me als
A icle
Flow S ess and Ho De o ma ion Ac i a ion Ene gy
o 6082 Aluminium Alloy In luenced by Ini ial
S uc u al S a e
I o Schindle 1,* , Pe Kawulok 1, Vladi oj Oˇcenášek 2, Pe Opˇela 1, Ros isla Kawulok 1
and S anisla Rusz 1
1Facul y o Ma e ials Science and Technology, VŠB – Technical Uni e si y o Os a a, 17. lis opadu 2172/15,
70800 Os a a, Czech Republic; pe [email p o ec ed] (P.K.); pe [email p o ec ed] (P.O.);
os isla [email p o ec ed] (R.K.); s anisla . [email p o ec ed] (S.R.)
2SVÚM a.s., To á ní2053, 25088 ˇ
Celáko ice, Czech Republic; [email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +420-596995215
Recei ed: 11 Oc obe 2019; Accep ed: 20 No embe 2019; Published: 22 No embe 2019


Abs ac :
S ess-s ain cu es o he EN AW 6082 aluminium alloy wi h 1.2 Si-0.51 Mg-0.75 Mn
(w .%) we e de e mined by he uniaxial comp ession es s a empe a u es o 450–550
◦
C wi h
a s ain a e o 0.5–10 s
−1
. The ini ial s uc u e s a e co esponded o h ee p ocessing ypes: as-cas
s uc u e non-homogenized o homogenized a 500
◦
C, and he s uc u e a e homogeniza ion and
ho ex usion. Signi ican ly highe low s ess appea ed as a esul o low empe a u e o ming o
he non-homogenized ma e ial. Ho de o ma ion ac i a ion ene gy Q- alues a ied be ween 99
and 122 kJ
·
mol
−1
o bo h homogenized ma e ials and om 200 o 216 kJ
·
mol
−1
o he as-cas s a e,
while he Q- alues calcula ed om he measu ed s eady-s a e s ess we e always highe han hose
calcula ed om he peak s ess alues. Fo he ex uded s a e o he 6082 alloy, he physically-based
model was de eloped o eliably p edic he low s ess in luenced by dynamic so ening, empe a u e,
s ain a e, and ue s ain up o 0.6.
Keywo ds: aluminium alloy; mic os uc u e; ho de o ma ion; ac i a ion ene gy; low s ess model
1. In oduc ion
In addi ion o hei chemical composi ion, he ho o ming p ocesses o aluminium alloys a e
signi ican ly in luenced by he ini ial s uc u e. The s a e o he s uc u e a ec s he plas ic de o ma ion
ha can be achie ed, and, hus, a ec s he economic pa ame e s o he p oduc ion.
The wo k aimed o de e mine he in luence o he ini ial s uc u e on selec ed aspec s o ho
de o ma ion beha iou o he EN AW 6082 aluminium alloy (AlSi1MgMn). Due o he ine-g ained
mic os uc u e, his alloyexhibi sgood esis ance odynamicloading condi ions. I s ypicalapplica ions
a e as ollows: o sho e cons uc ions, au omo i e suspension componen s, ail coach pa s, and mobile
c anes componen s. The age-ha dened 6082 alloy o e s an excellen combina ion o mechanical
p ope ies and co osion esis ance [1].
Many au ho s ha e discussed he in luence o homogeniza ion annealing on he cou se o ho
o ming p ocesses and inal p ope ies o p oduc s made o 6082 alloy. The subjec o in e es is bo h he
in insic e ec o homogeniza ion on he s uc u e and o ma ion o in e me allic phases [
2
,
3
], as well as
on he ho o ming p ocess [
4
–
6
], o on he ec ys alliza ion and ha dening du ing hea ea men [
7
–
9
].
The pape [
10
] de ails he ansi ion om ex uded ods o he as-cas and homogenized s uc u e
in he p oduc ion o die o gings. The ine-g ained as-cas s uc u e does no change signi ican ly
du ing o ging. This s uc u e a oids he o ma ion o su ace ec ys allized laye s ha a e ypical
Me als 2019,9, 1248; doi:10.3390/me 9121248 www.mdpi.com/jou nal/me als
Me als 2019,9, 1248 2 o 15
o die- o ged ex uded ods. Since hese laye s dec ease he mechanical p ope ies and he o ging
su ace quali y, he ini ial as-cas s uc u e o die o ming is p omising a his poin .
The homogenizing annealing o he as-cas s uc u e o aluminium alloys be o e ho o ming is
cu en ly an essen ial pa o he ex usion echnology o ods, which a e mainly used o die o ging.
I s a ou able e ec on he low s ess is he eason why homogeniza ion annealing o con inuously
cas ma e ial is used in an e o o p oduce o gings o demanding use in he au omo i e indus y, i.e.,
ods (ho izon al di ec chill cas ing [
11
]) o s ips ( win-bel cas ing [
12
]). Omi ing homogeniza ion
annealing om he die o ging p ocess is no planned o his eason, despi e he indispu able ene gy
sa ings. The e o e, in o ma ion on es s o p oduc ion o die o gings om non-homogenized as-cas
ma e ials is cu en ly no a ailable.
