Void formation, void growth and tensile fracture in Ti6AI4V

Void Formation, Void Growth and Tensile Fracture in Ti-6AI-4V

HAROLD MARGOLIN AND YASHWANT MAHAJAN

The inf luence of m i c r o s t r u c t u r e on void format ion , void growth and tens i le f r ac tu re was invest igated for the Ti-6A1-4V alloy, aged to yield s t rengths of approximate ly 110 ks i (758 MN/m2), 130 ks i (896 MN/m 2) and 140 ks i (965 MNfm2). Void nuclea t ion occurs at a - a g e d m a r t e n s i t e in te r faces for both equiaxed (E) and Widmans t~ t ten plus g ra in bound- a ry (W + GB)a s t r u c t u r e s as well as within a pa r t i c l e s . Void growth appeared to depend on mar t ens i t e plate lengths for a given aging t r e a t me n t for E ot s t r u c t u r e s , whereas it depended on p r io r /3 gra in s ize and g ra in boundary a th ickness for W + GBa s t r u c t u r e s . Two separa te c r i t i c a l c rack s i z e - f r a c t u r e s t r e s s (cor rec ted for necking) r e l a t ionsh ips were found for E and W + GBa s t r u c t u r e s . The f r ac tu re energy for both s t r u c t u r e s was lower than the co r re spond ing f r ac tu r e energy p rev ious ly obse rved for the T i - 5.25A1- 5 .5V-0 .9Fe-0 .5Cu (Ti- 5- 5) alloy, 2 and the lower duct i l i t i es of aged T i - 6A1- 4V were a sc r ibed to this lower f r ac tu re energy .

HOLDEN, Ogden and Jaffee ~ in a study of the me- chan ica l p rope r t i e s of a-~3 T i - M n al loys showed that the duct i l i ty of equiaxed a (Eot) s t r u c t u r e s was higher than that for Widmans t~ t ten plus gra in boundary a (W + GBa) s t r u c t u r e s . La te r , in an inves t iga t ion to de t e rmine the r e a s o n for this d i f ference, Greenf ie ld and Margo l in 2 s tudied an a- f l T i - 5.25A1- 5.5V-0.9Fe (Ti -5-5) al loy. Fo r both Eot and W + GBa s t r u c t u r e s they found that f r ac tu r e depended on void nuclea t ion and growth, f r ac tu re occu r r i ng whenever the c r i t i ca l c r ack s i z e - s t r e s s r e l a t ionsh ip was reached for the T i- 5- 5 al loy.

It was found that void growth occur red more rapidly at the g ra in boundar ies of the W + GBa s t r u c t u r e s than in the case of Eot. Fo r the W + GBa s t r u c t u r e s the c r i t i c a l c rack s i z e - s t r e s s r e la t ionsh ip was reached at a lower s t r a i n p r i o r to f r ac tu re . (The void is con- s ide red a c rack when it r eaches the c r i t i c a l s ize for f rac tu re . )

Th i s study was under taken to study the mec ha n i sm of t ens i l e fa i lu re of the Ti-6A1-4V alloy in an a t tempt to tmders tand why the T i - 5 - 5 alloy can be heat t r ea ted to higher s t reng ths while main ta in ing or exceeding the Ti-6A1-4V duct i l i ty .

I. EXPERIMENTAL PROCEDURE

ELI Ti-6A1-4V, conta in ing 0.078 wt pct oxygen, 12.2 mm round ba r stock, which was ava i lab le f rom an e a r l i e r inves t igat ion, 3 was used for the cu r r en t s tudies . The t3- transus was d e t e r m i n e d as 1245 K. The mate - r i a l was heat t r ea ted to produce e i ther a W + GBa or an Ea s t ruc tu re , the fi phase of which t r a n s f o r m e d to m a r t e n s i t e on quenching. W + GBa s t r u c t u r e was p ro - duced by in i t ia l ly heat ing to 1266 K, then furnace cool- ing to 1199 K, hold for var ious t imes , W.Q. E a s t r u c - t u r e s were produced by d i rec t ly heat ing to 1199 K. For both types of s t r uc tu r e t imes at 1199 K va r i ed f rom 1 to 150 h to cont ro l the s ize of p r i m a r y a pa r t i -

HAROLD MARGOLIN is Professor and YASHWANT MAHAJAN is Graduate Student in the Department of Physical and Engineering Metallurgy, Polytechnic Institute of New York, Brooklyn, NY 11201.

Manuscript submitted April 28, 1977.

METALLURGICAL TRANSACTIONS A

c les . Aging t e m p e r a t u r e s were var ied f rom 755 to 1033 K to obtain yie ld s t reng ths f rom 110 to 140 ks i (748 to 965 MN/m2).

M e a s u r e m e n t of pa r t i c l e s i zes and volume f rac t ions was c a r r i e d out with a Hurlbut counter . Genera l ly , a m i n i m u m of 100 pa r t i c l e s was me a su r e d . To study void growth a number of spec imens were heat t rea ted to produce the same m i c r o s t r u c t u r e and yield s t r eng ths . These spec imens were s t r a ined var ious amounts , and sect ioned to a point s l ight ly l a rge r than midsec t ion th ickness . They were then inf i l t ra ted with epoxy, pol ished to midsect ion , e lec t ropol i shed and etched. The procedure is e s sen t i a l ly the same as the one used e a r l i e r . 2 Af ter pol ishing, the spec imens were ex- amined to de t e rmine void shape and locat ion cha rac - t e r i s t i c s and to m e a s u r e the s ize of the longest void which could be detected in the necked reg ion for the p a r t i c u l a r s t r a i n . P r i o r [3 g ra in s izes for E a s t r u c - t u r e s were de t e rmined by r e f e r r i n g the m e a s u r e d E a pa r t i c l e s ize to a graph which had e a r l i e r 3 es tab l i shed the r e l a t ionsh ip between E a t r a v e r s e pa r t i c l e s ize , d~, and p r io r /3 gra in d iamete r , Dl3 for annea l ing at 1199 K as d~ = - 1.55 + 0.92 D/3 in m i c r o n s . The procedure us ing for d e t e r m i n i n g D~ in the equiaxed ~-~3 s t r uc tu r e has been desc r ibed e a r l i e r , a Dl3 for the W + GBa s t r u c t u r e s were m e a s u r e d d i rec t ly .

IX. RESULTS AND DISCUSSION

A. T r u e S t r e s s - T r u e S t ra in Rela t ions

In the study of the T i - 5 - 5 al loy 2 the same t rue s t r e s s - t r u e s t r a i n d iagram, except for total s t r a in , was obtained for a l l spec imens because the same solut ion t e m p e r a t u r e and aging t r e a t m e n t were used. This is not the case in the p r e se n t ins tance .

T r u e s t r e s s - t r u e s t r a i n r e l a t i ons for the a s - quenched condit ion with a 0.2 pct yield s t r e s s of 130 ks i (896 MN/m 2) and for an aged yield s t rength of 110 Ksi (758/m 2) a re shown in Fig . 1. Resu l t s a re given in Fig . 2 for average aged yie ld s t reng ths of 130 ks i and 140 ks i (965 MN/m2). The n u m b e r s in pa ren theses for each curve indicate the number of spec imens used to e s t ab l i sh the curve . The data a re so n u m e r o u s and

ISSN 0360-2133/78/0612-0781 $00.75/0 �9 1978 AMERICAN SOCIETY FOR METALS AND VOLUME 9A, JUNE 1978 781

THE METALLURGICAL SOCIETY OF AIME

/ 26~ TRUE STRESS-TRUE STRAIN CURVE 250 1 FOR SET #IE (110 ksi,y.s.) (758 MN/m 2)

240

25O

220

210 t~ "~" 200

09 190 hi 13~ 180 p- {n 170 hJ

160 fE I-- 150

140

150

120

110 �9 0

Sp. No. [3 I �9 - Corresponds to fractured specimen 5EQ ..,,,, ~ O 2 E - Equioxed (Z t- Transformed ,8 Z~ 3 E Q - A s Quenched from cz+/9 Field A 4 W - Widman a + Grain boundary cz

.aooe x 5 of true stress I I 6 ~,:,"~= j'for As Quenched �9 7 I ,2 ~ 5 E q Samples

= } W+GB ( =,~5~ (5)

f, I I l I l I I I I

0.1 0.2 0.5 0.4 0.5 0.6 0.7 0.8 0.9

TRUE STRAIN, ~ n ~

1797-

1725

1655

1586

1517

1448

t379

131o E

1241 ~

1172

1103

10:54

965

896

827

758

Fig. 1--True s tress- true strain relations for as- quenched 130 ksi (896 MN/ m 2) and 110 ksi (758 MN/m 2) yield stress Ti-6A1-AV.

