me als
A icle
Re isi ing Fo mabili y and Failu e o AISI304 Shee s
in SPIF: Expe imen al App oach and
Nume ical Valida ion
Gab iel Cen eno 1,*ID , And és Jesús Ma ínez-Donai e 1ID , Isabel Bagudanch 2ID ,
Domingo Mo ales-Palma 1ID , Ma ía Luisa Ga cia-Romeu 2ID and Ca pó o o Vallellano 1ID
1Depa men o Mechanical and Manu ac u ing Enginee ing, School o Enginee ing, Uni e si y o Se ille,
41092 Se ille, Spain; [email p o ec ed] (A.J.M.-D.); [email p o ec ed] (D.M.-P.); [email p o ec ed] (C.V.)
2Depa men o Mechanical Enginee ing and Indus ial Cons uc ion, Uni e si y o Gi ona, 17071 Gi ona,
Spain; [email p o ec ed] (I.B.); [email p o ec ed] (M.L.G.-R.)
*Co espondence: [email p o ec ed]; Tel.: +34-954-485965
Recei ed: 11 Oc obe 2017; Accep ed: 24 No embe 2017; Published: 28 No embe 2017
Abs ac :
Single Poin Inc emen al Fo ming (SPIF) is a lexible and economic manu ac u ing p ocess
wi h a s ong po en ial o manu ac u ing small and medium ba ches o highly cus omized pa s.
Fo mabili y and ailu e in SPIF ha e been in ensi ely discussed in ecen yea s, especially because
his p ocess allows s able plas ic de o ma ion well abo e he con en ional o ming limi s, as his
enhanced o mabili y is only achie able wi hin a ce ain ange o p ocess pa ame e s depending on
he ma e ial ype. This pape analyzes o mabili y and ailu e o AISI304-H111 shee s de o med by
SPIF compa ed o con en ional es ing condi ions (including Nakazima and s e ch-bending es s).
Wi h his pu pose, expe imen al es s in SPIF and s e ch-bending we e ca ied ou and a nume ical
model o SPIF is pe o med. The esul s allow he au ho s o es ablish he ollowing con ibu ions
ega ding SPIF: (i) he se ing o he limi s o he o mabili y enhancemen when small ool diame e s
a e used, (ii) he e olu ion o he c ack when ailu e is a ained and (iii) he de e mina ion o he
condi ions upon which necking is supp essed, leading di ec ly o duc ile ac u e in SPIF.
Keywo ds: o mabili y; ailu e; shee me al o ming; Single-Poin Inc emen al Fo ming (SPIF)
1. In oduc ion
Inc emen al Shee Fo ming (ISF) p ocesses accomplish he cu en equi emen s o apid,
adap i e, economic and en i onmen ally iendly manu ac u ing. I is especially iable o small
ba ches o pa s made o shee and does no need expensi e dedica ed machines o equipmen . Indeed,
i is a ela i e no el p ocess ha has been in he spo ligh o he me al- o ming communi y o he las
wo decades. Al hough he inc emen al shee - o ming echnology is linked o he p ocess o spinning,
he cu en ISF p ocess has i s o igins in he la e 1960s ela ed o he pionee wo ks o Leszak [
1
] and
Be ghahn and Mu ay [
2
], bo h in 1967. Ne e heless, ollowing he analysis o he his o ical e iew by
Emmens e al. [
3
] only he la e can be ega ded as an ac ual e sion o mode n ISF. This in es iga ion
e eals ha hose 2 ini ial pa en s we e no he wo k leading o he p esen de elopmen s, bu he
Bachelo Thesis o Mason in 1978 [
4
] p esen ed o he scien i ic communi y la e in 1984 [
5
], which
would be he eal o igin o he cu en s a e o he a in ISF.
Single-Poin Inc emen al Fo ming (SPIF) is he simples ype wi hin ISF p ocesses, which make
use o a simple se up no equi ing any pa ial o ull die. As shown in Figu e 1, he SPIF echnology
consis s o a hemisphe ical end- o ming ool d i en by a CNC machine ha ollows p og essi ely
a p e-es ablished ajec o y, de o ming a pe iphe ally clamped shee blank in o a inal componen
wi hou he use o any speci ic o ming die.
Me als 2017,7, 531; doi:10.3390/me 7120531 www.mdpi.com/jou nal/me als
Me als 2017,7, 531 2 o 14
Me als 2017, 7, 531 2 o 14
(a)
(b)
Figu e 1. (a) Schema ic ep esen a ion o he SPIF p ocess and (b) expe imen al se up u ilized.
Fo mabili y and ailu e o shee me al de o med by SPIF is usually analyzed wi hin Fo ming
Limi Diag ams o FLDs, which include he limi s ains a he onse o local necking, ep esen ed by
he Fo ming Limi Cu e (FLC), as well as a duc ile ac u e, cha ac e ized by he F ac u e Fo ming
Line (FFL). The cu en me hods o he e alua ion o hese limi s ains a he onse o necking and
ac u e ha e been ecen ly discussed in [6]. In his ega d, high duc ili y me al shee s de o med by
con en ional o ming p ocesses usually s a ailing a he onse o necking, i.e., he ma e ial de o ms
con inuously wi hin his neck unde an uns able de o ma ion p ocess, ollowing app oxima ely a
nea plane s ain s a e, un il he duc ile ac u e akes place. On he con a y, me al shee s de o med
by SPIF (o any o he ISF a ie y) wi hin a ce ain ange o p ocess pa ame e s su e a s able s aining
abo e he FLC ha may lead di ec ly o duc ile ac u e. The s abiliza ion mechanisms p o iding he
enhanced o mabili y obse ed in ISF a e p esen ed and discussed in he e iew pape by Emmens
and an den Boogaa d [7].
Wi h his backg ound, Sil a e al. [8] ca ied ou es s ha e ealed he possible exis ence o bo h
de o ma ion mechanisms, ei he ac u e wi h a p e ious necking o ailu e by di ec duc ile ac u e,
depending on he a io be ween he ini ial hickness o he shee and he adius o he ool ( 0/R). Fo
la ge ool diame e s, ailu e by necking could s ill occu , whe eas o small ool diame e s, ac u e
in absence o necking would be p omo ed, and o mabili y should hen be ep esen ed by he FFL. A
mo e ecen s udy [9] demons a ed ha in bo h o he p e ious cases, i.e., ailu e con olled ei he
by necking o by duc ile ac u e, ac u e s ains a e always wi hin a sca e band o he FFL.
