California 94550, USA

[email protected]

ABSTRACT

The effect of irradiation on the mechanical properties of metals is considered withparticular attention being paid to the development of defect-free channels following uniaxialtensile loading. The in situ transmission electron microscope deformation technique iscoupled with dislocation dynamic computer simulations to reveal the fundamental processesgoverning the elimination of defects by glissile dislocations. The observations of preliminaryexperiments are reported.

1 INTRODUCTION

The effect of irradiation on the mechanical properties of materials has been studiedextensively, with numerous reviews being published for different material systems [1-3]. Theemphasis in this paper is not to repeat these reviews but rather to show new experimentalresults aimed at correlating the microstructural behavior with the mechanical properties.Before describing the approach, the effect of irradiation on the stress-strain behavior ofmaterials is summarized. Fig. 1 shows the stress-strain behavior in 316LN solution annealedaustenitic stainless steel [4], polycrystalline copper [4], and iron [5] in Figs. 1a, 1b and 1c,respectively, as a function of neutron dose and temperature. For the FCC materials, the yieldand tensile strength increase, the ductility decreases, and a distinct yield point appears withincreasing neutron dose. For BCC Fe, neutron irradiation causes a decrease in the ductilityand, initially, also a drop in the tensile strength and removal of the upper yield point [6]. Athigher neutron doses the strength increases and the yield point reappears. Similar effects areproduced in other materials, including 304SS [1,5,7], 316SS [7], Cu [5], Pd [5], Fe [5,8], Mo[5], Mo-5%Re [5], and zirconium alloys. Figs. 1d and 1e show that the same trends occurfollowing proton irradiation of copper single crystals and polycrystalline iron [5,7].

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Proceedings of the International Conference Nuclear Energy in Central Europe, Portorož, Slovenia, Sept. 10-13, 2001

The changes in the mechanical properties (strength, ductility, deformation behavior, andfracture mechanism) are intimately related to the evolution of the microstructure andmicrochemistry that occurs during irradiation. As such, the mechanical properties are affectedby the accumulation of radiation damage, the local environment (temperature, stress state,chemical), and material variables (structure, composition, and initial microstructure). It istherefore necessary to understand how these variables change with irradiation, how they areinterrelated, and how these relationships change with continued irradiation.

The changes in the yield strength and the ductility as a function of irradiation dose fordifferent irradiation temperatures are shown qualitatively in Figure 2 for austenitic stainlesssteels. With increasing dose, the yield strength initially increases, reaches a maximum andthen decreases. The effect on the yield strength is also dependent on the test temperature, aneffect that is more obvious in Figure 2b in which the peak yield strength is plotted as afunction of the irradiation temperature. The maximum in the peak yield strength occurs at atest temperature of about 573 K. Figure 2c shows how the ductility (uniform elongation)decreases with increasing dose and irradiation temperature. The variation in the ductility withtemperature is clearer in Figure 2d. The decrease at the higher temperatures is attributable tothe helium embrittlement.

To relate these property changes with microstructural ones it is necessary to considerhow the defect population evolves as a function of dose and temperature. Figure 2e showshow the square root of the product of the dislocation loop density, N, and the loop diameter, d,varies with neutron dose for different irradiation temperatures. The trend is similar at alltemperatures, in that Nd increases with dose, reaches a peak between 10 and 20 dpa andthen decreases. (Note Nd is used simply because of its importance in the dispersed barrier-hardening model, which is described later.) The curves are shifted towards lower values withincreasing temperature. The position of the maximum depends not only on the dose but alsoon the irradiation temperature and reflects the saturation dose at which network dislocations

a) b) c)

d) e)

Figure 1. Comparison of the stress-strain behavior for a) neutron irradiated SA 316 L (N)[4], b) neutron irradiated polycrystalline copper[4], c) neutron irradiated iron [5], d) protonirradiated single crystal Cu, [5], and e) proton irradiated iron [5].

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become more competitive than dislocation loops for interstitials. In Fig. 2f the square root ofthe product of the void density, Nv, and void diameter, dv, is plotted as a function of neutrondose for different temperatures. (Voids only appear at the higher irradiation temperatures,>573K in the austenitic stainless steels.) Initially, the value of vvdN increases rapidly withdose, which reflects the number density change, and then increases more gradually at higherdoses, which is due to the change in the void diameter.

To correlate mechanical property changes with microstructural differences there are twomain hardening models- the dispersed barrier hardening model [9] which is similar to that forprecipitates, and the source hardening model [10]. The dispersed-barrier hardening modelgives the change in the yield strength required to move a dislocation through a field ofobstacles of strength α and separated by a distance l as

NdbMy αµσ =∆ .