260 1792

250

240

230

220

~r 210

~ 200

~ 190

~ 180

~ 170

150

140

130

120

I10

(5)

(8)

/ ~ FRACTURE

2, 0'.~ 0!5 0!~ 0!~ 01~ 0'7 0% TRUE STRAIN, ~n-~

Fig. 2--True stress-true strain relations for 128-138 ksi (882-951 MN/m 2) yield stress Ti-6A1-4V.

1723

1655

1586

1517

E448

1379

13~0

1241

1172

1105

t034

965

896

827

01.9 758

so closely spaced that data for only one curve a re shown in Fig . 1. Up to s ix teen m e a s u r e m e n t s were made for each spec imen tes ted . As can be seen f rom an examina t ion of F igs . 1 and 2, s t r a i n hardening r a t e s a re not constant . This will be d i s cus sed in connect ion with void growth r a t e s .

B. Void F o r m a t i o n and Growth

1) VOID FORMATION

a) Eat S t ruc tu re s . Void fo rmat ion had some s i m i - l a r i t i e s to behavior observed e a r l i e r in the T i - 5 - 5 a l - loy heat t r ea ted to a yield s t r e s s of 165 ksi (1138 MN/ m 2) (Ref. 2) as well as some notable d i f fe rences . In Eat s t r u c t u r e s voids were found to nucleate at pa r t i - c l e - m a t r i x in te r faces , Fig. 3, as noted e a r l i e r , 2 but in

Fig. 3--Voids forming at equiaxed c~-aged matrix interface, Set 2E, c = 0.4, magnification 584 times.

addit ion voids were found to nuclea te within E~ pa r t i - c les as well, Fig. 4, and at subboundar ies within pa r t i c l e s , Fig. 3, at A. The large void in Fig. 4 is r e m i n i s c e n t of c racks which have been repor ted in of the T i - 5 - 5 al loy heat t r ea ted to 180 ksi (1241 MN/ m e) and tes ted for f r ac tu re toughness , s and of c racks in ~ of Ti-6A1-4V notched t ens i l e spec imens . 6

In the p r e se n t study voids were also found to nuc le - ate in the aged mar t ens i t e mat r ix , F ig . 5. S imi l a r void fo rmat ion in the aged m a r t e n s i t e ma t r ix was noted in the T i - 5 - 5 al loy heat t r ea ted to 1241 MN/ m2. s Void fo rmat ion in unaged m a r t e n s i t e of the Ti-6A1-4V alloy, quenched f rom 1199 K has a lso been seen, thus indica t ing that aging, subsequent to quench- ing, is not a n e c e s s a r y p r e r e q u i s i t e to void fo rmat ion in ma r t e ns i t e . The as -quenched samples also showed void format ion at o - m a t r i x in te r faces and within in the same m a n n e r as did the aged s amp le s . Cam-

782 VOLUME 9A, JUNE 1978 METALLURGICAL TRANSACTIONS A

Fig. 4--Voids forming within equiaxed ~ particles, Set 2E, = 0.4, magnification 584 times.

chan i sm is appl icable for nucleat ion, growth of the void must take place by mul t ip le s l ip.

2) VOID GROWTH

a) M i c r o s t r u c t u r a l Aspec t s . For E a s t r u c t u r e s void growth in the ea r ly s tages of s t r a i n produced sphe r i - ca l voids, F ig . 8. Voids read i ly " c o n s u m e d " both E and g ra in boundary (GB) o~ pa r t i c l e s , Fig. 8(a) and (b). Voids in i t ia l ly growing along m a r t e n s i t e - p l a t e l e t s , Fig. 5, subsequent ly conver ted to rounded voids . The longest voids a re most often e l l ip t ica l in shape, Fig. 8(a), the e l l ip t i ca l cha rac te r i n c r e a s i n g with i n c r e a s - ing s t r a in . In the case of W + GBa s t r uc t u r e voids at a p a r t i c l e - m a t r i x in te r faces a re , except for the ve ry e a r l i e s t s tages, e l l ip t ica l in cha rac t e r . The longest voids were always assoc ia ted with GBa .

b) Growth of the Longest Void. M i c r o s t r u c t u r a l p a r a m e t e r s a re shown in Table I and co r re spond ing t ens i l e and f r ac tu re data a re given in Tab le It. Fo r each s t r a in the sec t ioned tens i l e samples were ex- amined to de t e rmine the s ize of the longest void. F igu re 9 is a plot of longest void, L v s t rue s t r a in . As in the case of the T i - 5 - 5 alloy, L i n c r e a s e d l ine- a r ly with t rue s t r a in . This is t rue for all y ie ld

Fig. 5--Voids forming in aged martensite matrix, Set 2E, = 0.4, magnification 584 times.

p le te ly m a r t e n s i t i c s t r u c t u r e s produced by quenching f rom the fl f ield showed behavior quite s i m i l a r to that found in m a r t e n s i t e s produced by quenching f rom the a - ~ field at 1199 K.

b) W + GBa S t ruc tu re s . W + GBa s t r u c t u r e s show void fo rmat ion at g ra in boundary a - m a t r i x in te r faces s i m i l a r in fo rm to those r epor t ed e a r l i e r . 2 However con t r a ry to obse rva t ions on a T i - 5 - 5 al loy 2 voids were found to fo rm at Widmanst~itten (W) a - a g e d m a r t e n s i t e in te r faces and to grow along them, Fig . 6 at A. Voids, having a shape s i m i l a r to the cen t r a l r ec t angu la r void of Fig. 4, were a lso found in W a . The re the voids were pa ra l l e l to twins within the pa r t i c l e .

A c lea r indica t ion of void fo rmat ion a t a tw in -mothe r a in te r face is seen in F ig . 7. These two observa t ions , taken together , suggest that a void, fo rming at a twin- mother a in ter face , may grow p re f e r en t i a l l y into the twin, and that, l ike the subboundar ies of F ig . 3, twin boundar i e s a re s i tes where incompat ib i l i ty can de- velop.

The fo rmat ion of voids at twin and subboundar ies is r e m i n i s c e n t of S t roh ' s 7 cleavage m e c h a n i s m for Zn, in which a c rack is formed by a s ingle s l ip sys - t em d i sp lacemen t of a t i l t boundary . However, the rounded shape of these voids suggests that, if this me-

Fig. 6--Voids forming at Widmanst~itten c~ -aged martensite interface, Set i W, ~ = 0.37, magnification 475 times.

Fig. 7--Voids forming at twin-mother a interface in Widman- st~tten particle, Set 4W, c = 0.345, magnification 475 times.

