Chapter 18

Radiation Effects in Metals:

Hardening, Embrittlem ent, and Fracture

18.1 STRUCTURAL â4ETALS FOR

FAST REACTORS

The nr u tron ect›n omy of a fast reac for is not so sign i fican tl y affected by neutron capture in the structural materials in th e core as is th at of a th ermal reactor. First, most neutron-capture cross sections increase with de- creasin g n eu tron ‹ n ergy’, an d the ne u tro n population of the liquid - metal fast breeder reactor ( U4 FEH ) co n tains a far lower perce n tage of thermal nt utrons th an does that uf a ligh t- wate r reactor ( LW It ) . Secs nd. th e ratici of the mass of structural me tal tO th £' mass of fissile materials is much smaller in a fast reactor than in a thermal reactor. Co nst q uv n tl y, mt'tals th at in :i thermal reactor would se very 1 y imp ai r neu tr old vc'on‹›mj‘ are acceptable in a last re actor, and th ‹' sent'cti o n of core str ttctu ral ma t.e ri all ror tlu Ight FBIi can bt basc•d primarily on cost anri me chan ical arid chemical prope rties. The d own grading of ne utro n- absorption characteristics from the ' It's tio n c rite ria for core strti ctural metals me ans th at the' r'ostl j zirvonium all oys used in the rmal reactors need not be emp loyed in fast reactors. Hoz'ever, parasitic nem tron ‹i bsorptioii by non f uel compont n Is is important enough ter c atise I âI FH 11 core de.signers to be q trite sparing in using cert‹iin structu ral me tals. The irradiation properties of high-ni ckel all oys, for example, are ge nerall y su perior to those of ‹ oiwen tional stainless steel, bti t nil'kel has a seriously large vr‹iss section for absorption of fas I It nitrous.

The most important metallic c omponent of a reactor core is th e fuel cladding; tti is iriember provides structural integrity tr› the t'uel element, presents fission products frum escaping t‹i the pri mark’ cixil a n I system, and separates the soriiu m coolant fro m the ceramic onto n«i i 'ith w hich it reacts ) . ’F he cladding must be thin-w-alled tu bind I hat can remain in tact in a fast reactor environment ft›r periods tit up to 3 years at temperatu res IO 800 C, diametral .strains ‹›f 3’ , ‹ind l3 uences up to 3 x 10 2 ’ nvu tro ns ‹'iii ' svr . Th e clarlri ing allu y selected for the LII FB It is the austenitic stainless steel describetl as ty pe 31fi. Th is material has an fcc cr› st at structure. l .Austenite is th e fcc irio d ificat io n of‘

iron. I I is the stable form of pure iron bet z'een 910 and 1400 C. The add it ion of nickel stabilizes this strut ture above room temperature. ) lt has goud high temperature creep strength and resists corrosion by liq uid -sodiu m and hypustoichiometric mixed-oxide fuels. $Ioreover, it is cheaper than mo re exotic metals, a vailable in su rricient quantities for the fast react‹› r program, and is easy’ to fabricate. ’I'lie c‹inip‹›sitions ‹if two austenitic stainless steels are given in Table 18.1.

The austenitic stainless steels, h‹i w’ei'er, are h ighly susceptible t‹i smell ing ‹i wing to vo id formalin n and t‹› high ie inperat ure embri tile men t by the hel iu m prud need ill neutro n reac tio ns w ith co nstitu c n I.s of the alloj‘. Com- mere ial nickel allo ys I e.g.. 1 n‹ onel anri I nc‹il oy ) are bac kti p materials for ‹ o re struc'tural comp‹i nents in the liq uiri - metal fast brvt der rt'actor. I’m r'sv allo ys appear to be lvs.s prone to v o i ri s u' c' 1.1 i n g , b u I t li e i r n e u t ro n - a b so r p t i o n cross secti‹in is higher than that of steel. Vanad iu m-based

‹ind refrac tory'-metal alloys are lo ng-ran ge ‹'and iciates for LSIFBR fu‹ 1-vlemv n t cladd in g. ’l'hvse two classes of metals but h possess bcc lattice st ructures ated ‹me more resistant to Incl iu m emb rit tlemc'nt than are th e austc n itic' stainless steels or nickel alloys. I n ariditi‹in , th e refra‹-tory met als I e.¿. , mol \ ’bde n u m ) d‹› n ot f‹irm \ o ids under large r« i-nc'utro n l1 uences at th e vlad d ing s‹'rvice temporal tl rt s of the LII FB li. llCis’ever, f›oth vanadiu m alloys and the re fractCiry metals are mu‹'li mo re c'ostlj th an smirk le.ss steel, and th eir use as cladd ing vould significantly increas‹• the capital cost of a fast reactor.

