Download - 233 MeV Ne ion irradiation effects on the mechanical properties of copper

K. HAVANCSAE et al. : Irradiation Effects on the Mechanical Properties of Cu 37 1

phys. stat. sol. (a) 106, 371 (1988)

Subject classification: 61.80; 62.20; 51.2

Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna') (a ) and Institute for General Physics, Eotvos University, Budapestz) (b )

233 MeV Ne Ion Irradiation Effects on the Mechanical Properties of Copper

BY K. HAVANCSAK (a), G. SZENES (b), V. A. SKURATOV (a), YUN DUN MAN (a), W. MALINOWSKI (a), and V. A. SHCHEGOLEV (a)

The dose dependence of the deformation behaviour of copper irradiated by 233 MeV Nc ions is investigated. The irradiation experiments are carried out on an external beam of the U-400 cyclotron. The yield stress rises monotonically from a fluence of 3 x 1014ions cm-2, saturating at @t 3 x 1015 ions cm+. This saturation behaviour is described by a simple saturation model, which is based upon the assumption that the cluster concentration rate decreases with increasing fluence. It is assumed that this is caused by the interaction between the already existing clusters and the newly produced cascades. The changes of other parameters of the stress-strain curve are also given.

Die Dosisabhkngigkeit des Deformationsverhaltens von Kupfer, das mit 233 MeV Ne-Ionen be- strahlt wird, wird untersucht. Die Bestrahlungsexperimente werden an einem externen Strahl des U-400-Zyklotrons durchgefuhrt. Die Streckgrenze wachst monoton von einern FluB von 3 x x 1014 Ionen om-2 und sattigt sich bei @t = 3 x 1015 Ionen Dieses Sattigungsverhalten wird durch ein einfaches Sattigungsmodell beschrieben, das auf der Annahme beruht, daB die Cluster- konzentrationsrate mit wachsendem FluB abnimmt. Es wird angenommen, daB dies verursacht wird durch die Wech~elwirkung zwischen den schon existierenden Clustern und den neu produzier- ten Kaskaden. Die Anderungen der anderen Parameter der Spannungs-Dehnungskurve werden ebenfalls angegeben.

1. Introduction

The defect structure of copper irradiated by neutrons or charged particles has been examined extensively for many years. The interest in this material is explained by the fact that i t may serve as a model material for the investigation of the defect structure in irradiated f.c.c. metals, and by its possible use in fusion reactor technology in the near future. The defect structure of irradiated copper has been investigated mainly by electrical resistivity measurements [ 1 t o 51, transmission electron microscopy [6, 71, and by the measurements of mechanical properties [8 to lo]. Recently a grow- ing interest has been shown in heavy-ion irradiation experiments [ll to 141. The results extensively reveal the advantages and limitations of heavy-ion irradiation in the simulation of neutron irradiations, although many details have so far not been clarified. The investigation of the mechanical properties of materials irradiated by energetic heavy ions is also in progress at the Joint Institute for Nuclear Research (Dubna). This program is based on the U-400 cyclotron. The irradiation system devel- oped makes it possible to perform ion bombardment under controlled conditions [ 151,

*) SU-101 000 MOSCOW, USSR. a) Muzeum krt. 6-8, H-1088 Budapest VIII, Hungary.

372 K. HAVANCSAK et al.

rc- I 70-161 -

F k ~ 7 O - l ~ - - 0 L

70-18 7 -

I I I I

and our first results for Ne ion irradiated nickel [16] have shown the potential of this approach. I n the present work the deformation behaviour of polycrystalline copper irradiated by energetic Ne ions is investigated. The main experimental results are presented here, and a more detailed analysis will be made in a following paper.

