593
ISIJ In e na ional, Vol. 62 (2022), No. 3, pp. 593–601
h ps://doi.o g/10.2355/isijin e na ional.ISIJINT-2021-381
* Co esponding au ho : E-mail: [email p o ec ed]
© 2022 The I on and S eel Ins i u e o Japan. This is an open access a icle unde he e ms o he C ea i e Commons
A ibu ion-NonComme cial-NoDe i s license (h ps://c ea i ecommons.o g/licenses/by-nc-nd/4.0/).
E ec s o C ys allog aphic Tex u e on Subsu ace Fa igue C ack
Gene a ion in Ti–Fe–O Alloy a Low Tempe a u e
Osamu UMEZAWA1,2)* and Weibo LI3)
1) Facul y o Enginee ing, Yokohama Na ional Uni e si y, 79-5 Tokiwadai, Hodogaya, Yokohama, 240-8501 Japan.
2) Cen e o Ad anced Inno a ion Technologies, Vysoká Škola Báňská - Technical Uni e si y o Os a a, 17. lis opadu 15, 708
33 Os a a-Po uba, Czech Republic.
3) G adua e School o Enginee ing, Yokohama Na ional Uni e si y. Now a Cen al Resea ch Labo a o ies, Nihon Pa ke izing
Co., L d., 2784 Okami, Hi a suka, Kanagawa, 254-0012 Japan.
(Recei ed on Augus 18, 2021; accep ed on No embe 8, 2021; J-STAGE Ad ance published da e:
Decembe 29, 2021)
Subsu ace mic oc acks de eloped in a g oo e- olled and cold-swaged Ti–Fe–O alloy we e cha ac e ized
o cla i y he gene a ion o subsu ace a igue c ack. In addi ion, he e ec s o c ys allog aphic ex u e on
subsu ace c ack ini ia ion and g ow h we e discussed. A conside able numbe o mic oc acks we e
de ec ed in he
β
g ains,
α
g ains, and a he
α
-
β
in e ace. The mic oc acks in he
β
g ains g ew negligibly
in o he neighbo ing
α
g ains along he basal plane. This was because hese g ains we e o ien ed wi h
hei c-axis almos pe pendicula o he loading axis. The 10 10
{}
α
ibe ex u e p e en s he o ma ion o
basal ace and i s g ow h on he basal plane. The s ess concen a ion a ound he mic oc ack in he
β
g ains could assis he g ow h o he mic oc ack in o neighbo ing
α
g ains along he p isma ic plane
(which is inclined o he loading axis a a sui able angle) o occasionally a a 10 10
{}
α
wis bounda y. The
10 10
{}
α
ibe ex u e assis ed mic oc ack g ow h, and he eby, o med aligned ace s and yield longe
mic oc ack leng h. The combina ion o he shea s ess and opening s ess on 10 10
{}
α
esul s in a Mode
II o III mic oc ack and causes mic oc ack g ow h on he p isma ic plane in he neighbo ing g ain.
KEY WORDS: i anium alloys; high cycle a igue; ex u e; subsu ace c ack; elec on backsca e di ac-
ion.
1. In oduc ion
Subsu ace a igue c ack ini ia ion si es in nea -
α
ype
and
α
-
β
ype i anium alloys commonly consis o ans-
g anula c ack ( ace ) o c acks ( ace s) unde bo h no mal
cyclic a igue and dwell a igue. Each ace is i ed o he
α
g ain mo phology o mic os uc u e and he quasi-clea age
ace s ha a e mos ly o med on o nea he basal plane.1–7)
Thei inclina ion o he p incipal s ess axis e ealed a wide
ange o a ia ions owing o he ex u e o he alloys,2)
al hough he mic oc ack g ow h o each ma e ial showed
a dependence on he o ien a ion o g ain s uc u e and
p incipal s ess axis.3–5,8) The disloca ion mo emen in he
α
phase is es ic ed o he p ima y slip plane and is ai ly
plana so ha disloca ion a ays on 10 10 1120
{}
a e
piled-up in he icini y o he g ain bounda ies. The local
s ess concen a ion nea he
α
g ain bounda y owing o
he e ogeneous slip may cause subsu ace c ack ini ia ion.9,10)
Fu he mo e, ex u e and mic o ex u e (mac ozone) s ongly
a ec subsu ace c ack ini ia ion and high-cycle a igue
s eng h.11–14) The s ess edis ibu ion be ween “so ”
(plas ically de o med and wi h a high Schmid ac o ) and
“ha d” (elas ically de o med and wi h a low Schmid ac o )
α
g ains owing o s ain incompa ibili y a hei bounda y
is also a ac o ha causes he de elopmen o a ace in he
ha d g ain unde cyclic loading.10,15–19) Mul iple mic oc acks
we e de ec ed in he mac ozone o ien ed wi h hei main
c-axis ex u e componen . Mo eo e , he dominan c ack
g ew in he mac ozones owing o mic oc ack coalescence.
