Ci a ion: Ga mendia, I.; Vallejo, H.;
Osés, U. Composi e Mould Design
wi h Mul iphysics FEM
Compu a ions Guidance.
Compu a ion 2023,11, 41.
h ps://doi.o g/10.3390/
compu a ion11020041
Academic Edi o s: Ma ynas Pa ašius
and Riman as Ba auskas
Recei ed: 3 Janua y 2023
Re ised: 6 Feb ua y 2023
Accep ed: 13 Feb ua y 2023
Published: 17 Feb ua y 2023
Copy igh : © 2023 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/).
compu a ion
A icle
Composi e Mould Design wi h Mul iphysics FEM
Compu a ions Guidance
Iñaki Ga mendia 1,* , Ha i z Vallejo 2and Usue Osés1
1Mechanical Enginee ing Depa men , Enginee ing School o Gipuzkoa, Uni e si y o he Basque Coun y
UPV/EHU, Plaza de Eu opa, 1, E-20018 Donos ia-San Sebas ián, Spain
2TECNALIA, Basque Resea ch and Technology Alliance (BRTA), Mikele egi Pasealekua, 7,
E-20009 Donos ia-San Sebas ián, Spain
*Co espondence: [email p o ec ed]; Tel.: +34-43-018-630
Abs ac :
Composi e moulds cons i u e an a ac i e al e na i e o classical me allic moulds when
used o componen s ab ica ed by p ocesses such as Resin T ans e Moulding (RTM). Howe e , he e
a e many ac o s ha ha e o be accoun ed o i a co ec design o he moulds is sough a e . In
his pape , he Fini e Elemen Me hod (FEM) is used o help in he design o he mould. To do so, a
he mo-elec ical simula ion has been pe o med h ough MSC-Ma c in he p ehea ing phase in o de
o ensu e ha he mould is able o be hea ed, h ough he Joule’s e ec , acco ding o he he mal cycle
speci ied unde ope a ing condi ions. Mean empe a u es o 120
◦
C and 100
◦
C a e p edic ed o
he lowe and uppe semi-mould pa s, espec i ely. Addi ionally, a he mo-elec ical-mechanical
calcula ion has been comple ed wi h MSC-Ma c o calcula e he ensile s a e along he sys em du ing
he p ehea ing s age. Fo he illing phase, he illing p ocess i sel has been simula ed h ough
RTM-Wo x. Bo h he uni o m- and non-uni o m empe a u e dis ibu ion app oaches ha e been
used o assess he esul ing e ec . I has been ound ha his piece o so wa e canno model he
empe a u e dependency o he esin and a nume ical ick mus ha e been applied in he second
case o o e come i . Resul s ha e been ound o be e y dependen on he app oach, he illing ime
being 73% g ea e when modelling a non-uni o m empe a u e dis ibu ion. The co ec beha iou
o he mould du ing he illing s age, as a consequence o he illing p essu e, has been also p o ed
wi h a speci ic mechanical analysis conduc ed wi h MSC-Ma c. Finally, he he mo-elas ic esponse
o he mould du ing he cu ing s age has been nume ically assessed. This analysis has been made
h ough MSC-Ma c, paying special a en ion o he cu ing o he esin and he exo he mic eac ion
ha akes place. Fo he sake o accu acy, a use sub ou ine o include speci ic cu ing laws has been
used. Ma e ial p ope ies employed a e also desc ibed in de ail ollowing a modi ied e sion o he
Sco model, wi h cu ing p ope ies ex ac ed om expe imen s. All hese de ailed calcula ions ha e
been he co ne s one o designing he composi e mould and ha e also un eiled some capabili ies
ha we e missed in he comme cial codes employed. Fu u e e sions o hese comme cial codes will
ha e o deal wi h hese weak poin s bu , as a whole, he Fini e Elemen Me hod is shown o be an
app op ia e ool o helping in he design o composi e moulds.
Keywo ds:
composi e moulds; cu ing simula ion; illing simula ion; ini e elemen me hod; he mo-
elec ical simula ion
1. In oduc ion
To his day, me als (mainly s eel and aluminium alloys) a e he mos easonable
op ion o he ab ica ion o ools and moulds, as hey mee he basic equi emen s o
mass p oduc ion p ocesses [
1
]. Howe e , me als as ooling ma e ials p esen a numbe
o se ious disad an ages such as much highe coe icien s o he mal expansion (CTE)
han he ma e ials o he p oduced pa s, aw ma e ial consump ion, and high cos s o
machining [2].