The s a e o he ini ial s uc u e be o e ho o ming (ex uded, as-cas homogenized, as-cas
non-homogenized) signi ican ly a ec s no only he ac ual ho o ming p ocess bu is also e lec ed
in he a ea o hea ea men . The esul ing mechanical, du abili y, and co osion p ope ies o he
o gings a e he esul o in e ac ion o he ini ial s uc u e, he ho de o ma ion pa ame e s, solu ion
annealing, and a i icial aging. The e o e, hese ela i ely complica ed connec ions ha e been he
subjec o se e al esea ch wo ks (see Re e ences [13–16]).
2. Cha ac e is ics o he Expe imen al Ma e ial
Th ee a ian s o he s uc u al s a e o he 6082 alloy we e in es iga ed (see Table 1 o chemical
composi ion).
Table 1. Chemical composi ion o expe imen al ma e ial in w . %.
Alloy Si Fe Cu Mn Mg C Zn Ti Al
EN AW 6082
0.7–1.3
max.
0.50
max.
0.10
0.4–1.0 0.6–1.2
max.
0.25
max.
0.20
max.
0.10
emainde
Ex uded od 0.93 0.16 0.06 0.68 0.76 0.14 0.01 0.05
emainde
As-cas od 0.93 0.15 0.07 0.53 0.74 0.13 0.01 0.03
emainde
Theywe econ inuouslycas odswi h a diame e o 55 mm in homogenized and non-homogenized
s a es as well as he ex uded od o he same diame e . The homogenizing annealing o he cas od
was ca ied ou a 530
◦
C o 8 h ollowed by slow ai cooling. Homogeniza ion was also ca ied
ou be o e ex usion. The cu ings om h ee di e en ods we e u ilized o p oduce samples o
subsequen ho comp ession es ing. The cu ings we e sec ioned pa allel o he axis along he
cen eline and me allog aphically p epa ed. Me allog aphic cu s we e e ched wi h he Kelle ’s eagen
o 30 s and obse ed on he in e ed ligh mic oscope ZEISS Axio Obse e Z1m (ZEISS, Jena,
Ge many). The s uc u e o he cas non-homogenized od is shown in Figu e 1, and he s uc u e
a e homogeniza ion is shown in Figu e 2. The e ec o homogeniza ion is appa en on he shape and
size o he in e me allic phases deposi ed a he bounda ies o he as-cas g ains. Homogeniza ion
annealing pa ially dissol es hese pa icles and ounds hem.
The s uc u e o he ex uded od (see Figu e 3) is ib ous in he di ec ion o pe o med ex usion
wi h appa en sub-g ains in he so ened aluminium ma ix.
Me als 2019,9, 1248 3 o 15
Me als 2019, 9, x FOR PEER REVIEW 3 o 16
Figu e 1. S uc u e o as-cas g ains and in e me allic phase cas od, which is non-homogenized.
Figu e 2. S uc u e o as-cas g ains and in e me allic phase–cas od, homogenized.
The s uc u e o he ex uded od (see Figu e 3) is ib ous in he di ec ion o pe o med
ex usion wi h appa en sub-g ains in he so ened aluminium ma ix.
Figu e 1. S uc u e o as-cas g ains and in e me allic phase cas od, which is non-homogenized.
Me als 2019, 9, x FOR PEER REVIEW 3 o 16
Figu e 1. S uc u e o as-cas g ains and in e me allic phase cas od, which is non-homogenized.
Figu e 2. S uc u e o as-cas g ains and in e me allic phase–cas od, homogenized.
The s uc u e o he ex uded od (see Figu e 3) is ib ous in he di ec ion o pe o med
ex usion wi h appa en sub-g ains in he so ened aluminium ma ix.
Figu e 2. S uc u e o as-cas g ains and in e me allic phase–cas od, homogenized.
The as-cas s uc u e is o med by he
α
-Al solid solu ion wi h he in e me allic phases a g ain
bounda ies. The di e en na u e o he in e me allic phases in he as-cas and ex uded s uc u es
is appa en om Figu es 4–6ob ained by he SEM me hod (seconda y elec on imaging). Scanning
elec on mic oscope ZEISS EVO 10 (ZEISS, Jena, Ge many) wi h backsca e de ec o and he Elemen
EDS sys em was used. In acco dance wi h esul s published in Re e ence [
8
], he in e me allic phases
β
-AlFeSiand
α
-AlFeMnSican beassumedaswell assomecoa se
β
-Mg
2
Sipa icles. The changeinphase
mo phology due o homogeniza ion annealing wi h slow cooling is e y e iden om a compa ison o
Figu es 1and 2, espec i ely (Figu es 4and 5). Homogeniza ion leads o he ans o ma ion o he
β
-AlFeSi phase in o he smalle ounded dispe soids o he
α
-AlFeMnSi ype. The ine p ecipi a es
should be he pa icles o he
β
-Mg
2
Si phase, o med by p ecipi a ion om he dissol ed pa icles
du ing slow cooling a e homogeniza ion [
17
,
18
]. Plas ic de o ma ion causes he in e me allic phases
o be c ushed in o lines pa allel o he di ec ion o ex usion ha was pe o med (see Figu e 6).