METALLURGICAL TRANSACTIONS A VOLUME 9A, JUNE 1978 783

(5)

(b) Fig. 8--(a) Spherical voids in Set 1E, E = 0.47, magnification 365 times, (b) voids growing in grain boundary a of Set 2W, e = 0.4, magnification 182.5 times.

s trengths studied. There i s s o m e ev idence for co- a l e s c e n c e of vo ids in F i g s . 4 to 8. The c o a l e s c e n c e of these voids occurs as a r e s u l t of loca l growth of inde- pendently formed voids , rather than as a resu l t of voids forming ahead of a major void and later joining the leading vo ids . As pointed out prev ious ly 2 the lat- ter m e c h a n i s m of void growth would cause a c c e l e r a t - ing growth rather than the l inear behavior seen here . Fur thermore , l oca l i zed flow at a void tip without void format ion ahead of the void was observed in the present work. This was s een in s p e c i m e n s which, after s tra in beyond the start of necking were sect ioned, pol ished, etched and res tra ined . This behavior has a l so been reported for the T i - 5 - 5 a l loy , s Consequently , it is con- cluded that in the T i -6A1-4V al loy the longest void, in the s i z e s encountered, grows by loca l i zed deforma- tion at the void tip. However, the longest void may have reached its s i z e by c o a l e s c e n c e with one or more voids as it grew.

c) Void Growth Rates of Ea Structures . Void growth rates , the s lope of the l ines of F ig . 9, are des ignated G L and are plotted in F ig . 10 as a function of s t ra in hardening rates , ca lculated from the reg ions of the curves of F ig s . 1 and 2 beyond s t ra ins of 0 .2. With

150

140

130

120

I I 0

J 9o 0 > 8o

I.- 7o if) w (.9 6o z 0 5o ._1

40

30

20

Sp. No

o ~ �9 3E �9 4E [ ] 5EQ E~ 7 E

I W [3 2W • 3W

/ V 4W "~ 5W

LONGEST VOID AT FRACTURE

[3 /

T R U E S T R A I N

F i g . 9 - - L o n g e s t v o i d a s a f u n c t i o n o f t r u e s t r a i n .

LO

2

f E

:=L

I-- <[ cr

T"

0

r

>

(,.9

360

520

28O

240

200

160

120

80

"E 4O

0 70

483

s~

4W

IW

W g~

�9 3E � 9

4E

' I ,[.)10~ [ 80 910 [olo lJO 130 140

k s i / s t r o i n I [ [ i l I i

551 620 689 758 82? 896 965

M N / m 2 / s t r o i n

STRAIN HARDENING RATE Fig. 10--Void growth rate, G L , v s strain hardening rate.

the except ion of the data for set 1E and 2E, G L values for Eo~ s tructures are independent of s tra in hardening ra tes . This is c l ear ly not the case for the W + GBa s tructures , where G L markedly dec l ines with in- c r e a s i n g s tra in hardening rate, but r e m a i n s above the va lues observed for equiaxed s t ruc tures .

The re la t ive constancy of void growth rate for Eo~ s tructures shown in Fig . 10 and the data for se t s 1E and 2E suggest , according to Table I, that void growth i s independent of D~, d~, and the mean free path be- tween o~ part i c l e s , ~, for the s i z e s encountered. The y ie ld s trengths of the constant void growth rate s p e c i - men se t s are in the range 882 to 951 M N / m 2, and these y ie ld s trengths are p r i m a r i l y produced by the aged martens i t e . Thus one must look to the martens i t e for the constancy of void growth rate .

Since there is a r e l a t i v e l y s m a l l range of prior grain s i z e s for the Eo~ s truc tures of se t s 3E, 4E, and 7E the martens i t e d imens ions must be r e l a t i v e l y con- stant. Voids generated at the s ide s of martens i t e laths in i t ia l ly appear to prefer to grow along the laths, Fig . 5 and Fig . 5 of Ref . 5. It would s e e m , therefore , that when a void r e a c h e s a lath at an angle to the void, this l a t h m u s t s e r v e as an obstac le or r e s i s t a n c e to void

7 8 4 - V O L U M E 9 A , J U N E 1 9 7 8 M E T A L L U R G I C A L T R A N S A C T I O N S A

Table I. Microstructure Parameters

Type Interparticle Set Structures Volume Pct Volume Volume Spacing No. Heat Treatment E/W* d~,, pm D~, pm l,~, pm dw,/am . Primary ot Pct Wa G.B. a ~, pan

IE 2E 3E 4E 5EQ

6E 1200 K, 3 �89 h W.Q. 7E 1200 K, 24 h W.Q. lW 1266 K, 25 min

"h200 K, 2�89 h W.Q. 2W 1266 K, 25 min

1200 K, 46�89 h W.Q. 3W 1266 K, 25 min

$1200K, 1 hW.Q. 4W 1266 K, 25 min

r K, 150h W.Q 5W 1266 K, 25 rain

$1200 K, 3 h W.Q. ~ 6W 1266K, 25 min [

$1200K, 1 hW.Q. [ 1M} 1266 K, 1 hW.Q | 2M

1200K, 3h W.Q. l Agedl005 K E 3.2 5.1 44 4.2 1200K, 65ShW.Q:J 1ShW.Q. E 12.2 15 34 23.4 1200K, 24hW.Q. ] Aged922K E 8.8 11.4 39 13.7 1200 K, 3h W.Q. J 45 min W.Q. E 3.7 5.7 30 8.6 1200K, 3 h W.Q. E

(quenched E 4.5 E 6.4 W

Aged 755 K 6.7 49 4.6 4 h W.Q. 8.8 46 7.5

180 8.6 5.3 44 40 4 18.9

W 188 t4.5 8.6 44 37 7 14 Aged 1033 K 1�89 h W.Q. 160 7.9 5.5 41 30 11 14.3

189 21 16.5 41 26 15 26.7

W 177 9.2 5.5 15.4 Aged 894 K 6 h A.C. W 234 5.9 4.5 13

Martensite

*E = Equiaxed a; W = Widmanst~itten ct; G.B. = Grain Boundary a; d~ = traverse diameter of equiaxed a; D~ = traverse diameter of prior ~ grains; la = traverse thickness of grain boundary t~; and d w = traverse thickness of Widmanst~tten ct.

Table II. Mechanical Property and Fracture Data for Table I Specimens

0.2 Pct, Set Yield Strength

No. Ksi MN/m 2

ale Corrected, Lortgest Void Fracture Strength Fracture at Fracture,

Ksi MN/m 2 Strain, ef L f, pm

1E 110 758 216.5 1493 0.64 60 2E 109 751 218 1503 0.59 59 3E 128 882 231 1593 0.707 30 4E 132 910 232 1599 0.685 23.5 5EQ 128 882 265 1827 0.86 47 6E 128.5 886 222 1531 0.537 19 7E 138 951 240 1655 0.675 33 lW 109 751 183 1262 0.46 75 2W 108 744 182 1255 0.43 109 3W 110 758 188.5 1300 0.445 50 4W 108 744 182.5 1258 0.438 123.5 5W 128 882 190 1313 0.387 42 6W 129 889 184 1269 0.392 138 1M 123 848 203 1400 0.38 2M 128 882 188 1296 0.33

g r o w t h a c r o s s t he new la th .* On t h i s b a s i s one would

*Specimens of sets 1E and 2E were closely examined to determine whether voids originating and growing along martensite laths would change direction at the end of the lath, Generally the voids stopped at the end of the platetet along which they were growing and tended to become oval in shape. The longest void at a par- ticular strain was associated with an c~ particle.

