polyme s
A icle
E ec s o he Tempe a u e–Time Regime o Cu ing o
Composi e Pa ch on Repai P ocess E iciency
And ii Kond a ie 1, Václa Píš ˇek 2, Lina Smo ziuk 3, Ma yna She so a 4, Anna Fomina 5, Pa el Kuˇce a 2
and Aleš P okop 2,*


Ci a ion: Kond a ie , A.; Píš ˇek, V.;
Smo ziuk, L.; She so a, M.; Fomina,
A.; Kuˇce a, P.; P okop, A. E ec s o
he Tempe a u e–Time Regime o
Cu ing o Composi e Pa ch on Repai
P ocess E iciency. Polyme s 2021,13,
4342. h ps://doi.o g/10.3390/
polym13244342
Academic Edi o : An onio Pizzi
Recei ed: 13 No embe 2021
Accep ed: 9 Decembe 2021
Published: 11 Decembe 2021
Publishe ’s No e: MDPI s ays neu al
wi h ega d o ju isdic ional claims in
published maps and ins i u ional a il-
ia ions.
Copy igh : © 2021 by he au ho s.
Licensee MDPI, Basel, Swi ze land.
This a icle is an open access a icle
dis ibu ed unde he e ms and
condi ions o he C ea i e Commons
A ibu ion (CC BY) license (h ps://
c ea i ecommons.o g/licenses/by/
4.0/).
1
Depa men o Building Technology and Cons uc ion Ma e ials, O.M. Beke o Na ional Uni e si y o U ban
Economy in Kha ki , Ma shal Bazhano S . 17, 61002 Kha ki , Uk aine; [email p o ec ed]
2Ins i u e o Au omo i e Enginee ing, B no Uni e si y o Technology, Technická2896/2,
616 69 B no, Czech Republic; [email p o ec ed].cz (V.P.); [email p o ec ed].cz (P.K.)
3
Depa men o In e na ional P ojec s and P og ams, Na ional Ae ospace Uni e si y “Kha ki A ia ion Ins i u e”,
Chkalo a S . 17, 61070 Kha ki , Uk aine; [email p o ec ed]
4Depa men o Composi e S uc u es and A ia ion Ma e ials, Na ional Ae ospace Uni e si y
“Kha ki A ia ion Ins i u e”, Chkalo a S . 17, 61070 Kha ki , Uk aine; [email p o ec ed]
5
Depa men o Railway, Au omobile T anspo and Handling Machines, Ins i u e o T anspo and Logis ics,
Volodymy Dahl Eas Uk ainian Na ional Uni e si y, Cen al A enue 59a, 93400 Sewe odone sk, Uk aine;
[email p o ec ed]
*Co espondence: ales.p okop@ u b .cz; Tel.: +420-541-142-261
Abs ac :
Repai p ocedu es wi h he use o composi e pa ches a e conside ed o be he mos e ec i e
among he cu en echnologies o epai o he s uc u es o a ious applica ions. In he p ocess o
moulding-on o a pa ch made o polyme ic composi e ma e ial by means o cu ing, echnological
s esses a ise in he pa ch. De e mina ion o esidual echnological s esses is a p io i y ask o he
modelling o he epai p ocess. Reduc ion o esidual s esses can be achie ed by op imiza ion
o he mode o epai pa ch cu ing. Fo mee ing his objec i e, he me hod o de e mina ion
o echnological s esses, which a ise in he s uc u e unde epai in he p ocess o cu ing o a
composi e pa ch, has been de eloped. The me hod akes in o accoun he sh inkage, change in
physico-mechanical cha ac e is ics, heological p ocesses occu ing in he binde du ing moulding
p ocess, and de e mina ion o s esses in he s uc u e unde epai a any ime. The e o e, p ema u e
ailu e o he epai join a he s age o epai can be a oided. I is shown ha he me hod adequa ely
desc ibes he le el o de o ma ions and s esses in he s uc u e being epai ed a he s age o hea ing
and holding o he composi e pa ch. Inc ease in he moulding empe a u e leads o a educ ion in
esidual s esses in he s uc u e unde epai . Howe e , cu en s esses a he s ages o hea ing and
empe a u e holding a e inc eased signi ican ly. Reliabili y o assump ions and de eloped me hod is
con i med by he compa ison wi h he expe imen al da a. The ob ained expe imen al g aph o o al
de o ma ion o he composi e pa ch allowed us o clea ly de e mine he momen o esidual s ess
occu ence in he s uc u e unde epai . This momen ma ches qui e exac ly (wi h he disc epancy
no exceeding 5 min) he gel poin de e mined analy ically based on dependence o he deg ee o
cu ing on he moulding mode. Consequen ly, he esea ch oge he wi h he esul s p e iously
ob ained allows making an in eg a ed choice o geome ic pa ame e s o he epai composi e pa ch
and empe a u e– ime egime o i s cu ing in o de o ensu e he speci ied le el o s eng h and
s i ness o he s uc u e unde epai .