In equation (1), b is the magnitude of the Burgers vector of the glissile dislocation, M ≅ 3.06[11] and relates the shear stress on a slip plane in a single crystal to the applied stress neededto move a dislocation in a polycrystal, and µ is the shear modulus. The barrier strengthdepends on the nature of the obstacle, ranging from 1 for voids, to between 0.33 and 0.45 forFrank loops, and to < 0.2 for dislocations. Ando et al. have suggested that the value of unityfor voids is too high [12]. The contribution from the different barriers is obtained using asuperposition law of the form

(1)

Figure 2. a) The yield strength dependence on the neutron dose for different irradiationtemperatures. b) The peak in the yield stress as a function of temperature. c) Thedependence of the uniform elongation as a function of dose for different irradiationtemperatures. d) The approximate variation of the uniform elongation as a function oftemperature for irradiated and unirradiated material. e) The variation of the square root ofthe product of the loop density and loop diameter with dose and temperature. f) Thevariation of the square root of the product of the void density and void diameter with doseand temperature. Comparison of data trend with dispersed barrier hardening modelprediction for irradiations at g) 373K and h) 673 K. 1 represents dislocation hardening, 2loops, 3 voids, and 4 bubbles. Trends are for austenitic stainless steels (adapted from Lucas[3]).

a) c) e) g)

b) d) f) h)

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( ) LRi

iSRTotaly σσσ ∆+∆=∆ ∑ 2

, .

In equation (2) ∆σSR is the change in the yield strength due to the interaction of dislocationswith short-range obstacles such as loops, voids and bubbles, and ∆σLR is due to theirinteraction with long-range obstacles such as other matrix dislocations. The effectiveness ofthis type of superposition model is shown in Figs. 2g and 2h for irradiation temperatures of373 and 673 K. In these figures the thicker line represents the trend in the experimental data.At 373 K, black dot damage (small dislocation loops, stacking-fault tetrahedral, etc.,)accounts for much of the increase in the yield strength at lower doses and networkdislocations at the higher doses. At 673 K, black dot damage still accounts for the increase atlow dose. Above 20 dpa, the contributions from voids and dislocation networks dominate.

In the source-hardening model [10], it is assumed that an atmosphere of small interstitialloops decorate the pre-existing line dislocations [13] (i.e., they form a Cottrell-likeatmosphere) and prevent them from acting as sources. These interstitial clusters are generatedwithin the cascade and glide to these dislocations where they are trapped. These interstitialclusters are an output of molecular dynamic computer simulation models. A TEM study of iondamage in copper has, however, failed to identify a significant population of these smallinterstitial clusters[14]. For the source-hardening model, the stress necessary to unlockdislocations is given by

21

1.0

=

yd

lbµτ .

Here, y is the distance from the line dislocation to the loop atmosphere and l is the separationdistance between the loops in the atmosphere.

Singh et al. [4] have argued against the usefulness of the dispersed barrier mechanism,as it cannot account for the increase in the yield strength with increasing dose and theappearance of the yield drop in FCC materials. They suggest that the increase represents adifficulty in generating dislocations or releasing them from their atmospheres rather thanmoving them through the obstacle field.

However, the decrease in the work hardening and uniform elongation (Figs. 2d and 2e)that accompanies the increase in the hardness is generally attributed to interactions betweendislocations and obstacles. In the case of irradiated materials the interaction between thelattice dislocations and the radiation defects (loops and stacking-fault tetrahedra) can lead todestruction of the defects and the creation of defect-free channels. The formation of suchchannels has been reported in a number of materials with different crystal structures and forirradiation with different energetic particles [5,7]. In addition to channel formation,deformation twinning is observed for particular combinations of strain rate and testtemperature in 304L [5] and J316 [15]. The twins are also free from the radiation defects. Athigher deformation temperatures dislocation channels are again produced in these steels.Some models [16-18] have been presented to explain the annihilation of the defects due to theinteraction with glissile dislocations but there is no direct experimental evidence to supportthem. However, if fully predictive models are to be developed it is necessary to understandwhat controls the initiation of slip, the nature of the interaction of the dislocations and thedefects, and the basic processes by which the defects are annihilated. In this paper somerecent real-time in situ TEM observations of the dislocation interactions with radiationproduced defects and computer simulations of the interactions are summarized.

(2)

(3)

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2 EXPERIMENT

For the in situ transmission electron microscope studies rectangular (dimensions 2.7 x11 x 0.2 mm) samples of 99.999% pure copper were used. An electron transparent region wasproduced in the center of the foil by using a jet-electropolishing apparatus. The samples wereirradiated in the thinned condition with 200 keV Kr+ ions to ensure a loop population wascreated throughout the sample thickness. The samples were deformed at room temperature insitu in the transmission electron microscope and the dynamic events were recorded onvideotape with a time resolution of 1/30th second. The nature of the defect population was notdetermined in these initial studies, but from previous work [19] it is expected that it consistsof stacking-fault tetrahedra, truncated stacking-fault tetrahedra, and Frank loops.

