ma e ials
A icle
The E ec o P ede o ma ion on C eep S eng h o
9% C S eel
Pe K ál1,* , Jiˇ íD oˇ ák1, Wol gang Blum 2, Václa Skleniˇcka 1, Zenji Ho i a 3,4,5,
Yoichi Takizawa 6, Yongpeng Tang 7, Lenka Kunˇcická1, Radim Kocich 8, Ma ie K apilo á1
and Ma ie S obodo á9
1Ins i u e o Physics o Ma e ials, Academy o Sciences o he Czech Republic,
Zizko a 22, 616 62 B no, Czech Republic; [email p o ec ed] (J.D.); [email p o ec ed] (V.S.);
[email p o ec ed] (L.K.); [email p o ec ed] (M.K.)
2Depa men o Ma e ials Science, Ins i u e I, Uni e si y o E langen-Nu embe g,
D-91058 E langen, Ge many; [email p o ec ed]
3Depa men o Ma e ials Science, Kyushu Ins i u e o Technology, Ki akyushu 804-8550, Japan;
[email p o ec ed]
4Magnesium Resea ch Cen e , Kumamo o Uni e si y, Kumamo o 860-8555, Japan
5Synch o on Ligh Applica ion Cen e , Saga Uni e si y, Saga 840-8502, Japan
6Technology Depa men , Nagano Fo ging Co., L d., Nagano 381-0003, Japan; [email p o ec ed]
7Wo ld P emie In e na ional Resea ch Ini ia i e,
In e na ional Ins i u e o Ca bon-Neu al Ene gy Resea ch (WPI-I2CNER), Kyushu Uni e si y,
Fukuoka 819-0395, Japan; [email p o ec ed]
8Facul y o Ma e ials Science and Technology, Technical Uni e si y o Os a a,
17. Lis opadu 15, 708 00 Os a a, Czech Republic; [email p o ec ed]
9UJP PRAHA a.s., 156 10 P aha-Zb asla , Czech Republic; [email p o ec ed]
*Co espondence: [email p o ec ed]
Recei ed: 2 No embe 2020; Accep ed: 23 No embe 2020; Published: 25 No embe 2020


Abs ac :
Ma ensi ic c eep- esis an P92 s eel was de o med by di e en me hods o se e e plas ic
de o ma ion such as o a ion swaging, high-p essu e sliding, and high-p essu e o sion a oom
empe a u e. These me hods imposed signi ican ly di e en equi alen plas ic s ains o abou
1–30. I was ound ha o a ion swaging led o o ma ion o he e ogeneous mic os uc u es wi h
elonga ed g ains whe e low-angle g ain bounda ies p edomina ed. O he me hods led o o ma ion
o ul a ine-g ained (UFG) mic os uc u es wi h high equency o high-angle g ain bounda ies.
Cons an load ensile c eep es s a 873 K and ini ial s esses in he ange o 50 o 300 MPa e ealed
ha he specimens p ocessed by o a ion swaging exhibi ed one o de o magni ude lowe minimum
c eep a e compa ed o s anda d P92 s eel. By con as , UFG P92 s eel is signi ican ly so e han
s anda d P92 s eel, bu di e ences in hei s eng hs dec ease wi h inc easing s ess. Mic os uc u al
esul s sugges ha c eep beha io o P92 s eel p ocessed by se e e plas ic de o ma ion is in luenced
by he equency o high-angle g ain bounda ies and g ain coa sening du ing c eep.
Keywo ds: c eep- esis an 9% C s eels; se e e plas ic de o ma ion; mic os uc u e
1. In oduc ion
Sligh p ede o ma ion (up o 0.2) o ma e ials can cause bo h imp o emen and de e io a ion o
c eep p ope ies [
1
]. In es iga ion o c eep beha io o p ede o med hea esis an aus eni ic s eels
e ealed ha he e ec o p ede o ma ion on c eep beha io depends on de o ma ion mode. I was
demons a ed ha p ede o ma ion in ension leads o imp o emen o c eep esis ance [
2
]. Howe e ,
he opposi e e ec was ound a e applica ion o comp ession p ede o ma ion [
1
]. De e io a ion o
Ma e ials 2020,13, 5330; doi:10.3390/ma13235330 www.mdpi.com/jou nal/ma e ials
Ma e ials 2020,13, 5330 2 o 17
c eep p ope ies was also obse ed in 2.25C –1Mo e i ic s eel p ocessed by ension p ede o ma ion a
873 K. Kikuchi and Ilschne [
3
] in es iga ed he e ec o 1% p ede o ma ion a di e en empe a u es
on c eep and e ealed ha he highe he p ede o ma ion empe a u e, he smalle he di e ence in
c eep esis ance wi h espec o he unde o med s a e.
Simila esul s we e ound in P92 s eel p ocessed by ho bending a 1193–1233 K and subsequen
c eep a 873 K. I was shown [
4
] ha ho bending caused insigni ican di e ences in c eep s eng h
alling wi hin a sca e band o he unben pipe. Howe e , insigni ican di e ences in c eep s eng h o
9% o C s eels we e obse ed a e cold bending [5].
F. Abe [
6
] in es iga ed c eep beha io o P91 s eel a 873 K and 78 MPa a e cold olling wi h
plas ic s ains o 0.2 and 0.4. I was ound ha ime o ac u e dec eases wi h inc easing cold
olling de o ma ion.
Cu en me hods o se e e plas ic de o ma ion (SPD) allow signi ican ly la ge s ain o be
imposed in compa ison wi h s anda d o ming me hods such as olling o bending [
7
–
9
]. In he case
whe e ex emely la ge de o ma ion is imposed o he ma e ial, ans o ma ion o a coa se-g ained
s uc u e o an ul a ine-g ained one (g ain size 0.1–1
µ
m) occu s [
7
]. Ne e heless, ans o ma ion o
he mic os uc u e using SPD me hods p oceeds subsequen ly. A he beginning o he ans o ma ion,
he mic os uc u e con ains, in pa icula , cell walls con aining angles wi h e y high disloca ion
densi y. The u he de o ma ion leads o subsequen inc easing o miso ien a ion be ween cells and
o ma ion o an ul a ine-g ained mic os uc u e. Thus, he mic os uc u es o med by SPD con ain
a ious p opo ions o low-angle (LA) and high-angle (HA) g ain bounda ies (GB), depending on he
le el o imposed plas ic s ain. Fo his eason, SPD echniques p o ide a unique oppo uni y o s udy
he in luence o signi ican ly di e en mic os uc u es on c eep beha io o me als. Recen esul s
showed ha di e ences in he c eep s eng h o SPD-p ocessed s a e and i s unde o med coun e pa
depend on he alue o plas ic s ain imposed in o he ma e ial [
10
–
14
], empe a u e, and applied s ess
used du ing c eep es ing [15–17].