Compu a ion 2023,11, 41. h ps://doi.o g/10.3390/compu a ion11020041 h ps://www.mdpi.com/jou nal/compu a ion
Compu a ion 2023,11, 41 2 o 16
Despi e o ha ing a much sho e use ul li e han me al ools and en ailing mo e
p oblems ela ed o mic o-c acking and po osi y, composi e ooling o e s many ad an ages
as i is a ligh weigh , less cos ly solu ion ha has lowe he mal ine ia and is ela i ely easy
o p oduce. They o e po en ially dec eased ab ica ion ime, easy epai /main enance,
lowe CTE misma ches, ailo ed he mal and s uc u al p ope ies, and educed heal h and
sa e y isks as well.
Consequen ly, i seems app op ia e o de elop inno a i e, obus and easy o hea
composi e moulds (bo h closed and open), h ough add essing all hose issues ha cu en ly
p e en composi e ooling om being a iable al e na i e o he indus ial p oduc ion o
plas ic and composi e pa s ac oss a wide ange o manu ac u ing ou es.
Resin T ans e Moulding (RTM) is one o he manu ac u ing p ocesses ha can be
s udied h ough he Fini e Elemen Me hod (FEM) [
3
–
8
]. I in ol es no only he RTM
p ocess i sel , bu also he design o he mould and i s beha iou om a he mal, elec ical,
mechanical, illing, and cu ing poin o iew. Du ing a ypical RTM p ocess (see Figu e 1),
ou s eps can be dis inguished: (1) P ehea ing o he mould un il i eaches an adequa e
empe a u e, (2) Filling h ough esin injec ion, (3) Cu ing o he esin, and (4) Cooling o
he mould.
Compu a ion 2023, 11, x 2 o 16
Despi e o ha ing a much sho e use ul li e han me al ools and en ailing mo e
p oblems ela ed o mic o-c acking and po osi y, composi e ooling o e s many
ad an ages as i is a ligh weigh , less cos ly solu ion ha has lowe he mal ine ia and is
ela i ely easy o p oduce. They o e po en ially dec eased ab ica ion ime, easy
epai /main enance, lowe CTE misma ches, ailo ed he mal and s uc u al p ope ies,
and educed heal h and sa e y isks as well.
Consequen ly, i seems app op ia e o de elop inno a i e, obus and easy o hea
composi e moulds (bo h closed and open), h ough add essing all hose issues ha
cu en ly p e en composi e ooling om being a iable al e na i e o he indus ial
p oduc ion o plas ic and composi e pa s ac oss a wide ange o manu ac u ing ou es.
Resin T ans e Moulding (RTM) is one o he manu ac u ing p ocesses ha can be
s udied h ough he Fini e Elemen Me hod (FEM) [3–8]. I in ol es no only he RTM
p ocess i sel , bu also he design o he mould and i s beha iou om a he mal, elec ical,
mechanical, illing, and cu ing poin o iew. Du ing a ypical RTM p ocess (see Figu e
1), ou s eps can be dis inguished: (1) P ehea ing o he mould un il i eaches an adequa e
empe a u e, (2) Filling h ough esin injec ion, (3) Cu ing o he esin, and (4) Cooling o
he mould.
(a) (b)
(c) (d)
Figu e 1. Di e en s ages o a ypical RTM p ocess: (a) p ehea ing o he mould, (b) esin illing, (c)
cu ing s age, and (d) cooling down phase.
In e e ence [3], Zade e al. simula ed he RTM and cu e p ocess o a wing lap
composi e pa h ough he comme cial FEM code ANSYS. They paid special a en ion o
he ma e ial p ope ies o he esin, ob ained h ough Di e en ial Scanning Calo ime y
(DSC). They also simula ed he illing p ocess wi h di e en numbe o injec ion and en
poin s. Howe e , hey did no simula e he p ehea ing phase o he p ocess and assumed
a uni o m ini ial empe a u e o 120 °C in he mould, which hea ily condi ioned hei
illing esul s. In e e ence [4], Joo e al. concen a ed hei simula ion e o s on he
mechanical s eng h ob ained o an au omo i e composi e on bumpe assemble. The
composi e pa was ob ained by High P essu e Resin T ans e Moulding P ocess and
shows good ag eemen when compa ing FEM esul s ob ained wi h LS-DYNA and he
expe imen al esul s. Re e ence [5] shows he wo k pe o med by Simacek e al. They used
he LIMS FEM so wa e o simula e a Comp ession RTM p ocess. Thei geome y was a
eal 3-D B-pilla , bu hey ecognized ha some simpli ica ions had o be accep ed i an
a o dable nume ical calcula ion was o be pe o med. Once again, p ehea ing was no
Figu e 1.
Di e en s ages o a ypical RTM p ocess: (
a
) p ehea ing o he mould, (
b
) esin illing,
(c) cu ing s age, and (d) cooling down phase.