In his ega d, he au ho s s udied in a p e ious wo k [10] he e ec o he localized bending
induced by he o ming ool, e alua ed h ough he abo e men ioned 0/R a io, in he s abiliza ion
o plas ic de o ma ion abo e he FLC du ing ISF. I was obse ed ha o highe ool diame e
(20 mm), he ailu e mode was due o necking ollowed by duc ile ac u e. Howe e o he lowes
ool diame e s conside ed (10 mm), ailu e occu ed by ac u e in he absence o necking.
Figu e 1. (a) Schema ic ep esen a ion o he SPIF p ocess and (b) expe imen al se up u ilized.
Fo mabili y and ailu e o shee me al de o med by SPIF is usually analyzed wi hin Fo ming
Limi Diag ams o FLDs, which include he limi s ains a he onse o local necking, ep esen ed by
he Fo ming Limi Cu e (FLC), as well as a duc ile ac u e, cha ac e ized by he F ac u e Fo ming
Line (FFL). The cu en me hods o he e alua ion o hese limi s ains a he onse o necking and
ac u e ha e been ecen ly discussed in [
6
]. In his ega d, high duc ili y me al shee s de o med by
con en ional o ming p ocesses usually s a ailing a he onse o necking, i.e., he ma e ial de o ms
con inuously wi hin his neck unde an uns able de o ma ion p ocess, ollowing app oxima ely a nea
plane s ain s a e, un il he duc ile ac u e akes place. On he con a y, me al shee s de o med by
SPIF (o any o he ISF a ie y) wi hin a ce ain ange o p ocess pa ame e s su e a s able s aining
abo e he FLC ha may lead di ec ly o duc ile ac u e. The s abiliza ion mechanisms p o iding he
enhanced o mabili y obse ed in ISF a e p esen ed and discussed in he e iew pape by Emmens
and an den Boogaa d [7].
Wi h his backg ound, Sil a e al. [
8
] ca ied ou es s ha e ealed he possible exis ence o bo h
de o ma ion mechanisms, ei he ac u e wi h a p e ious necking o ailu e by di ec duc ile ac u e,
depending on he a io be ween he ini ial hickness o he shee and he adius o he ool (
0
/R).
Fo la ge ool diame e s, ailu e by necking could s ill occu , whe eas o small ool diame e s, ac u e
in absence o necking would be p omo ed, and o mabili y should hen be ep esen ed by he FFL.
A mo e ecen s udy [
9
] demons a ed ha in bo h o he p e ious cases, i.e., ailu e con olled ei he
by necking o by duc ile ac u e, ac u e s ains a e always wi hin a sca e band o he FFL.
In his ega d, he au ho s s udied in a p e ious wo k [
10
] he e ec o he localized bending
induced by he o ming ool, e alua ed h ough he abo e men ioned
0
/R a io, in he s abiliza ion o
plas ic de o ma ion abo e he FLC du ing ISF. I was obse ed ha o highe ool diame e (20 mm),
Me als 2017,7, 531 3 o 14
he ailu e mode was due o necking ollowed by duc ile ac u e. Howe e o he lowes ool
diame e s conside ed (10 mm), ailu e occu ed by ac u e in he absence o necking.
Fu he mo e, conside ing ha o a ce ain ange o p ocess pa ame e s co esponding o
high
0
/R a ios ailu e will occu wi hou p e ious necking in SPIF, Isik e al. [
11
] p oposed a
new me hodology o de e mine he maximum s ains a ac u e di ec ly om he in-plane s ain
measu emen s wi hou e alua ing he gauge leng h s ains, which simpli ies he p ocedu e o
ob aining he FFL. Wha is equi ed is a se ies o es s on pa s wi h a a iable wall angle: unca ed
conical pa s (plane s ain condi ions) and unca ed py amidal pa s (plane s ain condi ions in he
walls o he py amid and biaxial s e ching a he co ne s). Isik e al. also in oduced he concep
o Shea F ac u e Fo ming Limi line o SFFL, co esponding o mode II o he ac u e mechanics
(in-plane shea ), which can also be exci ed unde ce ain loading condi ions in ISF. In-plane o sion
es s and plane shea es s a e equi ed o ep esen his new o ming limi . In o de o simpli y
and acili a e he de e mina ion o SFFL, a new geome y manu ac u ed by ISF has been ecen ly
p oposed [
12
]. This p oposal in ol es using a unca ed lobe conical shape wi h a ying wall angle
and measu ing he in-plane s ains a ac u e, hus a oiding he need o measu e gauge leng h s ains,
which is equi ed wi h ypical es specimens (in-plane o sion and plane shea es s).
In his scien i ic amewo k o SPIF, his pape allows he au ho s p esen ing he ollowing
con ibu ions o he cu en s a e o he a in ISF ega ding he SPIF p ocess applied o AISI304-H111
shee s: (i) he se ing o he limi s o he o mabili y enhancemen when small ool diame e s a e used,
(ii) he e olu ion o he c ack when ailu e is a ained and (iii) he condi ions, alida ed by he FEA,
upon which necking is supp essed, leading di ec ly o duc ile ac u e in SPIF.
A e con ex ualizing his s udy wi hin he s a e o he a in SPIF, Sec ion 2p esen s he ma e ial
and expe imen al me hods u ilized, Sec ion 3 ocuses on he nume ical modelling o he SPIF p ocess
ca ied ou and Sec ion 4discusses he expe imen al and nume ical esul s ob ained. Finally, he
con ibu ions o he pape a e exposed in Sec ion 5“Conclusions”.
2. Ma e ials and Expe imen al Me hods
This sec ion s a s p esen ing he mechanical cha ac e iza ion o he AISI304-H111 me al shee s
ob ained om uniaxial ensile es s and p o iding a powe law con aining he plas ic beha io o he
ma e ial o be used in he nume ical simula ions.
In Sec ion 2.2, he o ming limi s o he ma e ial a e gi en by means o con en ional Nakazima
es s, which combined by a se ies o s e ch-bending es s ca ied ou wi h a se o cylind ical punches
p o ide he FLD o he shee me al including bending e ec s.
Finally, he expe imen al plan and he expe imen al me hods used in he case o he SPIF es s a e
p esen ed in Sec ion 2.3.
2.1. Mechanical Cha ac e iza ion
The ma e ial analyzed is s ainless s eel AISI 304-H111 shee me al o 0.8 mm hickness.
The mechanical p ope ies ob ained om he ensile es s a e summa ized in Table 1[
10
]. As poin ed
ou in he ci ed p e ious wo k o he au ho s [
10
], he plas ic beha io o he ma e ial i s a Swi ’s
powe law as shown in Equa ion (1).
σ=Kε0+εP(1)
whe e Eis he elas ic modulus,
σy0.2
is he yield s ess, UTS he ul ima e ensile s ess, K,nand
ε0
a e
cons an s o he Swi ’s powe law depending on he ma e ial,
εP
is he equi alen plas ic s ain and
σ
he equi alen s ess.
Me als 2017,7, 531 4 o 14
Table 1. Mechanical p ope ies om ensile es s and Swi ’s powe law pa ame e s.
E(GPa) σy0.2 (MPa) UTS (MPa) K(GPa) nε0
207 503 669 1.55 0.594 0.055
2.2. Fo ming Limi Diag am
A se ies o Nakazima es s we e ca ied ou using a hemisphe ical punch o 100 mm diame e
using specimens co esponding o uniaxial, close o plane s ain and biaxial s ain condi ions.
The con en ional o ming limi s ep esen ed by he FLC and he FFL we e ob ained. In addi ion,
s e ch-bending es s using cylind ical punches o
Φ
20,
Φ
10 and
Φ
6 mm we e pe o med wi h he aim
o e alua ing he e ec o he bending induced by he ool adius in pos poning he onse o necking
due o he signi ican h ough- hickness s ain g adien induced by he cu a u e o he punches.
These o me cases led o s ain pa hs in be ween plane and uniaxial s ain. A leas 3 eplica es o
e e y es we e ca ied ou in o de o p o ide s a is ical meaning o he esul s ob ained.
The es s we e pe o med in a uni e sal shee me al es ing machine E ichsen 142-20 unde he
es ing condi ions o he s anda d ISO 12004-2:2008 [
13
]. The punch eloci y was se o 1 mm/s and he
lub ican a he in e ace punch-shee was Vaseline + PTFE + Vaseline. The sys em ARAMIS
®
, based
on digi al image co ela ion (DIC), was used a a a e o 12 ames pe second o e alua e he onse o
necking by using a me hodology p oposed by he au ho s [14].
Once he onse o necking is a ained, he majo s ain (
ε1
) o he poin s dis ibu ed a ound he
ailu e zone de elops uns ably close o plane s ain condi ions un il he ac u e s ains is eached,
being his beha io cha ac e is ic in he necking-con olled ailu e obse ed in all o he Nakazima and
s e ch-bending es s. Acco ding o his, he p ocedu e o cons uc ing he FFL s a s by measu ing
he hickness a ac u e a se e al places along he c ack in o de o ob ain he a e age hickness
s ain, which is e alua ed using he measu emen s a bo h sides o he c ack o e e y es ed specimen.
The a e age mino s ain is e alua ed along he ac u e line a he las image eco ded by ARAMIS®
be o e he c ack appea ance. The majo s ain is hen calcula ed by olume cons ancy as exp essed in
Equa ion (2).
ε1, =−ε2, −ε3, (2)
whe e
ε2,
and
ε3,
a e he a e age mino and hickness s ains e alua ed in a se ies o poin s along he
c ack line. In addi ion, i mus be poin ed ou ha some es ed specimens we e cu pe pendicula ly
o he c ack and he hickness was measu ed om a p o ile iew in o de o alida e he p e ious
hickness measu emen s along he c ack. This me hodology o de e mining he s ains a ac u e
is based on he wo k o A kins [
15
] and has been success ully used by he au ho s in ecen esea ch
wo k o measu ing ac u e s ains in o ming o shee me al [
10
], polyme ic shee s [
16
,
17
], o e en
o he p ocesses such as ube-end o ming [18].
Figu e 2depic s he o ming limi diag am o he AISI 304-H111 shee s including bending e ec s.
The e alua ion o he FLC and he FFL was pe o med by using he me hodologies exposed abo e and
only aking in o accoun he Nakazima es s. The a e age necking and ac u e s ains a e p o ided
o he 3 s ain pa hs conside ed. As can be seen, he FLC p esen s he expec ed V-shape whe eas he
FFL alls o he i s quad an o p incipal s ain ollowing he s aigh line
ε1
+ 0.69
ε2
= 1.08 wi h a
slope no a om he heo e ical alue o “
−
1” p oposed by A kins in [
15
]. The kink o he s ain
pa hs om he onse o necking owa ds ac u e is almos e ical in he i s quad an whe eas his
ansi ion in he second quad an su e s om a sligh le wa d slope, acco ding again o he ci ed
wo k o A kins. As can be seen, he bending e ec is ep esen ed by means o he a e age necking
and ac u e s ains (no used o ob aining he FLC and FFL) in he s e ch-bending es s. No ice ha
al hough he signi ican enhancemen o o mabili y a ained abo e he FLC due o his bending e ec
(which is u he discussed in [14]), he ac u e s ains a e placed on he FFL egion.
Me als 2017,7, 531 5 o 14
Me als 2017, 7, 531 5 o 14
Figu e 2. FLD o AISI 304-H111 shee s including bending e ec s.
2.3. Single Poin Inc emen al Fo ming Tes s
A Compu e Nume ic Con ol (CNC) 3-axis milling machine Kondia® HS1000 equipped wi h
he expe imen al se up shown in Figu e 1b was used o ca ying ou he SPIF es s. As shown in
Figu e 3a he es ing geome y was a conical us um wi h ci cula gene a ix o adius 40 mm, ini ial
diame e o he unca ed cone 70 mm, and ini ial d awing angle 20°. Tool diame e s o 20, 10 and 6
mm we e u ilized. The s ep down was se al e na i ely o 0.2 mm and 0.5 mm/pass. The s ep down
mo emen was in he same place du ing he es , ollowing he o ming ool al e na i ely in-plane
clockwise o coun e clockwise ajec o ies o consecu i e s ep downs (see Figu e 3b) in o de o
a oid o sion e ec s in he inal pa (see Figu e 3c). The ool o a ion was ee. Special me al- o ming
lub ican Hough on TD-52 was used wi h he aim o minimizing ic ion.
(a) (b) (c)
Figu e 3. (a) T unca ed coned geome y, (b) ool ajec o y and (c) inal pa a e es ing.
Table 2 shows he SPIF es s ca ied ou wi hin he expe imen al plan designed, which was
al eady p esen ed in [10]. Once again, h ee eplica es o e e y SPIF es we e ca ied o p o ide
s a is ical meaning o he esul s ob ained. The able p o ides he inal dep h eco ded in he ins an
in which he ailu e ook place and as well he p opo ional inal o ming angle calcula ed om he
p edic ed ajec o ies o o m he inal es ing pa geome y.
Figu e 2. FLD o AISI 304-H111 shee s including bending e ec s.
2.3. Single Poin Inc emen al Fo ming Tes s
A Compu e Nume ic Con ol (CNC) 3-axis milling machine Kondia
®
HS1000 equipped wi h he
expe imen al se up shown in Figu e 1b was used o ca ying ou he SPIF es s. As shown in Figu e 3a
he es ing geome y was a conical us um wi h ci cula gene a ix o adius 40 mm, ini ial diame e
o he unca ed cone 70 mm, and ini ial d awing angle 20
◦
. Tool diame e s o 20, 10 and 6 mm we e
u ilized. The s ep down was se al e na i ely o 0.2 mm and 0.5 mm/pass. The s ep down mo emen
was in he same place du ing he es , ollowing he o ming ool al e na i ely in-plane clockwise
o coun e clockwise ajec o ies o consecu i e s ep downs (see Figu e 3b) in o de o a oid o sion
e ec s in he inal pa (see Figu e 3c). The ool o a ion was ee. Special me al- o ming lub ican
Hough on TD-52 was used wi h he aim o minimizing ic ion.
Me als 2017, 7, 531 5 o 14
Figu e 2. FLD o AISI 304-H111 shee s including bending e ec s.
2.3. Single Poin Inc emen al Fo ming Tes s
A Compu e Nume ic Con ol (CNC) 3-axis milling machine Kondia® HS1000 equipped wi h
he expe imen al se up shown in Figu e 1b was used o ca ying ou he SPIF es s. As shown in
Figu e 3a he es ing geome y was a conical us um wi h ci cula gene a ix o adius 40 mm, ini ial
diame e o he unca ed cone 70 mm, and ini ial d awing angle 20°. Tool diame e s o 20, 10 and 6
mm we e u ilized. The s ep down was se al e na i ely o 0.2 mm and 0.5 mm/pass. The s ep down
mo emen was in he same place du ing he es , ollowing he o ming ool al e na i ely in-plane
clockwise o coun e clockwise ajec o ies o consecu i e s ep downs (see Figu e 3b) in o de o
a oid o sion e ec s in he inal pa (see Figu e 3c). The ool o a ion was ee. Special me al- o ming
lub ican Hough on TD-52 was used wi h he aim o minimizing ic ion.
(a) (b) (c)
Figu e 3. (a) T unca ed coned geome y, (b) ool ajec o y and (c) inal pa a e es ing.
Table 2 shows he SPIF es s ca ied ou wi hin he expe imen al plan designed, which was
al eady p esen ed in [10]. Once again, h ee eplica es o e e y SPIF es we e ca ied o p o ide
s a is ical meaning o he esul s ob ained. The able p o ides he inal dep h eco ded in he ins an
in which he ailu e ook place and as well he p opo ional inal o ming angle calcula ed om he
p edic ed ajec o ies o o m he inal es ing pa geome y.
Figu e 3. (a) T unca ed coned geome y, (b) ool ajec o y and (c) inal pa a e es ing.
Table 2shows he SPIF es s ca ied ou wi hin he expe imen al plan designed, which was al eady
p esen ed in [
10
]. Once again, h ee eplica es o e e y SPIF es we e ca ied o p o ide s a is ical
meaning o he esul s ob ained. The able p o ides he inal dep h eco ded in he ins an in which
Me als 2017,7, 531 6 o 14
he ailu e ook place and as well he p opo ional inal o ming angle calcula ed om he p edic ed
ajec o ies o o m he inal es ing pa geome y.
Table 2. Expe imen al plan o SPIF es s.
Tool Diame e Φ
(mm)
S ep Down ∆z
(mm/pass)
Final Dep h Z
(mm)
Final Fo ming Angle α
(◦)
20 0.2 23.8/23.8/23.8 69.8/69.8/69.8
0.5 24.5/24.0/24.0 70.9/70.1/70.1
10 0.2 28.0/28.2/28.2 76.1/76.4/76.4
0.5 27.5/28.0/28.0 70.9/70.1/70.1
60.2 28.2/28.0/28.8 76.4/76.1/77.3
0.5 28.0/28.5/28.0 76.1/76.9/76.1
The inal s ain s a e o he es ing specimens de o med by SPIF was e alua ed o -line by using
he 3D de o ma ion digi al measu emen sys em ARGUS
®
based on ci cle g id analysis. To his aim
a g id pa e n o 1 mm diame e was elec o-chemically edged on he shee blank p io o he es s.
Figu e 4a depic s he g id on he inal pa de o med by SPIF using a hemisphe ical o ming ool
o 20 mm diame e , whe eas Figu e 4b depic s he con ou o he majo p incipal s ain e alua ed
by ARGUS
®
(no ice he simila pa o ien a ion in Figu e 4a,b). The zone o maximum majo s ain
was loca ed a he icini y o he c ack co esponding o he in e pola ion o he s ains h oughou i
pe o med by ARGUS
®
. F ac u e s ains in SPIF we e ob ained ollowing he me hodology ha was
p e iously explained in Sec ion 2.2.
Me als 2017, 7, 531 6 o 14
Table 2. Expe imen al plan o SPIF es s.
Tool Diame e Φ (mm) S ep Down
Δz (mm/pass)
Final Dep h
Z (mm) Final Fo ming Angle α (°)
20 0.2 23.8/23.8/23.8 69.8/69.8/69.8
0.5 24.5/24.0/24.0 70.9/70.1/70.1
10 0.2 28.0/28.2/28.2 76.1/76.4/76.4
0.5 27.5/28.0/28.0 70.9/70.1/70.1
6 0.2 28.2/28.0/28.8 76.4/76.1/77.3
0.5 28.0/28.5/28.0 76.1/76.9/76.1
The inal s ain s a e o he es ing specimens de o med by SPIF was e alua ed o -line by using
he 3D de o ma ion digi al measu emen sys em ARGUS
®
based on ci cle g id analysis. To his aim
a g id pa e n o 1 mm diame e was elec o-chemically edged on he shee blank p io o he es s.
Figu e 4a depic s he g id on he inal pa de o med by SPIF using a hemisphe ical o ming ool o
20 mm diame e , whe eas Figu e 4b depic s he con ou o he majo p incipal s ain e alua ed by
ARGUS
®
(no ice he simila pa o ien a ion in Figu e 4a,b). The zone o maximum majo s ain was
loca ed a he icini y o he c ack co esponding o he in e pola ion o he s ains h oughou i
pe o med by ARGUS
®
. F ac u e s ains in SPIF we e ob ained ollowing he me hodology ha was
p e iously explained in Sec ion 2.2.
(a) (b)
Figu e 4. (a) Final g id and (b) con ou o ue majo p incipal s ain o a es ed pa by SPIF.
In o de o e alua e he p incipal s ains on he ou e su ace o he inal es ed pa s de o med
by SPIF wi hin he FLD o he ma e ial, se e al sec ions a e selec ed in e e y case, such as he sec ion
L1 o L3 shown in Figu e 4b. The alues o he in e pola ion o p incipal s ains p o ided by ARGUS
®
jus on he c ack line a e no aken in o accoun in he FLD, as a as he s ains a ac u e a e
calcula ed using he p ocedu e explained abo e.
3. Nume ical Modelling
This sec ion p esen s he nume ical model ca ied ou using DEFORM™-3D wi h he aim o
analyzing i ually o p o iding in o ma ion abou he ailu e p edic ion and he mechanisms
in ol ed in he enhancemen o o mabili y a ained in SPIF.
DEFORM™-3D is a comme cial Fini e Elemen Analysis (FEA) ool based on low o mula ion
and wi h implici compu a ion. Is i a powe ul nume ical ool ha has been mainly used ecen ly o
modelling manu ac u ing p ocesses such as cu ing [19] and bulk o ming o me als [20], bu i has
been also used o simula ing shee me al- o ming p ocesses [21,22].
The nume ical model in DEFORM™-3D was de eloped using 3D e ahed ons, ha ing he ini ial
mesh 50,000 elemen s. As can be seen in Figu e 5a, h ee ci cula meshing zones we e conside ed,
ha ing he in e media e annulus a smalle size o elemen s in o de o p o ide accu a e esul s wi hin
he ool-shee con ac egion co esponding o highe alues o majo s ain. Au oma ic emeshing
was used, allowing DEFORM™-3D o adap he mesh size in he zones a aining he highes s ain
alues. The punch is conside ed o be a igid body and ollows he eal ajec o y o he expe imen s.
Figu e 4. (a) Final g id and (b) con ou o ue majo p incipal s ain o a es ed pa by SPIF.
In o de o e alua e he p incipal s ains on he ou e su ace o he inal es ed pa s de o med by
SPIF wi hin he FLD o he ma e ial, se e al sec ions a e selec ed in e e y case, such as he sec ion L1 o
L3 shown in Figu e 4b. The alues o he in e pola ion o p incipal s ains p o ided by ARGUS
®
jus
on he c ack line a e no aken in o accoun in he FLD, as a as he s ains a ac u e a e calcula ed
using he p ocedu e explained abo e.
3. Nume ical Modelling
This sec ion p esen s he nume ical model ca ied ou using DEFORM
™
-3D wi h he aim o
analyzing i ually o p o iding in o ma ion abou he ailu e p edic ion and he mechanisms
in ol ed in he enhancemen o o mabili y a ained in SPIF.
DEFORM
™
-3D is a comme cial Fini e Elemen Analysis (FEA) ool based on low o mula ion
and wi h implici compu a ion. Is i a powe ul nume ical ool ha has been mainly used ecen ly o
modelling manu ac u ing p ocesses such as cu ing [
19
] and bulk o ming o me als [
20
], bu i has
been also used o simula ing shee me al- o ming p ocesses [21,22].
Me als 2017,7, 531 7 o 14
The nume ical model in DEFORM
™
-3D was de eloped using 3D e ahed ons, ha ing he ini ial
mesh 50,000 elemen s. As can be seen in Figu e 5a, h ee ci cula meshing zones we e conside ed,
ha ing he in e media e annulus a smalle size o elemen s in o de o p o ide accu a e esul s wi hin
he ool-shee con ac egion co esponding o highe alues o majo s ain. Au oma ic emeshing
was used, allowing DEFORM
™
-3D o adap he mesh size in he zones a aining he highes s ain
alues. The punch is conside ed o be a igid body and ollows he eal ajec o y o he expe imen s.
The elemen s co esponding o he a ea o shee me al in con ac wi h he backing pla e a e conside ed
o be clamped, as shown in Figu e 5b. The shee me al beha es as an elas ic-plas ic a e-independen
ma e ial wi h kinema ic ha dening. The elas ic-plas ic beha io is supposed o be iso opic ollowing
he Swi ’s powe law p esen ed in Sec ion 2.1. Due o he high compu a ional cos and aking in o
accoun he negligible in luence o he s ep down in o mabili y igge ed in [
10
], he s ep down was
se o 0.5 mm/pass in o de o educe he simula ion s eps. The simula ions we e pe o med un il a
e e ence inal dep h ela ed o he ool dep hs a ailu e p esen ed in Table 2, which we e chosen o be
24 mm o he case o a ool diame e o Φ20 mm and 28 mm o he case o Φ10 mm espec i ely.
Me als 2017, 7, 531 7 o 14
The elemen s co esponding o he a ea o shee me al in con ac wi h he backing pla e a e
conside ed o be clamped, as shown in Figu e 5b. The shee me al beha es as an elas ic-plas ic a e-
independen ma e ial wi h kinema ic ha dening. The elas ic-plas ic beha io is supposed o be
iso opic ollowing he Swi ’s powe law p esen ed in Sec ion 2.1. Due o he high compu a ional
cos and aking in o accoun he negligible in luence o he s ep down in o mabili y igge ed in [10],
he s ep down was se o 0.5 mm/pass in o de o educe he simula ion s eps. The simula ions we e
pe o med un il a e e ence inal dep h ela ed o he ool dep hs a ailu e p esen ed in Table 2, which
we e chosen o be 24 mm o he case o a ool diame e o Ф20 mm and 28 mm o he case o Ф10
mm espec i ely.
(a)
(b)
Figu e 5. (a) Meshing zones conside ed and (b) bounda y condi ions (clamped condi ion in “ ed”).
Figu e 6a,b depic s he de o med shape o he simula ion o he SPIF p ocess conside ing a s ep
down o 0.5 mm/pass using a ool o Ф20 and Ф10 mm espec i ely. Figu e 6c shows he con ou o
majo p incipal s ains co esponding o he case o a ool o Ф20 mm (shown in Figu e 6a). No ice
ha in his case, he maximum alue o he majo s ain (ε
1
) p o ided by he FEA was 0.879.
(a)
(c)
(b)
Figu e 6. (a) De o med shape p o ided by DEFORM™-3D o he inal es ing pa in SPIF using a ool
o Ф20 diame e and (b) Ф10 mm. (c) con ou o p incipal s ain o he case o Ф20 mm.
Finally, i is wo h men ioning ha he o e all cen al p ocessing uni (CPU) ime o a ypical
analysis shown in Figu e 6c, which include 6 emeshing p ocesses, was app oxima ely 85 h on a
lap op using one In el i7-6500U CPU (2.60 GHz) p ocesso .
4. Resul s and Discussion
In his sec ion, he expe imen al and nume ical esul s ega ding o mabili y and ailu e o
AISI304-H111 shee s de o med in SPIF a e p esen ed. In Sec ion 4.1, he limi s o he o mabili y
enhancemen o small ool diame e s a e e alua ed wi hin he FLD o he ma e ial. A ac og aphy
analysis is used o cla i y he mode o ailu e a ained, he loca ion whe e he c ack ini ia es and how
Figu e 5. (a) Meshing zones conside ed and (b) bounda y condi ions (clamped condi ion in “ ed”).
Figu e 6a,b depic s he de o med shape o he simula ion o he SPIF p ocess conside ing a s ep
down o 0.5 mm/pass using a ool o
Φ
20 and
Φ
10 mm espec i ely. Figu e 6c shows he con ou o
majo p incipal s ains co esponding o he case o a ool o
Φ
20 mm (shown in Figu e 6a). No ice
ha in his case, he maximum alue o he majo s ain (ε1) p o ided by he FEA was 0.879.
Me als 2017, 7, 531 7 o 14
The elemen s co esponding o he a ea o shee me al in con ac wi h he backing pla e a e
conside ed o be clamped, as shown in Figu e 5b. The shee me al beha es as an elas ic-plas ic a e-
independen ma e ial wi h kinema ic ha dening. The elas ic-plas ic beha io is supposed o be
iso opic ollowing he Swi ’s powe law p esen ed in Sec ion 2.1. Due o he high compu a ional
cos and aking in o accoun he negligible in luence o he s ep down in o mabili y igge ed in [10],
he s ep down was se o 0.5 mm/pass in o de o educe he simula ion s eps. The simula ions we e
pe o med un il a e e ence inal dep h ela ed o he ool dep hs a ailu e p esen ed in Table 2, which
we e chosen o be 24 mm o he case o a ool diame e o Ф20 mm and 28 mm o he case o Ф10
mm espec i ely.
(a)
(b)
Figu e 5. (a) Meshing zones conside ed and (b) bounda y condi ions (clamped condi ion in “ ed”).
Figu e 6a,b depic s he de o med shape o he simula ion o he SPIF p ocess conside ing a s ep
down o 0.5 mm/pass using a ool o Ф20 and Ф10 mm espec i ely. Figu e 6c shows he con ou o
majo p incipal s ains co esponding o he case o a ool o Ф20 mm (shown in Figu e 6a). No ice
ha in his case, he maximum alue o he majo s ain (ε
1
) p o ided by he FEA was 0.879.
(a)
(c)
(b)
Figu e 6. (a) De o med shape p o ided by DEFORM™-3D o he inal es ing pa in SPIF using a ool
o Ф20 diame e and (b) Ф10 mm. (c) con ou o p incipal s ain o he case o Ф20 mm.
Finally, i is wo h men ioning ha he o e all cen al p ocessing uni (CPU) ime o a ypical
analysis shown in Figu e 6c, which include 6 emeshing p ocesses, was app oxima ely 85 h on a
lap op using one In el i7-6500U CPU (2.60 GHz) p ocesso .
4. Resul s and Discussion
In his sec ion, he expe imen al and nume ical esul s ega ding o mabili y and ailu e o
AISI304-H111 shee s de o med in SPIF a e p esen ed. In Sec ion 4.1, he limi s o he o mabili y
enhancemen o small ool diame e s a e e alua ed wi hin he FLD o he ma e ial. A ac og aphy
analysis is used o cla i y he mode o ailu e a ained, he loca ion whe e he c ack ini ia es and how
Figu e 6.
(
a
) De o med shape p o ided by DEFORM
™
-3D o he inal es ing pa in SPIF using a ool
o Φ20 diame e and (b)Φ10 mm. (c) con ou o p incipal s ain o he case o Φ20 mm.
Finally, i is wo h men ioning ha he o e all cen al p ocessing uni (CPU) ime o a ypical
analysis shown in Figu e 6c, which include 6 emeshing p ocesses, was app oxima ely 85 h on a lap op
using one In el i7-6500U CPU (2.60 GHz) p ocesso .
4. Resul s and Discussion
In his sec ion, he expe imen al and nume ical esul s ega ding o mabili y and ailu e o
AISI304-H111 shee s de o med in SPIF a e p esen ed. In Sec ion 4.1, he limi s o he o mabili y
enhancemen o small ool diame e s a e e alua ed wi hin he FLD o he ma e ial. A ac og aphy
Me als 2017,7, 531 8 o 14
analysis is used o cla i y he mode o ailu e a ained, he loca ion whe e he c ack ini ia es and how i
e ol es once ailu e is eached. Sec ion 4.2 discusses he nume ical esul s ob ained, p esen ing he
condi ions upon which necking is supp essed, leading di ec ly o duc ile ac u e in SPIF.
4.1. Expe imen al Resul s
Figu e 7depic s he p incipal s ain s a e a he ou e su ace o he inal es ing pa de o med by
SPIF using ool diame e s o
Φ
20,
Φ
10 and
Φ
6 mm ep esen ed wi hin he FLD o he AISI 304 me al
shee s o a s ep down o 0.5 mm/pass (as discussed in [
10
], a ia ions o s ep down in he ange
o 0.2–0.5 mm did no ha e a ele an in luence in o mabili y). Al hough he h ee cases show an
impo an enhancemen o o mabili y well abo e he FLC, he inc ease o o mabili y as well as he
mode o ailu e di e s o he di e en punch adii. In his ega d, he ansi ion be ween he las
poin s o o mabili y p o ided by ARGUS
®
and he p incipal s ains a ac u e e alua ed wi h he
p ocedu e exposed in Sec ion 2.2, is ep esen ed in Figu e 7in do ed line. As i was discussed in [
10
],
in he case o a o ming ool o
Φ
20 mm diame e he ailu e mechanism was pos poned necking
ollowed by duc ile ac u e, whe eas in he case o
Φ
10 mm, he ac og aphy showed a se ies o
g oo es, which has been ela ed o an incipien necking [
23
]. In his sense, he s ain s a e a ained in
he case o
Φ
6 mm (see Figu e 7) almos coincides wi h he ob ained in he case o
Φ
10 mm. Howe e ,
in o de o e alua e he mode o ailu e, a ac og aphy analysis is pe o med. Besides, i mus be
no iced ha he ac u e s ains in SPIF a e sligh ly abo e he sca e band o
±
10% wi h espec o he
FFL (which conside ed only he ac u e s ains a ained in he Nakazima es s). This expe imen al ac
also ound in o he wo ks [
8
,
10
], implies ha o some ma e ials Nakazima es s migh no be sui able
o e alua ing he FFL o be used in SPIF. Indeed, he le el o iaxiali y in s e ching (e.g., Nakazima)
is much highe han in ISF and hen, he abili y o each he ac u e limi will depend on he sensi i i y
o he ma e ial o he iaxiali y s a e o ac u e.
Me als 2017, 7, 531 8 o 14
i e ol es once ailu e is eached. Sec ion 4.2 discusses he nume ical esul s ob ained, p esen ing he
condi ions upon which necking is supp essed, leading di ec ly o duc ile ac u e in SPIF.
4.1. Expe imen al Resul s
Figu e 7 depic s he p incipal s ain s a e a he ou e su ace o he inal es ing pa de o med
by SPIF using ool diame e s o Ф20, Ф10 and Ф6 mm ep esen ed wi hin he FLD o he AISI 304
me al shee s o a s ep down o 0.5 mm/pass (as discussed in [10], a ia ions o s ep down in he ange
o 0.2–0.5 mm did no ha e a ele an in luence in o mabili y). Al hough he h ee cases show an
impo an enhancemen o o mabili y well abo e he FLC, he inc ease o o mabili y as well as he
mode o ailu e di e s o he di e en punch adii. In his ega d, he ansi ion be ween he las
poin s o o mabili y p o ided by ARGUS® and he p incipal s ains a ac u e e alua ed wi h he
p ocedu e exposed in Sec ion 2.2, is ep esen ed in Figu e 7 in do ed line. As i was discussed in [10],
in he case o a o ming ool o Ф20 mm diame e he ailu e mechanism was pos poned necking
ollowed by duc ile ac u e, whe eas in he case o Ф10 mm, he ac og aphy showed a se ies o
g oo es, which has been ela ed o an incipien necking [23]. In his sense, he s ain s a e a ained in
he case o Ф6 mm (see Figu e 7) almos coincides wi h he ob ained in he case o Ф10 mm. Howe e ,
in o de o e alua e he mode o ailu e, a ac og aphy analysis is pe o med. Besides, i mus be
no iced ha he ac u e s ains in SPIF a e sligh ly abo e he sca e band o ±10% wi h espec o he
FFL (which conside ed only he ac u e s ains a ained in he Nakazima es s). This expe imen al
ac also ound in o he wo ks [8,10], implies ha o some ma e ials Nakazima es s migh no be
sui able o e alua ing he FFL o be used in SPIF. Indeed, he le el o iaxiali y in s e ching (e.g.,
Nakazima) is much highe han in ISF and hen, he abili y o each he ac u e limi will depend on
he sensi i i y o he ma e ial o he iaxiali y s a e o ac u e.
Figu e 7. P incipal s ain s a e o he inal es ing pa de o med by SPIF using ool diame e s o Ф20,
Ф10 and Ф6 mm ep esen ed wi hin he FLD o he ma e ial.
Figu e 7.
P incipal s ain s a e o he inal es ing pa de o med by SPIF using ool diame e s o
Φ
20,
Φ10 and Φ6 mm ep esen ed wi hin he FLD o he ma e ial.
Me als 2017,7, 531 9 o 14
In o de o e alua e he ailu e mode and se he limi s ain condi ions a ailu e ega ding he
enhancemen o o mabili y a ained in SPIF ela ed o he
0
/R a io, he ac u e zone was analyzed
by mic oscope o he case o he smalles ool diame e o
Φ
6 mm. Figu e 8depic s he ac og aphy
a wo sec ions o he inal unca ed cone. Sec ion A-A’ co esponds o he zone in which i seems
ha he c ack is abou o ini ia e whe eas sec ion B-B’ is placed wi hin he c ack line close o i s end.