A simila
α
-g ain o ien a ion p omo es cyclic s ain accu-
mula ion, because localized de o ma ion in one g ain can be
s aigh o wa dly accommoda ed in adjacen g ains.14) Thus,
he c ys allog aphic o ien a ions in neighbo ing g ains and
he mic o ex u e play impo an oles in he gene a ion o
mic oc acking owing o he s ain incompa ibili y and s ess
edis ibu ion du ing a igue p ocesses.20)
The mic oc acking on (0001) in a ha d
α
-g ain may
be gene a ed by he combina ion o he opening s ess
and shea s ess componen s unde cyclic loading. This is
because he shea s ess componen p omo es he de elop-
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ 594
men o he slip band on (0001). The no mal di ec ion o
he (0001)
α
quasi-clea age ace s is inclined a 15° o 60°
o he p incipal s ess axis,1,2,5,11) because he no mal s ess
on (0001) is excep ionally high when he ace is no mal o
he applied s ess.10,15) Howe e , he ace o ma ion modes
a lowe s ess le els di e and depend signi ican ly on
he mic os uc u es o he alloys. The mac ozones whose
main c-axis ex u e componen is almos pe pendicula o
he p incipal s ess axis obs uc mic oc ack g ow h.12) The
10 10
{}
α
ace was de ec ed, a he han he (0001)
α
ace .
This was pa icula ly so in he dwell a igue es o highly
ex u ed alloys wi h <0001> pe pendicula o he ensile
axis.19) The p isma ic c ack was consis en wi h a high
Schmid ac o o p isma ic slip. Howe e , i is no e iden
as o which ace ini ia es he o ma ion o c ack.19,21)
The e inemen o he
α
-g ain s uc u e and/o g ain
dis ibu ion wi h andom o ien a ion (elimina ion o mic o-
ex u e) can e ec i ely lowe he maximum s ess concen-
a ion a a bounda y. This is because a sho e slip leng h
esul s in subs an ial imp o emen s in a igue s eng h.3,22) A
Ti-6Al-4V olled ma e ial whose
α
-g ain s uc u e displayed
a andom o ien a ion dis ibu ion owing o a highe wo king
a io exhibi ed a igue s eng h ha was signi ican ly highe
han ha o a o ged ma e ial wi h a colony s uc u e a low
empe a u e.22,23)
The nea -
α
ype Ti–Fe–O alloy which p o ided a cha ac-
e is ic s uc u e o
α
phase wi h dispe sed small amoun o
β
phase clea ly exhibi ed subsu ace a igue c ack ini ia ion a
77 K, whe e he ace was de ec ed as a (0001)
α
c ack.10,24,25)
C yogenic empe a u e a igue could be mos a o able o
cha ac e ize he subsu ace c ack gene a ion, because he
subsu ace c ack ini ia ion and he s ain incompa ibili y
p e ail mo e a lowe empe a u es wi h highe he c i ical
esol ed shea s esses (CRSSs) o indi idual slip sys ems
and hei di e ences.26) Such he e ogeneous slip de o ma-
ion manne e ealed ha he in e nal s ess in he
α
g ain
had accumula ed no mal o (0001)
α
by he ull cons ain s
model analysis, in which esul ed in (0001)
α
c acking.27)
Ti–Fe–O alloy olled ma e ials p o ided a mic o ex u e
(mac ozone) wi h a he clea ly di ided in o eco e ed
(so )
α
g ain and ec ys allized (ha d)
α
g ain egions.
Fu he mo e, he mic os uc u e o he Ti–Fe–O alloy was
modi ied by g oo e- olling and cold-swaging o e ine he
α
-g ain s uc u e and a oid he mic o ex u e (mac ozone).
A ine globula
α
-g ain s uc u e and a weak 10 10
{}
α
ibe
ex u e we e achie ed. Howe e , he e was no imp o emen
in he a igue s eng h a 107 cycles.24) Al hough he (0001)
α
ace p o ided an o igin o he subsu ace c ack ini ia ion,
he 10 10
{}
α
ace s mainly co e ed he c ack ini ia ion si e.
The e o e, in he p esen s udy, he cyclic de o ma ion
s uc u e and mic oc acks de eloped in he modi ied mic o-
s uc u e o he Ti–Fe–O alloy we e cha ac e ized o discuss
he subsu ace c ack gene a ion.
2. Expe imen al
2.1. Ma e ial and Fa igue Tes ed Samples
The a igue es ed samples o a cold-swaged and annealed
nea -
α
ype Ti-0.994%Fe-0.386%O (mass%) ma e ial we e
examined in his s udy. The de ails o he ma e ial we e
desc ibed in he e e ence 24). The ec angula ba s cu om
he hick pla e a e ho - o ged (1 273 K hea ing) and ho -
olled (1 123 K hea ing) we e g oo e- olled (1 023 K hea -
ing, equi alen s ain
η
=1.3) and cold-swaged (
η
=0.48)
in o a ound ba wi h a diame e o 20 mm. The ound ba
was annealed a 1 023 K o 3.6 ks ollowed by ai cooled,
and he cylind ical es pieces we e cu pa allel o he olling
di ec ion (RD) di ec ion.
Fa igue es s we e pe o med using a c yogenic se o-
hyd aulic a igue machine unde load con ol a a s ess
a io, R o 0.01, in liquid ni ogen (77 K) and in ambien
ai (293 K).24) The es condi ions a e gi en in he e e ence
23). Table 1 lis s he ensile p ope ies o he es ma e ial.
Figu e 1 shows maximum cyclic s ess s. he numbe o
cycles o ailu e (N ) da a o he es ma e ial.24) The sam-
ples ha ailed a 77 K and 293 K in highe cycles exhibi ed
subsu ace c ack ini ia ion (solid plo s in Fig. 1). He ein,
hei maximum cyclic s ess was signi ican ly lowe han
0.2% p oo s ess,
σ
0.2. The samples ha ailed by subsu -
ace c ack ini ia ion we e selec ed o he p esen analyses.