2. Experimental The irradiation facility and the experimental procedure have been described else- where [15 to 171. Therefore, only the most important features will be given here. Tensile specimens were prepared from 30 p n cold-rolled copper sheet. The material used was 99.998 wt% pure with Fe(0.0013 wt%) arid Ni(0.0004 wt%) as the main im- purities. The specimens were of standard tensile form, with a 15 mm gauge length and 3 mm width. Before irradiation these were annealed a t 350 "C for 1 h in vacuum. This temperature produced a fully recrystallized grain structure with a mean intercept grain diameter of 5 pm. The irradiations were performed in air by passing the acceler- ator Ne ion beam through a thin aluminium window. The ion energy a t the entry surface of the specimens was 233 MeV. During the ion bombardment the specimens were cooled by a room temperature air jet so that the temperature did not exceed 100 "C. The temperature was indirectly controlled on special samples by measuring the changes in length when the ion beam was switched on.

The depth distribution of the defect production cross-section for a Ne projectile and Cu target is shown in Fig. 1. This distribution function was calculated by a com- puter code [18] using the relation

where cd(z) is the Frenkel-pair production cross-section per atom, as a function of the projectile range, v(T) is the damage function, i.e. the number of Frenkel pairs produced by a primary knock-on host atom of energy T, do/dT is the differential cross- section for producing host atom recoil of energy T, Ed the effective threshold energy for a displacement, yEi the maximum energy transferred, and @ ( E i , Of, 2) the distribution of the projectile as function of energy Ei and angle 8, a t depth Z. I n the calculations the modified Kinchin-Pease formula was used as Y ( T), Lindhard's differen-

233 MeV Ne Ion Irradiation Effects on the Mechanical Properties of Copper 373

tial scattering cross-section was taken as du/dT, Ed = 29 eV, and @(Ei, 8,) x) was the distribution given by Bardos [lS].

The non-uniformity of defect production is not too large throughout the specimen thickness, as we worked in the transmission mode. As shown by Fig. 1, the defect production cross-section varies in the range of (0.77 t o 1.15) x ern2. The uniformity of the ion beam distribution along the gauge length of the samples was controlled using a multifoil secondary electron-emission monitor system [ 151. By this means, the non-uniformity did not exceed 10%.

The mean defect production rate was 1.2 x 10-7 atom-l s-l (at a beam intensity of 1.2 x loll ions cm-2 s-l).

After the irradiation, the stress-strain curve was measured a t room temperature by an Instron tensile testing machine. A croeshead speed of 0.1 mm/min was used, cor- responding to a strain rate of 1.1 x lod4 s-l.

3. Results and Discussion

The dose dependence of some representative stress-strain curves is shown in Fig. 2 to demonstrate the effect of Ne ion irradiation. It can be seen that there are a) a large increase in yield stress, b) a large decrease in strain to fracture, and c) only a small influence of the Ne irradiation on the ultimate tensile strength. These results are similar to those for nickel irradiated by energetic heavy ions of Ne [16], and the results for neutron irradiated copper [lo, 201. However, the dose dependence of the yield stress is different (see below).

3.1 Change in yield stvess

The yield stress, according to the E = 0.002 plastic deformation, was determined from the stress-strain curves. Changes in yield stress Au versus ion irradiation fluence (@t ) are shown in Fig. 3. At some fluences measurements have been repeated several times to determine the uncertainty in data. This does not exceed t 3 MPa as shown by Fig. 3. The initial value of the yield stress, measured on the unirradiated specimens, was u = 35.5 MPa.

It can be seen in Fig. 3 that Au rises monotonically saturating a t the fluence @t = 3 x 1015 ions cm-2.

0 5 70 75 20 &(XI -

Fig. 2. The stress-strain curves for copper showing their dose dependence. The curves (I), (2), (3) have been shifted by 6, 4, and 2%, respectively. (1) annealed sample, (2) @t = 1 X 1015, (3) 5 X x 1015, (4) 6 x 1015 ions


I I I I I I I 0 I 2 3 4 5 6 7

Pt p ~ ~ ~ i ~ ~ ~ cm-2~ - Fig. 3. The yield stress vs. Ne ion-irradiation fluence for Cu. Curves (l), (2), and (3) correspond to relations ( 5 ) , (9), and (lo), respectively

The yield stress increase is presumably caused by irradiation defect clustering. These clusters prevent the dislocation propagation according to the relation [22]

Ao = apb VZ, (2)

1vhei.e x is a constant, p the shear modulus, h the Burgers vector, and c the cluster density with the mean diameter 2.