Although the generally t'avorable high-temperature properties of the austenitic stainless steel are utilize‹l in the fast react or core co mpoun ds l e.g., in c 1 ad ding and asse mb ly w'rappers ) , the lo wer flu x, lo wer ie mpc•ratu re ens'i ro n ment outsi d e the core per rn its less ex pensii e steels to be used for tlir reac'tur pressu re vesse 1. I n froth UIF B It and L \ VR syste as, t›rdinar \ fe rri tic or ‹ill os steel i.s used for th is coiripone n t. ( Fe rri te is a b‹‘c mo d i fic'ati‹›n ci f i r‹›n . ) ’I'y pi cal alloy -steel c omposi tions are sh u \ vn in ’I'able lH. 2. ’I’ll is material does nOt possess, n Or does it need to possess, the high -temperature sire ngt li and t o rrosicin resistanc'e of stain-

418

4 9

Table 18.1 Composition o f A ustenitic Sta in less Steels

T y pe 30 4, T y pe 316.

E le me nt

def‹irmati‹in o‹-ctirs at high strc*sses and rather q uie k ly . Uo wevt'r, the strct'yth ‹› I fuel-ele ment clacld ink in must accuratel y rcprescntccl h \ ’ the resistance uf the metal tu sl‹›w defurmati‹›n by creep, since the internal luacliny un

the cladcliny ne›’er reaches the yield stress. 1‘he creep

Fe 70

;g

Ni 9

6 S

1 7

1 .3

M j‹› strength of a metal is usuall}’ determined by thL tinJo c‹›i sti£utnts requirccl fur failure undtr a fixed applied stress ( i.t*.. a Stress

ru pt u re test ) .

E mbrittlement of a metal is measured by the amou nt u f plasti c or creep deformation that occurs before fracture. Fast- neu Iron irrad iati‹i n in vari abl y renders a metal less ductile than the unirradiated material. Fractu re ‹!an be of the brittle ty pe in whic h a small crack swiftly pr‹ipagates across an entire piece, or it can occur onl y a fte r lo log ti mcs at stress and after appreciable deformation. Failu re by stress ru ptu re tak es place by I ink u p o f small interbranular cracks or cavities that have d eveloped th rougliou t the interi‹›r of the metal.

Table 18. 2 Co mposition o f P remsure-Vessel Steels

18.2 EVOLUTION OF THE MIC ROSTRUC-

he ment

Fe

M n P

S i s

N:'

Mo

A 302- B,

wt. ”/•

97

( J 2

0. 01

0. 02

0. 2

0. F›

A 21 2- B,

96

0. .1

0.0 1

0. 3

0. 0 J

0.2

0.2

U.02

I ntei'st i t ial

S u be I i r u tir› na 1

TURE OF STEEL DURING NEUTRON IRRADIATION

The radiation -produced en lilies responsible fo r c hanges in the mechanical pr‹›pcrties of neutron-b‹imbarded metals can be identi fied , cOu nted, and sized with the aid of the electro n rnicrosvopt'. When an electron beam o r several- hu ndred k iloelectron vol ts energy passes th r‹›ugh a thin metal specimen, s‹i mc of the electrons are transmitted th mug li the fo il, and others a rv d i ff ractcd in rnu ch the' same way that X rays are ‹li ffrai ted by parallel atomic plaiic's near the su rracv of a c rystal. 2’he foil is su rii‹ icntl y th in

— ( 1000 to 5000 . \ ) and the incident electro n bean en f-

less steel, but it is much cheaper. 1 n co m mon wi th most bcc metals, ferritic steel ex hib its one potentially serious rad ia- tion effect. Belo iv a certain temperature k nown as the ductile—brittle transition temperature ( DBT"F ) , or nil- du ctility tempcratu re ( N DT ) , the metal is susce pti ble to brittle fracture. As long as the lo west operating temperature is greater than the nil-ductility temperature, the metal is ductile. Ho wever, the nil-ductility temperatu re increases d ramatically with neu tro n exposure, and, toward the end of a 30-year lifetime, a pressure vessel can be subject to brittle failure. Such catastrophic fa ilures have occasionally oc- curred in bridges, large storage tanks, and ships. Usually the entire structure breaks apart when brittle fracture occurs.

Four broad categories of mechanical behavio r are pertinent to reacto r performance:

1. Radiation hardening.

2. Embrittlement and fractu re.

3. Swelling.

4. Irradiation creep.

This chapter deals with the first two of these features. Swelling and irrad ia tio n c reep are considered in the following chapter.