2.2. Analyses
The ac u ed samples we e cu o nea he subsu ace
c ack ini ia ion si es pa allel o he di ec ion o ini ial c ack
g ow h as shown in Fig. 2.21) The mic os uc u es a ound
mic oc acks benea h he c ack p opaga ion planes we e
analyzed in he longi udinal c oss-sec ion. The mechanically
and elec ochemically polished su aces we e examined by
scanning elec on mic oscopy (SEM). Elec on backsca e
di ac ion (EBSD) pa e n analysis in SEM was employed
o de e mine he mic os uc u e a ound he mic oc ack.
The hin disk o ansmission elec on mic oscopy
(TEM) analysis was sec ioned om benea h he ac u e
su ace pe pendicula o he p incipal s ess axis and was
mechanically g ound. Each disk diame e was measu ed and
i s maximum cyclic s ess,
σ
max, was calib a ed, because he
Fig. 1. S–N da a o he es ed ma e ial a 77 K and 293 K.
Table 1. Tensile p ope ies o he es ed ma e ial a 77 K and
293 K.
Tempe a u e
(K)
0.2% p oo
s ess,
σ
0.2 (MPa)
Ul ima e ensile
s eng h,
σ
B (MPa)
To al
elonga ion (%)
77 1 257 1 326 11.3
293 659 799 29.5
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ595
Fig. 2. Schema ic illus a ion o analysis samples cu om he
ailed specimens.
Fig. 3. Mic os uc u e o es ma e ial: EBSD image quali y maps
o he RD plane (a) and o a longi udinal sec ion (b).
Fig. 4. Disloca ion s uc u e in
α
and
β
g ains o he es ed ma e-
ial on he RD plane.
Fig. 5. Disloca ion s uc u es in
α
g ains a e cyclic de o ma ion a 293 K: (a)
σ
max = 549 MPa, N = 388 010 cycles,
and (b)
σ
max = 597 MPa, N = 72 424 cycles.
a igue es specimens had an hou glass shape. TEM oils
we e p epa ed by elec ochemical winje polishing a 243 K
in a s i ed solu ion o 6% pe chlo ic acid, 35% bu anol,
and 59% me hanol. A JEM-2100F elec on mic oscope
equipped wi h a double- il goniome e s age was ope a ed
a 200 keV.
2.3. Mic os uc u e
Figu e 3 shows he mic os uc u e o he ma e ial as
EBSD image quali y maps. The ma e ial consis ed o
equiaxed
α
g ains and ine od-like
β
g ains, which we e
andomly dis ibu ed along he RD. The a e age
α
-g ain
size was app oxima ely 13
μ
m. Indi idual disloca ions we e
dis ibu ed in bo h
α
and
β
g ains as shown in Fig. 4, so
ha he equiaxed
α
g ains could be eco e ed ully. The
α
mic os uc u e showed a weak 10 10
{}
ibe ex u e in which
he maximum pole densi y o 10 10
{}
was less han h ee.24)
Fu he mo e, he c-axis is andomly dis ibu ed pe pendicu-
la o he p incipal s ess axis (RD).24)
3. Resul s
3.1. Cyclic De o ma ion S uc u e
A e cyclic de o ma ion a 293 K and 77 K, disloca ion
a ays we e de eloped in he
α
g ains a each s ess le el
as shown in Figs. 5(a) and 6(a). A ays we e blocked a
he g ain bounda ies o he
α
-
β
in e aces as indica ed by
an a ow in Fig. 6(a). Du ing he cyclic de o ma ion, p e-
exis ing mo eable disloca ions ea anged hemsel es and
mul iplied in he
α
g ain. Ce ain disloca ion loops we e
obse ed on he p isma ic plane a low empe a u es (Fig.
6(b)). When a disloca ion sou ce emi s a se ies o disloca-
ions all lying on he same slip plane, disloca ions pile up
behind he leading disloca ion and in e ac elas ically. The
dominan de o ma ion mode is ia he p isma ic slip sys em,
and he glide p ocess is ma kedly plana . Nea ly all he dis-
loca ions in coplana a ays obse ed in he
α
g ains (Figs.
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ 596
5(a) and 6(a)) we e o he sc ew ype as discussed in he
e e ences 9) and 10), and he mo emen was es ic ed o
hei slip planes. Disloca ions can pass h ough he bounda -
ies and in o he neighbo ing g ains a highe s ess le els.
Tangled disloca ions we e also de ec ed in
α
g ains a a
highe s ess le el a bo h es empe a u es (see Figs. 5(b)
and 6(c)). In addi ion, many disloca ions wi h mul iple slip
sys ems we e obse ed in he
β
g ains a bo h es empe a-
u es a any s ess le el (see Fig. 7).
3.2. Mic oc acks in
ββ
G ains
Rega dless o he s ess le el, a conside able numbe
o mic oc acks and oids we e de ec ed nea he ac u e
su ace on he c oss-sec ion o he ailed specimens a bo h
es empe a u es (see Fig. 8). Mos o he mic oc acks we e
de ec ed in he
β
g ains wi hin a dep h o 100
μ
m om
he ac u e su ace. All he de ec ed
β
mic oc acks we e
oughened a he
α
-
β
in e ace. A ew o oids we e also
de ec ed in he
α
g ains and a he
α
-
β
in e aces. Figu e
9 shows a mic oc ack gene a ed and g own a he
β
g ain
bounda y whe e he miso ien a ion be ween he
β
1 and
β
2
g ains was app oxima ely 42° (Figs. 9(b) and 9(d)). The ips
o he mic oc ack a e a he iple poin s o
α
1-
β
1-
β
2 and
α
2-
β
1-
β
2, and he localized plas ic de o ma ion is gene a ed
in neighbo ing
α
1 and
α
2 g ains (Fig. 9(c)). The c-axis o
each
α
g ain is nea ly pe pendicula o he p incipal s ess
axis (Fig. 9(b)). The Schmid ac o s in he indi idual
α
g ains a e high as M=0.46 (in
α
1) and M=0.48 (in
α
2) o
he p isma ic slip sys em (Table 2) and M=0.07 and 0.05,
espec i ely, o he basal slip sys em.
