ma e ials
A icle
Full-Field Tempe a u e Measu emen o S ainless S eel
Specimens Subjec ed o Uniaxial Tensile Loading a Va ious
S ain Ra es
K zysz o ˙
Zaba 1,* , Tomasz T zepieci´nski 2, S anisla Rusz 3, Sand a Puchle ska 1and Maciej Balce zak 1


Ci a ion: ˙
Zaba, K.; T zepieci´nski, T.;
Rusz, S.; Puchle ska, S.; Balce zak, M.
Full-Field Tempe a u e Measu emen
o S ainless S eel Specimens Subjec ed
o Uniaxial Tensile Loading a Va ious
S ain Ra es. Ma e ials 2021,14, 5259.
h ps://doi.o g/10.3390/ma14185259
Academic Edi o s: Qing Liu and
Jiangshan Zhang
Recei ed: 28 June 2021
Accep ed: 7 Sep embe 2021
Published: 13 Sep embe 2021
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 il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1Depa men o Me al Wo king and Physical Me allu gy o Non-Fe ous Me als, Facul y o Non-Fe ous
Me als, AGH—Uni e si y o Science and Technology, al. Adama Mickiewicza 30, 30-059 C acow, Poland;
[email p o ec ed] (S.P.); [email p o ec ed] (M.B.)
2Depa men o Manu ac u ing and P oduc ion Enginee ing, Facul y o Mechanical Enginee ing and
Ae onau ics, Rzeszow Uni e si y o Technology, al. Pows . Wa szawy 8, 35-959 Rzeszów, Poland;
[email p o ec ed]
3Depa men o Mechanical Technology, Facul y o Mechanical Enginee ing, VŠB—Technical Uni e si y o
Os a a, 17 lis opadu 15, CZ 708 33 Os a a–Po uba, Czech Republic; s anisla [email p o ec ed]
*Co espondence: [email p o ec ed]
Abs ac :
This a icle p esen s a s udy on he e ec o s ain a e, specimen o ien a ion, and plas ic
s ain on he alue and dis ibu ion o he empe a u e o dog-bone 1 mm- hick specimens du ing
hei de o ma ion in uniaxial ensile es s. Full- ield image co ela ion and in a ed he mog aphy
echniques we e used. A i anium-s abilised aus eni ic 321 s ainless s eel was used as es ma e ials.
The dog-bone specimens used o uniaxial ensile es s we e cu along he shee me al olling di ec ion
and h ee s ain a es we e conside ed: 4
×
10
−3
s
−1
, 8
×
10
−3
s
−1
and 16
×
10
−3
s
−1
. I was
ound ha inc easing he s ain a e esul ed in he in ensi ica ion o hea gene a ion. High-quali y
eg ession models (Ra > 0.9) de eloped o he aus eni ic 321 s eel e ealed ha sample o ien a ion
does no play a signi ican ole in he hea gene a ion when he sample is plas ically de o med. I was
ound ha a he momen o o ma ion o a necking a he highes s ain a e, he maximum sample
empe a u e inc eased mo e han ou imes compa ed o he ini ial empe a u e. A syne gis ic
e ec o he s ain ha dening exponen and yield s ess e ealed ha hea is gene a ed mo e apidly
owa ds small alues o s ain ha dening exponen and yield s ess.
Keywo ds:
digi al image co ela ion; mechanical p ope ies; s ainless s eel; empe a u e; he mo i-
sion; uniaxial ensile es
1. In oduc ion
Me als and hei alloys ha e a c ys alline s uc u e, which is cha ac e ised by a egula
a angemen o a omic co es. Technical me als ob ained by con en ional me allu gical
me hods ha e a polyc ys alline s uc u e [
1
,
2
]. This means ha me als a e made up o g ains
cha ac e ised by app oxima ely he co ec c ys al s uc u e. Polyc ys alline ma e ials
consis o g ains wi h a ious o ien a ions. Fo many polyc ys alline ma e ials, he g ain
o ien a ions a e andom be o e any wo king (de o ma ion) o he ma e ial is unde aken.
The e o e, e en i he indi idual g ains a e aniso opic, he p ope y di e ences end o
a e age ou and, o e all, he ma e ial is iso opic. When a ma e ial is o med, he g ains
a e usually dis o ed and elonga ed in one o mo e di ec ions which makes he ma e ial
aniso opic [3].