In e e ence [
3
], Zade e al. simula ed he RTM and cu e p ocess o a wing lap
composi e pa h ough he comme cial FEM code ANSYS. They paid special a en ion o
he ma e ial p ope ies o he esin, ob ained h ough Di e en ial Scanning Calo ime y
(DSC). They also simula ed he illing p ocess wi h di e en numbe o injec ion and en
poin s. Howe e , hey did no simula e he p ehea ing phase o he p ocess and assumed a
uni o m ini ial empe a u e o 120
◦
C in he mould, which hea ily condi ioned hei illing
esul s. In e e ence [
4
], Joo e al. concen a ed hei simula ion e o s on he mechanical
s eng h ob ained o an au omo i e composi e on bumpe assemble. The composi e
pa was ob ained by High P essu e Resin T ans e Moulding P ocess and shows good
ag eemen when compa ing FEM esul s ob ained wi h LS-DYNA and he expe imen al
esul s. Re e ence [
5
] shows he wo k pe o med by Simacek e al. They used he LIMS FEM
so wa e o simula e a Comp ession RTM p ocess. Thei geome y was a eal 3-D B-pilla ,
bu hey ecognized ha some simpli ica ions had o be accep ed i an a o dable nume ical
calcula ion was o be pe o med. Once again, p ehea ing was no simula ed and ini ial
Compu a ion 2023,11, 41 3 o 16
empe a u es o he p ocess we e aken based on p e ious expe ience. Re e ence [
6
] shows
he RTM p ocess simula ion o ano he ca componen , a cab on , pe o med wi h he
comme cial so wa e PAM-RTM by Kuppusamy e al. They simula ed he ai en apmen
ha can happen in such a p ocess and simula ed he illing o di e en mould empe a u es.
In e e ence [
7
], Xiong e al. inco po a ed he idea o mul iobjec i e op imiza ion o he
design o ligh weigh ca componen s. Finally, in e e ence [
8
], Mal e al. in es iga ed he
RTM p ocess o hin componen s and he e ec o mechanical dispe sion on he gene al
hea ans e .
These e e ences show he impo ance o simula ion by FEM in he con ex o indus ial
p ocesses, such as RTM and o he s. In ac , compu a ional simula ion ia he Fini e Elemen
Me hod b ings ad an ages compa ed o expe imen al and/o analy ical s udies, such
as as e esul s and lowe cos . The objec i e o his pape is o show ha he Fini e
Elemen Me hod is an adequa e ool o ensu e an app op ia e design o a composi e
mould and o sho en de elopmen cos s and imes. Consequen ly, many design decisions
can be aken now based on simula ion esul s, which will be con i med a e wa ds by
app op ia e expe imen a ion.
2. Me hodology
FEM calcula ions can be a guide and a sui abili y check o a mould design in he
con ex o an RTM p ocess [
9
]. In his pape , di e en aspec s ha we e aken in o accoun
o ensu e a p ope mould design will be shown.
As he mould was expec ed o be hea ed by means o he di ec esis ance me hod, he
p ehea ing was modelled h ough a he mo-elec ic analysis o de e mine he empe a u e
dis ibu ion o he mould due o he Joule’s e ec . A e ha , a mechanical analysis was
planned o accoun o he he mal s esses gene a ed by he hea ing. Howe e , a he mo-
elec ical-mechanical analysis was ca ied ou o ob ain he mechanical esponse o he
mould because o he he mal expansion: he en i e coupled analysis could be easily
pe o med wi h he simula ion code used, MSC-Ma c [10].
Based on he heo e ical he mal cycle, he illing o he mould was modelled assuming
iso he mal condi ions wi h a comme cial so wa e, RTM-Wo x [
11
]. Addi ionally, using he
empe a u e con ou on he ca i y de e mined in he p ehea ing s age, he illing p ocess
simula ion was epea ed assuming a non-iso he mal empe a u e dis ibu ion. In bo h
cases, he p essu e p o ile and he illing ime we e ob ained o compa e he e ec o he
app oach selec ed. Following, a s uc u al analysis was conduc ed o assess he mechanical
beha iou o he mould due o he in e nal p essu e.
Rega ding he cu ing o he esin [
12
–
15
], a he mal analysis was comple ed consid-
e ing he exo he mal eac ion ha ook place. Finally, a he mo-mechanical analysis was
conduc ed o de e mine he dimensional s abili y o he mould and he s ess s a e due o
he esul ing ansien empe a u e p o ile. The cooling down o he mould was no s udied.