3.3. G ow h o Mic oc acks in o
αα
G ains
Al hough mos o he mic oc acks in he
β
g ains we e
a es ed in he g ains, a ew o he mic oc acks we e
obse ed o ha e g own in o he neighbo ing
α
g ains.
Th ee mic oc acks (labeled as A, B and C in Fig. 10(a))
we e o med in indi idual
β
g ains. Mic oc ack A g ew in o
he neighbo ing g ains
α
3 and
α
4 (Fig. 10(b)). Acco ding
o he c ys allog aphic analysis, he mic oc ack g ew in o
he
α
3 g ain along i s p isma ic plane, which was inclined
Fig. 6. Disloca ion s uc u es in
α
g ains a e cyclic de o ma ion a 77 K wi h
σ
max = 978 MPa, N = 13 480 cycles.
Fig. 7. Disloca ions in
β
g ain o CS ma e ial a e cyclic de o ma ion: (a) 293 K,
σ
max = 513 MPa, N = 2 ×107 cycles,
no b oken, and (b) 77 K,
σ
max = 1 038 MPa, N = 6 590 cycles.
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ597
Fig. 8. Mic oc acks (indica ed by a ows) in he longi udinal sec ion benea h he ac u e su ace: (a) SEI (77 K,
σ
max =
995 MPa, N = 8 455 cycles), (b), (c) magni ied images indica ed in (a), and (d) SEI (77 K,
σ
max = 1 161 MPa,
N = 4 060 cycles).
Fig. 9. Mic oc ack (indica ed by an a ow) o med a he
β
-g ain bounda y in he longi udinal sec ion benea h he ac-
u e su ace (77 K,
σ
max = 995 MPa, N = 8 455 cycles): (a) SEI, (b) IPF o ien a ion map o (a), (c) KAM map o
he a ea indica ed in (b), and (d) miso ien a ion p o ile o line AB. (Online e sion in colo .)
o he p incipal s ess axis a app oxima ely 29° (see Table
3). Bo h he shea and ensile s esses on he c ack plane
we e ela i ely high. Mic oc ack A also g ew along he
10 10
{}
wis g ain bounda y be ween he g ains
α
4 and
α
9, which we e almos pe pendicula o he p incipal s ess
axis. The g ain
α
5 showed a c ys al o ien a ion ha was
almos iden ical o ha o g ain
α
4. Howe e , mic oc ack
B did no p opaga e in o he neighbo ing g ains
α
5 and
α
6. De o ma ion winning is supp essed as oxygen con en
inc eases. Howe e , 1122 1123
{}
comp essi e wins and

ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ 598
10 12 10 11
{}
ensile wins we e de ec ed in he g ains
α
6,
α
8, and
α
9 nea he mic oc ack ips, as shown in Fig. 10(b).
3.4. Localized Slips and Voids a
αα
-g ain Bounda ies
Figu e 11 shows a oid a he
α
-g ain bounda y. The
g ain
α
10 shown in Fig. 11(b) was o ien ed wi h a highe
p isma ic Schmid ac o (0.49). Fu he mo e, se e al p is-
ma ic slip bands de eloped he e. The g ain
α
11 was
o ien ed wi h p isma ic and basal Schmid ac o s o 0.42
and 0.25, espec i ely. The s ess concen a ion a he g ain
bounda y owing o he plana slip bands in
α
10 could
ha e gene a ed he oid. Al hough no mic oc acks we e
gene a ed a he oid, a localized p isma ic slip band was
emi ed om he oid in
α
11. Because he iaxial s ess
concen a ion ields we e de eloped a ound he oids, he
localized slip bands could ha e been de eloped by shea
s ess componen s. Howe e , no slip-o o he bands was
de ec ed unde any s ess le el.
Fig. 10. Mic oc ack (indica ed by an a ow) ha was o med a he
β
g ain bounda y and i s g ow h in o neighbo ing
α
g ains in he longi udinal sec ion benea h he ac u e su ace (77 K,
σ
max = 995 MPa, N = 8 455 cycles): (a)
SEI, (b) IPF o ien a ion map o (a). (Online e sion in colo .)
Fig. 11. Void o med a he
α
-g ain bounda y in he longi udinal sec ion benea h he ac u e su ace (293 K,
σ
max =
539 MPa, N = 1 166 619 cycles): (a) SEI and (b) IQ map. (Online e sion in colo .)
Table 2. Schmid ac o s o p isma ic slips o he
α
1 and
α
2
g ains neighbo ing he mic oc ack be ween
β
g ains
shown in Fig. 9 (
θ
: inclina ion o plane no mal o p inci-
pal s ess axis).
α
g ain Plane Slip sys em Schmid ac o , M
θ
(°)
α
1
P1
a
3
01 10 2110
()


0.08 6.8
P2
a
3
10 10 12 10
()


0.46 55.4
P3
a
3
1100 1 120
()


0.38 74.8
α
2
P4
a
3
01 10 2110
()


0.12 7.7
P5
a
3
10 10 12 10
()


0.48 52.8
P6  a
3
1100 1 120
()


0.36 67.3
Table 3. Schmid ac o s o p isma ic slip o he g ain
α
3 shown
in Fig. 10(b).