The aim o his wo k is o s udy he in luence o p ede o ma ion on c eep s eng h and he
mic os uc u e o P92 p ocessed by se e e plas ic de o ma ion (SPD), wi h equi alen s ains anging
om 1 o 20.
2. Ma e ials and Me hods
The expe imen al ma e ial used in he p esen wo k was ad anced ungs en-modi ied ma ensi ic
9%C P92 s eel. The chemical composi ion o P92 s eel (w .%) was as ollows: 0.11C, 8.58C , 0.33Mo,
1.67W, 0.37Si, 0.48Mn, 0.23V, 0.06Nb, 0.013P, 0.037N, 0.005S, 0.0015B, and 0.017Al. Hea ea men o
he as- ecei ed coa se-g ained (CG) s a e consis ed o no maliza ion a 1323 K o 60 min, ollowed by
empe ing a 1013 K o 140 min [4].
Discs o 30 mm diame e and 1.1 mm hickness and shee s wi h dimensions o 10
×
100
×
1.1 mm
3
we e cu om he as- ecei ed and ela i ely coa se-g ained P92 s eel (CG). The discs we e p ocessed
by 1 o a ion high-p essu e o sion (HPT) a oom empe a u e unde he p essu e o 6 GPa and
o a ion speed o 0.1 mm pe second. The shee s we e p ocessed by high-p essu e sliding (HPS) a
oom empe a u e wi h a sliding dis ance o 5 mm (HPS5) and 15 mm (HPS15) unde he p essu e o
4 GPa. The alue o on Mises equi alen s ain du ing HPT [
7
] g ows wi h he dis ance, , om he
cen e o he disc acco ding o
εSPD =
2
π N/√3
whe e Nis he numbe o u ns and is he hickness
o disc. The alue o on Mises equi alen s ain du ing he HPS p ocess [
18
] was es ima ed as
εSPD =x
√3
, whe e xis he sliding dis ance o he plunge wi h espec o he an il and is he hickness
o he sample.
The equi alen s ain imposed by o a ion swaging (RS) [
19
,
20
] was es ima ed by
εSPD
=ln(D
0
/D
n
)
2
,
whe e D
0
is he ini ial diame e ~30 mm and D
n
is he inal diame e ~15 mm a e applica ion o RS
a oom empe a u e. The alues o equi alen s ain
εSPD
imposed by selec ed me hods o SPD a e
shown in Table 1.
Ma e ials 2020,13, 5330 3 o 17
Table 1. P ede o ma ion (εSPD) imposed by me hods o se e e plas ic de o ma ion (SPD).
Ma e ial S a e o P92 S eel RS HPS5 HPS15 HPT
εSPD 1.4 2.6 7.9 25 ±5
Cons an load ensile c eep es s we e conduc ed a 873 K (~0.48 o mel ing empe a u e) in
p o ec i e a gon a mosphe e using la specimens wi h a gauge leng h o 10 mm and a c oss sec ion o
3
×
1 mm
2
. The es ed HPT specimens we e manu ac u ed om he disc egion wi h equi alen s ain
o abou 25
±
5 [
12
,
21
]. The gauge leng hs o he HPS ensile specimens we e aken om he cen al
pa o he shee .
Mic os uc u e in es iga ions we e pe o med in a scanning elec on mic oscope (SEM, Tescan
Ly a 3, (B no, Czech Republic), equipped wi h No dlysNano EBSD (High Wycombe, UK) de ec o
ope a ing a accele a ing ol age o 20 kV wi h specimen il ed a 70
◦
) and a ansmission elec on
mic oscope (TEM, JEOL 2100F, Tokyo, Japan). SEM was used o de e mine he miso ien a ions
θ
be ween neighbo ing g ains.
θ
=15
◦
was aken o dis inguish HAGBs om LAGBs consis en wi h
p e ious wo ks [
10
–
12
]. The mean spacing o LAGBs along es lines is called w, and he mean spacing
o HAGBs is called d. The ac ion o HAGBs is es ima ed as HAGB =w/d.
3. Resul s
3.1. Mic os uc u e be o e C eep
In he ollowing sec ion we epo mic os uc u al de ails o he P92 a ian s in es iga ed in his
wo k ega ding g ains and hei o ien a ions (Figu e 1), g ain miso ien a ions (Figu e 2), and bounda y
spacings (Figu e 3). They a y depending on he s ain
εSPD
applied du ing SPD (Figu e 3). As usual,
he as- ecei ed s a e CG consis s o p io aus eni e g ains con aining la hs bounda ies and o he LA
subg ain bounda ies (no isible in Figu e 1) in hei in e io s esul ing om ma ensi ic ans o ma ion.
The mic os uc u e o as- ecei ed s a e esul s om no maliza ion a 1323 K o 60 min in ai and
subsequen empe ing a 1013 K o 140 min.
Ma e ials 2020, 13, x FOR PEER REVIEW 3 o 19
Table 1. P ede o ma ion (εSPD) imposed by me hods o se e e plas ic de o ma ion (SPD).
Ma e ial S a e o P92 S eel RS HPS5 HPS15 HPT
εSPD 1.4 2.6 7.9 25 ± 5
Cons an load ensile c eep es s we e conduc ed a 873 K (~0.48 o mel ing empe a u e) in
p o ec i e a gon a mosphe e using la specimens wi h a gauge leng h o 10 mm and a c oss sec ion
o 3 × 1 mm2. The es ed HPT specimens we e manu ac u ed om he disc egion wi h equi alen
s ain o abou 25 ± 5 [12,21]. The gauge leng hs o he HPS ensile specimens we e aken om he
cen al pa o he shee .