As i can be deduced om his sho desc ip ion, se e al FEM analyses ha e been
pe o med in a ce ain o de , making some simpli ica ions. Some o he possibili ies and
coupled analyses ha e been dis ega ded and conside ed no needed, as he complexi y
would ha e been excessi e and he so wa e employed p esen ed some limi a ions, which
will be explained la e in he pape . Figu e 2summa izes he FEM calcula ions pe o med.
Compu a ion 2023,11, 41 4 o 16
Compu a ion 2023, 11, x 4 o 16
Figu e 2. So wa e amewo k o he mould design.
3. Mould Design
A composi e mould wi h a esis i e hea e sys em was de eloped o be used in he
simula ion and ab ica ion ac i i ies. As shown in Figu e 3, he mould was made up o
wo mica laye s, wo semi-moulds o composi e, a gaske and he esis i e hea e sys em.
Mica laye s we e used o he mal insula ion pu poses.
Figu e 3. Componen s o he mould and iews o he esul ing assembly.
Rega ding he hea e sys em concep , a esis i e ma e ial wi h needed elec ical
connec ions inside and an ex e nal housing o ib eglass ( o a oid elec ical leaks) was
conside ed. Main dimensions o he mould analysed a e p esen ed in Figu e 4.
Figu e 2. So wa e amewo k o he mould design.
3. Mould Design
A composi e mould wi h a esis i e hea e sys em was de eloped o be used in he
simula ion and ab ica ion ac i i ies. As shown in Figu e 3, he mould was made up o wo
mica laye s, wo semi-moulds o composi e, a gaske and he esis i e hea e sys em. Mica
laye s we e used o he mal insula ion pu poses.
Compu a ion 2023, 11, x 4 o 16
Figu e 2. So wa e amewo k o he mould design.
3. Mould Design
A composi e mould wi h a esis i e hea e sys em was de eloped o be used in he
simula ion and ab ica ion ac i i ies. As shown in Figu e 3, he mould was made up o
wo mica laye s, wo semi-moulds o composi e, a gaske and he esis i e hea e sys em.
Mica laye s we e used o he mal insula ion pu poses.
Figu e 3. Componen s o he mould and iews o he esul ing assembly.
Rega ding he hea e sys em concep , a esis i e ma e ial wi h needed elec ical
connec ions inside and an ex e nal housing o ib eglass ( o a oid elec ical leaks) was
conside ed. Main dimensions o he mould analysed a e p esen ed in Figu e 4.
Figu e 3. Componen s o he mould and iews o he esul ing assembly.
Rega ding he hea e sys em concep , a esis i e ma e ial wi h needed elec ical connec-
ions inside and an ex e nal housing o ib eglass ( o a oid elec ical leaks) was conside ed.
Main dimensions o he mould analysed a e p esen ed in Figu e 4.
Compu a ion 2023,11, 41 5 o 16
Compu a ion 2023, 11, x 5 o 16
Figu e 4. Main dimensions o he mould.
Table 1 collec s he physical, elec ical, he mal, mechanical, and iscosi y p ope ies
o he ma e ials in ol ed in he RTM p ocess. A composi e made o high conduc i i y
ib es was used o bo h semi-moulds. Fo he composi e o be manu ac u ed, p ope ies
om he AS43K ib es and he RTM6 esin we e conside ed. Rubbe , mica, and ib eglass
we e also used. Table 1 also shows ha se e al p ope ies o he sample ha e no been
conside ed (NC) as i s mechanical in luence (which is small) can be neglec ed.
Table 1. Ma e ial p ope ies.
P ope y
Composi e
Rubbe
Mica
Fibe glass
D y Fib e
Resin
Composi e Pa
Densi y (kg/m3) 1700 1150 2850 1800 1790 1150 1500
Elec ical esis i i y (ohm·m)
xx 5.88 × 10−6 5.88 × 10−6
yy 5.88 × 10−6 1 × 1014 2 × 1013 1 × 1014 5.88 × 10−6 NC NC
zz 5.88 × 10−4 5.88 × 10−5
The mal conduc i i y
W/(m·K)
xx 164 6.83 7
yy 164 0.15 0.35 0.58 6.83 0.3 7
zz 1 0.683 1
Speci ic hea J/(kg·K) 500 2000 880 795 1130 1500 1300
CTE (1/C), × 10−6
xx 1 × 10−3
yy 1 × 10−3 80 10 8 NC NC NC
zz 50
Emissi i y 0.9 - 0.75 - - - -
Young’s modulus (GPa)
xx 150
yy 150 7 × 10−3 172 18 NC NC NC
zz 4
Figu e 4. Main dimensions o he mould (in mm).