Atomistic simulation results have been coupled to a three-dimensional dislocationdynamics simulation to investigate the interaction between the radiation defects and thematrix dislocations. One such dislocation dynamics program produced by de la Rubia et al.simulates a 5mm cube of pure Cu that contains an initial density of randomly distributedFrank–Read dislocation sources [20]. The plastic deformation is obtained by following thedislocation motion and structure. The interaction of the mobile matrix dislocations with fullstacking-fault tetrahedra, truncated stacking-fault tetrahedra, and Frank loops have beenconsidered; see references [20,21] for details.

3 RESULTS

On deforming the sample in the electron microscope the matrix dislocations throughoutthe material move and interact with the dislocation loops. An example of this type ofinteraction is shown in Figure 3.

By using a computer-based image processing system, individual frames from thevideotape can be examined. The frame prior to breakaway of the dislocation from the obstaclecan be captured, allowing the effective pinning strength to be determined from the dislocationcurvature by using the Fleischer-Friedel dispersed-barrier hardening equation [22]. Thisanalysis was performed for 52 cases and the distribution of the obstacle strengths is shown inFigure 4. It should be noted that in these initial studies the dislocation line lengths were notcorrected for projection effects. Long dislocations lying in the plane of the foil were selectedfor analysis, which should minimize the projection error. The values are centered atapproximately 40 MPa, which is in good agreement with the value obtained from bulk studies.

Figure 3. The captured video frame contains a pinned dislocation at the instant beforebreaking free (a). The distance between obstacles, l, is measured. In an image editingcomputer application, circles are drawn to a size where a portion of the circleapproximates the dislocation curvature on both sides of the obstacle (b). Tangent linesare drawn on the circles with their origin at the pinning point. The angle 2φ is measuredbetween the tangent lines.

φ2l

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The interaction of dislocations with the defect does not result in its annihilation. Inmany cases, the same defect exists after the interaction with not just one but manydislocations.

Defect-free channels were produced during these in-situ studies in electron transparentfoils, indicating that the proximity of the free surfaces does not affect channel formation. Theorigin of the channels has yet to be identified, as has the mechanism by which the defects areannihilated, but channel formation appears to be associated with regions of high stressconcentration where the dislocation activity is high. Figure 5 shows an example ofdislocation channels emerging from the fracture surface. The two channels emerge from thesame point on the crack edge along two different slip planes. Figure 6 shows the complexdislocation structure that exists at the end of a defect-free channel and it is the motion of thesedislocations that must annihilate the defects.

An example of the interaction of a dislocation with an irradiation produced defect (anoverlapping stacking-fault tetrahedra) in the dislocation dynamics simulation is shown inFigure 7. Here the matrix dislocation is separated into partial dislocations, which move underan applied shear stress of 300 MPa. The leading partial dislocation interacts with, is pinned byand then absorbs part of the overlapping stacking-fault tetrahedra. The leading partial climbsas the trailing partial dislocation approaches. The trailing partial catches the leading partialdislocation at the defect, constricts and climbs by absorbing the remaining part of the

Figure 4. Distribution determined by experimental input to Fleischer-Friedel dispersed-barrier hardening theories.

( )( ) 23

2cos θµτ

= lb

Figure 5. Bright-field TEM image ofdefect-free channels extending fromthe edge of a crack.

g

Figure 6. The complexconfiguration at the end of a defect-free channel.

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stacking-fault tetrahedra. The matrix dislocation continues to move but with reduced mobilitybecause of the jogs on the constricted line segment. In this case the overlapping stacking-faulttetrahedra is absorbed by the interaction with the matrix dislocation. Simulations of theinteraction of matrix dislocations with stacking-fault tetrahedra show that the tetrahedra is notabsorbed, but is sheared by the passage of the dislocation. The stacking-fault tetrahedra is inthis case a relatively strong obstacle, with a breakaway angle of 80°. Continued dislocationactivity along the same slip plane generates the defect-free channels.

4 CONCLUSIONS

We have demonstrated that channels free of radiation-produced defects can be createdby deforming electron transparent foils in-situ in the transmission electron microscope. Thisvalidation was a necessary first step before the detailed interaction mechanism of defectannihilation was undertaken. The in-situ experiments will be used to provide input to and as ameans of verifying the defect annihilation mechanisms obtained from the computer simulationstudies. The combination of techniques will provide much needed insight to the basicprocesses responsible for defect annihilation and creation of channel, and, ultimately result inthe development of predictive models.

5 ACKNOWLEDGMENTS

IMR and JR would like to acknowledge support for this work from DOE underDEFG02-91ER45439, and in part (BW) under the auspices of the US Department of Energyby Lawrence Livermore National Laboratory. The use of the electron microscope facilities atArgonne National Laboratory and at the Frederick Seitz Materials Research Laboratory isappreciated.