Keywo ds: empe a u e– ime egime; binde sh inkage; gela ion
1. In oduc ion
In he p ocess o ope a ion o a ious s uc u es, de ec s may a ise in a numbe o
si ua ions, and de elopmen o such de ec s leads o damage ha p e en s u he use o
he s uc u e [
1
,
2
]. E ec i e epai o any de ec ed de ec s, including he epai in he ield
Polyme s 2021,13, 4342. h ps://doi.o g/10.3390/polym13244342 h ps://www.mdpi.com/jou nal/polyme s
Polyme s 2021,13, 4342 2 o 20
condi ions, allows o he p o ec ion o he damaged elemen s [3,4] and o he a oidance
o leng hy and cos ly capi al epai s [5,6].
Acco ding o esea ch [
7
,
8
], ins alla ion o epai pa ches is conside ed an e ec i e
me hod o he epai o de ec s such as den s, ailu es o bea ing skins and delamina ions
in he me al and composi e panel s uc u es. High physico-mechanical cha ac e is ics
o he mode n polyme ic composi e ma e ials (PCM) [
9
–
11
] de e mine success ul use
o he composi e pa ches o he epai o bo h polyme ic and me al s uc u es [
12
,
13
].
The composi e pa ch can also ha e po en ial applica ions in cons uc ing elec omagne ic
nanocomposi es o in elligen ma e ials, as he e is ca bon ma e ials in he composi e [
14
,
15
].
Howe e , s esses occu ing in he p ocess o cu ing he epai pa ch u he a ec he
bea ing capaci y o epai ed p oduc [
16
]. P esence o un eco ded ini ial s esses in he
epai ed s uc u e causes he appea ance o de ec s such as delamina ions, buckling and
mic oc acks in he binde [
17
,
18
], which in u n has a signi ican e ec on he s a ic and
a igue s eng h o he p oduc made wi h such s uc u es [19,20].
Reduc ion o esidual s esses can be achie ed by op imiza ion o he mode o epai
pa ch cu ing. Technological s esses a e caused by sh inkage o he polyme ic binde ,
as well as he di e ence in he linea he mal expansion coe icien s o ma e ials o be
joined [
21
]. Cu ing o he mo- eac i e polyme ic binde as he mos commonly used binde
in he epai pa ches o a ious applica ions [
22
] is, in ac , he combina ion o a numbe
o physico-chemical p ocesses. Thei mu ual in luence de e mines he beha iou o he
binde and he na u e o changes in i s main cha ac e is ics. Assessmen o he in luence
o pa ame e s o he cu ing mode on he s ess–s ain beha iou o he s uc u e unde
epai and choice o hei a ional alues can be pe o med only wi h a se o in e ela ed
ma hema ical models o de e mine he cu en alues o iscosi y, sh inkage, deg ee o
cu ing and mechanical cha ac e is ics o he PCM a any ime. A signi ican pa o pape s
such as [
23
,
24
] is ocused on he s udy o kine ics o he mo- eac i e binde cu ing and
analy ical modelling o he change in he cu ing deg ee depending on he empe a u e– ime
pa ame e s o he p ocess. This ocus is d i en by he ac ha achie emen o high cu ing
a es is a p e equisi e o he manu ac u ing o high-s eng h composi e s uc u es [
25
]. The
a ie y o phenomenological models o cu ing kine ics ound in he li e a u e is explained
by signi ican di e ences in he beha iou o a ious binde s [26,27].