Table 1collec s he physical, elec ical, he mal, mechanical, and iscosi y p ope ies o
he ma e ials in ol ed in he RTM p ocess. A composi e made o high conduc i i y ib es
was used o bo h semi-moulds. Fo he composi e o be manu ac u ed, p ope ies om he
AS43K ib es and he RTM6 esin we e conside ed. Rubbe , mica, and ib eglass we e also
used. Table 1also shows ha se e al p ope ies o he sample ha e no been conside ed
(NC) as i s mechanical in luence (which is small) can be neglec ed.
Table 1. Ma e ial p ope ies.
P ope y
Composi e
Rubbe
Mica
Fibe glass
D y Fib e
Resin
Composi e Pa
Densi y (kg/m3) 1700 1150 2850 1800 1790 1150 1500
Elec ical esis i i y (ohm·m)
xx 5.88 ×10−65.88 ×10−6
yy 5.88 ×10−61×1014 2×1013 1×1014 5.88 ×10−6NC NC
zz 5.88 ×10−45.88 ×10−5
The mal conduc i i y W/(m·K)
xx 164 6.83 7
yy 164 0.15 0.35 0.58 6.83 0.3 7
zz 1 0.683 1
Speci ic hea J/(kg·K) 500 2000 880 795 1130 1500 1300
CTE (1/C), ×10−6
xx 1 ×10−3
yy 1 ×10−380 10 8 NC NC NC
zz 50
Emissi i y 0.9 - 0.75 - - - -
Young’s modulus (GPa)
xx 150
yy 150 7 ×10−3172 18 NC NC NC
zz 4
Compu a ion 2023,11, 41 6 o 16
Table 1. Con .
P ope y
Composi e
Rubbe
Mica
Fibe glass
D y Fib e
Resin
Composi e Pa
Poisson’s a io
xy 0.2
yz 0.015 0.495 0.3 0.3 NC NC NC
xz 0.015
T ans . elas ici y modulus (GPa)
xy 62
yz 2.75 - - - - - -
xz 2.75
Viscosi y (mPa·s) a 120 ◦C - - - - - 33 -
Pe meabili y (m2), ×10−11
xx - - - - - 1.05 -
yy - - - - - 1.05 -
The hea powe ha is p oduced du ing he cu ing p ocess ollows Equa ion (1):
Pc=dα
d ×(1−V )×ρ ×H ×VT(1)
whe e P
c
ep esen s he gene a ed powe (W), d
α
/d is he cu ing a e (s
−1
), V
is he ib e
olume ac ion (no uni s),
ρ
is he esin densi y(kg/m
3
), H
is he esin cu e eac ion hea
(J/kg), and VTis he o al olume (m3).
The esin cu ing deg ee α, no uni s, can be calcula ed acco ding o Equa ion (2):
α +∆ =α +∆ ×dα
d (2)
Finally, he cu ing a e ollows a modi ied e sion o he Sco model [16]:
dα
d =K1+K2×αm×(B−α)n(3)
whe e
K1=A1×e
−∆E1
RT (4)
K2=A2×e
−∆E2
RT (5)
m=m1+m2×T+m3×T2(6)
B=b1+b2×T+b3×T2(7)
n=n1+n2×T+n3×T2(8)
Values o he coe icien s and H a e collec ed in Table 2. These alues come om
p e ious expe imen s pe o med in a p e ious p ojec , no epo ed in he open li e a u e.
Compu a ion 2023,11, 41 7 o 16
Table 2. Coe icien s alues o he cu ing a e equa ion.
Coe icien Value Coe icien Value
A11451.873 s−1H 480,000 J/kg
A216,797.24 s−1b11.04578
∆E17739.757 J/mol b2−7.9×10−4K−1
∆E27725.694 J/mol b31.4708 ×10−6K−2
m10.75079 n1−1.44997
m22.4 ×10−4K−1n20.0606 K−1
m34.4432 ×10−7K−2n3−7.6515 ×10−7K−2
4. Resul s and Discussion
4.1. P ehea ing
In an RTM p ocess, he empe a u e o he ca i y is he con ol a iable ha mus be
imposed. This he mal cycle depends on he esin and is he key pa ame e ha de ines
he e olu ion o he illing and he cu ing o he esin and, consequen ly, he esul ing pa
quali y. The he mal cycle conside ed in his case is p esen ed in Figu e 5.
Compu a ion 2023, 11, x 7 o 16
Table 2. Coe icien s alues o he cu ing a e equa ion.