Plane Slip sys em Schmid ac o , M
θ
(°)
P7
a
3
01 10 2110
()


0.38 29.2
P8
a
3
10 10 12 10
()


0.44 35.9
P9
a
3
1100 1 120
()


0.06 86.4
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ599
4. Discussion
4.1. De o ma ion Modes
The dominan de o ma ion mode in
α
i anium is he
10 10 1120
{}
slip ope a ion (pa icula ly a lowe em-
pe a u es), and he glide p ocess is ma kedly plana . The
disloca ion mo emen s a e es ic ed o hei slip planes,
and c oss-slip om a p ism plane on o ano he is di icul .
He e ogeneous mic oplas ici y owing o plana slip and
es ic ed sys ems causes s ain incompa ibili y a a bound-
a y. A p ocess o s ess dis ibu ion be ween weak and
s ong g ains owing o s ain incompa ibili y may be he
cause o he gene a ion o (0001) mic oc acks in i anium
alloys unde a igue loading. Co-plana a ays in
α
g ains
may pass h ough he bounda y and in o he neighbo ing
g ain o be blocked a he g ain bounda y whe e s ain
incompa ibili y is de eloped. Because he ma e ial exhibi s
10 10
{}
ibe ex u e, a shea mode is likely o be de eloped
on bo h (0001) and 10 10
{}
planes by s ain incompa ibili y.
The elaxa ion unde he simple shea mode is mo e s aigh -
o wa d han ha unde he ension mode. Fu he mo e, he
localized slip on hose planes unde he simple shea mode
may assis he g ow h o mic oc acks. The e o e, he e ine-
men o he
α
-g ain s uc u e should be accompanied by a
andom dis ibu ion o g ain o ien a ion o an imp o emen
in he a igue s eng h o
α
and
α
-
β
ype i anium alloys in
which subsu ace c ack ini ia ion is dominan .
Al hough ewe de o ma ion wins we e de ec ed in he
α
g ains, 1122 1123
{}
in comp ession and 10 12 10 11
{}
in
ension we e ope a ed nea he mic oc ack ips (Fig. 10(b)).
In gene al, winning occu s in polyc ys alline
α
i anium
and i s alloys because o an inadequa e numbe o slip
sys ems o accommoda e an a bi a y plas ic s ain. Fou
winning modes ha e been epo ed in
α
i anium. He e,
10 12 10 11
{}
and 1121 1 126
{}
a e ex ension wins,
and he 1122 1123
{}
and 10 11 10 12
{}
a e con ac ion
wins.28,29) The p edominan winning mode a oom em-
pe a u e is he 10 12
{}
ensile win, which co esponds o
a o a ion o 85° a ound he axis. A 77 K, he amoun o
10 12
{}
winning inc eased conside ably, and he 1121
{}
ensile and 1122
{}
comp essi e wins we e also obse ed.30)
Because he 1121
{}
win can o m in egions comple ely
cons ained by su ounding g ains owing o a shea s ess
highe han a c i ical alue,31) he 1122 1123
{}
and
10 12 10 11
{}
ope a ions we e de ec ed in his expe imen .
These ope a ions elaxed he in e nal s ess no mal o he
(0001).
4.2. Mic oc acks in
ββ
G ains
Less a en ion has been paid o he ole o he
β
phase in
subsu ace a igue c ack ini ia ion. Ruppen e al.4) p oposed
ha he piled-up disloca ions in
α
-g ain-induced slip in he
neighbo ing
β
phase and he o ma ion o a Co ell clea age
kni e {001} in he
β
phase p o ided a si e o subsu ace
c ack ini ia ion. Howe e , no expe imen al e idence o
clea age c acking has been epo ed. A quali a i e mic o-
mechanical model was also p oposed in which mic oc acks
we e gene a ed in a specimen’s in e io by he coalescence
o shea -induced ca i ies o med a he
α
-
β
in e aces along
localized slip bands.32) Howe e , ca i y nuclea ion was
de ec ed in a lamella s uc u e wi h hin
β
la hs unde high
applied s ess.
Void (o mic oc ack) nuclea ion in
β
g ains was de ec ed
a he
α
-
β
in e aces. I de eloped s ain incompa ibili y
be ween a eco e ed
α
(so ) g ain and a ec ys allized
α
(ha d) g ain in he c oss- olled Ti–Fe–O alloy a e cyclic
de o ma ion.25) The s ain incompa ibili y be ween ec ys al-
lized
α
g ains and
β
g ains could ha e induced mic oc ack
(o oid) nuclea ion, and he ea angemen o disloca-
ions in he neighbo ing eco e ed
α
-g ains enhanced he
s ain incompa ibili y. In he p esen s udy, a conside able
numbe o mic oc acks in
β
g ains we e de ec ed in highly
s ained egions such as nea he ac u e su ace. This is
no wi hs anding ha ew combina ions o so -
α
-g ain-
β
-g ain-ha d-
α
-g ain we e o med in he ma e ial because
o he ibe ex u e. The mic oc ack gene a ed a he iple
poin o
α
-
β
1-
β
2 could ha e p opaga ed along he
β
g ain
bounda y, as shown in Fig. 8(d). The densi y o disloca ions
in he
β
g ains as shown in Fig. 7 was highe han ha in
he
α
g ains.33) Because he hickness o
β
g ains was la ge
han ha o he c oss- olled ma e ial,25) he longe mean
ee slip leng h in he
β
phase could ha e induced a highe
local s ess concen a ion a he
α
-
β
in e ace, pa icula ly
a he iple poin o
α
-
β
1-
β
2 (see Fig. 9). This could ha e
caused he mic o oid gene a ion a he iple poin . The eby,
he opening s ess on he
β
g ain bounda y ha is nea ly
pe pendicula o he loading di ec ion could ha e assis ed
he mic oc ack g ow h om he mico oid, as illus a ed in
Fig. 12. Figu e 13 shows he o ien a ions o he indi idual
β
g ains in which oids we e de ec ed. The dis ibu ed
β
g ains de ia ed om <111> because o he high Schmid
Fig. 12. Schema ic illus a ion o mic oc ack g ow h a
β
-g ain
bounda y om he mic o oid a iple poin .
Fig. 13. O ien a ion dis ibu ion o indi idual oids de ec ed in
β
g ains. (Online e sion in colo .)
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ 600
ac o s o he {011}<111> slip. Mos o he mic oc acks
o med a he
β
g ain bounda ies e ealed a miso ien a ion
o 40°–60°, as shown in Fig. 13. Fu he mo e, Young’s
modulus o
β
-Ti alloys is lowe han ha o
α
-Ti (e.g.
app oxima ely 106 GPa o comme cially pu e i anium),
al hough Young’s modulus depends on he alloy composi-
ion.34) A he elas ic o plas ic de o ma ion s age, he p is-
ma ic slip sys ems in
α
phase we e ac i a ed p e e en ially
a he han slip sys ems in
β
phase owing o lowe CRSS.35)
The s ess in he
α
phase hen eleases and ans e s o he
β
phase. I also suppo s he local yielding in he
β
phase in
he low plas ic-s ain egime.
4.3. In luenceo Tex u eonMic oc ackGene a ion
The s ess concen a ion by he mic oc acks de eloped a
he
β
-g ain bounda y may igge (0001) mic oc acking in
he neighbo ing
α
g ain. Al hough (0001)
α
mic oc acks con-
s i u ed he main c ack in he c oss- olled ma e ial,25) ew
(0001)
α
mic oc acks we e de ec ed in he p esen ma e ial.
The subsu ace c ack ini ia ion si es (pa icula ly a 77 K)
consis ed mos ly o 10 10
{}
α
ace s and we e a he de oid
o (0001)
α
ace s.24) The
α
mic os uc u e in he p esen
ma e ial showed a weak 10 10
{}
ibe ex u e, and he c-axis
o he
α
g ains we e andomly dis ibu ed and we e nea ly
pe pendicula o he p incipal s ess axis. The e o e, bo h he
shea s ess and no mal s ess on he basal plane we e low,
and negligible (0001)
α
mic oc acking could be gene a ed in
he neighbo ing g ain. Al hough a (0001)
α
mic oc ack p o-
ides a s ess ield wi h mul iaxial modes in he neighbo ing
g ain, he combina ion o shea s ess and opening s ess on
10 10
{}
α
may also esul in Mode II o III mic oc acking.
The localized shea s ess as well as he opening (Mode I)
s ess owing o he p incipal s ess is likely o ha e caused
he mic oc ack g ow h on he p isma ic plane in he neigh-
bo ing g ain. In addi ion, Ban ounas e al.12) obse ed ha
α
g ains whose main c-axis ex u e componen was almos
pe pendicula o he loading di ec ion unc ioned as ba -
ie s o ace ed c ack g ow h. Then, 10 10
{}
α
ace s may
appea ,24) and he modi ied mic os uc u e o small
α
-g ains
wi h c-axis andomly dis ibu ed no mal o he loading axis
p e en s he g ow h o (0001)
α
ace .
Bo h su ace and subsu ace c acks o med along a p is-
ma ic plane in
α
g ains o ien ed wi h a e y high Schmid
ac o ha e been epo ed o unc ion as ini ia ion si es.5,21,36)
The mic oc ack o med along a p isma ic plane was in an
α
g ain and p opaga ed negligibly o he neighbo ing g ain.21)
Tha is, he p isma ic c ack o ma ion is consis en wi h he
su ace oughening mechanism a he han he ace o ma-
ion in he specimen in e io . Sacke e al.19) obse ed ha
p isma ic c acks in he in e io o a specimen we e almos
pe pendicula o he ensile loading di ec ion. This can be
explained by he s ess edis ibu ion models such as he
E ans-Bache model.19) In he p e ious s udy,24) he models
o ming 10 10
{}
α
ace o ace s we e p oposed, whe e he
(0001)
α
ace may gi e a igge o gene a e he subsu ace
c ack ini ia ion si e wi h 10 10
{}
α
ace s. In he p esen
wo k, he mic oc acks in he
β
g ains p opaga ed negligibly
in o hei neighbo ing
α
g ains, al hough hey displayed a
high Schmid ac o (see he g ains
α
1 and
α
2 in Fig. 9 and
Table 2). In addi ion, no mic oc acks we e de ec ed on he
p isma ic plane ha was nea ly pe pendicula o he loading
axis. Howe e , mic oc acks we e de ec ed a he 10 10
{}
α
wis bounda y and on he p isma ic planes inclined o he
loading axis, as shown in Fig. 10. Conside ing he edis ib-
u ed shea s ess caused by he s ess concen a ion a ound
he
β
-g ain mic oc ack and he s ain incompa ibili y a he
Fig. 14. Schema ic illus a ion o subsu ace a igue c ack ini ia ion: (a) a model based on he subc ack obse a ion and
(b) a modi ied model a 77 K in e . 24). (Online e sion in colo .)
ISIJ In e na ional, Vol. 62 (2022), No. 3
© 2022 ISIJ601
α
-g ain bounda y, he local p isma ic slip in he neighbo ing
g ain should be selec ed on he p isma ic plane wi h a high
Schmid ac o . Howe e , he in ense p isma ic slip o slip-
o in he neighbo ing g ain may ha e caused he mic oc ack
g ow h. The e o e, a combina ion o high ensile s ess and
shea s ess on he p isma ic plane is necessa y o
β
-g ain
mic oc ack p opaga ion. Thus, a simple explana ion o he
10 10
{}
α
ace o ma ion model is p oposed, as shown in
Fig. 14(a). When he inclined 10 10
{}
α
mic oc ack g ows
in he
α
1 g ain o i s bounda y, he mic oc ack may p opa-
ga e in o he neighbo ing
α
2 g ain along he p isma ic plane
because o he c oss slip. The combina ion o shea s ess
(Mode II o III) and opening s ess (Mode I) on 10 10
{}
α
may esul in mic oc acking on he p isma ic plane, which
is nea ly pe pendicula o he loading axis.
Because de o ma ion cons ain s in he
α
g ains on he
specimen su ace a e mo e lexible han he in e nal ones,
s ain incompa ibili y may be in oduced nea he speci-
men su ace. In ou p e ious wo k, we discussed a model
o subsu ace c ack ini ia ion based on he ac og aphical
analysis, whe e he ole o he
β
phase was omi ed.23) In he
model, he sc ew disloca ions o 10 10 1120
{}
pile-ups in
an
α
-g ain nea he specimen su ace in oduce he mic o-
c acking by (0001)
α
slip-o , as shown in Fig. 14(b). He ein,
he
β
mic oc ack may assis in he o ma ion o he shea
s ess on (0001)
α
. Because he (0001)
α
mic oc ack also p o-
ides a s ess ield wi h mul iaxial modes in he neighbo ing
g ain, he combina ion o shea s ess and opening s ess on
10 10
{}
α
esul in Mode II o III mic oc acking.
5. Conclusions
The cha ac e is ics o subc acks in Ti–Fe–O alloy o med
by high-cycle a igue a low empe a u e we e in es iga ed.
The phenomenological de ails o mic oc ack gene a ion,
pa icula ly he igge and beginning o he mic oc ack, a e
cla i ied as ollows:
(1) Mos o he mic oc acks we e in
β
g ains and a ew
p opaga ed in o
α
g ains along he p isma ic plane. A ew
oids we e p esen in he
α
g ains and a he
α
-
β
in e aces.
(2) The s ess concen a ion a ound he mic oc acks in
he
β
g ains assis s mic oc acking on he 10 10
{}
α
ace .
(3) The combina ion o shea s ess and opening s ess
on 10 10
{}
α
esul s in Mode II o III mic oc acking on he
p isma ic plane, which is pe pendicula o he loading axis.
Fu he mo e, he 10 10
{}
α
ex u e signi ican ly assis s mic o-
c ack g ow h on he 10 10
{}
α
plane.
Acknowledgmen
This pape was suppo ed by p ojec No. CZ.02.1.01/0.0/
0.0/17_049/0008441, “Inno a i e The apeu ic Me hods o
Musculoskele al Sys em in Acciden Su ge y” wi hin he
Ope a ional P og amme Resea ch, De elopmen and Educa-
ion inanced by he Eu opean Union and by he s a e budge
o he Czech Republic.
REFERENCES
1) O. Umezawa and K. Nagai: ISIJ In ., 37 (1997), 1170. h ps://doi.
o g/10.2355/isijin e na ional.37.1170
2) W. Li and O. Umezawa: Key Eng. Ma e ., 741 (2017), 76. h ps://doi.
o g/10.4028/www.scien i ic.ne /KEM.741.76
3) A. L. Pilchak, R. E. A. Williams and J. C. Williams: Me all. Ma e .
T ans. A, 41 (2010), 106. h ps://doi.o g/10.1007/s11661-009-0064-2
4) J. Ruppen, P. Bhowal, D. Eylon and A. J. McE ily: Fa igue Mecha-
nisms, ASTM STP 675, ed. by J. Fong, Ame ican Socie y o Tes -
ing and Ma e ials, Philadelphia, (1979), 47. h ps://doi.o g/10.1520/
STP35884S
5) I. Ban ounas, D. Dye and T. C. Lindley: Ac a Ma e ., 57 (2009),
3584. h ps://doi.o g/10.1016/j.ac ama .2009.04.018
6) M. R. Bache, M. Cope, H. M. Da ies, W. J. E ans and G. Ha ison:
In . J. Fa igue, 19 (1997), Suppl. 1, S83. h ps://doi.o g/10.1016/
S0142-1123(97)00020-0
7) V. Sinha, M. J. Mills and J. C. Williams: Me all. Ma e . T ans. A, 37
(2006), 2015. h ps://doi.o g/10.1007/s11661-006-0144-5
8) Y. Mine, S. Ka ashima, R. Ding, P. Bowen and K. Takashima: Sc .
Ma e ., 165 (2019), 107. h ps://doi.o g/10.1016/j.sc ip ama .2019.02.029
9) O. Umezawa, K. Nagai and K. Ishikawa: Ma e . Sci. Eng. A, 129
(1990), 223. h ps://doi.o g/10.1016/0921-5093(90)90269-9
10) H. Yokoyama, O. Umezawa, K. Nagai, T. Suzuki and K. Kokubo:
Me all. Ma e . T ans. A, 31 (2000), 2793. h ps://doi.o g/10.1007/
BF02830339
11) I. Ban ounas, D. Dye and T. C. Lindley: Ac a Ma e ., 58 (2010),
3908. h ps://doi.o g/10.1016/j.ac ama .2010.03.036
12) I. Ban ounas, T. C. Lindley, D. Rugg and D. Dye: Ac a Ma e ., 55
(2007), 5655. h ps://doi.o g/10.1016/j.ac ama .2007.06.034
13) K. Le Bia an , S. Pommie and C. P ioul: Fa igue F ac . Eng.
Ma e . S uc ., 25 (2002), 527. h ps://doi.o g/10.1046/j.1460-
2695.2002.00480.x
14) C. J. Szczepanski, S. K. Jha, J. M. La sen and J. W. Jones: Me all.
Ma e . T ans. A, 39 (2008), 2841. h ps://doi.o g/10.1007/s11661-
008-9633-z
15) M. R. Bache, W. J. E ans and H. M. Da ies: J. Ma e . Sci., 32
(1997), 3435. h ps://doi.o g/10.1023/A:1018624801310
16) M. R. Bache: In . J. Fa igue, 25 (2003), 1079. h ps://doi.o g/10.1016/
S0142-1123(03)00145-2
17) A. N. S oh: P oc. R. Soc. Lond. A, 223 (1954), 404. h ps://doi.
o g/10.1098/ spa.1954.0124
18) M. R. Bache, W. J. E ans, B. Suddell and F. R. M. He ouin: In .
J. Fa igue, 23 (2001), Suppl. 1, 153. h ps://doi.o g/10.1016/S0142-
1123(01)00124-4
19) E. E. Sacke , L. Ge main and M. R. Bache: In . J. Fa igue, 29 (2007),
2015. h ps://doi.o g/10.1016/j.ij a igue.2006.12.011
20) W. J. E ans and M. R. Bache: In . J. Fa igue, 16 (1994), 443. h ps://
doi.o g/10.1016/0142-1123(94)90194-5
21) F. B idie , P. Villechaise and J. Mendez: Ac a Ma e ., 56 (2008),
3951. h ps://doi.o g/10.1016/j.ac ama .2008.04.036
22) O. Umezawa, K. Nagai and K. Ishikawa: Te su- o-Hagané, 76 (1990),
924 (in Japanese). h ps://doi.o g/10.2355/ e su ohagane1955.76.6_924
23) O. Umezawa and K. Ishikawa: Ma e . Sci. Eng. A, 176 (1994), 397.
h ps://doi.o g/10.1016/0011-2275(92)90353-C
24) O. Umezawa, T. Yuasa and W. Li: ISIJ In ., 58 (2018), 1332. h ps://
doi.o g/10.2355/isijin e na ional.ISIJINT-2017-673
25) W. Li, O. Umezawa and N. Koga: ISIJ In ., 58 (2018), 359. h ps://
doi.o g/10.2355/isijin e na ional.ISIJINT-2017-514
26) K. Kishida, J. G. Kim, T. Nagae and H. Inui: Ac a Ma e ., 196 (2020),
168. h ps://doi.o g/10.1016/j.ac ama .2020.06.043
27) M. Mo i a and O. Umezawa: Ma e . T ans., 52 (2011), 1595. h ps://
doi.o g/10.2320/ma e ans.L-M2011815
28) M. H. Yoo: Me all. T ans. A, 12 (1981), 409. h ps://doi.o g/10.1007/
BF02648537
29) L. Wang, Y. Yang, P. Eisenloh , T. R. Biele , M. A. C imp and
D. E. Mason: Me all. Ma e . T ans. A, 41 (2010), 421. h ps://doi.
o g/10.1007/s11661-009-0097-6
30) S. Mahajan: Encyclopedia o Ma e ials: Science and Technology (2nd
ed.), ed. by K. H. J. Buschow e al., Else ie , Ams e dam, (2002), 1.
h ps://doi.o g/10.1016/b0-08-043152-6/01809-x
31) C. J. Bee e s and M. D. Halliday: Me . Sci. J., 3 (1969), 74. h ps://
doi.o g/10.1179/msc.1969.3.1.74
32) P. Le anc, V. Doque , M. Ge land and C. Sa azin-Baudoux: Ac a
Ma e ., 56 (2008), 4450. h ps://doi.o g/10.1016/j.ac ama .2008.04.060
33) W. Li and O. Umezawa: P oc. 13 h Wo ld Con . on Ti anium, ed. by
V. Venka esh e al., TMS, Wa endale, PA, (2016), 843. h ps://doi.
o g/10.1002/9781119296126.ch144
34) T. Ozaki, H. Ma sumo o, S. Wa anabe and S. Hanada: Ma e . T ans.,
45 (2004), 2776. h ps://doi.o g/10.2320/ma e ans.45.2776
35) R. Shi, Z. Nie, Q. Fan and G. Li: J. Alloy. Compd., 688 (2016), 787.
h ps://doi.o g/10.1016/j.jallcom.2016.07.105
36) J. E e ae s, D. Gon cha o , B. Ve linden and M. We e s: In . J.
Fa igue, 98 (2017), 203. h ps://doi.o g/10.1016/j.ij a igue.2017.01.043