The simpli ied model o he binde in he p ocess o cu ing, aking in o accoun s ess
elaxa ion, is p oposed in [
28
]. This model p o ides he balance o he modelling accu acy
and e iciency, which is ex emely necessa y in p ac ice.
Modelling and analysis o he he mo- eac i e binde cu ing aking in o accoun
g adual changes in he he mal and mechanical p ope ies is p esen ed in [
29
]. I is shown
ha empo al and spa ial changes in he physical p ope ies o epoxy esin in he cou se o
cu ing a ec he elas ic modulus o he cu ed PCM specimens.
The pape [
30
] p esen s a iscoelas ic model o epoxy esin, depending on empe a u e
and deg ee o cu ing. The esul s we e ob ained based on he hypo hesis o ime and
empe a u e o e lap. The e ec o he deg ee o cu ing was aken in o accoun h ough
glass ansi ion empe a u e, dependen on he cu ing, used as a e e ence empe a u e o
he shea coe icien s.
The pa e n o modelling o esidual s esses and echnological de o ma ions in
he PCM is p oposed in [
31
]. Expe imen al compa ison o he modelling esul s o all
mechanical cha ac e is ics a all s ages o he phase ans o ma ion o he ma e ial is gi en.
Un o una ely, he equa ions ob ained o modelling o all key p ocesses associa ed wi h he
empe a u e cycle o ha dening o he he moplas ic ma ix a e p esen ed oge he wi h he
co esponding ma e ial cons an s using he example o polye he e he ke one
(PEEK) only.
The me hod o p edic ing he dis ibu ion o esidual s esses in PCM caused by he
echnological p ocess in he cou se o binde cu ing is p oposed in [
32
]. Dis ibu ions o
he empe a u e and deg ee o cu ing we e ob ained. The elas ic modulus o he binde
was de e mined using a model o ins an aneous linea elas ici y a cu ing.
Polyme s 2021,13, 4342 3 o 20
The analy ical model o eco ding o he mo iscoelas ic e ec s on he esidual s esses
o composi e pa s du ing he cu ing p ocess is de eloped in [
33
]. Viscoelas ic e ec s on
he esidual s esses and elas ici y due o angen ial and adial he mochemical expansion
a e conside ed sepa a ely in o de o help unde s and hei indi idual in luence.
The pape s [
34
,
35
] deal wi h he change in dis ibu ion o he ield o esidual s esses
in he specimen o ma e ial AS4/8552-1 wi h he lay-up o (0
◦
/90
◦
) in he p ocess o cu ing.
To simula e he cu ing, he coupled he mal and s eng h p oblem is sol ed unde plane
de o ma ion condi ions.
A common disad an age o he pape s conside ed is ha hey ocus only on he
me hod o s ess de e mina ion, wi hou paying due a en ion o he cu ing p ocess i sel .
As a esul , hey do no ake in o accoun he change in he PhMC o he composi e ma e ial
du ing he cu ing p ocess, and conside he esidual s esses caused by he empe a u e
componen , only wi hou aking in o accoun he sh inkage. In many pape s, only he
cooling s age is conside ed, i.e., s esses a ising du ing he hea ing p ocess a e un easonably
neglec ed. An excep ion is [
36
], whe e he s ess–s ain beha iou is de e mined, aking
in o accoun he p e iously de eloped kine ic model o he binde pe o mance in he
cu ing p ocess, as well as [
34
,
35
], p o iding he model o beha iou o iscoelas ic ma e ial
o desc ibe he PCM ope a ion in he manu ac u ing p ocess, including he p ocesses o
o ma ion, polyme iza ion, and de elopmen o esidual de o ma ions and s esses.
