Pulsed irradiation creep in nickel

1281

Journal of Nuclear Materials 103 & 104 (1981) 1281.1286 North-Holland Publishing Company

PULSED

IRRADLATION

E. P. Simonen

CREEP IN NICKEL

and C. H. Henager,

Jr.

Pacific Northwest Laboratory Richland, Washington 99352 Results from a series of pulsed irradiation creep tests have indicated a signifiA pulsing effect cant effect of beam heating on pulsed irradiation creep behavior. due to intermittent atomic displacement damage was not observed. Sheet metal specimens were irradiated at 473 K using 15 MeV-deuterons and a stress of 200 MPa. The oulse cvcle consisted of 1000 seconds of irradiation followed bv 100 seconds Pulsed irradiation creep behavior was compared with steady irradiaof annealing. The experimental results were interpreted using models of tion creep behavior. intermittent displacement damage and theories of temperature history effects.

1.

isolated influences were identified by performing multiple irradiations on single specimens.

INTRODUCTION

Dimensional stability, stress relaxation and creep rupture are engineering properties diThese rectly affected by irradiation creep. property changes must be accounted for in the prediction of structural materials performance for fusion reactor operation. A unique environmenta~ concern for fusion is the proposed intermittent, i.e., pulsed, time structure of the irradiation flux. In a previous pulsed irradiation creep test [l] using a Tokamak-like pulsing schedule, we found a three-fold enhancement in the creep rate when comparing pulsed-irradiation creep with steadyThe steady-jrradjation irradiation creep. creep rates were shown to be compatibie with the climb-glide creep mechanism. Furthermore, the pulsed enhancement of creep was rationalized with rate theory calculations of transient point defect annihilation rates at climbing dislocations. For the conditions used in the light-ion pulsed experiment we found that the transient climb distance induced by pulsinq was on1.y on the order of a single Burgers vector or lkss.[2] This oredicted small climb distance has motivated'this additional theoretical and experimental evaluation of pulsed irradiation creep mechanisms. 2.

EXPERIMENTAL

RESULTS

The present pulsing experiments have revealed that the temperature excursions which are induced during light-ion irradiation pulsing can influence the enhancement of irradiation creep. This conclusion has emerged from the results of a series of pulsed irradiation creep tests. These tests were performed to isolate effects of point defect dynamics and pulsing effects on the creep specimen thermal history. The

Three irradiation modes were used: i) steadystate beam, ii) pulsing with the beam being brought on and off the specimen rapidly as in our prior study, and iii) pulsing with the beam being brought on and off the specimen slowly, i.e., over ten seconds. The speed of beam action was varied to compare the creep response with a large temperature excursion with that for a small excursion. Furthermore, the creep rate transitions from steady mode to pulsed modes allowed a comparison of steady-irradiation creep rate to pulsed-irradiation creep rate for a constant state of microstructure. This comparison can be made since the microstructure does not change discontinuously when the irradiation mode is changed because the microstructure is a slowly varying function of time. The nickel foil specimens were bombarded with 15 MeV deuterons at 473 K at a tensile stress The PNL light-ion irradiation of 200 MPa. creep apparatus was used for these tests. The deuteron beam current induced an atomic displacement rate of 5 x 1O-7 dpalsecond as calculated from the EDEP-1 displacement damage computer code.[3] The beam pulsing was produced in one of two ways: i) by manually steering the beam slowly on or off the specimen, which we choose to call slow-beam-action pulsing, or ii) by rapidly interrupting the beam in less than a second with a Faraday cup, which we choose to call fast-beam-action pulsing. The nominal pulsing characteristics were 1000 seconds of irradiation followed by 100 seconds of annealing. The specimen strain was measured continously during the test using a noncontacting laser extensometer. The 0.15 mm, 80-90% cold worked sheet specimens were from the same lot of material used in our prior pulsing study. The level of

1282

E.P. Simonen, C.H. Henager, Jr. /Pulsed irradiation creep in nickel

cold working for this lot of material was 80-90% and not 25% as previously reported.[l] The TEM microstructures of deuteron bombarded creep specimens are discussed by Henager et a1.[4] The creep response of a single specimen exposed sequentially to the three modes of irradiation is shown in Figure 1. The consistent observation that is apparent in this experiment is that pulsing with a fast-beam-action results in an enhanced creep rate when compared with either slow-beam-action pulsing or steady The six irradiations and their irradiation. creep rates were i) steady irradiation (transient rate), ii) slow-beam-action (2 x 10-g set-I), iii) fast-beam-action (3.1 x 10-g set-I), iv) slow-beam-action (1.6 x 10-g see-I), v) fast-beam-action (3.7 x and vi) steady irradiation 10-g set-1 (1.5 x lo- A1 set-l). The important consequence of the fast-beamaction pulsing is the large temperature increase that is induced in the specimen at the onset of each irradiation pulse. The temperature increase of about 100 K existed for approximately In contrast, the slow-beam-action one second. pulse induced a temperature rise of less than 30 K over a time of about ten seconds. A second irradiation run was performed using a single transition from a steady irradiation to This a slow-beam-action pulsed irradiation. transition revealed no effect of beam pulsing on the irradiation creep rate. The creep strain response for this run is shown in

Figure 2. The absence of a pulsing influence on creep rate in this test indicates that periodic annealing of the atomic displacement damage did not cause an increase in the creep rate when compared with the uninterrupted steadyirradiation creeo rate. 3.