Radiation hardening usually means the increase in the yield stress and the ultimate tensile stress as a function of fast- neutron fl uence and temperature. The y ield stren gth and ultimate strength are measured in tests in wh ich

that only a part of a si n Lily tirain is probed. \ V ills in th is single -crystal region of the material, some atomic planes are properl y oriented to di ff ract the incident electro n beam. ’Phe angle of the diffracted beam relative to the incident electron beam is determined by the Bragg co nd it ion based on the de Broglie wavelength of the incident electrons and the spacing of the atomic planes of the solid. The intensity of the transmitted beam is red uced to the extent that the intervening solid satisfies the Bragg conditio n and produces

strong diffraction. Figure 18.1 is a sketch of the setup for brigh I-field transmission-electrun microscopy. The trans- mitted electrons are brought into focus at an aperture by means of an electrostatic lens. ’I'he position of the aperture is adjusted so that only transmitted elec trons are permitted to pass; the diffracted beams are stopped. Any defect that

locally destroys the perfection of the crystal lattice also alters the di rrractio n conditions at th is point. \ Y hen the orientatio n and/or spacing of the atomic planes arou nd the defect more closely satisfy the Bragg co nditio n than do the planes in the perfect crystal, the d i ff faction phenomena n is stro nger for the planes aruund the defect than for those in the perfect crystal. With reference to Fig. 18.1, if 1 I t , then the transmitted beam rrom the vicinity of the defect is weaker than that from the perfect crystal. The defect appears on the photographic plate behind the aperture as a dark image on a brigh I background. The co ntrast of the image is pro portio nal to Iq — IQ . Such photographs re prc-

420

I NCIUE NT ELECT RON BEAM I

PO R T ION OF SPECIMEN FOI L ( SI NGLE GR AIN )

UE FECT

E LECTROSTATIC O6JE CT I V E LE NS

sent the projected image of the three-dimensiona l crystal de feet. Atomic planes that are out of register ( as those near a grain boundary or a stacking fatilt ) or zones of the crystal that are distorted by a strain field ( as around dislocations ) produce interference patterns and can therefore be imaged. Gas- filled bu bbles at equilibriu m ( i.e., gas pressure balanced by surface tension ) do not strain the surround ing solid, whic h therefore behaves as undistorted c rystal. Even when the cavity conta ins no gas ( a void ) , the strain field iii the vicinity of the defect is negligible. Bubbles and voids are detectable by virtue of the smaller absorptio n of the electro n beam passing th rough the cavity compared with the electrons that pass thro ugh a sectio n of the foil

consisting entirely of solid.

Figure 18. 2 sho we the microstructure of a typical

APE R TU RE

PHOTOGRAPHIC

unirradiated austenitic stainless steel used for fast reactor fuel-element cladding. t°igure 18. 2 ( a ) shows an ordinary photomicrograph of a polished specimen. The grains arc clcarl y visible and average 25 pm in size. The trans mission- electron micrograph of Fig. 18. 2 ( b ) contains only seg ments of the dislocation network of the as-fabricated metal.

IMAG E OF UE FECT

PLATE

18.2.1 Black-Dot Structure

Fig. 18.1 Illustration of image formation in bright-field electron microsco py. The values I2 and Ip denote the intensities of the transmitted and dif fracted beams for incident electrons passing t h rough a region of perfect crystal. T he primed quantiti‹'s d‹'note the arialogo us intensi- ties from the region of the defect.

Figure 15. 3 sh ows the microstructure of a specimen irradiated at 100 C by a fast-neuCron fluence of ‘10* ' neutrons/cm 2 . ’f'he defects produced at these conditions appear zs black dots in the electron micrograph. The defects arc too small to permit their structu re to be revealed by the electron microscope, but they are he lie ved

( a ) ( b )

Fig. 18.2 Microstructure of unirradiated type 304 stainless steel ( a ) Photomicrograph showing grain struc- ture. ( b ) Electron micrograph showing dislocatio n structure. ( From E. E. B loom, A n I nvestigatio n of Fast Neutron Radiation Damage in A n A ustenitic Stainless Steel, USA EC Report ORN L-45 SO, Oak Ridge Na- tio nal Laboratory, 1970. )

HA It DENIN G, EMD ft I TTL EMEN T, A ND FR A C TIRE

421

Fig. 18.3 Type 304 stainless steel irradiated at 93° C. [ From E. E. Bloom, W. R. Martin, J. 0. Stiegler, and J. R. Weir, J. N ucl. Mater., 22: 68 ( 1967 ) . }

to represent the depleted zones or vacancy clusters pre- dicted by radiation-damage theory ( Figs. 17. 2?› a nd 17 30 ) . As long as the irradiation temperature is belo w 350°C,

increasing Fluence simply increases the density of the black-dot damage.