Tiiasmuch as the yield stress obviously shows a saturation character, i t is worth trying to apply a simple saturation model. This model is based upon the assumption that no new cluster is formed in the vicinity of the already existing one within a volume v. According to the model, the cluster concentration rate is given by

where c is the cluster concentration, or the initial rate of cluster concentratioii change, and v the effective interaction volume between the defect clusters. The solution of (3) gives the dose dependence of the cluster concentration,

exp (-o,v@t) } . (4) 1

c = - { l - li'

The dose dependence of the yield stress is determined from (2) incorporating (4),

AG = A { 1 - exp ( - B@t) }I/* , (5)

where A and B are related to physical parameters as follows:

B : oCv . (7)

Curve 1 in Fig. 3 demonstrates (5), fitted to the experimental data. There is a fairly good agreement between the data and the mathematical curve, including the satura-

233 MeV Ne Ion Irradiation Effects on the Mechanical Properties of Copper 375

tion, too. The parameters A and B, given by the least-squares method are as follows:

A = 51 MPa,

B = 0.8 x 1015 om2 . In order to estimate the physical reality of such a model in our case, the initial rate

of cluster concentration change can be expressed in terms of microscopical parameters as follows :

The parameters incorporated in (8) are as follows: od is the Frenkel-pair production cross-section, e the atomic density of copper, 5 the defect-production efficiency, i.e. the ratio of defects avoiding the subthreshold annihilation to the number which theo- retically is calculated according to the modified Kinchin-Pease expression [ 131, and n is the mean number of defects in a cluster a t a low dose. To obtain an estimate of the interaction volume v, the following values of the parameters were taken: c d = cm2, e = 8.5 x loz2 5 = 0.5 [13], n = 10. The evaluation leads to a prediction of v = 9.4 x 10-20 cm3. Assuming the spherical form of this volume, we obtain its radius to be r = 3 nm.

It cannot be expected that such a simple model can describe the details of the com- plex interaction and annihilation processes in the high-energy (5 to 10 keV) displacement cascades, Nevertheless i t is hoped that the main features are reflected. According to this model, the saturation is explained by the decreasing cluster concentration rate with increasing fluence, which is caused by the interaction between the already existing clusters and the newly produced cascades. The above measurements do not give information about the precise mechanism of this interaction. How- ever, it may be not too far from reality if i t is assumed that the focussed interstitial propagation and the residual agitation of the lattice by the “thermal spike” may play an important role.

As a consequence of the interaction, no new cluster is formed, if a new cascade arises in the vicinity of a cluster already existing, within the interaction volume. How- ever, it can lead to changes in the dimensions of the already existing cluster depending on the type of the interacting clusters. In extreme cases the old cluster can disappear completely. There is experimental evidence for such annihilation of clusters 1191. In this sense the given interaction volume (9.4 x 10-20 cm3) is physically acceptable, but i t is clear that i t is an effective volume resulting from more concurrent processes.

It is important t o note that the model presented here implies that the mean diameter of the clusters @) can be a function of fluence. However, i t is t o be noted that this is a slowly changing function, and it is so for @ I 2 to a greater extent. Consequent- ly the exponential term dominates in the yield stress changes, which results in its saturation character.

Some comments must be made a t this point. (i) The majority of the earlier measurements for neutron-irradiated copper pro-

duced a different dose dependence of the yield stress Ao. In order t o compare with our data, two of them are given in Fig. 3. Curve 2 is plotted according to the relation

A c = e(@,t)l12 , (9)

as proposed by Seeger 1211. It can be seen from the figure that whereas the first points lie on the curve, i t rises much more rapidly than the experimental data.