Mic os uc u e in es iga ions we e pe o med in a scanning elec on mic oscope (SEM, Tescan
Ly a 3, (B no, Czech Republic), equipped wi h No dlysNano EBSD (High Wycombe, UK) de ec o
ope a ing a accele a ing ol age o 20 kV wi h specimen il ed a 70°) and a ansmission elec on
mic oscope (TEM, JEOL 2100F, Tokyo, Japan). SEM was used o de e mine he miso ien a ions θ
be ween neighbo ing g ains. θ = 15° was aken o dis inguish HAGBs om LAGBs consis en wi h
p e ious wo ks [10–12]. The mean spacing o LAGBs along es lines is called w, and he mean spacing
o HAGBs is called d. The ac ion o HAGBs is es ima ed as HAGB = w/d.
3. Resul s
3.1. Mic os uc u e be o e C eep
In he ollowing sec ion we epo mic os uc u al de ails o he P92 a ian s in es iga ed in
his wo k ega ding g ains and hei o ien a ions (Figu e 1), g ain miso ien a ions (Figu e 2), and
bounda y spacings (Figu e 3). They a y depending on he s ain εSPD applied du ing SPD (Figu e 3).
As usual, he as- ecei ed s a e CG consis s o p io aus eni e g ains con aining la hs bounda ies and
o he LA subg ain bounda ies (no isible in Figu e 1) in hei in e io s esul ing om ma ensi ic
ans o ma ion. The mic os uc u e o as- ecei ed s a e esul s om no maliza ion a 1323 K o 60
min in ai and subsequen empe ing a 1013 K o 140 min.
Figu e 1. Con .
Ma e ials 2020,13, 5330 4 o 17
Ma e ials 2020, 13, x FOR PEER REVIEW 4 o 19
Figu e 1. G ain mic os uc u e (o ien a ion con as wi h high-angle g ain bounda ies (HAGB) only,
no mal di ec ion (ND) and ex u e (poles o {110} planes) a oom empe a u e be o e c eep o (a) as-
ecei ed coa se-g ained (CG), (b) o a ion swaging (RS), and (c) high-p essu e sliding, HPS5 and (d)
HPS15; high-p essu e o sion (HPT) is simila o HPS15. Rolling di ec ions (RD) a e pa allel wi h he
pipe axis in CG s a e and shea di ec ion in SPD-p ocessed s a es.
RS has a he e ogeneous g ain s uc u e wi h bands o ine nea ly equiaxed submic on g ains and
la ge g ains exceeding 30 μm ha a e signi ican ly elonga ed pa allel o he di ec ion o swaging. The
g ain s uc u e o HPS5 is also ela i ely coa se bu mo e homogeneous. HPS15 has much mo e
e ined g ains simila o HPT.
Figu e 2. Miso ien a ion: cumula i e equency (F) o bounda ies wi h miso ien a ions θ in CG (as-
ecei ed) and p ede o med P92. In e sec ion wi h he dashed line θ = 15° gi es he low-angle g ain
bounda ies (LAGB) ac ion 𝑓 =𝐹(15°).
Figu e 1.
G ain mic os uc u e (o ien a ion con as wi h high-angle g ain bounda ies (HAGB) only,
no mal di ec ion (ND) and ex u e (poles o {110} planes) a oom empe a u e be o e c eep o
(
a
) as- ecei ed coa se-g ained (CG), (
b
) o a ion swaging (RS), and (
c
) high-p essu e sliding, HPS5 and
(
d
) HPS15; high-p essu e o sion (HPT) is simila o HPS15. Rolling di ec ions (RD) a e pa allel wi h
he pipe axis in CG s a e and shea di ec ion in SPD-p ocessed s a es.
Ma e ials 2020, 13, x FOR PEER REVIEW 4 o 19
Figu e 1. G ain mic os uc u e (o ien a ion con as wi h high-angle g ain bounda ies (HAGB) only,
no mal di ec ion (ND) and ex u e (poles o {110} planes) a oom empe a u e be o e c eep o (a) as-
ecei ed coa se-g ained (CG), (b) o a ion swaging (RS), and (c) high-p essu e sliding, HPS5 and (d)
HPS15; high-p essu e o sion (HPT) is simila o HPS15. Rolling di ec ions (RD) a e pa allel wi h he
pipe axis in CG s a e and shea di ec ion in SPD-p ocessed s a es.
RS has a he e ogeneous g ain s uc u e wi h bands o ine nea ly equiaxed submic on g ains and
la ge g ains exceeding 30 μm ha a e signi ican ly elonga ed pa allel o he di ec ion o swaging. The
g ain s uc u e o HPS5 is also ela i ely coa se bu mo e homogeneous. HPS15 has much mo e
e ined g ains simila o HPT.
Figu e 2. Miso ien a ion: cumula i e equency (F) o bounda ies wi h miso ien a ions θ in CG (as-
ecei ed) and p ede o med P92. In e sec ion wi h he dashed line θ = 15° gi es he low-angle g ain
bounda ies (LAGB) ac ion 𝑓 =𝐹(15°).
Figu e 2.
Miso ien a ion: cumula i e equency Fo bounda ies wi h miso ien a ions
θ
in CG
(as- ecei ed) and p ede o med P92. In e sec ion wi h he dashed line
θ
=15
◦
gi es he low-angle g ain
bounda ies (LAGB) ac ion HAGB =F(15◦).
Ma e ials 2020,13, 5330 5 o 17
Ma e ials 2020, 13, x FOR PEER REVIEW 5 o 19
Figu e 1 shows a sligh endency in CG o o ien a e {101} c ys allog aphic planes nea ly pa allel
o he pipe axis, which is iden ical o he s ess axis du ing c eep es ing. The mic os uc u e o he
RS s a e con ains a s ong ibe ex u e {hkl}<101> pa allel o he swaging axis (Figu e 1b).