This c ea es a ib ous s uc u e and he size o he la ge pa icles can dec ease. The
α
-pa icle size is
mo e han 10 µm in he cas s a e. A e homogeniza ion, i d ops o an a e age size o abou 2 µm.
Me als 2019,9, 1248 4 o 15
Me als 2019, 9, x FOR PEER REVIEW 4 o 16
Figu e 3. S uc u e o g ains in longi udinal di ec ion–ex uded od (ex usion di ec ion indica ed by
he ed a ow).
The as-cas s uc u e is o med by he α-Al solid solu ion wi h he in e me allic phases a g ain
bounda ies. The di e en na u e o he in e me allic phases in he as-cas and ex uded s uc u es is
appa en om Figu es 4 o 6 ob ained by he SEM me hod (seconda y elec on imaging). Scanning
elec on mic oscope ZEISS EVO 10 (ZEISS, Jena, Ge many) wi h backsca e de ec o and he
Elemen EDS sys em was used. In acco dance wi h esul s published in Re e ence [8], he
in e me allic phases β-AlFeSi and α-AlFeMnSi can be assumed as well as some coa se β-Mg2Si
pa icles. The change in phase mo phology due o homogeniza ion annealing wi h slow cooling is
e y e iden om a compa ison o Figu es 1 and 2, espec i ely (Figu es 4 and 5). Homogeniza ion
leads o he ans o ma ion o he β-AlFeSi phase in o he smalle ounded dispe soids o he
α-AlFeMnSi ype. The ine p ecipi a es should be he pa icles o he β-Mg2Si phase, o med by
p ecipi a ion om he dissol ed pa icles du ing slow cooling a e homogeniza ion [17,18]. Plas ic
de o ma ion causes he in e me allic phases o be c ushed in o lines pa allel o he di ec ion o
ex usion ha was pe o med (see Figu e 6). This c ea es a ib ous s uc u e and he size o he la ge
pa icles can dec ease. The α-pa icle size is mo e han 10 µm in he cas s a e. A e homogeniza ion,
i d ops o an a e age size o abou 2 µm.
Figu e 4. In e me allic α-AlFeMnSi phase in he cas non-homogenized od.
Figu e 3.
S uc u e o g ains in longi udinal di ec ion–ex uded od (ex usion di ec ion indica ed by
he ed a ow).
Me als 2019, 9, x FOR PEER REVIEW 4 o 16
Figu e 3. S uc u e o g ains in longi udinal di ec ion–ex uded od (ex usion di ec ion indica ed by
he ed a ow).
The as-cas s uc u e is o med by he α-Al solid solu ion wi h he in e me allic phases a g ain
bounda ies. The di e en na u e o he in e me allic phases in he as-cas and ex uded s uc u es is
appa en om Figu es 4 o 6 ob ained by he SEM me hod (seconda y elec on imaging). Scanning
elec on mic oscope ZEISS EVO 10 (ZEISS, Jena, Ge many) wi h backsca e de ec o and he
Elemen EDS sys em was used. In acco dance wi h esul s published in Re e ence [8], he
in e me allic phases β-AlFeSi and α-AlFeMnSi can be assumed as well as some coa se β-Mg2Si
pa icles. The change in phase mo phology due o homogeniza ion annealing wi h slow cooling is
e y e iden om a compa ison o Figu es 1 and 2, espec i ely (Figu es 4 and 5). Homogeniza ion
leads o he ans o ma ion o he β-AlFeSi phase in o he smalle ounded dispe soids o he
α-AlFeMnSi ype. The ine p ecipi a es should be he pa icles o he β-Mg2Si phase, o med by
p ecipi a ion om he dissol ed pa icles du ing slow cooling a e homogeniza ion [17,18]. Plas ic
de o ma ion causes he in e me allic phases o be c ushed in o lines pa allel o he di ec ion o
ex usion ha was pe o med (see Figu e 6). This c ea es a ib ous s uc u e and he size o he la ge
pa icles can dec ease. The α-pa icle size is mo e han 10 µm in he cas s a e. A e homogeniza ion,
i d ops o an a e age size o abou 2 µm.
Figu e 4. In e me allic α-AlFeMnSi phase in he cas non-homogenized od.
Figu e 4. In e me allic α-AlFeMnSi phase in he cas non-homogenized od.
Me als 2019, 9, x FOR PEER REVIEW 5 o 16
Figu e 5. In e me allic phase and p ecipi a es in he cas homogenized od.
Figu e 6. Disin eg a ed in e me allic phases in he ex uded od.
3. S ess-S ain Cu es
Cylind ical samples wi h a diame e o 10 mm and a heigh o 15 mm we e p oduced om he
supplied ma e ial. On he Hyd awedge II module (componen o he Gleeble 3800 ho de o ma ion
simula o (DSI, Poes enkill, NY, USA), he samples we e subjec ed o uniaxial comp ession wi h he
heigh educ ion co esponding o a ue s ain o 0.7. The samples we e hea ed up o he o ming
empe a u e, i.e., 450 °C, 500 °C, and 550 °C. The holding ime o 500 s was ollowed by de o ma ion
a nominal s ain a es o 0.5 s−1, 1 s−1, 5 s−1, and 10 s−1. The dange o alling o he usually welded
he mocouples du ing he es s was elimina ed by s u ing he K- ype he mocouple wi es in o he
holes d illed in o he used samples. These holes we e uni o mly 1.0 mm in diame e and 1.5 mm
deep. The de o med samples we e cooled eely, wi hou s uc u e ixa ion, because only he ini ial
s uc u e o all h ee ypes o ma e ial was in es iga ed wi h espec o he esea ch objec i es. The
ob ained cu es o low s ess σ [MPa] depending on he ue s ain e [–], empe a u e T [°C], and
s ain a e ė [s−1] we e smoo hed in he O igin so wa e and digi ized wi h a s ain s ep o 0.02.