The esul s o a numbe o expe imen al s udies a e o g ea impo ance o unde -
s anding he mechanisms o occu ence o empe a u e s esses in he p ocess o cu ing
o he epai pa ch and possible ways o educe hem [
37
,
38
]. S udy o he empe a u e
de o ma ions occu ing in he s uc u e unde a ious empe a u e and ime condi ions
o polyme iza ion a e deal wi h in [
39
,
40
]. Howe e , he expe imen al measu emen o
esidual s esses a cu ing is o en an expensi e and di icul p ocess [
41
]. The e o e, esul s
o expe imen al s udies in a numbe o wo ks a e supplemen ed wi h he da a ob ained
using he ini e elemen modelling [
42
,
43
]. I allowed he au ho s o gi e some ecom-
menda ions ega ding he choice o op imal pa ame e s o he epai p ocess [
44
]. The
pape [
45
] p oposes a mul iscale model o p edic ion o esidual s esses o composi es in
he p ocess o cu ing. Howe e , he main disad an age o he nume ical app oach is ha
he ini e elemen model is c ea ed o a s ic ly de ined s uc u e and canno be a bi a ily
ex ended o simila elemen s and manu ac u ing p ocesses [46].
Thus, i can be said ha , e en as he p oblem o de e mining he esidual echno-
logical s esses in panels epai ed by a composi e pa ch is discussed in mode n li e a u e
om a ious posi ions, he s udies conside ed do no ake in o accoun a numbe o
signi ican ac o s.
The objec i e o he wo k is o de elop a me hod o de e mining he echnological
s esses a ising in he s uc u e unde epai in he p ocess o cu ing o he composi e pa ch,
which would ake in o accoun he sh inkage, changes in physico-mechanical cha ac e is ics
and heological p ocesses occu ing in he binde du ing he moulding p ocess. Figu e 1
shows he esea ch low cha .
Polyme s 2021,13, 4342 4 o 20
Polyme s 2021, 13, x FOR PEER REVIEW 4 o 22
Figu e 1. The esea ch low cha .
2. Ma e ials and Me hods
To de e mine he s ess–s ain beha iou o he s uc u e in he p ocess o cu ing o
he composi e pa ch, ad anced ma hema ical model o a panel o s ep- a iable hickness
was used [47]. The ma hema ical model o he change in he PCM physical and
mechanical cha ac e is ics in he p ocess o cu ing o he composi e pa ch was de eloped
o aking in o accoun he echnological s esses a ising in he p ocess o he composi e
pa ch moulding-on. In he amewo k o his model, o he de e mina ion o kine ics o
cu ing, iscosi y and sh inkage o he binde , empi ical dependences o hese pa ame e s
on he empe a u e and ime o cu ing ob ained in [48,49] on he esul s o iso he mal and
dynamic calo ime ic es s o he epoxy binde Hysol EA9396 (Henkel, Bay Poin , CA,
USA) we e used. In he p ocess o cons uc ion o he ma hema ical model, aking in o
accoun a sha p change in he binde iscosi y du ing ansi ion om he liquid o he
elas ic s a e, i was assumed ha echnological s esses would a ise in he s uc u e a e
gela ion o he binde only. The linea dependence o he elas ic modulus on he deg ee o
cu ing was aken. Addi ionally, i was assumed ha Poisson’s a io and coe icien o
linea he mal expansion o he binde we e no dependen on he deg ee o cu ing, wi h
he linea he mal expansion coe icien being he known unc ion o empe a u e.
Dependences o he cu en elas ic cha ac e is ics o he monolaye a a pa icula momen
o cu ing on he cha ac e is ics o he ib e and ma ix we e de e mined om he known
dependences o he ein o ced media mechanics [50,51]. Wo en ein o cing ma e ial was
conside ed as a package, consis ing o wo iden ical monolaye s wi h laying angles o [0°,
90°]. Technological s esses in he s uc u e unde epai we e de e mined as a sum o
s esses a ising in sepa a e ime in e als, wi hin which he empe a u e and sh inkage
Figu e 1. The esea ch low cha .