e x p e c t a c o n s t a n c y of m a t r i x r e s i s t a n c e to vo id g r o w t h . T h e y i e l d s t r e n g t h of t h e E a p l u s a g e d m a r t e n s i t e

s t r u c t u r e i s a f u n c t i o n of the c o n t r i b u t i o n s of t h e i n - d i v i d u a l c o n s t i t u e n t s . At a s p e c i m e n y i e l d s t r e n g t h of 758 M N / m 2 it i s l i ke ly t ha t t h e r e i s l i t t l e d i f f e r e n c e b e t w e e n the i n d i v i d u a l y i e l d s t r e n g t h s of t he E a and the a g e d m a r t e n s i t e , and c o n s e q u e n t l y , i t i s not l i ke ly tha t e q u i a x e d a p a r t i c l e s would s e r v e a s c r a c k s t o p - p e r s a s t h e y d id w h e n y i e l d s t r e n g t h s of 1138 M N / m 2 w e r e a t t a i n e d in the T i - 5 - 5 aUoy . 2 F u r t h e r m o r e , the

t e n d e n c y f o r m e c h a n i c a l t w i n n i n g to o c c u r and v o i d s to " c o n s u m e " t w i n s would a l s o r e d u c e the ab i l i t y of

to s t o p c r a c k s . No s u c h b e h a v i o r w a s s e e n in e a r l i e r e x a m i n a t i o n of vo id f o r m a t i o n in the T i - 5 - 5 a l l oy . %5

T h e r e a r e i n s u f f i c i e n t d a t a a t y i e l d s t r e n g t h s of 886 and 951 M N / m 2 to p e r m i t c o m m e n t s to be m a d e on the c r a c k s t o p p e r c h a r a c t e r i s t i c s of E a at t h e s e h i g h e r s t r e n g t h s . H o w e v e r , it i s i n t e r e s t i n g to no te t ha t s e t 7E, w i t h a y i e l d s t r e n g t h of 951 M N / m 2 had the h i g h e s t f r a c t u r e s t r e n g t h of the a g e d s p e c i m e n s of T a b l e II .

d) Vo id G r o w t h R a t e s of W + G B a S t r u c t u r e . Bo th G L and s t r a i n h a r d e n i n g r a t e s f o r the W + GBo~ s t r u c - t u r e s a r e a f u n c t i o n of Dfi as i n d i c a t e d in F i g s . 11 and 12. T h e s e f i g u r e s have m a d e no d i s t i n c t i o n b e t w e e n y i e l d s t r e s s of 758 and 889 M N / m e. T h e c u r v e of F i g . 11 h a s b e e n d r a w n t h r o u g h the d a t a of 3 W, 1 W and 6 W b e c a u s e the g r a i n b o u n d a r y a t r a v e r s e t h i c k n e s s , l a , i s r o u g h l y e q u a l in t h e s e t h r e e c a s e s , w h i l e f o r 2 W and 4 W it i s m u c h l a r g e r .

T h e i n f l u e n c e of t he g r a i n b o u n d a r y (~ t h i c k n e s s on G L i s s h o w n in F i g . 13. I t c an be s e e n t h a t G L at a 0.2 pc t y i e l d s t r e s s of 758 M N / m 2 i n i t i a l l y i n c r e a s e s qu i t e m a r k e d l y o v e r a g r a i n s i z e v a r i a t i o n of abou t 11 pc t , T a b l e I. T h e d a t u m fo r 6 W, c o r r e s p o n d i n g to a y i e l d s t r e s s of 899 M N / m 2, r e v e a l s a m u c h h i g h e r G L f o r i t s , l~ , and t h i s m a y be r e l a t e d , a s F i g . 11 i n d i c a t e s , to i t s l a r g e r g r a i n s i z e .

T h e d e c r e a s i n g s l o p e of F i g . 13 w i t h i n c r e a s i n g la i s r e m i n i s c e n t of the b e h a v i o r of vo id g r o w t h in W i d - m a n s t ~ t t e n p l u s g r a i n b o u n d a r y a s t r u c t u r e s of t he T i - 5 - 5 a l loy , 2 w h e r e , a f t e r a l i n e a r i n c r e a s e in G L , wi th l a , a p l a t e a u w a s r e a c h e d a t l a of 5.5 ~ m . T h e G L v a l u e s a t a g i v e n Dfi and la w e r e m u c h l a r g e r in t he e a r l i e r w o r k . 2

It i s of i n t e r e s t to c o n s i d e r b o t h the s t r a i n h a r d e n i n g d e p e n d e n c y on g r a i n s i z e and vo id g r o w t h d e p e n d e n c i e s on b o t h g r a i n s i z e and a p a r t i c l e s i z e fo r t he W + G B a

METALLURGICAL TRANSACTIONS A VOLUME 9A, JUNE 1978-785

c u r v e s s i m i l a r to F ig . 12 to s m a l l e r g ra in s i z e s unti l no fu r t he r change in s t r a i n ha rden ing r a t e with g r a i n s i ze was o b s e r v e d .

A D~/2 dependency of void growth r a t e on p r i o r /3 g r a i n s i ze had p r e v i o u s l y been noted by Green f i e ld and M a r g o l i n 2 but no p h y s i c a l exp lana t ion had been of- f e r e d . Examina t ion of the r e l a t i o n s h i p of D/3 to the longes t void at f r a c t u r e , Lf* , in Tab le I, for W + GB~

*Obtained by extrapolating the void growth curves of Fig. 9 to the fracture strain.

s t r u c t u r e s r e v e a l s that D/3 > Lf , with Dp be ing as much as 4.2 LZ. This s u g g e s t s that g r a i n edges a r e p robab ly not inf luencing void growth and th is i n fe rence is sup- p o r t e d by the o b s e r v a t i o n that mos t vo ids do not in i t ia te at t r i p l e junc t ions .

Work on/3 b r a s s b i c r y s t a l s and t r i c r y s t a l s has shown that ro ta t ion , due to s l ip , of g r a in s on e i t he r s ide of the boundary p roduced a torque at the bound- a r y . 9,t~ Th i s to rque was d i r e c t l y p r o p o r t i o n a l to the

Fig. l l - -Void growth rate, GL, vs f l -matr ix grain size, D/3.

Fig. 12--Strain hardening rate vs f l -matr ix grain size, D/3.

s t r u c t u r e s . In o r d e r to do so, it is d e s i r a b l e f i r s t to c o n s i d e r a plot of s t r a i n ha rden ing r a t e vs the L a r s o n - M i l l e r p a r a m e t e r , M, for equiaxed s t r u c t u r e s , F ig . 14. B a s e d on d i f fe ren t hea t t r e a t m e n t s , which p r o - duced a p p r o x i m a t e l y the s a m e y ie ld s t r eng th , 3 it was p o s s i b l e to ca l cu l a t e the cons tant , C, in the e x p r e s s i o n M = T(C + log t ) as 11.96 for T in K and t in min.

It can be seen f rom F ig . 14 that as M i n c r e a s e s , i . e . , as the y ie ld s t r eng th d e c r e a s e s , Tab le II, the s t r a i n ha rden ing r a t e i n c r e a s e s . F o r the da ta of F ig . 14, D/3 s i z e s v a r y f r o m about 5 to 15 /~m, Tab le I, without inf luencing the y ie ld s t r e s s , Tab le II, o r the s t r a i n ha rden ing r a t e s (see da t a for 1E-2E and 3E- 4E). Thus F ig . 14 can be c o n s i d e r e d to show the s t r a i n ha rden ing behav io r as a function of M, when g ra in s i ze i s s m a l l enough to have no ef fec t . On this b a s i s F ig . 12 would be i n t e r p r e t e d as showing the de - c r e a s e in s t r a i n h a r d e n i n g - r a t e , for a p p r o x i m a t e l y cons tan t M (within 10 pct) as g r a i n s i ze i n c r e a s e s . F i g u r e 14 would in tu rn be c o n s i d e r e d the locus of the l i m i t s of a s e r i e s of cu rves with a p p r o x i m a t e l y con- s tunt M , the l im i t s be ing obta ined by e x t r a p o l a t i n g

786-VOLUME 9A, JUNE 1978

GRAIN BOUNDARY ALPHA TRAVERSE THICKNESS,~a(/.&m) Fig. 13--Void growth ra t e ,GL, vs grain boundary ce t raverse thickness /a.