Examples o he esul ing s ess-s ain cu es a e shown in compa a i e Figu es 7 and 8. The le e C
indica es he as-cas s a e, he le e H shows he s a e a e homogeniza ion, and he le e E
indica es he s a e a e ho ex usion. S ess alues co esponding o he peak (i.e., maximum alues
in indi idual es s) σp [MPa] and s eady-s a e low σss [MPa] we e de e mined o each cu e. Since
Figu e 5. In e me allic phase and p ecipi a es in he cas homogenized od.
Me als 2019,9, 1248 5 o 15
Me als 2019, 9, x FOR PEER REVIEW 5 o 16
Figu e 5. In e me allic phase and p ecipi a es in he cas homogenized od.
Figu e 6. Disin eg a ed in e me allic phases in he ex uded od.
3. S ess-S ain Cu es
Cylind ical samples wi h a diame e o 10 mm and a heigh o 15 mm we e p oduced om he
supplied ma e ial. On he Hyd awedge II module (componen o he Gleeble 3800 ho de o ma ion
simula o (DSI, Poes enkill, NY, USA), he samples we e subjec ed o uniaxial comp ession wi h he
heigh educ ion co esponding o a ue s ain o 0.7. The samples we e hea ed up o he o ming
empe a u e, i.e., 450 °C, 500 °C, and 550 °C. The holding ime o 500 s was ollowed by de o ma ion
a nominal s ain a es o 0.5 s−1, 1 s−1, 5 s−1, and 10 s−1. The dange o alling o he usually welded
he mocouples du ing he es s was elimina ed by s u ing he K- ype he mocouple wi es in o he
holes d illed in o he used samples. These holes we e uni o mly 1.0 mm in diame e and 1.5 mm
deep. The de o med samples we e cooled eely, wi hou s uc u e ixa ion, because only he ini ial
s uc u e o all h ee ypes o ma e ial was in es iga ed wi h espec o he esea ch objec i es. The
ob ained cu es o low s ess σ [MPa] depending on he ue s ain e [–], empe a u e T [°C], and
s ain a e ė [s−1] we e smoo hed in he O igin so wa e and digi ized wi h a s ain s ep o 0.02.
Examples o he esul ing s ess-s ain cu es a e shown in compa a i e Figu es 7 and 8. The le e C
indica es he as-cas s a e, he le e H shows he s a e a e homogeniza ion, and he le e E
indica es he s a e a e ho ex usion. S ess alues co esponding o he peak (i.e., maximum alues
in indi idual es s) σp [MPa] and s eady-s a e low σss [MPa] we e de e mined o each cu e. Since
Figu e 6. Disin eg a ed in e me allic phases in he ex uded od.
3. S ess-S ain Cu es
Cylind ical samples wi h a diame e o 10 mm and a heigh o 15 mm we e p oduced om he
supplied ma e ial. On he Hyd awedge II module (componen o he Gleeble 3800 ho de o ma ion
simula o (DSI, Poes enkill, NY, USA), he samples we e subjec ed o uniaxial comp ession wi h he
heigh educ ion co esponding o a ue s ain o 0.7. The samples we e hea ed up o he o ming
empe a u e, i.e., 450
◦
C, 500
◦
C, and 550
◦
C. The holding ime o 500 s was ollowed by de o ma ion a
nominal s ain a es o 0.5 s
−1
, 1 s
−1
, 5 s
−1
, and 10 s
−1
. The dange o alling o he usually welded
he mocouples du ing he es s was elimina ed by s u ing he K- ype he mocouple wi es in o he
holes d illed in o he used samples. These holes we e uni o mly 1.0 mm in diame e and 1.5 mm deep.
The de o med samples we e cooled eely, wi hou s uc u e ixa ion, because only he ini ial s uc u e
o all h ee ypes o ma e ial was in es iga ed wi h espec o he esea ch objec i es. The ob ained
cu es o low s ess
σ
[MPa] depending on he ue s ain e[–], empe a u e T[
◦
C], and s ain a e
˙
e
[s
−1
] we e smoo hed in he O igin so wa e and digi ized wi h a s ain s ep o 0.02. Examples o he
esul ing s ess-s ain cu es a e shown in compa a i e Figu es 7and 8. The le e C indica es he
as-cas s a e, he le e H shows he s a e a e homogeniza ion, and he le e E indica es he s a e a e
ho ex usion. S ess alues co esponding o he peak (i.e., maximum alues in indi idual es s)
σp
[MPa] and s eady-s a e low
σss
[MPa] we e de e mined o each cu e. Since he e a e some s ess
changes e en in he s eady s a e, he
σss
alues we e de e mined by linea eg ession o he ele an
da a (pa allel o he ho izon al axis).