ANALYSIS

AND DISCUSSION

The observed pulsed irradiatiun creep response was analyzed from two points of view: i) the pulsing influence on the instantaneous point defect fluxes and ii) the pulsing influence on the light-ion beam heating transients produced at the onset of each irradiation pulse. The transient beam heating effects were found to have a potentially significant influence on the irradiation creep rate. The climb rate of network dislocations and the growth rates of irradiation induced clusters were found to have only a small dependence on the transient instantaneous point defect fluxes. 3.1

Pulsing

Effects on Climb

The cyclic creep mechanism proposed in our previous studies [1,2] was based on the out-ofphase fluctuations in the vacancy and interstitial concentrations induced by irradiation At the onset of the irradiation pulsing. pulse a surplus annihilation of interstitials at sinks is caused by the limited slow vacancy mobility during the first several minutes of Conversely, during the pulse the irradiation. annealinq period there is a surplus of vacancy annihilaiibn due to their delayed diffusion

1

TIME x10’. SECONDS

Figure 1 : Irradiation creep strain versus time for sequential irradiations using three different modes of irradiation

TIME

xlo“,SECONDS

Figure 2 : Irradiation creep strain versus time comparing steady irradiation creep with pulsed irradiation creep using slowbeam-action pulsing

E. P. Simonen,

C H. Henager, Jr. /Pulsed

irradiation

1283

creep in nickel

to sinks when compared to interstitial diffuAn important consequence of sion to sinks. this dvnamic effect is the WediCtiOn that dislocation climb will be induced in alternating positive and negative directions during each The result can be an enhancement pulse cycle. in the climb-glide creep rate. This pulsed irradiation creep enhancement, however, can have a limited effectiveness due to the small climb amplitudes that are predicted. The climb amplitude Xc was shown to be [2]

xc=

CV bp

d

x

where b and Pd are the Burgers vector and dislocation density, respectively. D, is the vacancy diffusivity; k,2 is the vacancy sink strength and ta is the annealing time. At steady state the vacancy concentration, C,, and interstitial concentrations are given by the rate equations.

dcV -=

dt

dCi = dt

0

0 =

=

K -

aCiCv - kv2DvCv

(2)

K - aCiCv - ki2DiCi

Zi and Zv where kv2 is Zvpd and ki2 is ZiPd. are the bias oarameters for interstitials and vaK is the atomic displacecancies, respectively. ment rate, 5 x 1O-7 dpalsec and Q is the recombination parameter, 8.21 x 1016 set-l. We assume that Di equals 8 x 1O-7 exp (-O.l5/kT)m2/sec and Dv = 1.9 x 10-5 exp (-Ei/kT)mP/sec. Thermal emission terms have been neglected in this analysis due to the low temperature and the short annealing period. At our low irradiation temperatures, i.e., 473 K, there is evidence for divancancy reaction processes.[5] In the present analysis we assumed effective migration energies for vacancies which are less than the monovacancy migration energy of 1.38 eV. A family of curves showing calculated climb amplitudes as a function of effective vacancy migration energy for several dislocation densities are shown in Figure 3. The effective vacancy diffusivity is also shown as a coordinate in Figure 3. The pulsing influence on climb is a maximum at intermediate vacancy diffusivities. To affect the climb process the vacancy must have sufficient mobility to anneal out during the

EV,,

eV

Figure 3: Climb distance induced by pulsing as a function of vacancy migration energy (vacancy diffusion) and dislocation density, m-2. Moreover, a too annealing period of the pulse. high mobility results in a low vacancy concentration in the matrix and therefore the number of vacancies that can contribute to climb becomes negligible as the diffusivity increases. The result is a limited range of diffusivities, i.e., temperatures.or migration energies, where the pulsing influence on climb can be significant. Within reasonable limits of parameter assumptions, the climb amplitude at 473 K, as seen in Figure 3, is not great enough to overcome glide obstacles larger than a single Burgers vector. For this reason, we conclude that the proposed point defect dynamic mechanism cannot rationalize the pulsed irradiation creep enhancement observed in the PNL creep experiments. 3.2

Pulsing Effects on Irradiation-Induced Microstructure

In addition to perturbing the climb of dislocations, the intermittent irradiation may also perturb the growth histories of irradiationinduced clusters when compared with steadyirradiation behavior. These perturbations may result in modified irradiation induced microstructures due to the imposed pulsing conditions. To illustrate the pulsing effect on cluster growth we have calculated the influence of the pulse annealing of vacancies on void growth behavior. During this annealing period the void experiences an incremental growth supported by the vacancy annihilation which occurs in the absence of interstitial annihilation. The number of vacancies annihilated at each void during the annealing period, NV, can be estimated from

1284

E.P. Simonen.