2. Ma e ials and Me hods
To de e mine he s ess–s ain beha iou o he s uc u e in he p ocess o cu ing
o he composi e pa ch, ad anced ma hema ical model o a panel o s ep- a iable hick-
ness was used [
47
]. The ma hema ical model o he change in he PCM physical and
mechanical cha ac e is ics in he p ocess o cu ing o he composi e pa ch was de eloped
o aking in o accoun he echnological s esses a ising in he p ocess o he composi e
pa ch moulding-on. In he amewo k o his model, o he de e mina ion o kine ics o
cu ing, iscosi y and sh inkage o he binde , empi ical dependences o hese pa ame e s
on he empe a u e and ime o cu ing ob ained in [
48
,
49
] on he esul s o iso he mal and
dynamic calo ime ic es s o he epoxy binde Hysol EA9396 (Henkel, Bay Poin , CA,
USA) we e used. In he p ocess o cons uc ion o he ma hema ical model, aking in o
accoun a sha p change in he binde iscosi y du ing ansi ion om he liquid o he
elas ic s a e, i was assumed ha echnological s esses would a ise in he s uc u e a e
gela ion o he binde only. The linea dependence o he elas ic modulus on he deg ee
o cu ing was aken. Addi ionally, i was assumed ha Poisson’s a io and coe icien
o linea he mal expansion o he binde we e no dependen on he deg ee o cu ing,
wi h he linea he mal expansion coe icien being he known unc ion o empe a u e.
Dependences o he cu en elas ic cha ac e is ics o he monolaye a a pa icula momen
o cu ing on he cha ac e is ics o he ib e and ma ix we e de e mined om he known
dependences o he ein o ced media mechanics [
50
,
51
]. Wo en ein o cing ma e ial was
conside ed as a package, consis ing o wo iden ical monolaye s wi h laying angles o
[
0◦, 90◦
]. Technological s esses in he s uc u e unde epai we e de e mined as a sum
o s esses a ising in sepa a e ime in e als, wi hin which he empe a u e and sh inkage
Polyme s 2021,13, 4342 5 o 20
s esses we e caused by co esponding changes in empe a u e and sh inkage; he elas ic
modulus and he coe icien o linea he mal expansion o he binde we e cons an .
The numbe o a eas o di ision was de e mined by he equi ed compu a ional
accu acy. Reliabili y o he cons uc ed ma hema ical model is con i med by compa ison
wi h he esul s o expe imen al s udies o de o ma ions a ising in he aluminium panel
and ca bon ib e composi e pa ch in he moulding-on p ocess. To do his, a ca bon ib e
composi e pa ch (EA9396/Ca bon 3K-70-P, Henkel, Bay Poin , CA, USA) wi h a lay-up
pa e n o (0
◦
; 90
◦
) was laid on p e ab ica ed specimen o he aluminium alloy 2024T3 (TW
Me als Co po a e Headqua e s, Ex on, PA, USA) by we me hod. Thickness o he pa ch
a e cu ing was 2.2
±
0.07 mm. De o ma ions a ising in he es ed s uc u e in he p ocess
o cu ing o he composi e pa ch we e measu ed using KF5P1-20-400 (VEDA G oup o
Companies, Kyi , Uk aine) s ain gauges. To implemen he selec ed cu ing modes o he
epai pa ch, he he mal o en p o iding he uni o m hea ing o e he en i e a ea o he
specimen was used. Fo mo e accu a e empe a u e con ol, an addi ional he mocouple
was ins alled di ec ly on he es specimen. Due o small hickness o he specimen and wo-
way hea ing p o ided in he u nace, une en empe a u e dis ibu ion o e he hickness
was no aken in o accoun . To p e en he impac o he in e nal empe a u e de o ma ions
o he s ain gauge on he esul s o he expe imen , s ain gauges we e connec ed o he
measu ing sys em aking in o accoun he he mal compensa ion
3. Theo e ical Backg ound
As s a ed abo e, i is no possible o cons uc he gene al cu ing model sui able o
any he mo- eac i e binde [
23
,
24
]. This is due o signi ican di e ence in he beha iou o
a ious ypes o polyme s [22].