Me als 2019, 9, x FOR PEER REVIEW 6 o 16
he e a e some s ess changes e en in he s eady s a e, he σss alues we e de e mined by linea
eg ession o he ele an da a (pa allel o he ho izon al axis).
Figu e 7. S ess-s ain cu es o a empe a u e o 450 °C.
Figu e 8. S ess-s ain cu es o a empe a u e o 550 °C
4. Ho De o ma ion Ac i a ion Ene gy
The appa en ac i a ion ene gy alue Q [J·mol−1] in ho o ming is conside ed o be an
impo an ma e ial cons an , used p ima ily o calcula ing he Zene -Hollomon pa ame e Z [s−1]
ep esen ing he empe a u e-compensa ed s ain a e [19].
𝑍=𝑒󰇗·exp𝑄
𝑅·𝑇 (1)
whe e T [K] is empe a u e and R = 8.314 J·mol−1·K−1 is he gas cons an .
Knowledge o he Q alue o he gi en ma e ial enables, among o he s, o quickly p edic he
maximum low s ess alue a he gi en empe a u e and s ain a e [20]. The Q alue is ideally he
ma e ial cons an ha depends only on he chemical composi ion and mic os uc u e o he
pa icula ma e ial. The hype bolic law in he A henius- ype equa ion is con en ionally used o i s
de e mina ion [21].
𝑒󰇗=𝐶·exp−𝑄
𝑅·𝑇·sinh𝛼·𝜎 (2)
whe e C [s−1], n [–], and α [MPa−1] a e o he ma e ial cons an s. This ela ionship is o en sol ed by a
simple g aphic me hod based on he epea edly used linea eg ession [22]. A pa icula i y o he
Figu e 7. S ess-s ain cu es o a empe a u e o 450 ◦C.

Me als 2019,9, 1248 6 o 15
Me als 2019, 9, x FOR PEER REVIEW 6 o 16
he e a e some s ess changes e en in he s eady s a e, he σss alues we e de e mined by linea
eg ession o he ele an da a (pa allel o he ho izon al axis).
Figu e 7. S ess-s ain cu es o a empe a u e o 450 °C.
Figu e 8. S ess-s ain cu es o a empe a u e o 550 °C
4. Ho De o ma ion Ac i a ion Ene gy
The appa en ac i a ion ene gy alue Q [J·mol−1] in ho o ming is conside ed o be an
impo an ma e ial cons an , used p ima ily o calcula ing he Zene -Hollomon pa ame e Z [s−1]
ep esen ing he empe a u e-compensa ed s ain a e [19].
𝑍=𝑒󰇗·exp𝑄
𝑅·𝑇 (1)
whe e T [K] is empe a u e and R = 8.314 J·mol−1·K−1 is he gas cons an .
Knowledge o he Q alue o he gi en ma e ial enables, among o he s, o quickly p edic he
maximum low s ess alue a he gi en empe a u e and s ain a e [20]. The Q alue is ideally he
ma e ial cons an ha depends only on he chemical composi ion and mic os uc u e o he
pa icula ma e ial. The hype bolic law in he A henius- ype equa ion is con en ionally used o i s
de e mina ion [21].
𝑒󰇗=𝐶·exp−𝑄
𝑅·𝑇·sinh𝛼·𝜎 (2)
whe e C [s−1], n [–], and α [MPa−1] a e o he ma e ial cons an s. This ela ionship is o en sol ed by a
simple g aphic me hod based on he epea edly used linea eg ession [22]. A pa icula i y o he
Figu e 8. S ess-s ain cu es o a empe a u e o 550 ◦C
4. Ho De o ma ion Ac i a ion Ene gy
The appa en ac i a ion ene gy alue Q[J
·
mol
−1
] in ho o ming is conside ed o be an impo an
ma e ial cons an , used p ima ily o calcula ing he Zene -Hollomon pa ame e Z[s
−1
] ep esen ing
he empe a u e-compensa ed s ain a e [19].
Z=.
e·expQ
R·T(1)
whe e T[K] is empe a u e and R=8.314 J·mol−1·K−1is he gas cons an .
Knowledge o he Q alue o he gi en ma e ial enables, among o he s, o quickly p edic he
maximum low s ess alue a he gi en empe a u e and s ain a e [
20
]. The Q alue is ideally
he ma e ial cons an ha depends only on he chemical composi ion and mic os uc u e o he
pa icula ma e ial. The hype bolic law in he A henius- ype equa ion is con en ionally used o i s
de e mina ion [21].
.
e=C·exp−Q
R·T·hsinhα·σpin(2)
whe e C[s
−1
], n[–], and
α
[MPa
−1
] a e o he ma e ial cons an s. This ela ionship is o en sol ed by
a simple g aphic me hod based on he epea edly used linea eg ession [
22
]. A pa icula i y o he
hype bolic unc ion is used in his calcula ion, which simpli ies Equa ion (2) o low s ess alues (i.e.,
α·σp<0.8) in o he o m o he powe law.