When irradiation is carried out at temperatures greater than 350°C, the nature of the microstructure is entirely different from the black-dot pattern characteri.stic of low-temperature irradiation. In stainless steel irradiatt•d above 350‘C, the point defects created by the collision cascades are sufficiently mo bile to move about in the solid and agglomerate into larger defect clusters. The damage structure consists of dislocation loops and voids.

18.2.2 Loops

The defect agglomeratio n commonly called a loop is formed by condensation of radiation-produced vacancies or interstitials into roughly circular disks followed by collapse of the atomic planes adjacent to the platelet. Vacancy-loop formation is show n in Figs. 18.4 ( a ) and 18.4 ( b ) , and the corresponding process for interstitials is dep icted in Figs. 18.4 ( c ) and 18.4 ( d ) . The end result of the condensation collapse process is a region delineated by a circular edge

dislocation. In the fcc structure, loops invariably form on

The direction is indicated by the Stiller ind ices in the brackets. The sign depends on whether the loop was formed from vacancies or interstitials. The length of the b urgers vector is given by the square root of the sum of the squares of the Miller indices times the coefficient ap /3, or ( ap /3 ) 3'* - ap / 3 .

Edge dislocations can slip only in the direction of their Burgers vector. The cylinder normal to the loop on which the dislocation can move is not a 1110 ) glide direction for fee slip [ Fig. 8. 2 ( a ) l Therefore, the Frank dislocation loop cannot move in the direction of its Burgers vector and hence is immobile, or sessile. ’Fhe loop can change diameter by absorbing or emitting point defects ( i.e., by climb ) . Net

addition of the same type of point defect causes the loop to grow, whereas absorptio n of the opposite ty pe of point defect causes shrinkage. The stacking fault can be elimi- nated by moving the crystal above the loop relative to the solid belo w it. This shearing action is accomplished by passage of another ty pe of dislocation, called a Shock ley dislocation, across the faulted area. The Shock ley disloca- tion and the Frank dislocation react to form a dislocatio n loop at the same position as the original Frank loop but with the interior of the loop now in perfect stacking registry with the neighboring ( 111 ) planes. The loop unfaulting process occurs spontaneously in stainless steel at about 600°C. The Burgers vector of the un faulted loop is

a

b= " 2 [ 110] ( 18. 2 )

This Burgers vector is properly oriented for glide in the fee lattice [ Fig. 8. 2 ( a ) ] , and the loop is therefore mo bile. As it moves by slip, it sweeps out a cylindrical surface tilted at an

CON DE NSAT ION OF V ACAN C I ES IN

C RYSTA L PLAN E

( 111} planes. When a ( 111 ) plane is added to or removed from the lattice by agglomeratio n of a disk of interstitials or vacancies, the stack ing sequence of the perfect close- packed structure ( Sec. 3.6 ) is disturbed. The circular edge dislocation thus encloses a s Mac h ing fault.

The dislocation loops shown in Figs. 1 S.4 ( b ) and

18.4 ( d ) are called Fran h sessi/e dislocations or simpl v Frank loops. The term sessile means immobile. Because the dislocation encloses a stacking fault, Frank loops are also

I a I

CONDE NSATION OF

IN TE RST I T I ALS BE TWEEN C Ft YSTA L PLANE S

I b }

I NTE QSTITI A L LOOP

called [anlt ed loops. The Burgers vector of a Frank dislocation is perpendicular to the plane of the loop. and its

magnitude is equal to the separation of the 1111 l planes. ’This Burgers vector is denoted sy mbolicall y by

( d I

a„

b - * [ 111 j ( 18.1 )

Fig. 18.4 formation of vacanc y loops and interstitial loops.

422 FUNI9 AMFNTAL ABS PF. CT:S GB" N UCM."A R ft E A C TO ft K'UEL EL ISMENTS:

angle to the ( 111 ) plane. Because of the shape of slip pattern, the unfaulted loop is often called a prismatic loop. It is distinguished from the shear loop shown in Fig. 8.6 by the direction of the Burgers vector with respect to the plane of the loo p. The Burgers vector of a shear loop lies in the plane of the loop, whereas the Burgers vector of a prismatic loop lies outside the plane of the loop. The dislocation of the unfaulted loop given by Eq. 18. 2 is perfect in the sense that movement along the slip plane leaves the atoms in positions equivalent to those previously occupied. The dislocation characterizing the Frank sessile loop ( Eq. 18.1 ) does not satisfy this criterion, and the Frank loop is said to be imperfect.