Coe icien Value Coe icien Value
A1 1451.873 s−1 H 480,000 J/kg
A2 16,797.24 s−1 b1 1.04578
ΔE1 7739.757 J/mol b2 −7.9·10−4 K−1
ΔE2 7725.694 J/mol b3 1.4708 × 10−6 K−2
m1 0.75079 n1 −1.44997
m2 2.4 × 10−4 K−1 n2 0.0606 K−1
m3 4.4432 × 10−7 K−2 n3 −7.6515 × 10−7 K−2
4. Resul s and Discussion
4.1. P ehea ing
In an RTM p ocess, he empe a u e o he ca i y is he con ol a iable ha mus be
imposed. This he mal cycle depends on he esin and is he key pa ame e ha de ines
he e olu ion o he illing and he cu ing o he esin and, consequen ly, he esul ing pa
quali y. The he mal cycle conside ed in his case is p esen ed in Figu e 5.
Figu e 5. The mal cycle conside ed o RTM6.
In he eal RTM p ocess conside ed he e, in which he mould was hea ed by Joule’s
e ec , he se empe a u es depended on he elec ic po en ial applied. In his con ex , i
was necessa y o calcula e he elec ic po en ial ime e olu ion ha p oduced a ca i y
empe a u e e olu ion as close as possible o he one shown in Figu e 5. To do so,
empe a u es we e applied as he mal loads in he hea e pla es in a p elimina y hea
ans e calcula ion. As a esul , he hea powe (W) was ob ained and he elec ic po en ial
needed o p oduce his elec ic powe was also calcula ed. The elec ic po en ial
calcula ion was ob ained om he elec ic powe , conside ing he elec ical esis ance o
he hea e s. Figu e 6 shows he e olu ion o he elec ic powe and he elec ic po en ial
needed o ob ain he empe a u e e olu ion o Figu e 5.
0
25
50
75
100
125
150
175
200
0 30 60 90 120 150 180 210 240 270 300
Time (min)
Tempe a u e (ºC)
PREHEATING
(2ºC/min)
PREHEATING
(2ºC/min)
FILLINGFILLING
CURING
(1s phase)
CURING
(1s phase)
CURING
(2nd phase)
CURING
(2nd phase)
Figu e 5. The mal cycle conside ed o RTM6.
In he eal RTM p ocess conside ed he e, in which he mould was hea ed by Joule’s
e ec , he se empe a u es depended on he elec ic po en ial applied. In his con ex , i
was necessa y o calcula e he elec ic po en ial ime e olu ion ha p oduced a ca i y em-
pe a u e e olu ion as close as possible o he one shown in Figu e 5. To do so, empe a u es
we e applied as he mal loads in he hea e pla es in a p elimina y hea ans e calcula ion.
As a esul , he hea powe (W) was ob ained and he elec ic po en ial needed o p oduce
his elec ic powe was also calcula ed. The elec ic po en ial calcula ion was ob ained om
he elec ic powe , conside ing he elec ical esis ance o he hea e s. Figu e 6shows he
e olu ion o he elec ic powe and he elec ic po en ial needed o ob ain he empe a u e
e olu ion o Figu e 5.
Compu a ion 2023,11, 41 8 o 16
Compu a ion 2023, 11, x 8 o 16
Figu e 6. E olu ions o elec ic powe and ol age di e ence needed o each he equi ed
empe a u es.
Once he elec ical ol ages we e de e mined, a he mo-elec ic analysis was ca ied
ou o nume ically con i m ha he he mal cycle was ac ually ollowed. A e ha , he
s uc u al esponse caused by he he mal dila a ions was s udied h ough a he mo-
elec ical-mechanical analysis.
A ini e elemen mesh (Figu e 7) o med by 39,280 hexahed al elemen and 44,384
nodes was buil . Ma c Elemen numbe 7 (8 nodes linea hexahed al elemen ) was used
o mechanical calcula ions, while Ma c Elemen numbe 43 (8 nodes linea hexahed al
elemen ) was used o he mal, he mal–mechanical, he mal–elec ic, and cu e he mal–
mechanical calcula ions. Due o he exis ing symme y on he geome y, ma e ials, and
loads, jus hal o he en i e mould was modelled.
Figu e 7. Fini e elemen mesh used (hal model).
The elec ic ol age load applied was al eady ob ained om he p elimina y
calcula ion, shown in Figu e 6. Rega ding he mal bounda y condi ions, a na u al
con ec ion o 5 W/(m2K) and a adia ion o en i onmen condi ion we e de ined in he
ou e su aces. An ambien empe a u e o 20 °C was conside ed and a alue o 20 °C was
de ined as ini ial he mal condi ion.
0
50
100
150
200
250
300
350
400
0 30 60 90 120 150 180 210 240 270 300
Time (min)
Elec ic powe (W)
0
1
2
3
4
5
6
7
8
Elec ic po en ial di e ence (V)
Elec ic powe
Elec ic po en ial
Figu e 6.
E olu ions o elec ic powe and ol age di e ence needed o each he equi ed empe a u es.