.
e=C1·exp−Q
R·T·σpn(3)
Vice e sa, o high s ess alues (i.e.,
α·σp
>1.2), he unc ion simpli ies he equa ion in o he
o m o he exponen ial law.
.
e=C2·exp−Q
R·T·expβ·σp(4)
whe e C
1
,C
2
, and
β
a e he ma e ial cons an s. The cons an
α
in Equa ion (2) is gi en by he
ela ionship
α
=
β
/n. Fo a chosen high- empe a u e le el (i.e., o low s ess alues), he cons an n
is de e mined by he linea eg ession o he expe imen ally ound alues in he coo dina es ln
˙
e–ln
σp
. Fo a chosen low- empe a u e le el (i.e., o high s ess alues), he cons an
β
is ob ained by he
linea eg ession in he coo dina es ln
˙
e–
σp
. A e calcula ing he
α
quan i y, he cons an s Qand Cin
Equa ion (2) can be ob ained by he inal linea eg ession o all da a plo ed in he coo dina e sys em
ln ˙
e−n·ln(sinh(α·σp))–T−1.
Me als 2019,9, 1248 7 o 15
Such an es ima e o cons an s nand
β
is a weak poin o he desc ibed me hod since i can be
s ongly in luenced by he selec ion o he co esponding empe a u e le els. This de iciency can be
elimina ed by he applica ion o he specially de eloped so wa e ENERGY 4.0 (VŠB-TU Os a a,
Czech Republic) [
23
], which uses he abo e-men ioned alues o nand
β
only as he i s es ima e o
pa ame e s o he inal e ining nonlinea eg ession analysis o all da a co esponding o Equa ion (2).
Calcula ion o he ho de o ma ion ac i a ion ene gy om expe imen al
σp
- alues on he basis o
he hype bolic-sine Equa ion (2) is he adi ional me hod ha was success ully applied o di e en
ypes o ma e ials, such as o a ious ypes o s eel [
24
,
25
], in e me allic compounds [
26
], alloys based
on coppe [27], i anium [28], o magnesium [29].
Applica ion o he peak s ess
σp
is, in his case, physically jus i ied because i co esponds o
simila s uc u al s a es gi en by he cou se o dynamic ec ys alliza ion o di e en Z-pa ame e
alues. The same applies o he s eady-s a e s ess. By modi ying Equa ion (2), gene al dependence o
he low s ess σ[MPa] on pa ame e Zcan be exp essed.
σ=1
α·a csinh n
Z
C(5)
whe e low s ess should be σpo σss.
Table 2p esen s he Q alues calcula ed by he me hodology desc ibed abo e om he measu ed
alues o
σp
o
σss
o all h ee ini ial s uc u al s a es. An excep ionally low Q
p
alue o he ex uded
s a e is due o somewha g ea e sca e o σp alues measu ed a 450 ◦C.
Table 2. Ho de o ma ion ac i a ion ene gy alues calcula ed o a ious s uc u al s a es.
Ene gy As-Cas Homogenized Ex uded
Qp[kJ·mol−1] 200.2 116.3 98.6
Qss [kJ·mol−1] 216.1 121.9 120.6
5. Discussion o Resul s
The de o ma ion p ope ies o he as-cas s uc u e a e gene ally wo se o hose o he al eady
de o med s uc u e. The e o e, in die o ging o aluminium alloys, ho -ex uded cas ods a e usually
used as he s a ing s ock. One o he inno a i e echnological elemen s in o ging aluminium alloys o
he 6xxx se ies is he eplacemen o he ex uded ods wi h cas ods. This p ocedu e educes he cos
o he inpu ma e ial and he ene gy equi ed o he p oduc ion o ex uded ods. Di ec use o as-cas
ods o o gings, howe e , in ol es one majo echnological ope a ion, which is he homogeniza ion
o he as-cas s uc u e. High- empe a u e homogeniza ion o bille s o o gings is usually used be o e
he ods a e ex uded. This is a e y ene gy-in ensi e ope a ion, which signi ican ly inc eases he cos
o o gings. The e o e, he e is an e o o elimina e his ope a ion and o o ge a non-homogenized
ma e ial. The omission o homogeniza ion annealing has an in luence bo h on he s a e o s uc u e and
on i s de o ma ion beha iou as well as on he mechanical and a igue p ope ies o he inal o gings.
Since he as-cas s uc u e is s uc u ally and chemically he e ogeneous and coa se-g ained, i usually
exhibi s lowe mechanical p ope ies han he s uc u e o ex uded ods.
Ho de o ma ion beha iou o 6082 aluminium alloy, supplied in he o m o ods wi h a diame e
o 55 mm, was in es iga ed. Con inuous cas ing o such ba s is a demanding p ocess and o en la ge
cas ings (e.g., wi h a diame e o 101 mm [
30
]) a e used. Rods wi h a diame e o 55 mm can be used
o o ging p oduc s o he au omo i e indus y, e.g., o he on axle componen s. The use o cas
and non-homogenized ma e ial would esul in signi ican sa ings o e he con en ional ex uded
ba s. This would sa e on he cos o homogenizing he la ge diame e ods and he ba s’ ex usion.
Ye , i is necessa y o decide whe he o no homogenizing annealing o he cas ods is indispensable.
Figu es 7and 8demons a e ha he ini ial ex uded s a e esul s in mo e p onounced so ening
due o dynamic ec ys alliza ion o he ine g ains. S ess-s ain cu es co esponding o bo h as-cas
Me als 2019,9, 1248 8 o 15
s a es a e la e , wi h less o a di e ence be ween
σp
and
σss
alues. This is a sign o a delay in
dynamic ec ys alliza ion. Especially a low empe a u es, he as-cas non-homogenized ma e ial
exhibi s signi ican ly highe low s ess likely due o a speci ic cha ac e is ic o in e me allic phases in
he in e dend i ic spaces.
Table 2shows ha , in all cases, ela ionship Q
ss
>Q
p
came ou wi h an a e age di e ence o 12%.
This has con i med ha he Q alue is no s ic ly a ma e ial cons an bu depends on he amoun o
s ain. In mos cases, howe e , o me al alloys wi h signi ican peak s ess, he alue o he ac i a ion
ene gy mo e o less dec eases no qui e mono onically, wi h inc easing s ain. The esul s we e ob ained
o 17-4 PH s ainless s eel [
31
], Q420qE mic oalloyed s eel [
32
], T24 e i ic s eel [
33
], and Ti-6Al-4V
i anium alloy [
34
]. The p e ailing opposi e end was obse ed, e.g., in AZ81 magnesium alloy [
35
].
The disc epancy be ween Q
p
and Q
ss
alues should be due o a di e en disloca ion densi y and g ain
cha ac e a he espec i e s ains.
Co esponding Q alues a e e y close in case o he homogenized and ex uded s a e, bu abou
80% highe o he as-cas s a e. This indica es a e y p onounced e ec o homogeniza ion on he
de o ma ion beha iou o he as-cas s uc u e. Homogeniza ion annealing changes he size, shape,
and chemical composi ion o he in e me allic phases a g ain bounda ies (see Chap e 2 o mo e
de ails). As a esul o homogeniza ion, la ge
α
-AlFeMnSi phases (see Figu e 4) b eak down in o
smalle and ounded pa icles in o which he elemen s dissol ed in he ma ix di use. A he same
ime, dend i ic seg ega ion in he as-cas g ains is emo ed. Phases a e o med which, by hei
size and non-cohe ence wi h he su ounding ma ix, can esul in he ela i ely lowe low s ess
and ho de o ma ion ac i a ion ene gy in compa ison wi h he s uc u e p io o homogeniza ion.
The Q
ss
alues o he wo homogenized ma e ials indica e ha , a la ge s ains, he e a e no signi ican
di e ences in he s uc u e s a e o he ini ial as-cas and ex uded ma e ial. The Q alues calcula ed by
o he au ho s o a ious aluminium alloys including a 6082 ype a e shown in Table 3 o compa ison.
Table 3. Values o ho de o ma ion ac i a ion ene gy calcula ed o a ious aluminium alloys.
Alloy Q[kJ·mol−1] Re e ence
2024 (As-cas ) 345 [36]
2026 (Homogenized) 341 [37]
6082 (Homogenized) 191 [30]
6082 (Ex uded) 269 [38]
6082 (A i icially aged) 228 [39]
6082 (N/A) 175 [40]
6082 (Homogenized) 182 [41]
6082 (Na u ally aged) 245 [42]
7050 (As- olled) 237–241 [43]
Al-Mg-Si-Cu (Homogenized) 236 [44]
I should be emphasized ha he compa ison o he calcula ed Q alues wi h li e a y sou ces
can be signi ican ly in luenced by a ious expe imen al condi ions (speci ic chemical composi ion o
he ma e ial, ini ial s uc u e s a e, ype o de o ma ion es , ange o empe a u e, and s ain a e)
and, o a ce ain ex en , by he me hodology used o p ocess he expe imen al esul s [
23
]. In Table 3,
he ac i a ion ene gy alues o he 6082 alloy ange om 191 o 269 kJ
·
mol
−1
. Thei a e age alue o
215 kJ
·
mol
−1
co esponds e y accu a ely o he ac i a ion ene gy Q
ss
=216 kJ
·
mol
−1
o he as-cas s a e
in Table 2. Howe e , i is signi ican ly lowe han all Q alues calcula ed o he ma e ials subjec ed
o homogeniza ion annealing (see Table 2). The di e ence wi h he esul o Spiga elli, E angelis a,
and McQueen [
38
] (i.e., Q=269 kJ
·
mol
−1
) is pa icula ly signi ican . In his case, he ini ial s uc u es
we e somewha di e en o a ious es ing empe a u es (200–500
◦
C) when each sample was ea ed
a 530
◦
C o 2 h, and hen aged o 24 h a he empe a u e selec ed o he o sion es . This ea men
was in ended o p oduce a s able s uc u e, in e ms o pa icle popula ion, which a oids any signi ican
p ocess o p ecipi a ion and/o coa sening o he p ecipi a es du ing de o ma ion. The esul ing
Me als 2019,9, 1248 9 o 15
s ess-s ain cu es di e signi ican ly om hose in Figu es 7and 8when exhibi ing ma ked peaks
bu no signs o subsequen ansi ion o a s eady-s a e. The esul s conclude ha he high- empe a u e
de o ma ion o he 6082 alloys wi h s able dispe sion o p ecipi a es is eco e y-con olled.