Cl!. Henager, Jr. /Pulsed

(4)

where kf is ZvPd plus 4nrvpv. rv and pv are the void size and number density, respectively, and R is the atomic volume of nickel. The vacancy concentration at the onset of annealing, Cv, is obtained from Equations (Z)-(3). The number of vacancies annihilated per void during the annealing cycle is not large unless the dislocation density and the void densities are low. Figure 4 illustrates the dependence of vacancy annihilation per void as a function of the effective vacancy migration energy for two choices of dislocation density. We conclude that point defect transients do not result in large perturbations in the development of the irradiation induced microstructures. Furthermore, the discontinuous changes in creep responses illustrated in Figure 1 suggest that the pulsing effects on the creep rates were instantaneous and were not due to slowly varying influences on microstructural development. General conclusions can be drawn from Figures 3 and 4 for Tokamak pulsing periods at any temperature, i.e., any vacancy diffusivity, in the absence of vacancy thermal emission. Significant pulsing effects on the climb of

0, mVsec

E;,

eV

Figure 4 : The number of vacancies annihilated per void during each pulse annealing period as a function of vacancy migration energy and dislocation density, m-2. A void size of 0.1 nm and number density of 1021 m-3 was assumed.

irradiation

creep in nickel

dislocations and on the defect microstructures are only predicted for a limited range of temperatures and for materials with low sink densities. Predicted effects are greatest for well annealed materials with low dislocation densities and at low fluences when irradiationinduced sink strengths are small. 3.3 Thermal Cycling The measured thermal history provides a basis for calculating enhancement in rate processes caused by beam-induced temperature cycling. If a thermal rate process has an Arhennius temperature dependence, then an enhancement, a, due to an elevated time-averaged temperature can be calculated from

exp (- E /k T(t))dt

(5)

where E is the activation energy of the process and tp is the time of the irradiation pulse. The temperature, T(t), is the measured time dependent temperature and T, is the constant temperature which would exist with no thermal cycling. The results calculated from Equation (5) demonstrate that an activation energy of 2 eV is consistent with a two-fold enhancement in a rate process due to the beam-induced temperature exHence if the irradiation creep rate cursion. had an effective activation energy of 2 eV, the time-at-temperature calculation would account for the pulsed experimental behavior. This activation energy, however, is much larger than expected from rate theory calculations of the temperature dependence of climb-glide creep. At 473 K and 5 x 1O-7 dpalsecond, point defect recombination is the rate controlling The defect concentrations process in nickel. and hence climb-glide creep rate should have an effective activation energy of about one half that for vacancies, i.e.,.about 0.4 to 0.7 eV, which is much less than the necessary 2 eV found in this analysis. Enhancement in the thermal creep rate is expected due to the thermal excursion. Spingarn [6] suggests that at 473 K the activation energy for thermal creep of nickel is about 1.8 eV. The increase in thermal creep rate was estimated from Equation (5) and was found to be about 50% greater than for a steady temperature. The thermal creep component, however, is only about 10% of the total measured creep rate, i.e., thermal plus irradiation creep. Hence, the expected enhancement in the total creep rate due to an enhanced thermal creep rate is only about 5%. Thermal stresses induced by the instantaneous beam heating were calculated and were found to

E.P. Simonen, C.H. Henager, Jr. I Pulsed irradiation creep in nickel be much less than necessary to induce yielding Furthermore, these stresses of the specimen. existed for only less than a second and therefore should not contribute significantly to enNonetheless, the possihanced creep rates. bility remains that the periodic stress pulses may be producing contributions to the specimen strain due to ill-defined dislocation and/or micro~chanical effects. 4.

1285

ACKNOWLEDGMENTS This work was supported by the Office of Basic Energy Sciences of the U.S. Department of Energy under Contract DE-ACO6-76RL0 1830. REFERENCES

Cl1

Simonen, E. P. , and Hendrick, P. L., 3. Nucl. Mater. 85 and 86 (1979) 873,

c23

Simonen, 282.

CONCLUSIONS

Pulsed irradiation creep testing has revealed an enhanced creep rate caused by irradiationAn enhancement induced temperature excursions. in the creep rate was not observed when the pulsing was conducted in a manner which minimized the induced temperature excursion. The absence of a pulsing effect on the creep rate for a constant temperature is consistant with calculations of pulsed irradiation effects on climb and irradiation-induced microstructural The mechanism for the thermal development. cycling influence has not been identified; however, enhancement of thermally activated rate processes was shown to occur due to time-attemperature considerations. Also the possibility of strain effects induced by thermal stresses was suggested.

E. P., J. Nucl. Mater. 90 (1980)

c31 Manning, I., and Mueller, G. P., Computer Phys. Comm. 7 (1974) 85.

i-41 Henager, Jr., C. H., Simonen, E. P., Bradley, E. R., and Stang, R. G., J. Nucl. Mater., this volume.

[51

Yoo, M. H., Phil. Mag. A 40, 2 (1979) 193.

F61

Spingarn, J. R., Ph.D. Thesis, Dept. of Materials Science and Enaineerina. Stanford Univ. (April 19iS) *' SU-DMS-77-D-13.