Epoxy binde Hysol EA9396 (Henkel), widely used o epai s in he o eign a ia ion
indus y, was chosen o he esea ch. To de e mine he kine ics o cu ing, iscosi y and
sh inkage o he binde EA 9396, empi ical dependences cons uc ed in [
48
,
49
] unde
he in e na ional p ojec SENARIO (AST5-CT-2006-030982) wi h he inancial suppo o
he Eu opean Commission we e used, based on he esul s o iso he mal and dynamic
calo ime ic es s and expe imen al s udy o sh inkage. Figu e 2shows he g aphs o
changes in he abo emen ioned cha ac e is ics a he cu ing mode ecommended by he
binde manu ac u e .
Polyme s 2021, 13, x FOR PEER REVIEW 5 o 22
s esses we e caused by co esponding changes in empe a u e and sh inkage; he elas ic
modulus and he coe icien o linea he mal expansion o he binde we e cons an .
The numbe o a eas o di ision was de e mined by he equi ed compu a ional
accu acy. Reliabili y o he cons uc ed ma hema ical model is con i med by compa ison
wi h he esul s o expe imen al s udies o de o ma ions a ising in he aluminium panel
and ca bon ib e composi e pa ch in he moulding-on p ocess. To do his, a ca bon ib e
composi e pa ch (EA9396/Ca bon 3K-70-P, Henkel, Bay Poin , CA, USA) wi h a lay-up
pa e n o (0°; 90°) was laid on p e ab ica ed specimen o he aluminium alloy 2024T3 (TW
Me als Co po a e Headqua e s, Ex on, PA, USA) by we me hod. Thickness o he pa ch
a e cu ing was 2.2 ± 0.07 mm. De o ma ions a ising in he es ed s uc u e in he p ocess
o cu ing o he composi e pa ch we e measu ed using KF5P1-20-400 (VEDA G oup o
Companies, Kyi , Uk aine) s ain gauges. To implemen he selec ed cu ing modes o he
epai pa ch, he he mal o en p o iding he uni o m hea ing o e he en i e a ea o he
specimen was used. Fo mo e accu a e empe a u e con ol, an addi ional he mocouple
was ins alled di ec ly on he es specimen. Due o small hickness o he specimen and
wo-way hea ing p o ided in he u nace, une en empe a u e dis ibu ion o e he
hickness was no aken in o accoun . To p e en he impac o he in e nal empe a u e
de o ma ions o he s ain gauge on he esul s o he expe imen , s ain gauges we e
connec ed o he measu ing sys em aking in o accoun he he mal compensa ion
3. Theo e ical Backg ound
As s a ed abo e, i is no possible o cons uc he gene al cu ing model sui able o
any he mo- eac i e binde [23,24]. This is due o signi ican di e ence in he beha iou
o a ious ypes o polyme s [22].
Epoxy binde Hysol EA9396 (Henkel), widely used o epai s in he o eign a ia ion
indus y, was chosen o he esea ch. To de e mine he kine ics o cu ing, iscosi y and
sh inkage o he binde EA 9396, empi ical dependences cons uc ed in [48,49] unde he
in e na ional p ojec SENARIO (AST5-CT-2006-030982) wi h he inancial suppo o he
Eu opean Commission we e used, based on he esul s o iso he mal and dynamic
calo ime ic es s and expe imen al s udy o sh inkage. Figu e 2 shows he g aphs o
changes in he abo emen ioned cha ac e is ics a he cu ing mode ecommended by he
binde manu ac u e .
Wi h he use o hese models and based on he ac ha a sha p change in he binde
iscosi y co esponds o i s ansi ion om he liquid o elas ic s a e [25], calcula ions
showed ha , a he ime o gela ion, he deg ee o he binde cu ing was equal o 52%.
Wi h he inc ease in he deg ee o he binde cu ing, he change in i s elas ic
cha ac e is ics occu s [26,27,29].
Figu e 2. Change in iscosi y (η), sh inkage (ξ) and deg ee o cu ing (θ) o he binde EA 9396 a he
cu ing mode ecommended by he manu ac u e [48,49].
Figu e 2.
Change in iscosi y (
η
), sh inkage (
ξ
) and deg ee o cu ing (
θ
) o he binde EA 9396 a he
cu ing mode ecommended by he manu ac u e [48,49].