Curve 3 shown in the same figure follows from the relation

A0 = f (@t - g)lI4, (10) proposed by Zinkle and Kulcinski [5]. A small incubation dose is supposed by us in (lo), for the sake of a better f i t . It is seen that a rather good agreement is obtained except for the saturation region, starting a t about 3 x 1015 ioriscm-2. The parameters e , f , and g in (9) arid (10) are constant.

(ii) Makin and Minter have used the same mathematical model t o explain their measurements on neutron-irradiated polycrystallirie copper and nickel [20]. I n those experiments saturation was not actually observed, but only a tendency t o it. They also assumed that no new cluster can form i n the vicinity of an old one within a volume v. The microscopical mechanism of the saturation process was riot discussed by them.

(iii) The problem of incubation fluerice was also examined directly. The yield stress of an unirradiated specimen was measured by deforming it only slightly over the yield point, arid then releasing it. J n this condition the specimen was irradiated by a fluence of up to 0.05 x l O I 5 ions which is less than the incubation fluence pre- dicted by (10). The increase in stress observed a t subsequent deformation indicates the absence of incubation. It is worth mentioning that ( 5 ) does not imply an incnba- tion dose.

3.2 Other parameters of the stress-strain curve

Fig. 4 shows the change of strain to fracturo versus ion-irradiation fluerice. The re- duction in elongation from 10 to 3% is similar to the trend observed in the case of Ne ion-irradiated nickel [16].

The form of the ultimate tensile stress curve strongly differs from the behaviour of that of nickel [16]. A t the outset of the curve it falls, then passes through a minimum, and then slowly rises again (Fig. 5 ) .

The functional form of the stress-strain curves over the yield point has also heen examined. A s is usually proposed in the literature,

where 0 and E are the plastic parts of stress and strain, respectively, K is a constant, and rn is the work-hardening coefficient. In order to determine the coefficient m, the 111 &-In 0 plots were made, as shown in Fig. 6. It consists of straight lines which confirm the validity of (11). Tn the case of an uriirradiated sample the experimental point,s lie on a single straight line, while for the irradiated specimens a break is oh-

I I I I I I I 0 7 2 3 4 5 6 7

Fig. 4. The deformation to fracture as a function of the Ne ion fluence

o t ( 1 0 ~ ~ i 0 n ~ cm-2i -

233 MeV Ne Ion Irradiation Effects on the Mechanical Properties of Copper

0.8

377

I

-

Fig. 5. The ultimate tensile stress as a function of the Ne ion fluence

[n E - Fig. 6. The In E-ln (T plot for an unirradiated (1) and irradiated ( 2 ) copper sample

I 1 I I I I 0 7 2 3 4 5 6

mt (1075i0ns cm-21 ---+ Fig. 7. The dose dependence of the work hardening coefficients m, (0 ) and m2 (0 )

378 K. HAVANCSAK et al. : Irradiation Effects on the Mechanical Properties of Cu

served, i.e. two different values of the work-hardening coefficient, m, and m,, are associated with one fluence. As shown in Fig. 7, m, and m2 behave differently with regard t o fluence. At low fluences, m, rapidly falls, then passes through a minimum at about 1.5 x 1015 ions cm' 2, and rises t o the starting value. This trend resembles tha t of ultimate tensile stress. A t the same time, at low doses, nz, seems t o remain un- affected arid then i t starts decreasing a t a fluerice of about 1.5 x 1015 ions cm-2.

The results obtained clearly demonstrate tha t there are two well-separated parts of the deformation of the irradiated specimen, i.e. the mechanisms of deformation changes at a certain point of elongation. The first of them may be associated with the propagation of the Liiders band. This assumption is confirmed by the observation tha t the stress.-strain curves have a jerky charact,er immediately above the yield point, which is likely t o be the consequence of inhomogeneous deformation.

A t low fluences the coefficient m2 remains almost unchanged. A similar observation has been reported by Higgy [lo] for pure copper single crystals after a high neutron exposure. As far a s the ultimate tensile stress, the deformation t o fracture, and the work-hardening coefficient are concerned, the uncertainties in their measurement are usually greater than those of the yield point, and their features are not easy t o inter- pret without additional measurements.

The authors wish t o express their gratitude t o Academician (2 . N. Flerov and Prof. Yu. Ts. Oganessian for their permanent interest, as well as t o G. Bardos for the defect production cross-section calculations. We are indebted t o the personnel of the cyclotron U-400 for their careful work.

Acknowledgements

References [l] W. SCHILLING and K. SONNENBERG, J. Phys. F 3,322 (1973). [2] F. DWORSCHAK, R. LENNARTZ, and H. WOLLENBERG, J . Phys. I? 5,400 (1975). [3] R. C. BITCHER and T. H. BLEWITT, J. nuclear Mater. (Amsterdam) 98, 63 (1981). [4] R. S. AVERBACK end K. L. MERKLE, Phys. Rev. B 16,3860 (1977). [ 3 ] S. J. ZINKLE and G. L. KULCINSKI, J. nuclear Mater. (Amsterdam) 122/123, 449 (1984). [6] XI. RUHLE, F. HAUSSERMANN, and M. RAPP, phys. stat. sol. 39, 609 (1970). [7] C. A. ENGLISH, J. nuclear Mater. (Amsterdam) 108/10!), 104 (1982). [8] T. H. BLEWITT, R. R. COLTMAN, R. E. JAMISON, and J. K. REDMAN, J. nuclear Mater. (Am-

[9] &I. J. MAKIN and S. A. MANTHORPE, Phil. Mag. 8, 1725 (1961). sterdam) 2, 277 (1960).

[lo] H. R . HIGGY, J. nuclear Mater. (Amsterdam) 107, 90 (1982). [ll] A. IWASE, S. SASAKI, T . IWATA, and T . NIHIRA, J. nuclear Mater. (Amsterdam) 55,259 (1975). [12] A . D. MARWICK, J. nuclear ?/later. (Amsterdam) 55,259 (1975). [13] R. S. AVERBACK, J. nuclear Mater. (Amsterdam) 108/109,33 (1982). [14] R. S. AVERBACK, K. L. MERKLE, and L. J. THOMSON, Radiat. Eff. 51, 91 (1980). r1.51 K. HAVANCSAK, v. A. SKURATOV, A. ILLES, SIN HON CHER, W. MALINOWSKI, E. D. VARABEV,

[l6] K. HAVANCSAK, V. A. SKURATOV, G . SZENES, SIN HON CHER, W. MALINOWSKI, and V. A.

[17] K. HAVANCSAK, A. ILLES, P. HORVATH, I. IVANCSIK, B. FOGARASSY, and G. SZENES, Commun.

[18] G. BARDOS, Phys. Letters 8119,415 (1987). [19] S. ISHIANO and T. MUROGA, J. nuclear Mater. (Amsterdam) 133/134,78 (1985). [20] 31. J. MAKIN and I?. J. MINTER, Acta metall. 8, 691 (1960). [21] 9. SEEGER, 2nd United Nations Conf. Peaceful Uses of Atomic Energy, United Nations,

[22] A. J. E. FOREMAN, Phil. Mag. 17 , 353 (1968).

and V. A. SHCHEGOLEV, Commun. JINR, 13-84-601, Dubna 1984.

SRCHEGOLEV, Fiz. Metallov i Metallovedenie 62, 390 (1986).

JINR, P7-85-261, Dubna 1985.

Xew York 1958 (p. 250).

(Received July 31, 1987; in revised form December 11, 1987)

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