In me als subjec ed o plas ic wo king, he mos impo an de ec s o he c ys al la ice
a e disloca ions and g ain bounda ies. S ain ha dening—ha dening o a ma e ial wi h
de o ma ion— esul s om in e ac ion and mul iplica ion o disloca ions du ing plas ic
de o ma ion. G ain bounda ies ha e a much g ea e in luence on he mechanical p ope ies
o me als han disloca ions [
4
,
5
]. The high ene gy le el o g ain bounda ies de e mines
Ma e ials 2021,14, 5259. h ps://doi.o g/10.3390/ma14185259 h ps://www.mdpi.com/jou nal/ma e ials
Ma e ials 2021,14, 5259 2 o 15
he occu ence o many phenomena, such as con inuous mobili y o bounda ies leading o
g ain g ow h and lowe co osion esis ance [
6
–
8
]. G ain bounda ies also ha e a s ong
in luence on he duc ili y o me als. The deg ee o s ain ha dening o ma e ials by g ain
e ining is desc ibed by he Hall–Pe ch ela ionship [
9
,
10
] acco ding o which he yield
s eng h o he ma e ial inc eases wi h he deg ee o g ain e inemen . On he one hand,
g ain bounda ies inhibi he ee mo emen o disloca ions du ing g ain de o ma ion
while pa icipa ing in he p ocess o ma e ial s eng hening and in he o ma ion o he
de o ma ion ex u e [
1
]. On he o he hand, he g ain bounda ies a e he main a ea o
pe manen de o ma ion du ing c eep o supe plas ic low.
The de o ma ion o he ma e ial (elas ic o plas ic) occu s unde he in luence o a
load applied o i . Elas ic de o ma ion disappea s when he load is emo ed. Plas ic
de o ma ion emains a e he ma e ial is unloaded. The e a e wo main mechanisms o
plas ic de o ma ion: he gliding mo ion o disloca ions and de o ma ion winning [
11
,
12
].
The gliding mo ion does no occu simul aneously in all possible planes and di ec ions
o slip. De o ma ion occu s g adually, s a ing om he sliding planes and di ec ions
p io i ised in ela ion o he di ec ion o he applied load. Du ing de o ma ion, he numbe
o ac i e slip planes and ee disloca ions ha a e gene a ed du ing de o ma ion inc eases.
Fu he plas ic de o ma ion equi es he applica ion o g ea e s ess in o de o ini ia e
new disloca ions [
13
–
15
]. The p ocess by which s ess inc eases wi h de o ma ion is called
wo k ha dening. Plas ic de o ma ion is also accompanied by hea gene a ion due o he
in e nal esis ance o he ma e ial, which can be de ec ed a he mic os uc u e scale when
loading he ma e ial [16,17].
The in es iga ion o hea gene a ion and dissipa ion du ing plas ic de o ma ion was
e lec ed in scien i ic esea ch. Bodelo e al. [
18
] applied in a ed (IR) coupled ull- ield
measu emen s o obse e he he e ogenei ies o kinema ic and he mal da a a he g ain
scale o aus eni ic s ainless s eel. Specimens we e subjec ed o a cyclic loading. I was
ound ha he empe a u e was signi ican ly a ec ed by di usion and his obse a ion
ends o con i m ha empe a u e may no be used as a damage indica o . Boulange
e al. [
19
] ha e ocused on he de e mina ion o hea sou ces om a empe a u e ield
p o ided by an IR came a. They sepa a ely iden i ied he dissipa i e and he mo-elas ic
hea sou ces. The mal ull- ield measu emen s om in a ed he mog aphy we e used o
s udy he Po e in-Le Cha elie e ec [
20
]. The empe a u e ield p o ided insigh s in o
he dynamics o band o ma ion and mo ion.
The non-con ac op ical me hods o he measu emen o empe a u e displacemen in-
clude ideo ex ensome e s [
21
], lase speckle co ela ion [
22
], in e e ome y
me hods [23–25]
and empe a u e-calib a ed CCD came as [
26
]. In addi ion o IR he mog aphy, he o he
echnique ha allows empe a u e changes o be coupled wi h s ains is digi al image co e-
la ion (DIC), in which digi al images o an objec be o e and a e de o ma ion a e cap u ed
using a non-con ac op ic and ma e ial-independen measu ing ins umen , and hen hey
a e subjec o co ela ion analysis [
23
,
24
,
27
]. High-speed DIC allows de o ma ion and dam-
age mechanisms o be analysed in a quan i a i e manne [
28
]. DIC was used o ob ain s ain
ields and o in es iga e he p opaga ion o he Lüde s band in s eel specimens subjec ed o
he uniaxial ensile es [
29
]. The s ain s a es associa ed wi h localised necking and di use
s ains a e also in es iga ed. Resul s show ha he c oss-sec ion o a ensile specimen mus
be ega ded as a s uc u e, no as an elemen a y olume o ma e ial which is subjec ed o
he uni o m load. The esul s o in es iga ions o Hung and Voloshin [
30
] indica ed ha o
he uni o m ension es , DIC is a e y con enien and e icien ool o he measu emen o
in-plane s ain measu emen . Feng and Xue [
31
] applied in a ed he mog aphy es s and
DIC es s o he display o he he mal ield du ing mechanical ensile es s o 3D p in ed
bol s. Cholewa e al. [
32
] de eloped he me hod o calib a ed in a ed he mal came as
wi h a s e eo- ision DIC sys em applicable o scales o leng hs bo h la ge and small. ˙
Zaba
e al. [
33
] used DIC and IR he mog aphy o ind he ela ionship be ween yield s ess and
he Taylo –Quinney coe icien and hei change wi h he s ain a e du ing he s e ching o
nickel-based supe alloys. A coupled he mog aphy and DIC sys em was calib a ed using a
Ma e ials 2021,14, 5259 3 o 15
se ies o one sided hea exposu e expe imen s pe o med on loaded sandwich composi es.