Wi h he use o hese models and based on he ac ha a sha p change in he binde
iscosi y co esponds o i s ansi ion om he liquid o elas ic s a e [
25
], calcula ions
showed ha , a he ime o gela ion, he deg ee o he binde cu ing was equal o 52%.
Wi h he inc ease in he deg ee o he binde cu ing, he change in i s elas ic cha ac e -
is ics occu s [26,27,29].
Assuming he linea dependence o he elas ic modulus on he deg ee o cu ing and
aking in o accoun he sha p change in he elas ic modulus du ing passing h ough he gel

Polyme s 2021,13, 4342 6 o 20
poin expe imen ally p o en in [
50
], we use he unc ion below o se ing o he binde
elas ic modulus
Eb( ) = (0, < g
Eθ=100%
bθ, ≥ g
, (1)
whe e
θ
—cu en alue o he deg ee o cu ing;
g
—gela ion ime;
Eθ=100%
b
—binde elas ic
modulus a 100% deg ee o cu ing.
Assuming ha a e gela ion he Poisson’s a io and he binde linea he mal expan-
sion coe icien change insigni ican ly, we conside hem independen o he deg ee o
cu ing. Howe e , we ake in o accoun a signi ican change in he binde linea he mal
expansion coe icien on he empe a u e T. Dependence o he elas ic cha ac e is ics o
ini ial PCM componen s ( ib e and ma ix) on he empe a u e will be neglec ed because
o a sligh change in hese p ope ies a low cu ing empe a u es [
22
]. Dependences o
he cu en elas ic cha ac e is ics o he monolaye a a pa icula momen o cu ing on
he cha ac e is ics o he ib e and ma ix we e de e mined using he known dependen-
cies [51,52]:
E1( ) = E Θ+Eb( )(1−Θ),E2( ) = E Eb( )
Eb( )Θ+E (1−Θ),
G12( ) = G Gb( )
Gb( )Θ+G (1−Θ),µ12(T) = µ Θ+µb(1−Θ),
α1( ) = E α Θ+Eb( )αb(T)(1−Θ)
E Θ+Eb( )(1−Θ),
α2( ) = (α Θ+αb(T)(1−Θ))(E Θ+Eb( )(1−Θ))
E Θ+Eb( )(1−Θ)+
Θ(1−Θ)(αb(T)−α )(E µb−Eb( )µ )
E Θ+Eb( )(1−Θ),
ξ1( ) = Ebξb(1−Θ)
E Θ+Eb( )(1−Θ),
ξ2( ) = E Θ+Eb( )(1−Θ)+Θ(E µb−Eb( )µ )
E Θ+Eb( )(1−Θ)(1−Θ)ξb,











































(2)
whe e E
,E
b
,G
,G
b
,
µ
,
µb
,
ξ
,
ξb
—elas ic modulus, shea modulus, Poisson’s a ios, ib e
and binde sh inkage, acco dingly; Θ— ela i e olume ic con en o ib es.
Wo en ein o cing ma e ial is conside ed as a package consis ing o wo iden ical
monolaye s wi h laying angles o [0◦, 90◦], o which [34,46]:
Ex=Ey=E1
2+E2
2−2E2
1µ2
21
E1+E2;Gxy =G12,
αx=αy=(α1E1
2+α2E2
2+α1+α2
2E1µ21)( E1
2+E2
2−E1µ21)
(E1
2+E2
2)2−E2
1µ2
21
,
ξx=ξy=(ξ1E1
2+ξ2E2
2+ξ1+ξ2
2E1µ21)( E1
2+E2
2−E1µ21)
(E1
2+E2
2)2−E2
1µ2
21
,



















(3)
whe e E1=E1
1−µ12µ21 ,E2=E2
1−µ12µ21 .
In o de o de e mine he s ess–s ain beha iou o he s uc u e unde epai , we
apply he analy ical model o a panel o s ep- a iable hickness [
19
]. Now we shall analyse
he ex e nal and in e nal o ce ac o s leading o he appea ance o s esses in he s uc u e
unde epai , using he example o ypical empe a u e– ime dependence o he polyme ic
binde cu ing mode (Figu e 3) [19,22].