Fig. 14--Strain hardening rate vs Larson-Miller parameter .

METALLURGICAL TRANSACTIONS A

300 2068 X:

7, / t ' . ' -Ref. (2) Data 6.- 280 / 193o

,.n ~1~_. 260 / xSEQ 1792

(,9 2 4 0 1655

"-~ 2 2 0 (517 Z I---

~ 200 t579 ~

' f t . / 6 ~ ) f . o ~ . ? ~ " " xx x 5W Ld 180 ~ ~......,.~xx - - i~ / 5W 1241 t'-- (.O LU 160 E- EQUIAXED ALPHA 1103 Or" W" WIDMANST.~.TTEN PLUS 0 GRAIN BOUNDARY ALPHA ',.3 140 965

150 I I I I I I I B96 I 2 5 4 5 6 7 8

- I / 2 - I / 2 Lf ,ram

Fig . 1 5 - - C o r r e c t e d f r a c t u r e s t r e s s , Crfc, v s (void l e n g t h at fracture)-~, Lf-l #.

s ize of the components on e i ther s ide of the boundary . Once a void f o r m s at the boundary any torquing s t r e s s e s mus t be taken up by the m a t e r i a l at the ends of the void. Thus in addit ion to the s t r e s s concen t ra - t ion f rom the applied s t r e s s at the void tip, there is another component of s t r e s s concen t ra t ion at the void ends which is p ropor t iona l to the p r i o r /3 gra in s ize .

It is not c l ea r that an en t i r e p r i o r /3 gra in wil l be- have as a s ingle unit in view of the p rec ip i t a t ion of coarse ~ pa r t i c l e s and the fo rmat ion of m a r t e n s i t e in the t3. But the r e su l t s suggest that probably enough of the o r ig ina l g ra in does act as an individual unit to p ro - duce a gra in s ize dependency. The torquing effect would a lso explain, at leas t in par t , why GB voids grow fas te r than voids at W~ p a r t i c l e s . It may be for the p r e s e n t work that the D~/2 por t ion of the dependency is not s een because of the tendency for voids to have r e l a t ive ly l a rge r r ad i i of cu rva tu re at the i r ends than was seen for the T i - 5 - 5 a l loy. 2

The fact that G L values at p r i o r fi g ra in boundar ies a re affected by s t r a i n hardening r a t e s and g ra in bound- a ry ~ pa r t i c l e s ize while equiaxed ~ void growth r a t e s a re not, suggests that de format ion GB~ plays a ma jo r ro le in void growth. One would expect that within l imi t s the c o a r s e r this c~ and the lower the s t r a i n hardening r a t e s , the g rea t e r would be the GB void growth ra te and this expectat ion is in ag reemen t with observed behavior .

i n t e r e s t to note that sets 6 W, 889 MN/m z yield s t r e s s , and 7E, 951 MN/m e yield s t r e s s , fit the i r r e spec t ive curves as well as do the lower yield s t r e s s , 758 MN/ m e , data.

It is fu r ther of i n t e r e s t to note that the a s -quenched data, 5EQ, shows f rac tu re behavior close to that of the T i - 5 - 5 alloy, afc for set 5EQ is the average of two samples which differed by only 20.7 MN/m 2. Thus it would appear that the aging p rocess d r a s t i ca l l y reduced the f r ac tu r e r e s i s t a n c e of Ti-6A1-4V and was most damaging to the W + GB~ s t ruc tu r e .

Sets, lW, 2W, 3W, 4W, 1E and 2E were al l given the same f inal solut ion t r e a t me n t and were aged at t em- p e r a t u r e s , 1005 and 1033 K, where no major d i f fe rence in p rope r t i e s would be expected, as the common yield s t reng th indica tes . Thus the c lear separa t ion of the E and W + GB~ s t r uc t u r e se ts of data and the c lear dif- fe rence in the s lopes of the two curves suggest that there is a bas ic di f ference in void growth and f r ac tu re behavior of the two s t ruc tu re types . This d i f ference is not apparen t f rom the curves as drawn in Fig . 9.

The curves of Fig. 15 r e p r e s e n t a c r i t i c a l r e l a t i on - ship between void or c rack size and f r ac tu re s t r e s s . As pointed out e a r l i e r , 2 for those m i c r o s t r u c t u r e s which favor a rapid void growth, the c r i t i c a l r e l a t i on - ship between c rack s ize and s t r e s s is reached at a l a r g e r c r ack s ize tb_a~ for those m i c r o s t r u c t u r e s favor ing slow void growth. Thus, if there is a d i f fer - ence in void growth behavior between Eo~ and W + GBot s t r u c t u r e s , this should be seen in a plot of Lf vs G L. Such a di f ference is indeed evident in Fig . 16. A s im i - lar plot made f rom the data of the T i - 5 - 5 alloy, 2 but not included here , showed that the data for E and W + GBo~ s t r u c t u r e s fel l on a s ingle curve, which is in keeping with the fact that a s ingle curve fit the Crfc vs L] ~/2 data for that inves t igat ion.

In the e a r l i e r work on the T i - 5 - 5 al loy 2 void growth in both E and W + GBo~ s t r u c t u r e s occu r r ed at p r io r /3 g ra in boundar ies in the W + GBc~ s t r u c t u r e s but no d i rec t evidence of this type of void growth was found in the equiaxed s t r u c t u r e s . It may be that this poss i - ble di f ference in void path is r e spons ib l e for the sepa ra t ion of the data into two curves in the p re sen t study in the following m a n n e r . Higher A1 contents a re

140 I

120

C. Tens i l e F r a c t u r e ioo E

The longest voids which a r e found in the necked ~_ reg ion form at the cen te r of the sample , where, Br idg- :_ 80

J man n has pointed out, the s t r e s s is max imum. The d nomina l f r ac tu re s t r e s s de t e rmined by dividing the 5 60

> f r ac tu re load by the f r ac tu r e a r e a can be co r rec t ed

b- for the shape effect of the neck accord ing to a p rocedure worked out by Br idgman . n The s t r e s s obtained is the ~ z 40

O applied s t r e s s at the axis of the spec imen . This c a r - J r ec ted f r a c t u r e s t r e s s has been designated afc which 2o is plotted aga ins t L] ~/z in Fig . 15. Also shown in Fig . 15 is the curve obtained f rom e a r l i e r work on the T i - 5 - 5 al loy. 2 C o n t r a r y to the e a r l i e r work, the data for the Eat and W + GB~ s t r u c t u r e s appear to lie on two dif ferent curves with di f ferent s lopes . It is a lso of

�9 - AS QUENCHs / +

' ,;o ' 2;0 ' 3;0 '

GL. VOID GROWTH RATE, ,u.rn/slrain Fig . 1 6 - - P l o t of L f v s G L .

400

METALLURGICAL TRANSACTIONS A VOLUME 9A, JUNE I978-787

to be expec ted in GBot which p r e c i p i t a t e s out f i r s t and th is ~ would be m o r e s u s c e p t i b l e to e m b r i t t l e m e n t on aging a c c o r d i n g to r e c e n t work n which ind ica t e s TisA1 f o r m a t i o n in T i -6A1-4V.

I l l . GENERAL DISCUSSION

A. Void Nuc lea t ion

F i g u r e 17 at A shows that s l ip in Wot does not ex- tend r e a d i l y into the m a t r i x a s it does when the ma- t r i x i s l a r g e l y r e t a ined /3 , e This i m p l i e s that s l ip over l a r g e d i s t a n c e s in the aged m a r t e n s i t i c m a t r i x ap- p a r e n t l y does not p r e c e d e void f o r m a t i o n at m a r t e n s i t e la th i n t e r f a c e s .