6 REFERENCES

[1] E. Bloom."Irradiation Strengthening and Embrittlement", in Radiation Damage in Metals317 (ASM, Metals Park, Ohio, 1975).

[2] D. Franklin, G. E. Lucas and A. L. Bement."in Creep of Zirconium Alloys in NuclearReactors 815 (American Society for Testing and Materials, Philadelphia, PA, 1983).

Figure 7. The interaction of partial matrix dislocations with overlapping stacking-faulttetrahedra under 300MPa shear stress. (After Diaz de la Rubia et al.[20])

a) b) c)

d) e) f)

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[3] G. E. Lucas. "The evolution of mechanical property changes in irradiated austeniticstainless steels". J. of Nucl. Mater., 206, 1993, pp 287 - 305.

[4] B. N. Singh, A. J. E. Foreman and H. Trinkhaus. "Radiation Hardening Revisited: role ofintracascade clustering". J. of Nucl. Mater., 249, 1997, pp 103 - 115.

[5] M. Victoria, N. Baluca, C. Bailata, Y. Dai, M.I. Luppoa, R. Schaublina and B.N. Singh."The microstructure and associated tensile properties of irradiated fcc and bcc metals". J.of Nucl. Mater., 276, 2000, pp 114 - 122.

[6] K. Linga Murty. "Role and significance of source hardening in radiation embrittlementof iron and ferritic steels". J. of Nucl. Mater., 270, 1999, pp 115-28.

[7] C. Bailata, F. Groschela and M. Victoria. "Deformation modes of proton and neutronirradiated stainless steels". J. of Nucl. Mater., 276, 2000, pp 283 - 288.

[8] B. L. Eyre and A. F. Barlett. "An electron microscope study of neutron irradiationdamage on alpha-iron." Philosophical Magazine 12, 1965, pp 261–271.

[9] A. Seeger."in Proceedings 2nd International Conference on Peaceful uses of AtomicEnergy 258 (Geneva, 1958).

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[11] R. E. Stoller and S. J. Zinkle. "On the relationship between uniaxial yield strength andresolved shear stress in polycrystalline materials". J. of Nucl. Mater., 283-287, 2000, pp349-52.

[12] M. Ando, Y. Katoh, H. Tanigawa, A. Kohyama and T. Iwai. "The contribution ofvarious defects to irradiation-induced hardening in an austenitic model alloy". J. of Nucl.Mater., 283-287, 2000, pp 423-7.

[13] N. M. Ghoniem, B. N. Singh, L. Z. Sun and T. Diaz de la Rubia. "Interaction andaccumulation of glissile defect clusters near dislocations". J. of Nucl. Mater., 276, 2000,pp 166–177.

[14] M. A. Kirk, M. L. Jenkins and H. Fukushima. "The search for interstitial dislocationloops produced in displacement cascades at 20 K in copper". J. of Nucl. Mater., 276,2000, pp 50-8.

[15] N. Hashimoto, S. J. Zinkle, A. F. Rowcliffe, J. P. Robertson and S. Jitsukawa."Deformation mechanisms in 316 stainless steel irradiated at 60 degrees C and 330degrees C". J. of Nucl. Mater., 283-287, 2000, pp 528-34.

[16] J. Strudel and J. Wahburn. Phil. Mag., 9, 1964, pp 491.[17] A. J. E. Foreman and J. V. Sharp. "A mechanism for the sweeping-up of loops by glide

dislocations during deformation". Philosophical Magazine 19, 1969, pp 931.[18] D. S. Gelles."in Dislocation Modeling of Physical Sciences (ed. M. F. Ashby et al.) 158

(Pergamon, New York, 1981).[19] T. L. Daulton, M. A. Kirk and L. E. Rehn. "In-situ transmission electron microscopy

study of ion-irradiated copper: temperature dependence of defect yield and cascadecollapse". Phil. Mag. A 80, 2000, pp 809-42.

[20] Tomas Diaz de la Rubia, Hussein M. Zbib, Tariq A. Khraishi, Brian D. Wirth, MaxVictoria and Maria Jose Caturla. "Multiscale modelling of plastic flow localization inirradiated materials". Nature 406, 2000, pp 871 - 874.

[21] Hussein M. Zbib, Tomas Diaz de la Rubia, Moono Rhee and John P. Hirth. "3Ddislocation dynamics: stress-strain behavior and hardening mechanisms in fcc and bccmetals". J. of Nucl. Mater., 276, 2000, pp 154 - 165.

[22] J. Friedel. Dislocations (Pergamon, New York, 1964).

mechanical properties of irradiated materialscoupled with dislocation dynamic computer simulations...

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