The HPS-p ocessed specimens (Figu e 1c,d) exhibi ed a ibe ex u e <110> pe pendicula o he
shea di ec ion o HPS wi h {110}<111> and {110}<100> s ongly p onounced a ian s. A simila
ex u e was also obse ed in he HPT-p ocessed specimens [21].
Figu e 3. Bounda y spacings d and
w
e sus equi alen SPD s ain (εSPD) (a) a e SPD and (b) a e
annealing; CG da a a e displayed a εSPD = 0.6 o compa ison easons; he e ical ex ension o shaded
a ea sh inks wi h inc easing 𝑓.
Figu e 2 displays he cumula i e equency (F) o b ounda ies wi h miso ien a ions up o θ. Fo
θ = 15°, F equals he LAGB ac ion 𝑓 ≡1−𝑓
. The s eep inclina ion o he GC cu e shows
p edominance o LAGBs wi h θ < 15° and HAGBs wi h high θ > 40° and a concen a ion nea Σ 3
(60°/111). A e SPD, such a gap in he dis ibu ion is missing. In RS and HPS5, HAGB is s ongly aised
by SPD-induced LAGB gene a ion. Wi h inc ease o εSPD, s ain-induced LABGs ge con e ed in o
HAGBs, and HAGB inc eases o 0.85 o HPT.
Figu e 3a isualizes he exis ing da a o he mean bounda y spacings in he in es iga ed
ma e ial a ian s a e SPD. The w- and d-lines a e no p ima ily p ecise i s o he limi ed esul s. The
Figu e 3.
Bounda y spacings dand w e sus equi alen SPD s ain (
εSPD
) (
a
) a e SPD (
b
) a e annealing;
CG da a a e displayed a
εSPD
=0.6 o compa ison easons; he e ical ex ension o shaded a ea
sh inks wi h inc easing HAGB.
RS has a he e ogeneous g ain s uc u e wi h bands o ine nea ly equiaxed submic on g ains
and la ge g ains exceeding 30
µ
m ha a e signi ican ly elonga ed pa allel o he di ec ion o swaging.
The g ain s uc u e o HPS5 is also ela i ely coa se bu mo e homogeneous. HPS15 has much mo e
e ined g ains simila o HPT.
Figu e 1shows a sligh endency in CG o o ien a e {101} c ys allog aphic planes nea ly pa allel o
he pipe axis, which is iden ical o he s ess axis du ing c eep es ing. The mic os uc u e o he RS
s a e con ains a s ong ibe ex u e {hkl}<101>pa allel o he swaging axis (Figu e 1b).
The HPS-p ocessed specimens (Figu e 1c,d) exhibi ed a ibe ex u e <110>pe pendicula o he
shea di ec ion o HPS wi h {110}<111>and {110}<100>s ongly p onounced a ian s. A simila
ex u e was also obse ed in he HPT-p ocessed specimens [21].
Figu e 2displays he cumula i e equency (F) o b ounda ies wi h miso ien a ions up o
θ
.
Fo
θ
=15
◦
,Fequals he LAGB ac ion
LAGB ≡
1
− HAGB
. The s eep inclina ion o he GC cu e
shows p edominance o LAGBs wi h
θ
<15
◦
and HAGBs wi h high
θ
>40
◦
and a concen a ion nea
Σ
3 (60
◦
/111). A e SPD, such a gap in he dis ibu ion is missing. In RS and HPS5,
HAGB
is s ongly
aised by SPD-induced LAGB gene a ion. Wi h inc ease o
εSPD
, s ain-induced LABGs ge con e ed
in o HAGBs, and HAGB inc eases o 0.85 o HPT.
Figu e 3a isualizes he exis ing da a o he mean bounda y spacings in he in es iga ed ma e ial
a ian s a e SPD. The w- and d-lines a e no p ima ily p ecise i s o he limi ed esul s. The w-line
wi h
w∝
1
/ε0.5
SPD
is mo i a ed by pa abolic wo k ha dening,
σ∝ε0.5
SPD
, du ing SPD a oom empe a u e
owa d he inal s a iona y (sa u a ion) s age and o ma ion o quasi-s a iona y subg ain s uc u es

Ma e ials 2020,13, 5330 6 o 17
wi h
wqs ∝
1
/σ
. The
d
-line wi h
d∝
1
/εSPD
dec eases mo e s ongly wi h
εSPD
han w because
miso ien a ion o
θ
-dis ibu ion shi s owa d highe
θ
wi h
εSPD
by ans o ma ion o LAGBs in o
HAGBs. Ve ical ex ension o he shaded a ea ma ks
HAGB
; as he lines o dand wapp oach each
o he , LAGB sh inks and HAGB app oaches 1.
Imposing
εSPD
=1.4 by RS educes he g ain size d o 1.6
µ
m, and 35% o he bounda ies a e
HAGBs (Figu e 2) wi h ela i ely equal
θ
-dis ibu ion be ween 15–65
◦
. P ocessing wi h HPS wi h a
sliding dis ance o 5 mm o
εSPD
=2.6 gene a es a g ain size o abou 1.25
µ
m and a simila po ion
o HAGBs. Imposing
εSPD
=7.9 by HPS15 led o a signi ican dec ease o mean g ain size down o
0.35
µ
m and an inc ease o
HAGB
up o 0.7. The lowes g ain size, d, and he highes ,
HAGB
, a e ound
o HPT subjec ed o he highes SPD s ain, εSPD =25 ±5.
Howe e , g ain pa ame e s a e SPD a oom empe a u e a e no he ones de e mining c eep,
as he g ains coa sen du ing hea ing o he es empe a u e and subsequen soaking un il he beginning
o c eep. While his annealing ea men be o e c eep has li le e ec o mic on-sized g ains, i causes
signi ican coa sening o submic on g ains. This is seen in Figu e 3b (see a ow “ eco e y”).
Figu e 4shows he e ec o annealing o 5 h a 873 K; his ea men simula es he annealing e ec
o hea ing o he es empe a u e. Despi e di e en deg ees o
εSPD
in RS, HPS5, HPS15, and HPT,
he subg ain s uc u es look quali a i ely simila . Reco e y o disloca ion line leng h and bounda y
a ea in ol es mo ion o bo h ee disloca ions and bounda ies o si es o eco e y by ecombina ion
and annihila ion. While his occu s, many ela i ely s aigh ee disloca ions (see a ows) a e seen
o ex end be ween neighbo ing bounda ies. The subg ain sizes w(mean in e cep s) es ima ed om
mic og aphs like hose o Figu e 5a e plo ed in Figu e 3b. The w- and d-coa sening is small o he
ela i ely coa se g ains o RS and HPS5, bu i is p ominen o he ul a ine g ains o HPT whe e
dgoes up o 0.35 µm wi h a ac ion o HAGB a ea ( HAGB) ~90%.
Ma e ials 2020, 13, x FOR PEER REVIEW 6 o 19
w-line wi h 𝑤∝1/𝜀

. is mo i a ed by pa abolic wo k ha dening, 𝜎∝𝜀

. , du ing SPD a oom
empe a u e owa d he inal s a iona y (sa u a ion) s age and o ma ion o quasi-s a iona y subg ain
s uc u es wi h 𝑤 ∝1/𝜎. The 𝑑-line wi h 𝑑∝1/𝜀
 dec eases mo e s ongly wi h 𝜀 han w
because miso ien a ion o 𝜃-dis ibu ion shi s owa d highe 𝜃 wi h 𝜀 by ans o ma ion o
LAGBs in o HAGBs. Ve ical ex ension o he shaded a ea ma ks
HAGB; as he lines o d and w
app oach each o he , LAGB sh inks and HAGB app oaches 1.
Imposing εSPD = 1.4 by RS educes he g ain size, d, o 1.6 μm, and 35% o he bounda ies a e
HAGBs (Figu e 2) wi h ela i ely equal θ-dis ibu ion be ween 15–65°. P ocessing wi h HPS wi h a
sliding dis ance o 5 mm o εSPD = 2.6 gene a es a g ain size o abou 1.25 μm and a simila po ion o
HAGBs. Imposing εSPD = 7.9 by HPS15 led o a signi ican dec ease o mean g ain size down o 0.35
μm and an inc ease o HAGB up o 0.7. The lowes g ain size, d, and he highes , HAGB, a e ound o
HPT subjec ed o he highes SPD s ain, εSPD = 25 ± 5.
Howe e , g ain pa ame e s a e SPD a oom empe a u e a e no he ones de e mining c eep,
as he g ains coa sen du ing hea ing o he es empe a u e and subsequen soaking un il he
beginning o c eep. While his annealing ea men be o e c eep has li le e ec o mic on-sized
g ains, i causes signi ican coa sening o submic on g ains. This is seen in Figu e 3b (see a ow
“ eco e y”).
Figu e 4 shows he e ec o annealing o 5 h a 873 K; his ea men simula es he annealing
e ec o hea ing o he es empe a u e. Despi e di e en deg ees o εSPD in RS, HPS5, HPS15, and
HPT, he subg ain s uc u es look quali a i ely simila . Reco e y o disloca ion line leng h and
bounda y a ea in ol es mo ion o bo h ee disloca ions and bounda ies o si es o eco e y by
ecombina ion and annihila ion. While his occu s, many ela i ely s aigh ee disloca ions (see
a ows) a e seen o ex end be ween neighbo ing bounda ies. The subg ain sizes w (mean in e cep s)
es ima ed om mic og aphs like hose o Figu e 5 a e plo ed in Figu e 3b. The w- and d-coa sening
is small o he ela i ely coa se g ains o RS and HPS5, bu i is p ominen o he ul a ine g ains o
HPT whe e d goes up o 0.35 μm wi h a ac ion o HAGB a ea ( HAGB) ~90%.
(a) RS εSPD = 1.4
(b) HPS5 εSPD = 2.6
Ma e ials 2020, 13, x FOR PEER REVIEW 7 o 19
(c) HPS15 εSPD = 7.9
(d) εSPD ~ 25 ± 5
Figu e 4. Mic os uc u e (TEM) a e annealing a 873 K o 5 h in (a) RS, (b) HPS5, (c) HPS15, and (d)
HPT; no e he highe magni ica ion in (c,d).
Figu e 5. Mic os uc u e o P92 s eel p ocessed by HPT and annealed a 923 K o 500 h.
E en mo e (sub)g ain coa sening occu s in annealing o 500 h a 923 K (Figu e 5). He e he
g ains coa sen o d ~0.85 μm wi h HAGB ~87%. The high alue o HAGB is unde s andable as no LABGs
a e o med du ing s a ic annealing whe e no ne plas ic de o ma ion occu s.
3.2. C eep Beha io
Figu e 6 shows e olu ion o s ain a e (𝜀󰇗) wi h s ain in c eep a σ0 = 150 MPa o all P92 a ian s.
All cu es display a p onounced ela i e minimum o c eep a e (𝜀󰇗). HPT, HPS5, and HPS15 ha e
simila 𝜀󰇗. CG and RS c eep much mo e slowly. Duc ili ies o di e en SPD specimens di e
g ea ly. RS has he lowes duc ili y. The esul s will be discussed below in ela ion o mic os uc u e.
Figu e 7 shows he c eep a es o CG, RS, and HPS e sus s ess. Tes s a cons an load ha e he
ad an age o show bo h he e olu ion wi h s ain and he in luence o s ess in a single plo . This is
because s ess a ies a cons an load wi h s ain, as
Figu e 4.
Mic os uc u e (TEM) a e annealing a 873 K o 5 h in (
a
) RS, (
b
) HPS5, (
c
) HPS15,
and (d) HPT; no e he highe magni ica ion in (c,d).
Ma e ials 2020,13, 5330 7 o 17
Ma e ials 2020, 13, x FOR PEER REVIEW 7 o 19
(c) HPS15 εSPD = 7.9
(d) εSPD ~ 25 ± 5
Figu e 4. Mic os uc u e (TEM) a e annealing a 873 K o 5 h in (a) RS, (b) HPS5, (c) HPS15, and (d)
HPT; no e he highe magni ica ion in (c,d).
Figu e 5. Mic os uc u e o P92 s eel p ocessed by HPT and annealed a 923 K o 500 h.
E en mo e (sub)g ain coa sening occu s in annealing o 500 h a 923 K (Figu e 5). He e he
g ains coa sen o d ~0.85 μm wi h HAGB ~87%. The high alue o HAGB is unde s andable as no LABGs
a e o med du ing s a ic annealing whe e no ne plas ic de o ma ion occu s.
3.2. C eep Beha io
Figu e 6 shows e olu ion o s ain a e (𝜀󰇗) wi h s ain in c eep a σ0 = 150 MPa o all P92 a ian s.
All cu es display a p onounced ela i e minimum o c eep a e (𝜀󰇗). HPT, HPS5, and HPS15 ha e
simila 𝜀󰇗. CG and RS c eep much mo e slowly. Duc ili ies o di e en SPD specimens di e
g ea ly. RS has he lowes duc ili y. The esul s will be discussed below in ela ion o mic os uc u e.
Figu e 7 shows he c eep a es o CG, RS, and HPS e sus s ess. Tes s a cons an load ha e he
ad an age o show bo h he e olu ion wi h s ain and he in luence o s ess in a single plo . This is
because s ess a ies a cons an load wi h s ain, as
Figu e 5. Mic os uc u e o P92 s eel p ocessed by HPT and annealed a 923 K o 500 h.
E en mo e (sub)g ain coa sening occu s in annealing o 500 h a 923 K (Figu e 5). He e he g ains
coa sen o d~0.85
µ
m wi h
HAGB
~87%. The high alue o
HAGB
is unde s andable as no LABGs a e
o med du ing s a ic annealing whe e no ne plas ic de o ma ion occu s.
3.2. C eep Beha io
Figu e 6shows e olu ion o s ain a e
.
ε
wi h s ain in c eep a
σ0
=150 MPa o all P92 a ian s.
All cu es display a p onounced ela i e minimum o c eep a e
.
εmin
. HPT, HPS5, and HPS15 ha e
simila
.
εmin
. CG and RS c eep much mo e slowly. Duc ili ies o di e en SPD specimens di e g ea ly.
RS has he lowes duc ili y. The esul s will be discussed below in ela ion o mic os uc u e.
Ma e ials 2020, 13, x FOR PEER REVIEW 8 o 19
σ = σ0 exp(ε) (1)
p o ided ha de o ma ion is uni o m. Empi ically i is known ha uni o mi y o de o ma ion along
he gauge leng h is p o ided in ela i ely duc ile ma e ials un il he s ain has eached abou hal he
ac u e s ain [22]. Acco ding o Equa ion (1), he loga i hmic s ess axis co esponds o a linea
s ain axis.
Figu e 6. E olu ion o s ain a e wi h s ain in ensile c eep a cons an load wi h σ0 = 150 MPa o
di e en SPD s ains εSPD.
Thus, he indi idual cu es in Figu e 7 can be iewed as 𝜀󰇗–ε cu es like hose o Figu e 6 bu
shi ed along he abscissa. De o ma ion begins a 𝜎=𝜎
; he scale ba ma ks an in e al Δ𝜀 = 0.5 o
uni o m s ain. No only do he minima o he cu es displayed in Figu e 7 show dependence on
s ess, hey also show he ull e olu ion o a e om he beginning, ia s eng hening and so ening
up o he second hal o he cu es whe e ex e nal and in e nal necking cause an o e -exponen ial
inc ease o a e un il inal ac u e.
Figu e 7 shows wo main ea u es. Fi s , he global s ess dependences o a es di e s ongly
o he a ian s HPS and HPT wi h he highes εSPD and he a ian s RS and CG wi h he lowes εSPD.
Roughly speaking, he s ess exponen 𝑛 = 𝑑𝑙𝑜𝑔𝜀󰇗/𝑑𝑙𝑜𝑔𝜎 o he a es is abou 6 o 7 o HPS and HPT
and wice ha high o RS and CG. This la ge n-di e ence leads o he esul ha he minimum c eep
a es o all a ian s a e simila a a high s ess o abou 400 MPa, while CG and RS c eep much mo e
slowly a he lowe s ess o 150 MPa. Figu e 7 also displays so ening du ing c eep ha is e iden
om he p onounced minimum due o he ac ha he a e inc eases dis inc ly mo e s ongly a e
he minimum han would be expec ed om s ess sensi i i y alone. In he li e a u e, his s eep
inc ease is e med e ia y c eep and is o en linked o “damage” and ac u e. Howe e , i
de o ma ion is ai ly uni o m a e he minimum, as in ou ul a ine-g ained (UFG) ma e ials wi h
ac u e s ains > 0.5, he a e inc ease mus be a ibu ed o so ening by in e nal mic os uc u al
changes, e.g., coa sening p ocesses (see Discussion) a he han ac u e. The ollowing subsec ion
desc ibes he obse ed changes.
Figu e 6.
E olu ion o s ain a e wi h s ain in ensile c eep a cons an load wi h
σ0
=150 MPa o
di e en SPD s ains εSPD.
Ma e ials 2020,13, 5330 8 o 17
Figu e 7shows he c eep a es o CG, RS, and HPS e sus s ess. Tes s a cons an load ha e he
ad an age o show bo h he e olu ion wi h s ain and he in luence o s ess in a single plo . This is
because s ess a ies a cons an load wi h s ain, as
σ=σ0exp(ε) (1)
p o ided ha de o ma ion is uni o m. Empi ically i is known ha uni o mi y o de o ma ion along he
gauge leng h is p o ided in ela i ely duc ile ma e ials un il he s ain has eached abou hal he ac u e
s ain [22]. Acco ding o Equa ion (1), he loga i hmic s ess axis co esponds o a linea s ain axis.
Ma e ials 2020, 13, x FOR PEER REVIEW 9 o 19
Figu e 7. C eep a e–s ess cu es o HPT, CG, and RS.
3.3. Changes o Mic os uc u e du ing C eep Tes ing
The mic os uc u e o ac u ed ensile specimens was in es iga ed a di e en loca ions along
hei leng h. In he g ip pa s, he local s ess, σloc, is negligible. In he gauge leng h, he s esses and
s ains a y wi h loca ion. The local s ain was oughly es ima ed as εloc = ln(Sloc/S0) om he local
c oss sec ion, S, and he ini ial c oss sec ion, S0. The local s ess ollows om Equa ion (1) as σloc =
σ0exp(εloc).
Figu es 8 and 9 show examples o he mic os uc u e in SEM and TEM o he mode a ely
p ede o med a ian RS a e c eep o ac u e a di e en σ0 and di e en σloc.
(a) g ip pa , local s ain (εloc) ~ 0
Figu e 7. C eep a e–s ess cu es o HPT, CG, and RS.
Thus, he indi idual cu es in Figu e 7can be iewed as
.
ε
–
ε
cu es like hose o Figu e 6bu
shi ed along he abscissa. De o ma ion begins a
σ=σ0
; he scale ba ma ks an in e al
∆ε
=0.5 o
uni o m s ain. No only do he minima o he cu es displayed in Figu e 7show dependence on s ess,
he cu es also show he ull e olu ion o a e om he beginning, ia s eng hening and so ening
up o he second hal o he cu es whe e ex e nal and in e nal necking cause an o e -exponen ial
inc ease o a e un il inal ac u e.
Figu e 7shows wo main ea u es. Fi s , he global s ess dependences o a es di e s ongly o
he a ian s HPS and HPT wi h he highes
εSPD
and he a ian s RS and CG wi h he lowes
εSPD
.
Roughly speaking, he s ess exponen
n=dlog .
ε/dlogσ
o he a es is abou 6 o 7 o HPS and HPT and
wice ha high o RS and CG. This la ge n-di e ence leads o he esul ha he minimum c eep a es
o all a ian s a e simila a a high s ess o abou 400 MPa, while CG and RS c eep much mo e slowly
a he lowe s ess o 150 MPa. Figu e 7also displays so ening du ing c eep ha is e iden om he
p onounced minimum due o he ac ha he a e inc eases dis inc ly mo e s ongly a e he minimum
han would be expec ed om s ess sensi i i y alone. In he li e a u e, his s eep inc ease is e med
e ia y c eep and is o en linked o “damage” and ac u e. Howe e , i de o ma ion is ai ly uni o m
a e he minimum, as in ou ul a ine-g ained (UFG) ma e ials wi h ac u e s ains >0.5, he a e
inc ease mus be a ibu ed o so ening by in e nal mic os uc u al changes, e.g., coa sening p ocesses
(see Discussion) a he han ac u e. The ollowing subsec ion desc ibes he obse ed changes.
Ma e ials 2020,13, 5330 9 o 17
3.3. Changes o Mic os uc u e du ing C eep Tes ing
The mic os uc u e o ac u ed ensile specimens was in es iga ed a di e en loca ions along
hei leng h. In he g ip pa s, he local s ess,
σloc
, is negligible. In he gauge leng h, he s esses
and s ains a y wi h loca ion. The local s ain was oughly es ima ed as
εloc
=ln(S
loc
/S
0
) om he
local c oss sec ion, S
loc
, and he ini ial c oss sec ion, S
0
. The local s ess ollows om Equa ion (1) as
σloc =σ0exp(εloc).
Figu es 8and 9show examples o he mic os uc u e in SEM and TEM o he mode a ely
p ede o med a ian RS a e c eep o ac u e a di e en σ0and di e en σloc.
Ma e ials 2020, 13, x FOR PEER REVIEW 9 o 19
Figu e 7. C eep a e–s ess cu es o HPT, CG, and RS.
3.3. Changes o Mic os uc u e du ing C eep Tes ing
The mic os uc u e o ac u ed ensile specimens was in es iga ed a di e en loca ions along
hei leng h. In he g ip pa s, he local s ess, σloc, is negligible. In he gauge leng h, he s esses and
s ains a y wi h loca ion. The local s ain was oughly es ima ed as εloc = ln(Sloc/S0) om he local
c oss sec ion, S, and he ini ial c oss sec ion, S0. The local s ess ollows om Equa ion (1) as σloc =
σ0exp(εloc).
Figu es 8 and 9 show examples o he mic os uc u e in SEM and TEM o he mode a ely
p ede o med a ian RS a e c eep o ac u e a di e en σ0 and di e en σloc.
(a) g ip pa , local s ain (εloc) ~ 0
Ma e ials 2020, 13, x FOR PEER REVIEW 10 o 19
(b) gauge nea ac u e su ace, εloc ~ 0.09
Figu e 8. Mic os uc u e and ex u e o RS a e c eep a σ0 = 200 MPa in (a) g ip pa and (b) gauge
leng h nea he ac u e. RD di ec ions a e pa allel wi h he s ess axis.
G ain s uc u e and ex u e, subg ain, and disloca ion s uc u e look ela i ely simila o be o e
c eep (Figu es 1b and 4a). I is no ed ha he disloca ion s uc u es ha e all unde gone eco e y,
ei he be o e c eep o a e ac u e; he e o e, Figu e 9 p obably is no ep esen a i e o he
disloca ion s uc u e in si u unde c eep s ess.
Figu e 9. Disloca ion mic os uc u e in he gauge leng hs o specimens es ed: (a) 300 MPa and (b)
150 MPa.
Nex , we conside he mos se e ely p ede o med ma e ials HPS15 and HPT. Figu e 10 shows
g ain s uc u e and ex u e o HPS15 in dependence o εloc. Compa ed o he s a e be o e c eep
(Figu e 4c), he ul a ine g ains ha e coa sened s a ically in he g ip pa and e en mo e so in gauge
leng h. The ex u e did no change in he g ip pa and a e sligh c eep s ain in he gauge leng h
(Figu e 10a,b). The miso ien a ion dis ibu ion e ol es du ing c eep (Figu e 11). The e is a signi ican
inc ease o HAGB ac ion ( HAGB) du ing c eep as εloc inc eases o 0.12 and 0.38. I appea s ha LAGBs
mig a e as e du ing g ain coa sening by eco e y h ough ecombina ion wi h o he bounda ies
han HAGBs do and so disappea ea lie . Nea he ac u e su ace, he HAGB ac ion, HAGB,
dec eased again. This sugges s massi e de o ma ion connec ed wi h o ma ion o small subg ains in
la ge g ains a he high local s esses ac ing he e.
(a)
(b)
Figu e 8.
Mic os uc u e and ex u e o RS a e c eep a
σ0
=200 MPa in (
a
) g ip pa and (
b
) gauge leng h
nea he ac u e. RD di ec ions a e pa allel wi h he s ess axis.
Ma e ials 2020, 13, x FOR PEER REVIEW 10 o 19
(b) gauge nea ac u e su ace, εloc ~ 0.09
Figu e 8. Mic os uc u e and ex u e o RS a e c eep a σ0 = 200 MPa in (a) g ip pa and (b) gauge
leng h nea he ac u e. RD di ec ions a e pa allel wi h he s ess axis.
G ain s uc u e and ex u e, subg ain, and disloca ion s uc u e look ela i ely simila o be o e
c eep (Figu es 1b and 4a). I is no ed ha he disloca ion s uc u es ha e all unde gone eco e y,
ei he be o e c eep o a e ac u e; he e o e, Figu e 9 p obably is no ep esen a i e o he
disloca ion s uc u e in si u unde c eep s ess.
Figu e 9. Disloca ion mic os uc u e in he gauge leng hs o specimens es ed: (a) 300 MPa and (b)
150 MPa.
Nex , we conside he mos se e ely p ede o med ma e ials HPS15 and HPT. Figu e 10 shows
g ain s uc u e and ex u e o HPS15 in dependence o εloc. Compa ed o he s a e be o e c eep
(Figu e 4c), he ul a ine g ains ha e coa sened s a ically in he g ip pa and e en mo e so in gauge
leng h. The ex u e did no change in he g ip pa and a e sligh c eep s ain in he gauge leng h
(Figu e 10a,b). The miso ien a ion dis ibu ion e ol es du ing c eep (Figu e 11). The e is a signi ican
inc ease o HAGB ac ion ( HAGB) du ing c eep as εloc inc eases o 0.12 and 0.38. I appea s ha LAGBs
mig a e as e du ing g ain coa sening by eco e y h ough ecombina ion wi h o he bounda ies
han HAGBs do and so disappea ea lie . Nea he ac u e su ace, he HAGB ac ion, HAGB,
dec eased again. This sugges s massi e de o ma ion connec ed wi h o ma ion o small subg ains in
la ge g ains a he high local s esses ac ing he e.
(a)
(b)
Figu e 9.
Disloca ion mic os uc u e in he gauge leng hs o specimens es ed: (
a
) 300 MPa and (
b
) 150 Mpa.
Ma e ials 2020,13, 5330 16 o 17
5.
The he e ogeneous mic os uc u e o RS con aining la ge elonga ed g ains wi h subg ains exhibi s
he highes c eep esis ance bu he lowes duc ili y.
The obse ed c eep so ening ela ed wi h g ain e inemen by SPD indica es ha he e a e only
limi ed means o imp o e c eep esis ance. Howe e , he eno mous inc ease in duc ili y may be
a signi ican ad an age in some cases. In any case, he p esen indings seem o be o ele ance
o he p oblem o c eep a e y low s esses and c eep a es in long- e m applica ion o empe ed
ma ensi e C s eels. Due o in e se s ess dependence, he qs subg ain size becomes e y la ge unde
hese condi ions so ha he g ains become mo e and mo e subg ain- ee and he ac ion o LAGBs
app oaches and exceeds 0.5. In his si ua ion, one mus expec ha he s ess dependence o he
c eep a e changes compa ed o he con en ional CG case wi h d>> wbecause dynamic eco e y is
accele a ed by HAGB con ol. This expec a ion o so ening, accompanied by declining s ess exponen
o c eep a e, ag ees wi h many obse a ions made in he ange o e y slow c eep, which so a ha e
no ound a sa is ac o y and gene ally accep ed explana ion.
Au ho Con ibu ions:
Concep ualiza ion, P.K., W.B., V.S., and Z.H.; me hodology, P.K., W.B., V.S., J.D., R.K.
and Z.H.; so wa e, W.B.; alida ion, P.K., J.D., Z.H., Y.T. (Yoichi Takizawa), Y.T. (Yongpeng Tang) and M.S.; o mal
analysis, W.B. and P.K.; in es iga ion, P.K., J.D., V.S., L.K., M.K., M.S. and Y.T. (Yoichi Takizawa); esou ces, P.K., J.D.,
R.K., M.S., Y.T. (Yoichi Takizawa) and Y.T. (Yongpeng Tang); da a cu a ion, P.K., J.D. and W.B.; w i ing—o iginal
d a p epa a ion, P.K., W.B. and V.S.; w i ing— e iew and edi ing, P.K., W.B. and V.S.; isualiza ion, P.K., W.B.;
J.D., L.K., R.K. and M.K.; supe ision, W.B. and V.S. All au ho s ha e ead and ag eed o he published e sion o
he manusc ip .
Funding: This esea ch was unded by he Czech Science Founda ion, g an numbe 19-18725S.
Acknowledgmen s:
The au ho s acknowledge inancial suppo om he Czech Science Founda ion
(g an No. 19-18725S). The wo k was suppo ed in pa by a g an -in-aid om MEXT, Japan, o scien i ic
esea ch (A) (No. 19H00830). The HPT p ocess was ca ied ou a he In e na ional Resea ch Cen e o Gian
S aining o Ad anced Ma e ials (IRC-GSAM) a Kyushu Uni e si y, Fukuoka, Japan.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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2010
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Usami, S.; Mo i, T. C eep de o ma ion o aus eni ic s eels a medium and low empe a u es. C yogenics
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Kikuchi, S.; Ilschne , B. E ec s o a small p es ain a high empe a u es on he c eep beha iou o AISI
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Publishe ’s No e:
MDPI s ays neu al wi h ega d o ju isdic ional claims in published maps and ins i u ional
a ilia ions.
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