On sec ion A-A’, a e y incipien necking can be obse ed. On he con a y, sec ion B-B’ depic s a
duc ile ac u e co esponding o a mono onous dec ease o hickness un il ac u e. In bo h sec ions,
he inden a ion p oduced by he ool can be easily obse ed. This inden a ion p oduced in ce ain SPIF
condi ions, mos ly o small ool diame e s, has been also e alua ed using nume ical ools [24].
This ac og aphic analysis led o he conclusion o he ailu e mode a ained. In his sense,
i seems ha he pa could be de o med plas ically abo e he FLC p esen ing he ci ed mono onous
dec ease o hickness un il duc ile ac u e ook place, being only possible o egis e a much pos poned
incipien necking. Indeed, he e was a compe i ion be ween he bending e ec ep esen ed by he
0
/R
a io, which is he key ac o o he inc eased o mabili y in SPIF, and he ool inden a ion, ha made
his speci ic p ocess o each a h eshold o he enhancemen o o mabili y o a ool diame e wi hin
he ange o 10 mm o 6 mm.
Me als 2017, 7, 531 9 o 14
In o de o e alua e he ailu e mode and se he limi s ain condi ions a ailu e ega ding he
enhancemen o o mabili y a ained in SPIF ela ed o he 0/R a io, he ac u e zone was analyzed
by mic oscope o he case o he smalles ool diame e o Ф6 mm. Figu e 8 depic s he ac og aphy
a wo sec ions o he inal unca ed cone. Sec ion A-A’ co esponds o he zone in which i seems
ha he c ack is abou o ini ia e whe eas sec ion B-B’ is placed wi hin he c ack line close o i s end.
On sec ion A-A’, a e y incipien necking can be obse ed. On he con a y, sec ion B-B’ depic s a
duc ile ac u e co esponding o a mono onous dec ease o hickness un il ac u e. In bo h sec ions,
he inden a ion p oduced by he ool can be easily obse ed. This inden a ion p oduced in ce ain
SPIF condi ions, mos ly o small ool diame e s, has been also e alua ed using nume ical ools [24].
This ac og aphic analysis led o he conclusion o he ailu e mode a ained. In his sense, i
seems ha he pa could be de o med plas ically abo e he FLC p esen ing he ci ed mono onous
dec ease o hickness un il duc ile ac u e ook place, being only possible o egis e a much
pos poned incipien necking. Indeed, he e was a compe i ion be ween he bending e ec ep esen ed
by he 0/R a io, which is he key ac o o he inc eased o mabili y in SPIF, and he ool inden a ion,
ha made his speci ic p ocess o each a h eshold o he enhancemen o o mabili y o a ool
diame e wi hin he ange o 10 mm o 6 mm.
Figu e 8. F ac og aphy o he ac u e zone a 2 sec ions o a ool diame e o Ф6 mm. Sec ion A-A’
co esponds o he c ack ini ia ion whe eas sec ion B-B’ is placed close o i s end.
Mo eo e , ela ed o he de e mina ion o he ailu e mode, i is impo an o es ablish how he
c ack ini ia es and de elops in he SPIF p ocess. Wi h his aim, he online measu emen o he o ming
o ce allowed igge ing he ac ual dep h in which ailu e was a ained o e e y es (in o ma ion
shown in Table 2). Indeed, a he p ecise ins an in which ailu e is eached, he e is a d op down in
he e ical o ce e olu ion ha se es o s op he p ocess and calib a e he inal dep h.
Some ep esen a i e es s co esponding o a ool diame e o Ф6 mm (ma ked in bold in Table
2) we e selec ed o show he ini ia ion and e olu ion o he c ack. Figu e 9 depic s he de eloped
su aces con aining he c ack co esponding o he 3 es s o a s ep down 0.5 mm/pass (Tes 1 o 3 in
Table 2) eaching inal dep hs o 28.0, 28.5 and 28.0 mm and he second es (Tes 2) co esponding o
a s ep down o 0.2 mm/pass. Assuming he al e na i e mo emen o he ool o successi e passes
shown in Figu e 3b, i is easy o unde s and he di ec ion o he igh wa d c ack e olu ion in 3 o he
cases, and he le wa d c ack e olu ion in he case o eaching ailu e a a inal dep h o 28.5 mm (Tes
Figu e 8.
F ac og aphy o he ac u e zone a 2 sec ions o a ool diame e o
Φ
6 mm. Sec ion A-A’
co esponds o he c ack ini ia ion whe eas sec ion B-B’ is placed close o i s end.
Mo eo e , ela ed o he de e mina ion o he ailu e mode, i is impo an o es ablish how he
c ack ini ia es and de elops in he SPIF p ocess. Wi h his aim, he online measu emen o he o ming
o ce allowed igge ing he ac ual dep h in which ailu e was a ained o e e y es (in o ma ion
shown in Table 2). Indeed, a he p ecise ins an in which ailu e is eached, he e is a d op down in he
e ical o ce e olu ion ha se es o s op he p ocess and calib a e he inal dep h.
Some ep esen a i e es s co esponding o a ool diame e o
Φ
6 mm (ma ked in bold in Table 2)
we e selec ed o show he ini ia ion and e olu ion o he c ack. Figu e 9depic s he de eloped su aces
con aining he c ack co esponding o he 3 es s o a s ep down 0.5 mm/pass (Tes 1 o 3 in Table 2)
eaching inal dep hs o 28.0, 28.5 and 28.0 mm and he second es (Tes 2) co esponding o a s ep
down o 0.2 mm/pass. Assuming he al e na i e mo emen o he ool o successi e passes shown
in Figu e 3b, i is easy o unde s and he di ec ion o he igh wa d c ack e olu ion in 3 o he cases,
and he le wa d c ack e olu ion in he case o eaching ailu e a a inal dep h o 28.5 mm (Tes 2
co esponding o a s ep down o 0.5 mm/pass). This obse a ion o he c ack allows concluding ha
he c ack ini ia es a a ce ain loca ion whe e he limi ing p incipal s ains a e eached (o he FFL in