In a ed he mog aphy and DIC measu emen s a e no applicable o expe imen s wi h low
conduc i i y ma e ials o discon inuous ma e ials [
33
,
34
]. Maynadie , e al. [
35
] de eloped
an in a ed image co ela ion sys em equipped wi h a single IR came a o measu e simul a-
neous he mal ields and de o ma ion. The disad an age o he p oposed me hod is ha
his echnique equi es he use o a special coa ing o displacemen measu emen using he
single came a. Ch ysochoos e al. [34] p oposed DIC and he mog aphy measu emen s o
he de e mina ion o he mechanical ene gy and hea sou ces in ol ed a local scale du ing
a he e ogeneous ensile es . The modynamic analysis o he ene gy balance showed he
in luence o he dissipa ed mechanism on he s ess–s ain esponse.
Many o s udies ake place a a mac oscopic scale wi h he measu emen o he a e age
empe a u e o he ma e ial [
36
,
37
]. Meanwhile, due o he g ain s uc u e o polyc ys alline
me als and he occu ence o a ious plas ic de o ma ion mechanisms, he empe a u e
o he body subjec ed o loading is no uni o m. The way o explain his phenomenon
is o ake ull- ield measu emen s. In his pape , he coupled IR and DIC measu emen s
we e conduc ed o assess he he momechanical esponse o s ainless s eel s ip samples
subjec ed o ensile load a di e en s ain a es. An analysis o a iance (ANOVA) was
used o gain in o ma ion abou he ela ionship be ween he s ain ha dening phenomenon,
yield s ess, sample o ien a ion in espec o he shee olling di ec ion, s ain a e, and
plas ic s ain o he specimen and empe a u e.
2. Ma e ials and Me hods
2.1. Ma e ial
The esea ch ma e ial was a i anium-s abilised aus eni ic s ainless s eel, 321 (AMS
5510). S eel 321 is a s eel wi h good o mabili y, weldabili y and esis ance o in e g anula
co osion ha is mainly used in he chemical and a ia ion indus ies. The hickness o he
shee s was 1 mm. The es samples we e cu om he shee in h ee di ec ions: he olling
di ec ion (RD), a an angle o 45
◦
o he RD and pe pendicula o he RD. The dimensions
o es samples (Figu e 1) we e in acco dance wi h he ASTM E8/E8M–11 s anda d [
38
].
The equi emen s o he chemical composi ion o he es s eel a e shown in Table 1and
a e in acco dance SAE AMS 5510 [39].
Ma e ials 2021, 14, x FOR PEER REVIEW 3 o 16
change wi h he s ain a e du ing he s e ching o nickel-based supe alloys. A coupled
he mog aphy and DIC sys em was calib a ed using a se ies o one sided hea exposu e
expe imen s pe o med on loaded sandwich composi es. In a ed he mog aphy and DIC
measu emen s a e no applicable o expe imen s wi h low conduc i i y ma e ials o
discon inuous ma e ials [33,34]. Maynadie , e al. [35] de eloped an in a ed image
co ela ion sys em equipped wi h a single IR came a o measu e simul aneous he mal
ields and de o ma ion. The disad an age o he p oposed me hod is ha his echnique
equi es he use o a special coa ing o displacemen measu emen using he single
came a. Ch ysochoos e al. [34] p oposed DIC and he mog aphy measu emen s o he
de e mina ion o he mechanical ene gy and hea sou ces in ol ed a local scale du ing a
he e ogeneous ensile es . The modynamic analysis o he ene gy balance showed he
in luence o he dissipa ed mechanism on he s ess–s ain esponse.
Many o s udies ake place a a mac oscopic scale wi h he measu emen o he
a e age empe a u e o he ma e ial [36,37]. Meanwhile, due o he g ain s uc u e o
polyc ys alline me als and he occu ence o a ious plas ic de o ma ion mechanisms, he
empe a u e o he body subjec ed o loading is no uni o m. The way o explain his
phenomenon is o ake ull- ield measu emen s. In his pape , he coupled IR and DIC
measu emen s we e conduc ed o assess he he momechanical esponse o s ainless s eel
s ip samples subjec ed o ensile load a di e en s ain a es. An analysis o a iance
(ANOVA) was used o gain in o ma ion abou he ela ionship be ween he s ain
ha dening phenomenon, yield s ess, sample o ien a ion in espec o he shee olling
di ec ion, s ain a e, and plas ic s ain o he specimen and empe a u e.
2. Ma e ials and Me hods
2.1. Ma e ial
The esea ch ma e ial was a i anium-s abilised aus eni ic s ainless s eel, 321 (AMS
5510). S eel 321 is a s eel wi h good o mabili y, weldabili y and esis ance o in e g anula
co osion ha is mainly used in he chemical and a ia ion indus ies. The hickness o he
shee s was 1 mm. The es samples we e cu om he shee in h ee di ec ions: he olling
di ec ion (RD), a an angle o 45° o he RD and pe pendicula o he RD. The dimensions
o es samples (Figu e 1) we e in acco dance wi h he ASTM E8/E8M–11 s anda d [38].
The equi emen s o he chemical composi ion o he es s eel a e shown in Table 1 and
a e in acco dance SAE AMS 5510 [39].
Figu e 1. Dimensions (in mm) o he samples o he ensile es .
Table 1. Chemical composi ion o 321 s eel (w .%) [39].
C (max.) Si Mo Mn
(max.)
P + S
(max. C Ni
Ti
(max.) N (max.) Fe
0.08 0.25–1.00 0.75 2.0 0.04 P
0.03 S 17.0–19.0 9.0–12.0 0.7 0.1 balance
Figu e 1. Dimensions (in mm) o he samples o he ensile es .
Table 1. Chemical composi ion o 321 s eel (w .%) [39].
C (Max.) Si Mo Mn (Max.) P + S (Max.) C Ni Ti (Max.) N (Max.) Fe
0.08 0.25–1.00 0.75 2.0 0.04 P
0.03 S 17.0–19.0 9.0–12.0 0.7 0.1 balance
2.2. Uniaxial Tensile Tes
Dog-bone samples (Figu e 1) we e s e ched in a uniaxial ensile es machine Zwick/Roell
Z100 (Figu e 2). Th ee di e en s ain a es we e used in he in es iga ions: 4
×
10
−3
s
−1
,
8×10−3s−1and 16 ×10−3s−1. The es s we e ca ied ou a a empe a u e o 24 ◦C.
Ma e ials 2021,14, 5259 4 o 15
Ma e ials 2021, 14, x FOR PEER REVIEW 4 o 16
2.2. Uniaxial Tensile Tes
Dog-bone samples (Figu e 1) we e s e ched in a uniaxial ensile es machine
Zwick/Roell Z100 (Figu e 2). Th ee di e en s ain a es we e used in he in es iga ions:
4 × 10–3 s−1, 8 × 10−3 s−1 and 16 × 10−3 s−1. The es s we e ca ied ou a a empe a u e o 24 °C.
Figu e 2. Tes s and.
2.3. Digi al Image Co ela ion Technique
The digi al image co ela ion A amis sys em (GOM, B aunschweig, Ge many) was
used o de e mine he cha ac e o he de o ma ion o he sample in a non-con ac manne
du ing he s e ching p ocess o samples. The measu ing sys em consis s o wo essen ial
componen s. The i s is a scanne , consis ing o wo high- esolu ion digi al came as (Fig-
u e 2) posi ioned in ela ion o each o he in such a way as o be able o build a spa ial
image. The second elemen o he se is a compu e wi h special so wa e o he nume ical
p ocessing o images.
P ope su ace p epa a ion o he samples is necessa y o DIC analysis. Fi s , he
samples a e co e ed wi h whi e pain , and hen a andom pa e n o con as ing black
spo s is applied. The selec ion o he size o he spo s depends on he size o he es objec
and he op ical p ope ies o he measu ing appa a us. The measu emen p ocess consis s
in aking a se ies o images o he sample by wo came as in successi e s ages o loading.
Co ela ion o images om hese came as makes i possible o de e mine he posi ion o
each pixel by gi ing hem coo dina es in a h ee-dimensional coo dina e sys em. Then he
images a e di ided in o so-called de o ma ion g ids, each o which con ains a unique pa -
e n o do s [40]. The ini ial se up becomes he e e ence s ep. Due o he de o ma ion o
he shee su ace, he spo s in each elemen o he mesh change hei posi ion in ela ion
o each o he , which makes i possible o calcula e he ull ield de o ma ion in ela ion o
he e e ence posi ion. Howe e , in o de o make such an analysis possible, he sys em
di ides he measu emen a ea in o ields o a ixed size called ace s. Local s ains a e
ob ained om he o mula:
𝜺𝒆𝒏𝒈 =𝐥𝐢𝐦
𝒍→𝟎 𝒍𝒊𝒏 +∆𝒍𝒅
𝒍𝒊𝒏 −𝟏∙𝟏𝟎𝟎% (1)
whe e lin is he ini ial dos ance be ween wo neighbou ing ace s and Δld is he dis ance
inc ease du ing uniaxial ensile es .
The dimension o s anda d ace is 21 × 21 pixels. The second cha ac e is ic alue is
he dis ance be ween he cen es o adjacen ace s. The A amis sys em o e s many bene-
i s, such as:
• a s able solu ion o ull- ield analyses o es objec s o jus a ew millime e s up o
s uc u al componen s o se e al me es in size,
Figu e 2. Tes s and.
2.3. Digi al Image Co ela ion Technique
The digi al image co ela ion A amis sys em (GOM, B aunschweig, Ge many) was
used o de e mine he cha ac e o he de o ma ion o he sample in a non-con ac manne
du ing he s e ching p ocess o samples. The measu ing sys em consis s o wo essen ial
componen s. The i s is a scanne , consis ing o wo high- esolu ion digi al came as
(Figu e 2) posi ioned in ela ion o each o he in such a way as o be able o build a spa ial
image. The second elemen o he se is a compu e wi h special so wa e o he nume ical
p ocessing o images.
P ope su ace p epa a ion o he samples is necessa y o DIC analysis. Fi s , he
samples a e co e ed wi h whi e pain , and hen a andom pa e n o con as ing black
spo s is applied. The selec ion o he size o he spo s depends on he size o he es objec
and he op ical p ope ies o he measu ing appa a us. The measu emen p ocess consis s
in aking a se ies o images o he sample by wo came as in successi e s ages o loading.
Co ela ion o images om hese came as makes i possible o de e mine he posi ion o
each pixel by gi ing hem coo dina es in a h ee-dimensional coo dina e sys em. Then
he images a e di ided in o so-called de o ma ion g ids, each o which con ains a unique
pa e n o do s [
40
]. The ini ial se up becomes he e e ence s ep. Due o he de o ma ion o
he shee su ace, he spo s in each elemen o he mesh change hei posi ion in ela ion o
each o he , which makes i possible o calcula e he ull ield de o ma ion in ela ion o he
e e ence posi ion. Howe e , in o de o make such an analysis possible, he sys em di ides
he measu emen a ea in o ields o a ixed size called ace s. Local s ains a e ob ained
om he o mula:
εeng =lim
l→0lin +∆ld
lin −1·100% (1)
whe e l
in
is he ini ial dos ance be ween wo neighbou ing ace s and
∆
l
d
is he dis ance
inc ease du ing uniaxial ensile es .
The dimension o s anda d ace is 21
×
21 pixels. The second cha ac e is ic alue
is he dis ance be ween he cen es o adjacen ace s. The A amis sys em o e s many
bene i s, such as:
•
a s able solu ion o ull- ield analyses o es objec s o jus a ew millime e s up o
s uc u al componen s o se e al me es in size,
•i is a ma e ial-independen and non-con ac measu ing sys em,
•
i pe o ms high-p ecision measu emen s wi h a 3D measu emen esolu ion in he
sub-mic ome e ange,
•i is a high- esolu ion o poin -based and ull- ield measu emen s.
Ma e ials 2021,14, 5259 5 o 15
2.4. In a ed (IR) The mal Mapping
The su ace empe a u e o he samples du ing he s e ching was measu ed using
a high-sensi i i y IR Fli T640 came a (Fli Sys ems AB, An enn ägen 6, 187 66 Täby,
Sweden). The measu emen s o empe a u e we e co ela ed wi h he measu emen o
s ain using he A0A amis sys em. Non-in asi e dis ance measu emen was pe o med
wi h an accu acy o he mog aphic measu emen s in he ange o +/
−
2
◦
C. The p incipal
pa ame e s o he Fli T640 came a a e lis ed in Table 2.
Table 2. Pa ame e s o a Fli T640 came a.
Pa ame e Uni Value
Resolu ion pixel 2048 ×1536
Measu ing ange ◦C−40 ÷+2000
Re esh a e Hz 30
The mal sensi i i y mK 30
2.5. Analysis o Va iance
Quad a ic mul idimensional ANOVA was used o de e mine he ela ionship be ween
ma e ial p ope ies (s ain ha dening exponen , yield s ess, sample o ien a ion), p ocess
pa ame e s (s ain a e and pe cen age s ain) and he maximum empe a u e appea ing
in he sample du ing he s e ching p ocess. The alues o he s ain ha dening exponen
we e de e mined by app oxima ing ue s ess- ue s ain cu es using he well known
Hollomon’s powe law.
ANOVA is a s a is ical me hod o examining obse a ions ha depend on one o
mo e ac o s ac ing simul aneously. Due o he di e en nume ical anges o he da a, hey
we e no malised o he ange [
−
1, +1] [
41
]. The min-max no malisa ion was applied by
means o a linea unc ion b inging he da a o a new in e al (Coded Low, Coded High).
Explana o y a iables should be independen o each o he . The inpu da a we e i ed
wi h a polynomial, and he in luence o indi idual a iables on he quali y o he model
was checked using backwa d elimina ion. The minimum and maximum alues o he inpu
a iables o samples made o 321 shee a e p esen ed in Table 3. In e media e alues o
inpu pa ame e s we e coded p opo ionally in he ange [−1, +1].
Table 3.
Fac o s and le els o analysis o a iance (ANOVA) o s e ching o specimens o 321 s eel.
Pa ame e Name Uni Type Minimum Maximum
A
S ain
ha dening
exponen
- Nume ic 0.35 0.392
BYield s ess MPa Nume ic 341 367
CS ain a e s−1Nume ic 4×10−316 ×10−3
DSample
o ien a ion deg. Nume ic 0 90
EPe cen age
s ain % Nume ic 12 117.7
The eg ession models ha we e buil we e subjec ed o signi icance es s. The me hod
o backwa d elimina ion o a iables was used in he analysis. I is a a iable selec ion
p ocedu e in which all he a iables a e en e ed in o he eg ession equa ion and hen
emo ed sequen ially. The a iable wi h he lowes pa ial co ela ion wi h he dependen
a iable is conside ed o emo al i s . I i mee s he elimina ion c i e ia, i is emo ed.
The basis o emo ing o lea ing a gi en a iable in he model is he calcula ion o Fishe
F s a is ics. The independen a iable wi h he highes p obabili y co esponding o he
Fishe pa ame e F is emo ed om he model i he p obabili y pis su icien ly high
( ypically p= 0.10). A e he i s a iable is emo ed, he nex one o be emo ed is he

Ma e ials 2021,14, 5259 6 o 15
one ha has he smalles pa ial co ela ion wi h he dependen a iable. The p ocedu e
exi s when he e a e no o he a iables in he equa ion ha mee he emo al c i e ia.
The signi icance o he eg ession model a a le el o
α
= 0.05 is de e mined based on he
a iance due o he e ec o a ac o and he a iance due o he e o e m.
3. Resul s and Discussion
3.1. Expe imen al In es iga ions
Figu e 3shows he e olu ion o he su ace empe a u e o he samples cu along he
shee olling di ec ion o he 321 s eel du ing i s s e ching wi h di e en s ain a es. I
is clea ly isible ha e en wi hin he ange o p opo ional de o ma ions he zone wi h
he highes empe a u e is loca ed app oxima ely a he cen al poin be ween he g ippe s
o he es ing machine. As a esul o hea con ec ion caused by in e nal ic ion o he
ma e ial, an inc ease in he empe a u e o he samples was also obse ed in he pa ha
is g ipped whe e no plas ic de o ma ion occu s. Inc easing he s ain a e esul ed in he
in ensi ica ion o hea gene a ion. A he momen o he o ma ion o a necking a he
highes s ain a e, he maximum sample empe a u e inc eased by mo e han 4 imes
compa ed o he ini ial empe a u e. Simila conclusions can be d awn o he samples cu
a an angle o 45◦wi h espec o RD and pe pendicula o RD (Figu e 4).
Only pa o he mechanical ene gy is con e ed in o hea in he de o ma ion p ocess.
The emainde is s o ed in he mic os uc u e o he ma e ial inc easing he in e nal ene gy
o he ma e ial. The o al ene gy spen on de o ming an elas ic-plas ic ma e ial is equal o
he wo k unde aken on elas ic ( e e sible) de o ma ion and pe manen (plas ic) de o ma-
ion. Mo eo e , he ene gy consumed on plas ic de o ma ion is di ided in o hea dissipa ed
in he o ming p ocess and ene gy s o ed in he ma e ial [
42
–
44
]. The e olu ion o he
mic os uc u e du ing de o ma ion depends on he ype o ma e ial, he ini ial empe a u e
and he loading si ua ion [
45
,
46
]. Changing he de o ma ion me hod usually leads o a
pa ial o comple e econs uc ion o he disloca ion sys ems o med in he p e ious s ages
o de o ma ion and he o ma ion o new sys ems [
47
,
48
]. The in e ac ion o he la ice
de ec s is ela ed o he o e lapping o hei s ess ields. I he o e lap o s ess ields
caused by de ec s educes he ene gy o he sys em, hen wi h a speci ic ac i i y o he
espec i e slip sys ems, hese de ec s will o m con igu a ions complian wi h he p inciple
o ene gy minimisa ion [49,50].
The plas ici y ma gin measu ed as he di e ence be ween ul ima e ensile s ess and
ield s ess is mo e p onounced in he case o 321 s eel han o 17-4PH s eel.
Figu e 5show he e ec o pe cen age s ain on he change in he maximum empe a-
u e o he specimens o 321 s eel. These dependencies, de e mined by he de e mina ion
coe icien R
2
, show a linea end wi h a high co ela ion alue R
2
> 0.93. In he case o he
sample made om 321 s eel cu a an angle o 45
◦
es ed a a s ain a e o
16 ×10−3s−1
,
he las poin co esponds o he ad anced s age o sample necking. The e o e, he R
2
- alue
o ha case is abou 0.9484 (Figu e 5c). In gene al, he highe he s ain a e he s eepe he
end lines. The samples made o 321 s eel show aniso opic ea u es, which a e pa icula ly
isible a a s ain a e o 8
×
10
−3
s
−1
(Figu e 5b). T end lines o samples cu a di e en
angles a e inclined a di e en angles wi h espec o he abscissa axis. T ue s ess-s ain
cu es o 321 s eel de e mined a a ious s ain a es a e shown in Figu e 6. T ue s ain is
de ined as ε :
ε =lnl
l0(2)
whe e land l0a e he cu en and ini ial gauge leng hs, espec i ely.
Ma e ials 2021,14, 5259 7 o 15
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Figu e 3. In a ed (IR) he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu along he shee
olling di ec ion, es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1and (c) 16 × 10−3 s−1.
Figu e 3.
In a ed (IR) he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu along he shee
olling di ec ion, es ed a he ollowing s ain a es: (a) 4 ×10−3s−1, (b) 8 ×10−3s−1and (c) 16 ×10−3s−1.
Ma e ials 2021,14, 5259 8 o 15
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Figu e 4. IR he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu
pe pendicula o he olling di ec ion (RD), es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8
× 10−3 s−1and (c) 16 × 10−3 s−1.
Figu e 5 show he e ec o pe cen age s ain on he change in he maximum empe -
a u e o he specimens o 321 s eel. These dependencies, de e mined by he de e mina ion
coe icien R2, show a linea end wi h a high co ela ion alue R2 > 0.93. In he case o he
sample made om 321 s eel cu a an angle o 45° es ed a a s ain a e o 16 × 10−3 s−1, he
las poin co esponds o he ad anced s age o sample necking. The e o e, he R2- alue
o ha case is abou 0.9484 (Figu e 5c). In gene al, he highe he s ain a e he s eepe
he end lines. The samples made o 321 s eel show aniso opic ea u es, which a e pa -
icula ly isible a a s ain a e o 8 × 10−3 s−1 (Figu e 5b). T end lines o samples cu a
di e en angles a e inclined a di e en angles wi h espec o he abscissa axis. T ue
s ess-s ain cu es o 321 s eel de e mined a a ious s ain a es a e shown in Figu e 6.
T ue s ain is de ined as ε :
Figu e 4.
IR he mog aphy images and digi al image co ela ion cha s o 321 s eel samples cu
pe pendicula o he olling di ec ion (RD), es ed a he ollowing s ain a es: (
a
) 4
×
10
−3
s
−1
,
(b) 8 ×10−3s−1and (c) 16 ×10−3s−1.
Ma e ials 2021, 14, x FOR PEER REVIEW 9 o 16
𝜺𝒕=𝒍𝒏𝒍
𝒍𝟎 (2)
whe e l and l0 a e he cu en and ini ial gauge leng hs, espec i ely.
Figu e 5. In luence o s ain on empe a u e o 321 s eel samples es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 ×
10−3 s−1 and (c) 16 × 10−3 s−1.
Figu e 6. T ue s ess- ue s ain cu es o 321 s eel de e mined a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1
and (c) 16 × 10−3 s−1.
3.2. Analysis o Va iance (ANOVA) o 321 S eel Samples
A quad a ic model con aining only s a is ically signi ican elemen s was chosen o i
he expe imen al da a. The empe a u e esponse su ace o he 321 s eel specimens is
gi en by:
𝑻=𝟕𝟔.𝟕𝟏−𝟏𝟖.𝟓𝟔𝑨−𝟏𝟎.𝟎𝟐𝑩−𝟒.𝟏𝟗𝑪+𝟒.𝟕𝟏𝑫+𝟒𝟖.𝟔𝟏𝑬−𝟒.𝟗𝟕𝑨𝑩
+𝟗.𝟓𝟖𝑨𝑪+𝟖.𝟐𝟕𝑨𝑫−𝟑𝟏.𝟒𝟏𝑨𝑬−𝟏𝟐.𝟗𝟗𝑩𝑪−𝟏𝟑.𝟏𝑩𝑬
−𝟐𝟏.𝟑𝟓𝑪𝑬−𝟏.𝟐𝟐𝑫𝑬+𝟏𝟑.𝟑𝟔𝑬𝟐
(3)
The signi icances o he in luence o he indi idual ma e ial pa ame e s as well as he
condi ions o he s e ching p ocess and hei in e ac ion in he eg ession model we e
de e mined on he basis o he ANOVA. The quali y o i o he model ob ained o he
alues measu ed o a gi en esea ch plan (Equa ion (3)) was hen de e mined on he basis
o he de e mina ion coe icien s R2 and he F es . The signi icance o he model is con-
i med by an F- alue o 53.30 (Table 4). This model can, he e o e, be used o p edic em-
pe a u e alues based on ma e ial de o ma ion. The p obabili y ha such a la ge F- alue
can esul om da a noise is only 0.01%.
The p obabili y alues p o E, AE, CE, E2 ha a e less han 0.0500 p o e ha hese
ac o s a e s a is ically signi ican . The pa ame e s he emo al o which will no educe
Figu e 5.
In luence o s ain on empe a u e o 321 s eel samples es ed a he ollowing s ain a es: (
a
) 4
×
10
−3
s
−1
,
(b) 8 ×10−3s−1and (c) 16 ×10−3s−1.
Ma e ials 2021,14, 5259 9 o 15
Ma e ials 2021, 14, x FOR PEER REVIEW 9 o 16
𝜺𝒕=𝒍𝒏𝒍
𝒍𝟎 (2)
whe e l and l0 a e he cu en and ini ial gauge leng hs, espec i ely.
Figu e 5. In luence o s ain on empe a u e o 321 s eel samples es ed a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 ×
10−3 s−1 and (c) 16 × 10−3 s−1.
Figu e 6. T ue s ess- ue s ain cu es o 321 s eel de e mined a he ollowing s ain a es: (a) 4 × 10−3 s−1, (b) 8 × 10−3 s−1
and (c) 16 × 10−3 s−1.
3.2. Analysis o Va iance (ANOVA) o 321 S eel Samples
A quad a ic model con aining only s a is ically signi ican elemen s was chosen o i
he expe imen al da a. The empe a u e esponse su ace o he 321 s eel specimens is
gi en by:
𝑻=𝟕𝟔.𝟕𝟏−𝟏𝟖.𝟓𝟔𝑨−𝟏𝟎.𝟎𝟐𝑩−𝟒.𝟏𝟗𝑪+𝟒.𝟕𝟏𝑫+𝟒𝟖.𝟔𝟏𝑬−𝟒.𝟗𝟕𝑨𝑩
+𝟗.𝟓𝟖𝑨𝑪+𝟖.𝟐𝟕𝑨𝑫−𝟑𝟏.𝟒𝟏𝑨𝑬−𝟏𝟐.𝟗𝟗𝑩𝑪−𝟏𝟑.𝟏𝑩𝑬
−𝟐𝟏.𝟑𝟓𝑪𝑬−𝟏.𝟐𝟐𝑫𝑬+𝟏𝟑.𝟑𝟔𝑬𝟐
(3)
The signi icances o he in luence o he indi idual ma e ial pa ame e s as well as he
condi ions o he s e ching p ocess and hei in e ac ion in he eg ession model we e
de e mined on he basis o he ANOVA. The quali y o i o he model ob ained o he
alues measu ed o a gi en esea ch plan (Equa ion (3)) was hen de e mined on he basis
o he de e mina ion coe icien s R2 and he F es . The signi icance o he model is con-
i med by an F- alue o 53.30 (Table 4). This model can, he e o e, be used o p edic em-
pe a u e alues based on ma e ial de o ma ion. The p obabili y ha such a la ge F- alue
can esul om da a noise is only 0.01%.
The p obabili y alues p o E, AE, CE, E2 ha a e less han 0.0500 p o e ha hese
ac o s a e s a is ically signi ican . The pa ame e s he emo al o which will no educe
Figu e 6.
T ue s ess- ue s ain cu es o 321 s eel de e mined a he ollowing s ain a es: (
a
) 4
×
10
−3
s
−1
,
(b) 8 ×10−3s−1and (c) 16 ×10−3s−1.
3.2. Analysis o Va iance (ANOVA) o 321 S eel Samples
A quad a ic model con aining only s a is ically signi ican elemen s was chosen o i
he expe imen al da a. The empe a u e esponse su ace o he 321 s eel specimens is
gi en by:
T=76.71 −18.56A−10.02B−4.19C+4.71D+48.61E−4.97AB
+9.58AC +8.27AD −31.41AE −12.99BC −13.1BE
−21.35CE −1.22DE +13.36E2(3)
The signi icances o he in luence o he indi idual ma e ial pa ame e s as well as
he condi ions o he s e ching p ocess and hei in e ac ion in he eg ession model we e
de e mined on he basis o he ANOVA. The quali y o i o he model ob ained o he
alues measu ed o a gi en esea ch plan (Equa ion (3)) was hen de e mined on he
basis o he de e mina ion coe icien s R
2
and he F es . The signi icance o he model is
con i med by an F- alue o 53.30 (Table 4). This model can, he e o e, be used o p edic
empe a u e alues based on ma e ial de o ma ion. The p obabili y ha such a la ge
F- alue can esul om da a noise is only 0.01%.
Table 4. Resul s o analysis o a iance o he eg ession model o 321 s eel samples.
Sou ce Sum o Squa es Deg ees o F eedom Mean Squa e F-Value p-Value Meaning
Model 8991.31 14 642.24 53.30 <0.0001 signi ican
A—s ain
ha dening
exponen 26.04 1 26.04 2.16 0.1723 -
B—yield s ess 39.77 1 39.77 3.30 0.0993 -
C—s ain a e 0.5708 1 0.5708 0.0474 0.8321 -
D—sample
o ien a ion 13.38 1 13.38 1.11 0.3167 -
E—plas ic s ain 989.76 1 989.76 82.14 <0.0001 -
AB 1.11 1 1.11 0.0920 0.7679 -
AC 9.23 1 9.23 0.7664 0.4019 -
AD 22.41 1 22.41 1.86 0.2025 -
AE 171.00 1 171.00 14.19 0.0037 -
BC 4.45 1 4.45 0.3696 0.5568 -
BE 36.85 1 36.85 3.06 0.1109 -
CE 758.38 1 758.38 62.94 <0.0001 -
DE 2.40 1 2.40 0.1992 0.6649 -
E266.37 1 66.37 5.51 0.0409 -
Residual 120.49 10 12.05 - - -
Co To al 9111.80 24 - - - -
The p obabili y alues p o E,AE,CE,E
2
ha a e less han 0.0500 p o e ha hese
ac o s a e s a is ically signi ican . The pa ame e s he emo al o which will no educe he
quali y o he model include, in e alia, C,AB,BC,DE. Due o he sa is ac o y alue o he