Once he elec ical ol ages we e de e mined, a he mo-elec ic analysis was ca ied
ou o nume ically con i m ha he he mal cycle was ac ually ollowed. A e ha , he
s uc u al esponse caused by he he mal dila a ions was s udied h ough a he mo-
elec ical-mechanical analysis.
A ini e elemen mesh (Figu e 7) o med by 39,280 hexahed al elemen and 44,384 nodes
was buil . Ma c Elemen numbe 7 (8 nodes linea hexahed al elemen ) was used o me-
chanical calcula ions, while Ma c Elemen numbe 43 (8 nodes linea hexahed al elemen )
was used o he mal, he mal–mechanical, he mal–elec ic, and cu e he mal–mechanical
calcula ions. Due o he exis ing symme y on he geome y, ma e ials, and loads, jus hal
o he en i e mould was modelled.
Compu a ion 2023, 11, x 8 o 16
Figu e 6. E olu ions o elec ic powe and ol age di e ence needed o each he equi ed
empe a u es.
Once he elec ical ol ages we e de e mined, a he mo-elec ic analysis was ca ied
ou o nume ically con i m ha he he mal cycle was ac ually ollowed. A e ha , he
s uc u al esponse caused by he he mal dila a ions was s udied h ough a he mo-
elec ical-mechanical analysis.
A ini e elemen mesh (Figu e 7) o med by 39,280 hexahed al elemen and 44,384
nodes was buil . Ma c Elemen numbe 7 (8 nodes linea hexahed al elemen ) was used
o mechanical calcula ions, while Ma c Elemen numbe 43 (8 nodes linea hexahed al
elemen ) was used o he mal, he mal–mechanical, he mal–elec ic, and cu e he mal–
mechanical calcula ions. Due o he exis ing symme y on he geome y, ma e ials, and
loads, jus hal o he en i e mould was modelled.
Figu e 7. Fini e elemen mesh used (hal model).
The elec ic ol age load applied was al eady ob ained om he p elimina y
calcula ion, shown in Figu e 6. Rega ding he mal bounda y condi ions, a na u al
con ec ion o 5 W/(m2K) and a adia ion o en i onmen condi ion we e de ined in he
ou e su aces. An ambien empe a u e o 20 °C was conside ed and a alue o 20 °C was
de ined as ini ial he mal condi ion.
0
50
100
150
200
250
300
350
400
0 30 60 90 120 150 180 210 240 270 300
Time (min)
Elec ic powe (W)
0
1
2
3
4
5
6
7
8
Elec ic po en ial di e ence (V)
Elec ic powe
Elec ic po en ial
Figu e 7. Fini e elemen mesh used (hal model).
The elec ic ol age load applied was al eady ob ained om he p elimina y calcula-
ion, shown in Figu e 6. Rega ding he mal bounda y condi ions, a na u al con ec ion o
5 W/(m
2
K) and a adia ion o en i onmen condi ion we e de ined in he ou e su aces.
An ambien empe a u e o 20
◦
C was conside ed and a alue o 20
◦
C was de ined as
ini ial he mal condi ion.
Addi ionally, some mechanical cons ain s we e applied o he he mo-elec ical–
mechanical analysis. Tha way, null displacemen s we e de ined in he X di ec ion a he
symme y plane, in he Y di ec ion a he cen e o he mould, and in he Z di ec ion a he
mould base.
Compu a ion 2023,11, 41 9 o 16
Resul s show ha a ime-dependen elec ic cu en was p oduced due o he imposed
ol age di e ence. A he end o he p ehea ing p ocess ( ime = 50 min), he alue o he
cu en densi y was abou 1.3
×
10
6
A/m
2
and i was nea ly uni o m in he whole hea e .
I was obse ed also ha he elec ic cu en was almos ze o a he ou e su aces, which
indica es ha he ib eglass insula es he hea e well enough and, consequen ly, he e will
be no isk o elec ocu ion.
The empe a u e dis ibu ion ob ained a e he p ehea ing can be seen in Figu e 8,
and i shows ha he maximum empe a u es we e eached in he esis i e hea e . The hea
gene a ed he e was hen ans e ed o he adjoining componen s. Due o he he mal insu-
la ions o mica, he empe a u e o he ou e su aces was no so high and he empe a u e
in he cen e was highe .
Compu a ion 2023, 11, x 9 o 16
Addi ionally, some mechanical cons ain s we e applied o he he mo-elec ical–
mechanical analysis. Tha way, null displacemen s we e de ined in he X di ec ion a he
symme y plane, in he Y di ec ion a he cen e o he mould, and in he Z di ec ion a he
mould base.