A r e c e n t f ini te e l emen t method s tudy x3 of s t r e s s d i s - t r i bu t ions in the a and/3 p h a s e s of a T i - M n a l loy showed that t r i a x i a l s t r e s s e s a r e l ike ly to deve lop at or-/3 i n t e r f a c e s , and this t r i a x i a l i t y would be expec ted to a s s i s t void f o r m a t i o n s . If s l ip can r e a d i l y be t r a n s - f e r r e d f rom a to ;3, one would expec t the extent of th is t r i a x t a l i t y to be r educed . Such a p o s s i b i l i t y ex i s t s for the B u r g e r s o r i en ta t ion 14 be tween a and/3, s ince s e v e r a l s e t s of s l ip s y s t e m s in a a r e p a r a l l e l to s l ip s y s t e m s in/3. It is p o s s i b l y for th is r e a s o n that no voids were found along Widmans t~ t t en a i n t e r f a c e s in the T i - 5 - 5 a l loy . 2

R o b e r t s and P a r t r i d g e 15 have found that a {10i2}~10il) twin boundary under fa t igue loading i s a b a r r i e r to d i s l oca t i on mot ion. D i s l o c a t i o n s we re found to co l l ec t at th is boundary on the untwinned s ide . A s i m i l a r co l l ec t ion of d e b r i s a t {1121} twin un- twin in t e r f ace in t i t an ium was d i s c u s s e d by Stubbing- ton. 6 The au tho r s a l so r e p o r t e d the f o r m a t i o n of mul - t ip le fine ho les in the i n t e r f ace be tween twin and ma- t r i x . H such voids also formed in uniaxial loading, this behavior would be consistent with macroscopically visible void nucleation at twin-untwin interfaces, Fig. 7, and the eventual "consumption" of the twin by the void. No evidence is available regarding twins in mar- t ens i t e and void fo rma t ion .

B. Void Growth

In F ig . 10 s p e c i m e n se t s 1E and 2E show s i m u l - t aneous ly the h ighes t s t r a i n ha rden ing and void growth r a t e s for the E a s t r u c t u r e s . F o r the W + GB~ s t r u c - t u r e s , however , h igher s t r a i n ha rden ing r a t e s w e r e a c c o m p a n i e d by lower void growth r a t e s . C o m p a r i - son of these da ta sugges t s that the high s t r a i n ha rden - ing and void growth r a t e s for s e t s 1E and 2E may a r i s e f rom the s a m e s o u r c e , a c c o r d i n g to the fo l low- ing specu la t ion .

In d i s c u s s i n g the aging behav io r of a s - q u e n c h e d hexagona l m a r t e n s i t e T i -6A1-4V, W i l l i a m s ~6 poin ts out that t e m p e r i n g o c c u r s by p r e c i p i t a t i o n of/3. P r e - sumab ly with i n c r e a s e d aging t ime the ;3 p a r t i c l e s a g g l o m e r a t e while s i m u l t a n e o u s l y i n c r e a s i n g the inter- /3 p a r t i c l e d i s t ance . Th is i n c r e a s e would e n l a r g e the s l ip d i s t ance in the m u r t e n s i t e b e f o r e d i s l oca t i ons would encounte r t3 p a r t i c l e s , which p r e s u m a b l y mus t offer r e s i s t a n c e to s l ip . If th is we re not the ca se , then h igher aging t e m p e r a t u r e s and longer t i m e s , i . e . , in- c r e a s e d va lues of M, should not r e s u l t in g r e a t e r sof t - ening. T h e r e i s some fu r t he r suppor t for th is sugges - t ion f rom work on the t e m p e r i n g of m a r t e n s i t e in the

Fig. 17--Specimen from 1 W sectioned after a strain of e = 0.37 polished etched and restrained; magnification 365 times. Slip in c~ does not readily proceed across aged mar- tensite matrix.

T i - 6 A 1 - 2 S n - 4 Z r - 6 M o a l loy , 17 which showed that a v e r y fine d i s p e r s i o n of/3 p a r t i c l e s , p r e c i p i t a t e d f r o m m a r - t ens i t e , p roduced l a rge i n c r e a s e s in h a r d n e s s .

Thompson, e t a118 have shown that s l ip d i s t ance and s t r eng then ing a r e d i r e c t l y r e l a t e d , i n c r e a s e d s t r e n g t h - ening be ing a c c o m p a n i e d by d e c r e a s e d s l ip d i s t ance . M a r g o l i n and S tanescu 1~ have shown a s i m i l a r r e l a - t ionsh ip be tween s t r eng th and s l ip l ine spac ing . The l a t t e r au thor s found mos t r a p i d ha rden ing a c c o m - pan ied the mos t r a p i d d e c r e a s e in spac ing . One may, t h e r e f o r e , sugges t for s p e c i m e n se t s 1E and 2E that, the l a r g e r the s l ip d i s t ance , the more r e a d i l y can it be r e d u c e d and t h e r e f o r e the m o r e r a p i d the ha rden ing . Since s l ip is r e q u i r e d for void growth, the longer the s l ip pa th be tween o b s t a c l e s , i . e . , the l a r g e r the s p a c - ing be tween/3 p a r t i c l e s , the m o r e r e a d i l y should void growth take p l ace . Th i s d i s c u s s i o n i m p l i e s that even at l a rge s t r a i n s the /3 p a r t i c l e s have an effect on s l ip pa th . No da ta is ava i l ab l e on/3 i n t e r p a r t i c l e d i s t a n c e s in T i -6A1-4V as a funct ion of aging.

It is p o s s i b l e to extend these ideas on s l ip d i s - t ances to the void growth b e h a v i o r in GBot, the c r i t i c a l r e g i o n for void growth in the W + GB~ s t r u c t u r e . Slip d i s t a n c e s in the GBa p a r t i c l e s t h e m s e l v e s a r e much l a r g e r than s l ip d i s t a n c e s in the aged m a r t e n s i t e . Thus one would expec t that the s l ip d i s t a n c e s in GB~ would be much m o r e s ens i t i ve to changes in s t r a i n ha rden ing r a t e than s l ip d i s t a n c e s in m a r t e n s i t e . One would a l so expec t that these s l ip d i s t a n c e s in GBoI could d e c r e a s e r a p i d l y as a function of the s t r a i n h a r d - ening i m p o s e d by the aged m a r t e n s i t e m a t r i x . Ac - co rd ing ly the extent of s l ip and t h e r e f o r e the r a t e of void growth would be r e d u c e d . The void growth be- hav io r of GB~ s t r u c t u r e s a r e , indeed, in keeping with t hese o b s e r v a t i o n s .

E a r l i e r d i s c u s s i o n p roposed , in a c c o r d a n c e with phenomeno log i ca l o b s e r v a t i o n s , that for a g iven va lue of M, s t r a i n ha rden ing r a t e s d e c r e a s e d with i n c r e a s e d p r i o r ;3 g ra in s i z e . Thompson, e t al x8 have shown that r e l a t i v e s t r a i n ha rden ing r a t e s , in the un i fo rm s t r a i n r ange , v a r y be tween g ra in s i z e s for A1 and Cu and that for o r - b r a s s the r e l a t i v e s t r a i n ha rden ing r a t e s a p p e a r to be unchanged. No da t a a r e a v a i l a b l e for the r e g i o n s

788-VOLUME 9A, JUNE 1978 METALLURGICAL TRANSACTIONS A

beyond necking. The ques t ion of how i n c r e a s i n g p r i o r fl g ra in s ize would reduce s t r a i n ha rden ing r a t e s in the reg ion of necking, therefore , r e m a i n s unc lea r .