Faulted and unfaulted dislocation loops are shown in Figs. 18.5 ( a ) and 18.5 ( b ) , respectively. Because of the stacking fault they enclose, the faulted loops in Fig. 18.5 ( a ) appear in the electron microscope as opaque circles. Removal of the faulted region renders the interior of the loop identical to the rest of the solid, and only the outline of the loop remains [ Fig. 18.5 ( b ) ] . Since the unfaulted dislocation loops are mobile, they easily lose their dis- tinctive circular shape by gliding under an applied stress and

( b )

Fig. 18.5 Dislocation loops in type 304 stainless steel. ( a ) Faulted. ( b ) Unfaulted. ( From E.E. Bloom and J. 0. Stiegler, in ASTâI Special Technical Publication 454,

p. 451, American Society for 'Testing and Materials, Phila- delphia, 1970. )

becoming tangled with the natural or deformation- produced dislocation network of the solid. Loops disappear from the irradiated solid at about 600 to 6 50°C.

18.2.3 Voids

Under some conditions the embryo collection of vacancies of Fig. 18.4 ( a ) can begin to grow in a th ree- dimensional manner rather than collapse into a dislocation loop. This route leads to the formation of voids in metals and consequent swelling of the structure ( Chap. 19 ) . Voids produced in stainless steel by high-fluence fast-neutro n bombard ment at 525°C are shown in Fig. 18.6. The voids are not spherical. Rather, they assume the shape of a regular octahedron with { 111 } planes as surfaces. The ends of the octahedron, however, are truncated by {100} planes. Voids are annealed out of the microstructure at about 7 50°C.

18.2.4 Carbide Precipitates

In pure metals, only vo ids and dislocation loops are produced by intermediate-temperature irradiation. In a material as complex as stainless steel, however, neutron irradiation also causes different solid phases to precipitate. Carbon is added to steel in the molten state, where the solubility of carbon is high. Carbon solu bility, whether in the solid or in the liquid forms of steel, decreases rapidly as the temperature is reduced. however, when the steel is rapidly quenched from the melt, the kinetics of carbon precipitation are too slow to keep u p with the rapid decrease in the mobility of the atomic species in the solid. Consequently, the 0.06 wt.% carbon in steel ( Table 18.1 ) is maintained in atomic form as a su persaturated solution. When the steel is heated to temperatures at which su per- saturation persists but atomic mobility is appreciable, the carbon can be expelled from solution and form a second phase in the metal. When steel is aged ( i.e., heated for long periods of time at elevated temperatures ) , dissolved carbon reacts with the matrix elements iron and chromium to form a compound M C, ( M - Cr and Fe ) which is insoluble in the austenite or gamma phase. These carbides are formed by the reaction

23M ( y ) + 6C ( y ) - Mt , C„ ( mixed carbide )

where denotes the austenitic phase. The carbide formed is a mixture of Fe, , C, and Cry fi„ . Since chromium is a strong carbide-forme r, the mixed carbide consists primarily of C •2 3 C, . The nickel constituent of stainless steel does not form stable carbides.

Neutron irradiation accelerates the diffusional processes that control the mobilities ‹if the atomic species in the lattice and hence the kinetics ot‘ the prece ding precipitation reaction. Carbide precipitation occurs at m uch lowe r temperatures and shorter times than those required for aging in the absence of irradiation. Radiation accelerates the rates of precipitation reactions when such processes are thermo- dy namicall ravorable. 11’ the irradiation temperature is above that at wli ie h the solut› il its li rni I o f‘ carbon is c•q ual to the carbon conte tit of the' stet'l. irradiatio n ‹ an not cause precipitatitin. for ty’pe 31G sta in lms steel containing 0.0fi*i

4 23

with the major constituents, principally nickel. At tempera- tures below t50”C, the he liu m atoms produced by stopping the al pha particles in the material are not mobile enough to migrate and nucleate bubbles. Consequently, heliu m remains in solution and is invisible to the electron microscope. A t high temperatures helium bub bles form in the meta 1 in the same way that fission-gas bub bles form in ceramic ox ide fuel material ( Chap. 13 ) . ’i'he helium bubbles in the metal are nearly spherical, wh ich suggests that the internal gas pressure is very nearly balanced by surface- tension f‘orces. Figure 18.8 shows the heliu m bubbles in stainless steel at 800°C. In this instance, the helium was injected into the specimen by a cyclotro n. 'rhe bubbles on the grain boundaries are larger than those in the matrix. "I'he intergranu lar helium plays an important role in the high temperatu re embrittleme nt of stainless steel. Short of melti rig, heliu m bubbles cannot be removed from the metal by an sealing.

18.3 MECHANICAL-PROPERTIES TESTS

Much of the mechanical testing designed to elucidate the effects of neutron irradiation on structural metals is perf‘ormed after irradiatic› n with conventional metallurgical testing machines. Usuall y the specimens are irradiated in a neutro n flux c›f‘ known energy spectrum for a fixed period of time and then removed for testing. 'rhe effects of large neutron fluences ( i,e., very long irradiations ) can be

Fig. 18.6 ’I'y pe 316 stainless-steel specimen irradiated at 5 25° C to 7.1 x 10° ne utrons/ c m ( P3 > 0.1 Me V ) . Mean void diameter, 640 A; void n umber density, 4.4 X 10' voids/cm°. [ from \ V. K. Appleby et al., in Radiation- Induced Voids in Me tale, A lba ny, N. Y., James W. Corbett and Louis C. lan niello ( I.ds. ) , U SA £?C S ymposiu m Series, CO N F 710601, p. UG, 197 1.

carbon, for example, carbide precipitation is thermo- dynamically un favorable at temperatu res greater than W00°C. At temperatures lower than 400°C, diffusional processes are too slow ( even when enhanced by irradiation ) to cause observable precipitation in reasonable irradiation times. Between 400 and 900°C, however, exposure of austenitic stainless steel to fast-neutron fluences between 10 2 ' and 10 2 2 neutrons mcm° produces carb ide precipita- tion. Figure 18.7 sho ws an electron micrograph of carb ide precipitation in ty pe 316 stainless steel. Carbide particles are found both within the grains of the 7 phase ( austenite ) and on the grain boundaries. "I'he presence of precipitates on the grain boundaries affects the cree p strength of the alloy.

18.2.8 Heliu m Bubbles

At temperatures above S00°C, dislocation loops and voids are not fou nd in irradiated steel. I n addition to grain boundaries, dislocations ( augmented by the un- faulted loops that have joined the original dislocation network ) , and carbide precipitates, the microstructure contains small helium- filled bub bles. Fleli u m is generated by ( n,a ) reactions with the boron impurity in the steel and

Fig. 18.7 Nearly continuous M› , C, precipitation along grain boundary of solutic›n treated type 316 irradiated at 850°C t‹i 5.1 X 10° neutrons/c m° [ Prom II. R. Brager and J. L. Straalsutid, J. .X"uc 1. Va te r., 46: 134 ( 197 3 ) . ]

4 24

irradiated at a fixed temperature provide information on the thermal stability of defects that are responsible for the change in strength brough t about by irradiation. For some properties, however, out-of-pile testing, even at a test temperature equal to the irradiation temperature, does not adequately represent the behavior of the metal in the reactor environ ment. This complication can be eliminated by performing mechanical tests during irradiation; such experiments, however, are difficult and costly. In pile testing is usually restricted to measurement of mechanical properties that depend critically on the neutron flux as well as on the neutron fluence ( e.g., irradiation creep ) .

This section reviews some of the conventional mechanical-property tests that are applied to irradiated structural steels.

18.3.1 Tensile Test

The tensile test provides a means of uniaxially loading a rod or bar-shaped specimen and of measuring the elongation for various applied loads ( Fig. 18.9 ) . When a specimen of initial length lp and cross sectional area Ay is subjected to an applied load in tension P, the length increases to 1, and the cross-sectional area is reduced to A. The engineering s Press in the test is defined as the ratio of the load to the initial cross sectional area, or PHA q. The true te nsile stress, ho wever, is based on the actual specimen area, or

"l'he engineering s tra in is the elongation divided by the initial specimen length, or ( I — lg ) /I . The /rue s/roi/t, on the other hand, is the integral of the increments of strain over the specimen length:

( 18.4 )

Fig. 18.8 Transmission electron micrographs of stainless steel injected with 5 x 10*' atom fraction helium, tested at 800°G. Large helium b ubbles are seen in ( a ) the grain boundary and ( b ) in the grain boundary, with smaller bubbles in the matrix. ( From D. Kramer et al., in ASTM Special Technical Publicatio n 484, p. 509, American Soci- ety for Testing and Materials, Philadelphia, 1970. )

determined by the simple expedient of removing core components of a reactor and fabricating test samples from them. Aside from the problems associated with handling and shielding radioactive samples, post-irradiation testing is a routine operation, and a large amount of mechanical- properties data can be accumulated quickly and in- expensively.

The mechanical properties of irradiated structural steels depend on the irradiation temperature. When testing is done after removal from the reactor, the testing tempera- ture is unavoidably introduced as an additional parameter. This additional d egree of flexib ility is often valuable; tensile tests over a range of test temperatures on specimens

The true strain is always somewhat larger than the engineering strain. The true strain defined by Eq. 18.4 is

( a l

Fig. 18.9 The tensile test. ( a ) Test specimen. ( b ) Uniform elongation. ( c ) Necking.

H.A R DEF'IE'G, E $'II1 R I TEL E.L IE.X'T, AL'D FR A C TL“R E 425

not equivalent to the strain components commonly em- ployed in elasticity the Ory ( i.e., Eq. A.10 of the Append ix ) . 3’he relation between the in finitesimal strain components and d isplacement is determined by Taylo r series ex pan- sio ns, which neglect products of strain compo nents. 'J‘he strain of Eq. 18.4 is applicable to finite deformations encountered in tensile tests far into the plastic region. It is also called the logarith mic strain.

In the elastic stress regiOn, the true stress—strain cu me obeys Hooke's law, ss’hich for the un iax ia1 tensile test is

‹ — Ec . Hose ever, tensile tests are generally intended to investigate the behavior of the metal at mut h larger stresses than those fr›r wh ich Ho‹i ke's law is follo z'ed. The large, irreversible plastic strains in must tensile tests ta ke place at essentiall y constant vulume because d eformation occurs primaril y by shear. \ Vit h the specimen volu me constant, area reduction is related to elongation by

dl dA

I A

’th us, the true strain c'an also be expressecl bY

( 18.5 )

( 16.6 l

STR AI N

Fig. 18. 10 Stress—stra in curvr fur fer ritic steel.

The pre‹'ed ing eg uati‹› ns apply' without quali fixation to the p‹› rtion ‹›f the deforms tion in wh ich the cross-sectional area of’ the specimen is reduced by the same amet unt t» er t he en ti re lengt h of the spe‹ imen. This mode ‹if def orma- tion is called uii //’r›i iii r In n ya I mo n | i'“ig. 1 8.S ( b ) ] . At a certa in l‹›ad the cruss sectional area of a localized section of the specimen he¿ins t‹› decrease more rapid I \ ' than the

remainder of I he bar | Fig. 18.9 ( ) I This plienomen‹in is called ii e c- k iiig, and the stress or stra in at wit ich it begins is the p‹›int ‹if jo las 1 ie iii s lab ili 1 s .

’I'he ntresswtrain r-urie.s for a ti pii'al { u nirrad iatecl ) l‹iss all ‹›y steel are show n in £ ig. 18. 1 0. 3’he general shapes of these ‹'urs'es arv t haracteristi‹ of most metals that crystallize in the bcc lat tice structure. The solid line depicts the end in eering stress—strain curve, which is a plot of P A„ vs. I I — 1 t, ) 1 i, . J“he ma terial deforms elast i‹-allv according to Htiok e's la u’ u p to the point U, where the specimen appears tO gis'e w'a ' or tt› iefrJ. ’the lt›ad then drops cvi t h itat'reasing el‹›ngati‹›n to the poin t L. The po ints I' and L are called the upper and I o over yield p‹›ints, rcspe‹ tively. The re'pur t ed

\ ’ield sire myth ‹if a material is usually’ the stress at the lower y’it'ld p‹›int. F“or a sh ort strain intvri at f‹›1lu wing p‹iint L, pt astic deformatir›n prr›ceeds w'i th no increase in loacl. Th is in teri'a1 is t'alled the L uders strain. The stress level characterizing the Luders strain regi‹›n is essentially the same as the l‹iw'er \ 'ield ptiint, altho ugh it is sometimes

£ ‹› 11 r›u'ing the L u'ders strain is a regiun ivh ere the stress red uired tt› produt e furtive r stra in increases. ’I'his portion of the stre.ss—strain curve is t'alled the ,str clit-/iorr/cftiiig or user/: /io›rJcn/iiJ region be‹'ause the material becomes

str‹›nger as a result Of the deformation process. Plastic instabilit y terminates the work - hardening portio n of the stress—strain curve at the poin t labeled U’fS, which stands for ulli'rnale fcrLsi/c ,sfres.s. This point represents the maximu m l‹›ad-bearin ¿ eapacit y o f the specimen. At all times rl u ring defurma I iun, the I‹›ad is equal to the prud uct r› I the ac I ual cr‹»s-sect i‹›nal area and the true stress. ur P ‹/ \ . At the L1*S, dP -- 0, ur

cl ‹ d A

‹i A

A‹'c‹›rding to Eq. IS.G, —d A A - dc‘, so the onset of necking, whic h occurs at the UTS, is located on the true stress—strain curve at the puint at ivli ich

( 18.T )

Up to plastic instab ility, the true stress—stra in curve ( the dashed curve in Fig. 18.10 ) can be constructed using Eqs. 18. 3 and 18.4. During neck ing, Eq. 18.4 does not appl y if the gau ge length 1 is interpreted as the total specimen length. Ho we ther, nowh ere has it been specified that I mu st be the entire specimen lenyth ; it could \ ’ery well have been cht›sen as a very short segment right in the necking region. Over this small segment, elongation is uniform. It is ex perimentally diffit'ult to measure length changes in a very tinv gauge length. However, Eq. 18.5 applies to the necked regio n prr›vid ed that the area A is the cross-sectional area at the most severely necked part of the specimen. Therefore, applicatio n ‹if Eqs. 18.3 and 18.6

426

with the nerked area taken for A permits the true stress—strain curve to be extended from the UTS to fracture ( point F“ ) . The true strain and stress at fractu re are always larger than those based on the engineering stress— strain curve. At small strains, however , the difference between the two stress—strain curves is negli gible. The yield stress, for example, can be represented by either curve with no appreciable error,

Pigure 18.11 sho avs the tensile behavior of a typical austenitic steel. The primary ct if ference between the stress— strain cu irises in F its. IS. 10 and 18.11 is the absence of a

\ •’elI-defined ¿’ield puint in Fiy. 18.11. For must metals with an f‹'c struc ture, the stress—strain curv-e continuously

Figs. 18.10 and 18.11. The yield stress is reduced at low strain rates because the slow mo ti•on of dislocations at low stress levels becomes sufficient to become manifest as plastic deformation. In unirradiated steels, ductility is not significantly affected by strain rate.

Strain rates of 0.01 min*' are characteristic of co nven- tional tensile tests. This figure is also approximately equal to the strain rates induced in cladding by ty pical reactor power transients ( shutdown, startu p, and power cycling ) .

\ Vhen the strain rate in the test is reduced to 10* min*’ and the temperature is high, the test is called a creep- ru pture test. This strain ra ie is ty pical of that imposed on clad ding by fuel sw'ell ing in the reactor.

18.3.2 Tube-Burst Tests—Biaxial Stress State

The tensile test described above is an experimentally conv'enien t u'ay of measuring the mechanical properties of a metal. In acid ition, theoretical interpretation of the stress— strain cuin'es is simpli fied by the fact t hat there is o nl y one n‹inxero component of the stress tensor, namely, the normal stress in the direction Of the applied load. However, the stress state Of fuel-eleme nt cladding loaded internally by fission-gas pressu re and fuel swelling more closely resembles that in a long thin -walled cy lindrical tube closed at both ends and pressurized by a gas. Since cladding fails by creep ru pture after long periods of being subjected to stresses w elf belci u' the yield stress, considerable creep- ru pture testing of unirradiated and irradiated steel tub ing has been performed by pressuriz ing closed tubing with an inert gas. These tests are called tube burst tests.

According to elastic it y theory, the normal stresses in ctused tu bes loaded by an internal gas pressure p are given b}’ ( see problem 1 d.6 )

ST R AI N

Fig. 18.11 Stress—strain curve for austenitic steel.

pD

‹i, 0

( 18.8a )

( 18.9b )

deviates from Hoo ke's law as the stress is increased , and it is impossible t‹i assign a definite stress at wh ich plastic deformation begins. That is, the me tal does not yield in an unequivocal manner. Hence, yielding tor the onset of plastic no iv ) in su ch metals is arbitrarily eo nsidered to uccur when the permanent strain in the tensile test is 0.?-’ . This stress, denoted by o j' in Fig. 18.11, is called the 0.?'."• r›//ief 5'ield s I i‘eiigth of the me tal.

Duc I ilil v is measured either by the amount of strain between the true fracture stress and the yield stress ( c;. — eg ) or mo re commonly by the total uni form elo nga- tion u p to necking. Einhrit I lr me ii I means a reduction in either of these two measures of ductil ity. A brittle material fails when yield occurs or, in the case of a material having no sharp yield point, when t‘ailu re occurs before 0. 2 ‹ offset strain.

The rate at which deformation is imposed in the tensile test, or the strain rate, affects the stress—strain curves of

where D is the tu be diameter and t is the wall th ie kness ( t D ) . The in finitesimal radial and tangential strains appropriate to conventional elasticity theory are ( t t„ ) /t‹, and ( D — D„ ) Di, , rvspe‹ tirel v . 'the logarith rrli‹ strains should be used u hen appreciable cteformation occurs. The true ( logarithmic ) strains are

( 1 H.9h )

( 15.Sc )

w here D„ and t ‹, are the initial tube diameter and u'all thick ness, respectivel y. By raryiny the gas pressure, p, plastic deformation ‹if the tu be can be induced. Because the tube wall is subject to twc› stress components or -