Resul s show ha a ime-dependen elec ic cu en was p oduced due o he
imposed ol age di e ence. A he end o he p ehea ing p ocess ( ime = 50 min), he alue
o he cu en densi y was abou 1.3 × 106 A/m2 and i was nea ly uni o m in he whole
hea e . I was obse ed also ha he elec ic cu en was almos ze o a he ou e su aces,
which indica es ha he ib eglass insula es he hea e well enough and, consequen ly,
he e will be no isk o elec ocu ion.
The empe a u e dis ibu ion ob ained a e he p ehea ing can be seen in Figu e 8,
and i shows ha he maximum empe a u es we e eached in he esis i e hea e . The
hea gene a ed he e was hen ans e ed o he adjoining componen s. Due o he he mal
insula ions o mica, he empe a u e o he ou e su aces was no so high and he
empe a u e in he cen e was highe .
Figu e 8. Tempe a u es (°C) dis ibu ion a he end o he p ehea ing.
The empe a u e o he ca i y was close o he a ge empe a u e 120 °C. In ac ,
a e age ca i y empe a u e was 120 °C in he lowe pa and 100 °C in he uppe pa .
Howe e , he dis ibu ion was no uni o m and highe (up o 134 °C in he lowe semi-
mould and 106 °C in he uppe one) and lowe alues (up o 92 °C in he lowe semi-
mould and 91 °C in he uppe one) could be ound. This empe a u e dis ibu ion has
in luence in he illing phase o he RTM p ocess. E olu ions o he maximum and
minimum empe a u es o he ca i y we e close o he se empe a u e and indica ed ha
he hea ing a e was nea ly linea . This e olu ion can be seen in Figu e 9.
Figu e 8. Tempe a u es (◦C) dis ibu ion a he end o he p ehea ing.
The empe a u e o he ca i y was close o he a ge empe a u e 120
◦
C. In ac ,
a e age ca i y empe a u e was 120
◦
C in he lowe pa and 100
◦
C in he uppe pa .
Howe e , he dis ibu ion was no uni o m and highe (up o 134
◦
C in he lowe semi-
mould and 106
◦
C in he uppe one) and lowe alues (up o 92
◦
C in he lowe semi-
mould and 91
◦
C in he uppe one) could be ound. This empe a u e dis ibu ion has
in luence in he illing phase o he RTM p ocess. E olu ions o he maximum and minimum
empe a u es o he ca i y we e close o he se empe a u e and indica ed ha he hea ing
a e was nea ly linea . This e olu ion can be seen in Figu e 9.
Looking a he mechanical beha iou p edic ed by his p ehea ing calcula ion, Table 3
summa izes he mos signi ican esul s.
Table 3. Maximum on Mises s esses and displacemen s.
Loca ion Max. Von Mises S ess (MPa) Max. Displacemen (mm)
Uppe mica co e 125 0.20
Uppe composi e mould 110 0.19
Sample 0 0.14
Gaske 0 0.10
Hea e sys em 70 0.09
Lowe composi e mould 110 0.10
Lowe mica co e 120 0.10
Compu a ion 2023,11, 41 16 o 16
11. RTM-Wo xs 2.8, Use s Documen a ion. A ailable online: h ps://www.polywo x.com/doc/ (accessed on 8 Decembe 2022).
12.
Yi, S.; Hil on, H.H.; Ahmad, M.F. A ini e elemen app oach o cu e simula ion o he mose ing ma ix composi es. Compu .
S uc . 1997,64, 383–388. [C ossRe ]
13.
Kim, J.; Moon, T.J.; Howell, J.R. Cu e Kine ic Model, Hea o Reac ion, and Glass T ansi ion Tempe a u e o AS4/3501-6
G aphi e–Epoxy P ep egs. J. Compos. Ma e . 2002,36, 2479–2498. [C ossRe ]
14.
Ride , A.N.; Wang, C.H.; Cao, J. In e nal esis ance hea ing o homogeneous cu ing o adhesi ely bonded epai s. In . J. Adhes.
Adhes. 2011,31, 168–176. [C ossRe ]
15.
Magui e, J.M.; Sha p, N.D.; Pipes, R.B.; B adaigh, C.M. Ad anced p ocess simula ions o hick-sec ion epoxy powde composi e
s uc u es. Compos. Pa A 2022,161, 107073. [C ossRe ]
16.
Kenny, J.M.; Ma ezzoli, A.M.; Nicolais, L.; Mazzola, M. A model o he he mal and chemo heological beha io o he mose
p ocessing: II) Unsa u a ed polyes e based composi es. Compos. Sci. Technol. 1990,38, 339–358. [C ossRe ]
Disclaime /Publishe ’s No e:
The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual
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people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .
