75
THE PREDICTION OF GRAIN SIZE OF THE HEAT AFFECTED ZONE OF WELDED
S304H STEEL TUBES USING A MATHEMATICAL MODEL
Ja omí Mo a ec
* Jose B adáč
** I a No áko á
*** Heinz Neumann
Technical Uni e si y o Libe ec
Facul y o Mechanical Enginee ing
Depa men o Enginee ing Technology
S uden ská 2, 461 17, Libe ec 1, Czech Republic
[email p o ec ed]
** [email p o ec ed]
*** [email p o ec ed]
* ŠkodaAu o Uni e si y
Au omobile Technology Depa men
Tř. V. Klemen a 869, 293 60, Mladá Bolesla , Czech Republic
* [email p o ec ed]
Abs ac
Supe 304H is an aus eni ic s eel, which is mainly used o boile s in he mal powe plan s
and he ene gy sec o . S eng h a high empe a u es has become one o he mos impo an
a ibu es in he design o boile ubes. The di e ences in ma e ial p ope ies, especially in i s
c eep esis ance compa ed o o he aus eni ic s eels o simila composi ion, a e mainly
achie ed by he addi ion o abou 3 w .-% o coppe . The o ma ion o ine Cu- ich
p ecipi a es du ing manu ac u e leads o an inc eased c eep s eng h du ing he p ocess o
p ecipi a ion ha dening. The impac o he welding cycle on he g ain coa seness in he hea -
a ec ed zone (HAZ) o S304H s eel will be demons a ed in his pape . The op ions and
p ocedu es o p edic ing g ain size by ma hema ical modeling o welding and hea ea men
will also be shown he e. The me hod o acqui ing he inpu da a o he ma hema ical models,
which p edic he g ain size, will also be desc ibed.
In oduc ion
The con inuous end o ope a ional pa ame e s o inc ease hei ene gy and chemical
condi ions also equi es he de elopmen o new ma e ials, which a e able o ope a e unde
such condi ions. Hea - esis an s eels can undoub edly be classed as one o hese ma e ials.
They ha e o ul ill many equi emen s, which a e o en con adic o y. The main equi emen
lies in i s enhanced esis ance agains long e m loading unde high empe a u es. No less
impo an is su icien esis ance agains co osion, which o ms an oxide laye on he s eel
su ace. [1]
Applica ions o such new ma e ials and he inclusion o he echnological p ocesses o
joining hem oge he a e o en accompanied by he use o welding simula ions and hea
ea men compu a ions. These compu a ions can la gely elimina e he isks, which a e
connec ed wi h he occu ence o unaccep able de ec s, o hey can lead o he elimina ion o
inne s esses caused by he p ocess. The Sysweld p og am is one o he mos commonly used
p og ams o his ype o compu a ion.
76
When p edic ing he s uc u e and esul ing p ope ies o he welded join s a ea, i is impo an
o know no only he g ain size in he ini ial s a e, bu also du ing he welding p ocess. Fo
his eason, his pape desc ibes he me hodical p ocedu es and he expe imen al esul s,
which lead o he de ini ion o a compu a ional model. This model hen enables he p edic ion
o he aus eni ic g ain size o he weldmen s made by S304H s eel, especially in he hea -
a ec ed zone, bu no in he weld a ea.
1 The Cha ac e is ics and Uses o S304H S eel
Gene ally speaking, aus eni ic s eels ha e good mechanical p ope ies and excellen co osion
esis ance e en a high empe a u es, a ying om 650-700°C. Howe e , his ad an age is
coun e ed by hei un a ou able he mal-physical p ope ies such as low he mal conduc i i y
and high he mal expansi i y. Ano he majo d awback is he possible damage o he ma e ial
h ough he mal a igue, especially when hese s eels a e used in powe s a ions whe e hey
a e wo king in cyclic he mal modes. The cos o hese s eels p ohibi s hei use on a la ge
scale. [6] Cu en ly aus eni ic hea esis an s eels g ade 304, a e used in Eu ope, USA and
Japan. Recen ly, S304H, which is a new ype o aus eni ic s ainless s eel con aining 3%
coppe , is being adop ed o he p oduc ion o supe -hea e / e-hea e ubes o 600°C USC
powe plan boile s. [2]
The s eng h o his ma e ial a high empe a u es is ele a ed and pa icula ly i s c eep
p ope ies a e imp o ed by adding abou 3 w .-% o coppe , inc easing he ca bon con en and
adding ce ain amoun s o niobium and ni ogen. The addi ion o ni ogen leads o a solid
solu ion hea s eng hening o he ma e ial. This inc eases he ensile s ess esis ance. The
s ess esis ance unde c eep condi ions is mainly inc eased by he p ecipi a ion o a Cu- ich
phase in he ma ix. [4]The Cu- ich phase is mainly composed o Cu and also a pa o Fe, C
and Ni. The con en o Cu in he Cu- ich phase is lowe han 20 a pc a ea ly s age o
p ecipi a ion a e 1 hou aging, and hen i is inc easing con inually wi h aging ime and
eaches almos 90 a pc a cen e when aging o 500 hou s. These esul s ep esen ha Cu
a oms g adually concen a e o Cu- ich pa icles and he o he elemen s (such as Fe, C , Ni
e c.) di use away om Cu- ich pa icles o ma ix wi h he inc easing o aging ime a
± 650°C. I is easonable o sugges ha Cu will be he only main composi ion in Cu- ich
phase when aging o e y long ime. [11]
Du ing manu ac u e, his Cu- ich phase and a niobium ca boni ide phase p ecipi a e
simul aneously. S304H is cha ac e ized by an excellen p ecipi a ion ha dening e ec . I
eaches peak ha dness (246 HV) a 1000 h and main ains almos he same le el ill 8000 h a
650°C. [3]
The di usion o ch omium o he su ace is accele a ed and he o ma ion o an adhe en and
dense ch omium oxide (C 2O3) laye is enhanced. This p o ec i e laye educes u he
oxida ion o a minimum.
Tubes o he ma e ial (ø 38 mm, wall hickness 6.3 mm) we e used o g ain size p edic ion.
I s chemical composi ion analysis is shown in Table 1. Figu e 1 shows he ini ial s a e
mic os uc u e o he es ed ma e ial.
Tab. 1: Chemical composi ion o es ed ma e ial
C
Mn
Si
P
S
C
Ni
Nb
Cu
N
w . %
0.090
0.873
0.243
0.005
0.015
18.8
8.449
0.508
3.515
0.091
Sou ce: Own
77
Sou ce: Own
Fig. 1: Ini ial s a e mic os uc u e o S304H s eel (80 ml HCl; 13 ml HF; 7 ml HNO3)
2 The compu a ion o g ain size using he Sysweld p og am
The educ ion o Gibbs su ace ee ene gy ac s as he he modynamic d i ing mechanism o
g ain g ow h. The g ain g owing p ocess esul s in he educ ion o he g ain su ace bounda y
and hus o a dec ease in ee ene gy. G ain size is impo an in wo espec s. I is impo an
wi h ega d o he mechanical p ope ies o he ma e ial (e.g. b i leness), bu also wi h espec
o he in luence on he ans o ma ion p ocesses. The i s models, which we e buil on he
physical basis, we e de eloped a he beginning o 1950s. In 1980, a new app oach based on
ma hema ical modelling was in oduced. On he basis o compu ed simula ions i was also
possible o moni o he p ocesses, which we e p e iously di icul o obse e, o example he
olume change a e o he indi idual g ains. Cu en ly, he mos commonly used simula ion
me hod is he “Mon e Ca lo Po s Model” me hod. A desc ip ion o his me hod is gi en as an
example in [5, 7]. An ideal ule o g ain g ow h is gi en by equa ion (1). [8]
eCDD TR
Q
aa  

0
(1)
D – g ain diame e (mm), D0 – ini ial g ain size (mm),
C – ma e ial cons an (mma·s-1), Q – ac i a ion ene gy (J·mol-1),
R – gas cons an (J·K-1·mol-1), T – empe a u e (K),
– ime (s) a – coe icien (-).
I was es ablished by expe imen s ha coe icien alues a y be ween 2 and 5. Value a=2
applies i he g owing p ocess is solely con olled by di usion. Value a=4 is de e mined in he
case whe e he e is p ecipi a ion and di usion along he g ain bounda y. G ain g owing is,
howe e , in luenced by o he ac o s, o example, hea ing a e and g ain g ow h ba ie s. The
compu a ion o g ain size p oceeds in he Sysweld simula ion p og am based on equa ion (2)
which exp esses he g owing a e o he g ain size.







 TR
Q
CDaexp

(2)
78
Cons an C is usually 0.4948·1014 mma.s-1. This compu a ional equa ion is designed o cases
when he amoun o aus eni e is cons an o is dec easing. I he amoun o aus eni e inc eases,
wo de elopmen s a e obse ed:
 Exis ing g ains inc ease in size.
 New g ains a e gene a ed wi h ze o ini ial g ain size.
By gene alizing he con en ional equa ion in o de o de e mine he g ain size, we a i e a
he ollowing equa ion (3).
aa D
TR
Q
CD 











exp
(3)
In his equa ion, he λ alue exp esses he aus eni e p opo ion while he alue


shows he
ans o ma ion a e o his phase. Fo


>0 he aus eni e is c ea ed. I he aus eni e is no
c ea ed, i.e.


 0 hen is he g ain size exp essed by he equa ion (2).
3 Expe imen al de e mina ion o g ain size
Fo nume ical analysis in Sysweld, i is impo an o know he inpu condi ions de ining he
g ain size changes, which depend on ime and he mal exposu e o he ma e ial. The es
samples we e 12 mm long ings cu om he gi en ube (ø 38 mm, wall hickness 6,3 mm).
Since i conce ned he moulding p oduc , he specimens we e measu ed longi udinally and
ans e sely, because o he ac ha he g ains could by de o med du ing he moulding
p ocess. The specimens we e he mally exposed in an o en a 1000°C, 1100°C o 4 and 8
hou s and we e subsequen ly cooled in wa e . While hea ing up o he es empe a u e he
hea ing a e o all specimens was 420°C/hou .
Specimens o alida ing he s uc u e we e p epa ed acco ding o a s anda d me allog aphic
p ocedu e. To accen ua e he g ain bounda ies he specimens we e cau e ized in solu ion
(80 ml HCl; 13 ml HF; 7 ml HNO3). This solu ion had o be used because cau e iza ion agen s
like Villela Bain o Vogel, which a e commonly used o alloy ma e ials, do no wo k wi h
he used ma e ial. The g ain size was e alua ed acco ding o CSN EN ISO 643 s anda d. The
e alua ion o he g ain size was exp essed by he in e sec ion me hod and by he planime ic
me hod. Based on hese measu emen s, he a e age numbe o sec ions o one millime e o
measu ed line NL was de e mined using he in e sec ion me hod. Then, da a such as he
a e age leng h o linea sec o l, he g ain size numbe G1 and he numbe o g ains in one
mm2 ma ked m we e also de e mined. Fo he planime ic me hod i is impo an o de e mine
he g ain size numbe , G2 (based on his da a i is possible o de e mine he a e age g ain
diame e
d
and he a e age g ain su ace a ea
a
). F om his, he eal a e age g ain su ace
a ea
s
a
, he eal a e age g ain diame e
d
and he numbe o g ains in one mm2 can also be
compu ed. [9] The de e mined alues o he g ain size o each se o expe imen al condi ions
o he in e sec ion and planime ic me hod a e shown in able 2.
79
Tab. 2: De e mined alues o g ain size
The da a de e mined by help o
in e sec ional me hod
The da a de e mined by help o planime ic
me hod
Specimens
S 304H
NL
l
G1
Numbe
o g ains
in 1mm2
G2
Numbe
o g ains
in 1mm2
Middle
g ain
su ace
[mm2]
Middle
g ain
diame e
[mm]
Ini ial
s a e
LD
52.326
0.01911
8
2048.0
8
2131.3
0.0004691
0.02166
TD
47.007
0.02127
8
2048.0
8
2325.7
0.0004301
0.02074
1000 °C
4 hou s
LD
40.716
0.02456
7-8
1536.0
8
2045.5
0.0004888
0.02211
TD
53.353
0.01874
8
2048.0
8
1949.6
0.0005129
0.02265
1000 °C
8 hou s
LD
45.857
0.02181
8
2048.0
8
1917.6
0.0005214
0.02284
TD
67.634
0.01479
9
4096.0
8
2365.1
0.0004228
0.02056
1100 °C
4 hou s
LD
41.222
0.02426
7-8
1536.0
7
847.8
0.0011794
0.03434
LD
35.911
0.02785
7
1024.0
7
949.0
0.0010537
0.03246
TD
45.880
0.02180
8
2048.0
7
1011.2
0.0009888
0.03145
TD
51.672
0.01935
8
2048.0
7
1337.9
0.0097474
0.02734
1100 °C
8 hou s
LD
21.842
0.04578
6
512.0
6
591.2
0.0016915
0.04113
TD
36.882
0.02711
7
1024.0
6
544.5
0.0018365
0.04286
NL – a e age numbe o g ains g ipped o he line uni leng h, l – a e age leng h o linea sec o , G1 – g ain size
numbe e alua ed wi h in e sec ional me hod, G2 – g ain size numbe e alua ed wi h planime ic me hod, LD –
longi udinal di ec ion, TD – ans e sal di ec ion
Sou ce: [9]
4 Ma hema ical compu a ion o g ain size using Sysweld
The expe imen ally de e mined alues o g ain size (see able 2) we e used as inpu da a o
he g ain size calcula ion in he Sysweld simula ion p og am. The compu a ions o his
p og am a e based on equa ions (2) and (3). The alue o he ac i a ion ene gy, Q, can be se
in he de ini ion o he compu a ion model by using a posi i e powe cons an , a, and he
cons an , C.
In he i s phase, he inpu da a leads o a compu ed g ain size, which co esponds o he
expe imen ally de e mined g ain size. Based on expe ience, i can be said ha he main
pa ame e o p edic ing g ain size by ma hema ical simula ion is he ac i a ion ene gy, Q.
Cons an C emain unchanged, C=0,4948·1014 mm4.s-1 and he powe cons an , a, usually
ma ches a=4 ( he case o p ecipi a ion and di usion along he g ain bounda y). Based on
hese esul s, he ac i a ion ene gy Q o he a io Q/R is hen de e mined. In he case o
S304H s eel i is op imal o keep he a io Q/R=73400 o a empe a u e o 1000°C and
Q/R=74800 o a empe a u e o 1100°C. [10]

80
This alida ed model is consequen ly used o he calcula ion o he g ain size based on non-
s a iona y empe a u e ields appea ing du ing welding. Figu e 2 depic s a 3D simula ion
model o a weld made up o h ee weld beads as well as he weld´s basic geome y. All he
weld beads on he simula ion model a e only c ea ed by using an addi ional ma e ial.
Howe e , he simula ion model he o hea sou ce co espond wi h mel ing bounda ies o he
eal weld geome y o indi idual weld beads.
Sou ce: [10]
Fig. 2: 3D simula ion model o he weld wi h h ee weld beads and he weld geome y
Figu e 3 shows he esul s o compu ing he g ain size in HAZ o he weld made on S304H
s eel ube ø 38, wall hickness 6.3 mm. The weld was made by an au oma ed machine using
GTAW me hod. Th ee weld beads we e made wi h a p ehea ing empe a u e o 180°C, an
in e pass empe a u e o 290 °C and using addi ional ma e ial The mani MTS 616. The edges
o he indi idual weld beads we e ecip ocally shi ed by 120° while he welding di ec ions o
he successi e beads we e e e sed. None o he weld beads was inished immedia ely a e
360°, hey all o e lapped hei edges a leas by 10 mm. Expe imen al welds we e made in
Ví ko ice S eel company and he welding pa ame e s a e hei know-how. The asyme ici y o
he aus eni e g ain dis ibu ion in HAZ in o a y symme ical model ( ig.3) occu s in he a eas
whe e he ends o o iginal beads we e ewelded by abou 10 mm.
Figu e 4 displays he de ails o g ain coa seness in HAZ on he bounda y o he second and
hi d weld bead.
81
Sou ce: [10]
Fig. 3: The esul s o compu ing g ain size in HAZ a e welding (S304H)
Sou ce: Own
Fig. 4: De ail De ails o g ain coa seness in HAZ a e welding on he bounda y o he
second and hi d weld bead (S304H)
Following he eal-li e welding expe imen , he compu ed da a o he g ain size and he eal-
li e g ain size o med in HAZ we e compa ed. Speci ically poin s 0.5; 1; 1.5; 2; 2.,5; 3 and 5
mm om he mel ing bounda y (MB) we e compa ed. Table 3 shows he compa ison o he
g ain size esul s compu ed nume ically and o med expe imen ally.
82
Tab. 3: Compa ison o he g ain size esul s compu ed nume ically and o med
expe imen ally
Dis ance om he MB [mm]
0.5
1.0
1.5
2.0
2.5
3.0
5.0
Middle g ain size [mm], expe imen
0.0880
0.0845
0.0272
0.0239
0.0209
0.0190
0,0207
Numbe o g ains in 1 mm2, expe .
129
140
1348
1749
2289
2752
2325
G ain size numbe G, expe .
G4
G4
G7
G8
G8
G8
G8
Middle g ain size [mm], compu a ion
0.0539
0.0512
0.0296
0.0243
0.0204
0.0204
0.0204
Numbe o g ains in 1 mm2, comp.
344
381
1141
1693
2403
2403
2403
G ain size numbe G, comp.
G5
G5
G7
G8
G8
G8
G8
Sou ce: Own
Conclusion
The compu a ional p og am module o he de e mina ion o g ain size using he Sysweld
p og am was de eloped as a ma ginal module, mainly mean o public pu poses. Howe e ,
we can now see an inc easing demand o his ype o simula ion compu a ion. Tha is why
one o he aims o he TA02010992 p ojec is he alida ion and, i necessa y, he
modi ica ion o his p og am module, hus he p edic ed alues o aus eni ic g ain size a e
welding o hea ea men co espond o he eal si ua ion. The mos impo an aspec is he
op imiza ion o he HAZ esul s, because he p ocesses a e e y dynamic he e and hus we
can expec in ensi e g ain g ow h in ha a ea.
F om Table 3 i is e iden ha he p edic ion o aus eni ic g ain size using ma hema ical
models e lec s he eali y e y well. This close ag eemen is especially e iden a 1.5 mm
om he mel ing bounda y. In he a ea wi h he highes he mal g adien s o he a ea 1.5 mm
om he mel ing bounda y, he g ains p edic ed by simula ions (G5) a e smalle han hose
de e mined expe imen ally (G4). This disc epancy is p obably caused by he compu a ional
p og am module design, which, a p esen , makes i impossible o inse he inpu da a in he
o m o empe a u e dependency. This pa icula inaccu acy could also be caused by he g ain
size de e mina ion me hod acco ding o CSN EN ISO 643 s anda d.
Acco ding o his no m, he g ain size is de e mined a he de ined su ace. The e is i egula
empe a u e dis ibu ion in he HAZ o he weld and he g ain size dec eases as he dis ance o
he mel ing bounda y inc eases. Howe e , he e a e no s anda d ins uc ions o p edic ing
g ain size in he HAZ and hus he selec ed me hod p o ides he mos ele an esul s.
Acknowledgemen s
The a icle was p epa ed wi hin he scope o he TA02010992 g an p ojec .
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Ing. Ja omí Mo a ec, Ph.D.; Ing. Jose B adáč, Ph.D.; Ing. I a No áko á, Ph.D.; doc. Ing.
Heinz Neumann, CSc.