C. F r a c t u r e

1) EVALUATION OF arc

As pointed out e a r l i e r Ofc , shown in Table H and plotted in Fig . 15, r e f e r s to the axial s t r e s s . However, the longest voids at the cen te r of the spec imen extend some d i s tance away f rom the cen te r and the quest ion, therefore , a r i s e s as to how well the axial s t r e s s r e p r e s e n t s the applied s t r e s s in the v ic in i ty of the void. P a r k e r , et al, 2~ by a p roces s of d r i l l i ng an axial hole and noting the d imens iona l changes in a 0.25 pct C s teel , have found that there is very l i t t le change in axial s t r e s s up to about 15 pct of the spec imen rad ius f rom the cen te r outward for a spec imen with 30 pct reduc t ion of a r ea . Thus it would appear for the p r e s e n t case where the longest void encounte red was about 140 ~m that the axial s t r e s s is e s sen t i a l l y con- s tant .

Another ques t ion which can be r a i s e d is, that in view of the fact that a n u m b e r of voids a re p re sen t , how well can the axial s t r e s s be said to r e p r e s e n t the ac tua l s t r e s s p r e sen t . Greenf ie ld and Margol in 2 have shown that for the spec imen FSB2 with a 56 pct r e d u c - t ion of a r e a (and the l a rges t volume f rac t ion of voids of a l l the spec imens tested) that 50 pct of the voids a re contained in 3.8 pct of the c ross sec t iona l a r ea lo- cated at the cen te r of the sample . If one a s s u m e s that on average the voids at the cen te r a re twice the s ize of the voids outside this a r ea , then 2/3 of the tota l of 1.5 pct of the voids in the f r ac tu r e a r e a a re contained in 3.2 pct of the c ros s sec t iona l a r ea . Thus the c ros s sec t iona l a r e a in this reg ion would be reduced by about 27 pct and the nomina l axial s t r e s s at the cen te r would be r a i s e d by 27 pct.

The volume f rac t ion of voids is a function of s t r a i n 2 and thus the dec rea se in c ross sec t iona l a r e a of the spec imen due to voids in the cen t r a l reg ion of the f r ac tu r e su r face will depend on s t r a in . The net r e - sul t of this behavior would be to i n c r e a s e the s lopes of the a f -L~ 1/~ plots of Fig. 15 without changing the re l a t ive pos i t ions of the cu rves . The s lopes would probably not be i nc r ea sed by more than a factor of 4 or 5.

2) FRACTURE ENERGY

a) Griff i th F r a c t u r e Energy . It was pointed out e a r l i e r ~ that a Griff i th f r ac tu re energy can be de- r ived f rom the s lopes of ~fc vs L] ~/2 cu rves . The f r ac tu re energy, without cons ide r ing the effect of volume f rac t ion of voids on the nomina l value of ~fc, was repor ted as 1.8 • l0 S e r g s / c m ~ for the T i - 5 - 5 a l - loy. The f r ac tu r e energy, ca lcula ted f rom the slopes of Fig. 15 for the Ti-6A1-4V alloy is about 0.6 • l0 S e r g s / c m 2 for the E~ s t r u c t u r e and about 0.3 • 105 e r g s / c m 2 for the W + GB~ conf igurat ion. If an e s t i - mate is made of the e las t i c energy per unit a r e a ava i l - able at f r ac tu re , the energy is roughly 50 t imes the f r ac tu re energy for the T i - 5 - 5 alloy. Thus even if the void volume f rac t ion co r r ec t i ons were made, the Griff i th ene rg ie s would be about 1/10 of the avai lable

energy . This s i tua t ion is cons i s ten t with the Griff i th r e q u i r e m e n t s for the onset of f r ac tu re .

b) A s s e s s m e n t of the Reason for the Difference in F r a c t u r e Energy for T i - 5 - 5 and Ti-6A1-4V. The fact that the f r ac tu re ene rg ies of the Ti-6A1-4V alloy a re s m a l l e r than that of the T i - 5 - 5 alloy mos t probably is not re la ted to the p r e s e n c e of the in ter face phase . 22'23 This conclus ion is based on the following specula t ion and support ing expe r imen ta l evidence. If one a s s u m e s that the in ter face phase is p r e se n t in the T i - 5 - 5 alloy, then s ince , p r e sumab ly the c h a r a c t e r i s t i c s of the in- t e r face phase would be s i m i l a r in both ins tances , the in te r face phase would not r a i s e the f r ac tu re s t r e s s in T i - 5 - 5 and lower it in Ti-6A1-4V. Fu r the r , if the as -quenched Ti-6A1-4V alloy e i ther does not have the in te r face phase or has an fcc or hcp in ter face phase s t r u c t u r e 22 yet behaves in a manne r s i m i l a r to the aged T i - 5 - 5 , this behavior mus t fu r the r s t r eng then the conclus ion that the in ter face phase does not affect energy absorp t ion dur ing f r a c t u r e .

The expe r imen ta l evidence in support of this con- c lus ion is the observa t ion that the in te r face phase is not e s s e n t i a l e i ther to void nuc lea t ion or void growth. F i gu r e s 3 to 5 and 7 indicate that voids can form at pos i t ions other than ~ -~ in te r faces . F igu re 8(a) r e - veals that voids grow ac ross ~-fi in te r faces in E~ s t r u c t u r e s while Fig . 8(b) r evea l s that a void can " c o n s u m e " an en t i r e gra in boundary ~ pa r t i c l e , i.e., void growth is not confined to a reg ion nea r the i n t e r - face.

We may next examine what in fo rmat ion is avai lable f rom void growth r a t e s . S imi l a r r a t e s of void growth occur red for E s t r u c t u r e s in the T i - 5 - 5 al loy z and in

the p r e se n t inves t iga t ions , speci f ica l ly se ts G-5 and Z-1 of Ref. 2 and sets 3E and 4E of the p r e s e n t work. However, the f r ac tu re s t r a i n s in the e a r l i e r work S were much l a r g e r . Thus, the ra te of growth of voids t hemse lves is not re la ted to the f r ac tu re energy. This was also apparent f rom the L f - ~ plot of the e a r l i e r work, 2 where data for the fast growing voids at GB~ and slow growing voids in E~ s t r u c t u r e s fell on the same afc -L~ 1/z curve . The lower f r ac tu re s t r a i n s in Ti-6A1-4V can be in t e rp re ted p r i m a r i l y as a consequence of the lower f r ac tu re energy of Ti-6A1- 4V. F o r example, a s s u m e that the voids leading to fa i lu re grow to the same c r i t i c a l s ize in the T i - 5 - 5 and Ti-6A1-4V al loys . At a given c r i t i ca l void s ize the s t r e s s will be higher in T i - 5 - 5 than in Ti-6A1-4V, Fig . 15. Because of the na tu re of the s t r e s s - s t r a i n cu rves this wil l r e s u l t in a higher s t r a i n for the T i - 5 - 5 al loy. It is of i n t e r e s t to note that those s i m i l a r void growth ra tes in the two al loys were achieved in both cases at different levels of s t r e s s , d i f ferent i n t e rpa r t i c l e spacings and p r i o r ~ gra in s i ze s .

c) As Quenched Mar t ens i t e . The high energy ab- so rb ing c h a r a c t e r i s t i c s of a s -quenched mar t ens i t e found by C r o s s l e y and Lewis 24 a re in a g r e e m e n t with the p r e s e n t high duct i l i ty -h igh f r ac tu re s t r e s s obse r - vat ion on the behavior of this s t r u c t u r e . It is not pos- s ible to a sc r ibe the loss in f r ac tu re toughness which comes on annea l ing or aging this s t r uc t u r e wholly to the fo rmat ion of Ti3A112 (or shor t range order ing) , as C r o s s l e y and Lewis have suggested, because p r e - c ipi ta t ion of/3 is a lso involved.

METALLURGICAL TRANSACTIONS A VOLUME 9A, JUNE 1978-789

d) Evaluat ion of no. In the work of Greenf ie ld and MargoUr/~ it was noted that the s t r e s s in te rcep t ob- tained, when the L~ 1/z to L] ~/z = 0, was afc v s curve was ex t rapola ted

e s sen t i a l ly the yield s t r e s s in the ma- t e r i a l . This was in t e rp re t ed as indicat ing that voids could not fo rm unt i l y ie ld ing took place. In the p r e s e n t ins tance ext rapola t ion of the arc v s L] ~/z curves pro- duees in te rcep ts somewhat above the value of the e a r l i e r work and in both ins tances the extrapola ted values a re above the yield s t r e s s .

In the p r e sen t work also the longest v o i d - s t r a i n curves , F ig . 9, as in the e a r l i e r work, 2 a re cons i s ten t with zero void length at ze ro plas t ic s t r a in , thereby also implying that voids form at or close to the onset of yielding.* On this bas i s the in te rcep t cannot be con-

*It has recently been shown that cracking at a-~ interfaces or within a can form at the surface of tensile specimens at strains just above the proportional unit. 2~

s ide red the s t r e s s which mus t be exceeded to c rea te a void, and r e f e r ence to F igs . 9, 1 and 2 indica tes that voids have been seen below this s t r e s s in te rcep t .

F u r t h e r it is obvious that % cannot be the s t r e s s at which f r ac tu re takes place when the c rack is in - f ini te in s ize, s ince this makes no phys ica l s ense . Since the E a and W + GBa s t r u c t u r e s appear to have different modes of f r ac tu re in the p r e s e n t study, i .e . , t r a n s g r a n u l a r void growth vs gra in boundary void growth, this suggests that % may in pa r t cha rac t e r i ze the void growth path.

e) Applicat ion of Observa t ions to Ducti le F r a c t u r e in Genera l . F ina l ly in view of var ious theor ies on duct i le f r ac tu re involving void growth and coa les - cence, 25-z7 one may ask how well the r e su l t s of Fig. 15 and the s i m i l a r e a r l i e r data on the T i - 5 - 5 al loy (see F ig . 15 and Fig . 17 of Ref. 2) can be said to r e - late to duct i le f r ac tu re . Havner and Glassco, 2s ana lyz ing c r i t e r i a for ducti le f r ac tu re , have concluded that the same re la t ionsh ip between energy and the on- set of uns table f r ac tu re ex is t s for both b r i t t l e and duct i le f r ac tu re . This ana lys i s would then indicate that a c r i t i c a l s r e s s s void s ize re la t ionsh ip can exis t in ducti le meta l s as was found here . A c r i t i c a l s t r e s s - c r ack s ize re la t ionsh ip s i m i l a r to the one found here was also observed for Z r - H alloys.2~

Calhoun and Stoloff s~ observed 50 to 100 /~m size voids on longi tudinal sec t ions of f r ac tu red Mg base al loy spec imens , typified by the i r Fig. 6. These authors were unable to find any re l a t ionsh ip between d imples on the f r ac tu re sur face and these voids . Since the f r ac tu r e sur face contained some of these la rge voids, and s ince there was no evidence of void coa lescence , these r e su l t s can be taken to imply the poss ib le ex is tence of a c r i t i c a l s t r e s s - c r a c k s ize r e - la t ionship a lso.

The ques t ion can be r a i s ed as to whether ducti le f r ac tu r e mus t always take place accord ing to a c r i t i - cal s t r e s s - c r a c k s ize re la t ionsh ip . If the deformat ion and r ecove ry p r o c e s s e s accompanying void growth and coa lescence can occur without, at any p a r t i c u l a r c rack length, r each ing the appl icable c r i t i c a l s t r e s s - c rack size re la t ionsh ip , then f rac tu re can occur by void growth and coalescence , unt i l local shear at the spec imen edges p e r m i t s f inal rup tu re to occur as demons t ra t ed by Put t ick for Cu.3~

IV. SUMMARY

1) Voids have been found to nuclea te at equiaxed and g ra in boundary a - a g e d mar t ens i t e in te r faces , and con- t r a r y to e a r l i e r r e su l t s z within a at m a t r i x - t w i n i n t e r - faces , at a subboundar ies , and at Widmanst~itten a - aged mar t ens i t e in t e r faces . Voids also nucleated at m a r t e n s i t e lath in t e r faces .

2) Growth of the longest void, L, at a p a r t i c u l a r s t r a i n is l i nea r with s t ra in , and the slopes of these l ines , the void growth ra tes , GL, a r e s m a l l e r for E a s t r u c t u r e s than for W + GBa s t r u c t u r e s . For the lat- t e r s t r u c t u r e s G L was l a rge r along GBa than along W a . G L i n c r e a s e d with p r i o r t3 gra in s ize and GBa th ickness but for E a s t r u c t u r e s appeared to depend for a given aging t r e a t me n t on m a r t e n s i t e plate s ize .

3) G L was marked ly dec reased with i nc r e a sed s t r a i n harden ing r a t e s for the W + GBa s t r u c t u r e s but was r e l a t i ve ly l i t t le changed in the E a s t r u c t u r e s .

4) When a c r i t i c a l void length, L f vs co r r ec t ed f rac - tu re s t r e s s , afc, re la t ionsh ip is reached unstable f r ac tu re takes p lace . The re la t ionsh ip has the form afc = (to + K L ] 1/2 " ~o and K have higher va lues for Ea s t r u c t u r e s than for Wa s t r u c t u r e s , thus r e su l t i ng in two separa te curves for the two s t r u c t u r e s . Slopes for both s t r u c t u r e s a re cons iderab ly s m a l l e r than that observed in e a r l i e r work z for the T i - 5 - 5 (Ti-5.25A1- 5 .5V-0.09Fe-0.5Cu) alloy. Although lower (rfc s t r e s s e s a re observed at a given c r i t i c a l c rack s ize for aged Ti-6A1-4V than for the T i - 5 - 5 alloy, a s -quenched E a s t r u c t u r e s for Ti-6A1-4V show afc s t r e s s e s s i m i l a r in magnitude to the e a r l i e r work. 2

5) A Griff i th f r ac tu r e energy was calcula ted f rom the slope of the arc vs L~ lie curve . The lower f r ac tu re s t r a i n s for the Ti-6A1-4V alloy a re a t t r ibu ted to its lower f r ac tu re energy va lues , which were lower than those for the T i - 5 - 5 alloy.

6) The di f ference between the a r c - L ] ~/2 curves for the E and W + GBa s t r u c t u r e s is cha rac t e r i zed by a d i f ference in L f - G L c u r v e s for the two s t r u c t u r e s , which sugges ts that % is a m a t e r i a l c h a r a c t e r i s t i c or constant .

7) A sugges t ion is made for when ducti le f r ac tu re wil l include a c r i t i c a l s t r e s s - c r a c k size re la t ionsh ip and when it will not.

ACKNOWLEDGMENTS

The authors wish to thank A. Procoppio, A. Pa te l and A. Sanghvi for c a r r y i n g out pa r t of the exper i - men ta l work and to acknowledge useful d i s cus s ions with A. W. Thompson and W. W. Gerbe r i ch . The con- t inued i n t e r e s t and encouragement of Dr . Bruce Mac- Donald of the Office of Naval R e s e a r c h is apprec ia ted . The authors wish to thank A. M. Adair and F. Gurney for the ex t rus ion and swaging of this m a t e r i a l . This work was c a r r i e d out on ONR Cont rac t N-00014-75-C- 0793.

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790 VOLUME 9A, JUNE 1978 METALLURGICAL TRANSACTIONS A

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METALLURGICAL TRANSACTIONS A VOLUME 9A, JUNE 1978-791