Li e al. [
45
] s udied he ho de o ma ion beha iou o he 6082 alloy a e semi-con inuous
cas ing and homogeniza ion a 545
◦
C o 24 h. Using Equa ions (2)–(4), hey calcula ed he ho
de o ma ion ac i a ion ene gy epea edly unde di e en s ains anging om 0.10 o 0.65. The esul s
a e demons a ed in Figu e 9. Dependence Q(e) is a he complica ed, and is o iginally desc ibed by
a 7 h o de polynomial i . The ac i a ion ene gy alue a ies signi ican ly wi hin a na ow ange
o abou 172-178 kJ
·
mol
−1
and is, he e o e, highe han he Q alues o he homogenized s a e in
Table 2(i.e., 116 o 122 kJ
·
mol
−1
), bu below hese alues o he as-cas s a e (i.e., 200 o 216 kJ
·
mol
−1
).
This may also be due o highe silicon con en o 1.30% e sus 0.93% (see Table 1). An unexplained
cou se o dependence Q(e) in Figu e 9demons a es he g ow h o he Q alue a he highes s ains
applied, which is consis en wi h he inding ha ela ionship Q
ss
>Q
p
aligns wi h he ma e ial
unde in es iga ion. Howe e , i is necessa y o d aw a en ion o he p incipal di e ences in he
calcula ion o Q alues om he s ess alues co esponding o pa icula de o ma ions, espec i ely
om he
σp
o
σss
alues. The speci ic s ess alues co esponding o he peak o s eady s a e on he
s ess-s ain cu e a e he esul o de o ma ion s eng hening and dynamic so ening p ocesses, and,
he e o e, ha e a simila physical signi icance o he di e en alues o he Zene -Hollomon pa ame e .
In con as , s esses co esponding o pa icula s ain alues a di e en Z alues may co espond o
quali a i ely di e en s uc u al s a es o he de o med ma e ial.
Me als 2019, 9, x FOR PEER REVIEW 10 o 16
Figu e 9. E ec o he ue s ain on he Q alue o he homogenized 6082 alloy, acco ding o
Re e ence [45].
Figu e 10 as well as he da a in Tables 2 and 4 clea ly show he di e en de o ma ion
beha iou s o he as-cas 6082 alloy and he ma e ial a e homogeniza ion annealing, especially a
lowe de o ma ion empe a u es. The indi idual lines in Figu e 10 we e ob ained by eg ession
analysis and co espond o a simple exponen ial unc ion.
Figu e 10. In luence o homogeniza ion on he σp alues measu ed a di e en empe a u es and
selec ed s ain a e alues.
Based on he knowledge o all ma e ial cons an s in Equa ion (5), he dependence o he s ess σp
o σss on he Z pa ame e could be plo ed in Figu es 11 and 12. These black lines can be compa ed o
he measu ed alues (colou -coded poin s), which a e also ela ed o he empe a u e-compensa ed
s ain a e. The di e en Z alues o he same combina ion o empe a u e and s ain a e a e he
esul o di e en ac i a ion ene gy alues (see Table 2) being applied in Equa ion (1). The accu acy
o he ma hema ical desc ip ion o he σp and σss alues wi h a o al o six equa ions is e y good in
he whole ange o applied de o ma ion condi ions, wi h an a e age s anda d de ia ion o only 1
MPa.
Table 4. Cons an s in Equa ion (5) calcula ed o he indi idual ini ial s uc u al s a es.
S ess Type Cons an As-Cas Homogenized Ex uded
n [–] 1.03 3.58 3.07
Figu e 9.
E ec o he ue s ain on he Q alue o he homogenized 6082 alloy, acco ding o
Re e ence [45].
Figu e 10 as well as he da a in Tables 2and 4clea ly show he di e en de o ma ion beha iou s o
he as-cas 6082 alloy and he ma e ial a e homogeniza ion annealing, especially a lowe de o ma ion
empe a u es. The indi idual lines in Figu e 10 we e ob ained by eg ession analysis and co espond
o a simple exponen ial unc ion.
Based on he knowledge o all ma e ial cons an s in Equa ion (5), he dependence o he s ess
σp
o
σss
on he Zpa ame e could be plo ed in Figu es 11 and 12. These black lines can be compa ed o
he measu ed alues (colou -coded poin s), which a e also ela ed o he empe a u e-compensa ed
s ain a e. The di e en Z alues o he same combina ion o empe a u e and s ain a e a e he
esul o di e en ac i a ion ene gy alues (see Table 2) being applied in Equa ion (1). The accu acy o
he ma hema ical desc ip ion o he
σp
and
σss
alues wi h a o al o six equa ions is e y good in he
whole ange o applied de o ma ion condi ions, wi h an a e age s anda d de ia ion o only 1 MPa.
Signi ican di e ences o compa able alues o
σp
and
σss
in he case o he ini ial as-cas s a e and
o bo h s a es a e homogeniza ion annealing illus a es how c ucial he e ec o homogeniza ion on