Polyme s 2021,13, 4342 7 o 20
Polyme s 2021, 13, x FOR PEER REVIEW 7 o 22
he ex e nal and in e nal o ce ac o s leading o he appea ance o s esses in he s uc u e
unde epai , using he example o ypical empe a u e– ime dependence o he polyme ic
binde cu ing mode (Figu e 3) [19,22].
Figu e 3. Typical empe a u e– ime dependence o he polyme ic binde cu ing mode
Taking in o accoun ha echnological s esses occu in he s uc u e only a e
gela ion (poin O) [25,29,31], he ypical cu ing p ocess can be oughly di ided in o ou
s ages, as shown in Figu e 3.
A he i s s age, occu ence and g ow h o s esses is de e mined by hea ing and
a ailable sh inkage de o ma ions. When me al s uc u es a e epai ed using he
composi e pa ch, he mal and sh inkage s esses can ha e he same sign a he de ini e
a io o he linea he mal expansion coe icien and s i nesses [19]. In his case,
empe a u e s esses supplemen ed wi h sh inkage ones may lead o occu ence o de ec s
al eady in he hea ing p ocess, since physico-mechanical cha ac e is ics o he pa ch
ma e ial a he i s s age a e conside ably lowe han he inal alues. I de e mines he
need o con ol he s esses a poin A.
Du ing he iso he mal holding (AC), s esses esul om he con inuing sh inkage
(II) and elaxa ion p ocesses (III) [28,32,33].
A he ou h s age, he occu ing s esses a e de e mined by cooling o he s uc u e
being epai ed and he ongoing elaxa ion p ocesses. The inal echnological s esses a
poin D summa ize he s esses a all p e ious s ages and a e subjec o con ol [22].
Unde ce ain condi ions, a each s age he e ec i e ol ages can exceed he cu en
pe missible alues. I de e mines he need o con ol bo h he esidual s esses (poin D),
and he cu en s esses a design poin s A, B and C [47].
In o de o de e mine he s ess–s ain beha iou o he s uc u e wi h he
cha ac e is ics changing in he cu ing p ocess, a ising s esses a e de e mined as a sum o
s esses on he ce ain a eas, wi hin which [19]:
• The mal and sh inkage s esses a e caused by co esponding inc ease in he
empe a u e and sh inkage
∆=−; ∆=−; (4)
• Elas ic modulus o he binde is aken o be cons an and equal o
=
󰇛󰇜

; (5)
• The binde linea he mal expansion coe icien is aken o be cons an and equal o

=
󰇛󰇜

. (6)
The numbe o a eas o di ision is de e mined by he equi ed compu a ional
accu acy.
Figu e 3. Typical empe a u e– ime dependence o he polyme ic binde cu ing mode.
Taking in o accoun ha echnological s esses occu in he s uc u e only a e gela ion
(poin O) [
25
,
29
,
31
], he ypical cu ing p ocess can be oughly di ided in o ou s ages, as
shown in Figu e 3.
A he i s s age, occu ence and g ow h o s esses is de e mined by hea ing and
a ailable sh inkage de o ma ions. When me al s uc u es a e epai ed using he composi e
pa ch, he mal and sh inkage s esses can ha e he same sign a he de ini e a io o he
linea he mal expansion coe icien and s i nesses [
19
]. In his case, empe a u e s esses
supplemen ed wi h sh inkage ones may lead o occu ence o de ec s al eady in he hea ing
p ocess, since physico-mechanical cha ac e is ics o he pa ch ma e ial a he i s s age a e
conside ably lowe han he inal alues. I de e mines he need o con ol he s esses a
poin A.
Du ing he iso he mal holding (AC), s esses esul om he con inuing sh inkage (II)
and elaxa ion p ocesses (III) [28,32,33].
A he ou h s age, he occu ing s esses a e de e mined by cooling o he s uc u e
being epai ed and he ongoing elaxa ion p ocesses. The inal echnological s esses a
poin D summa ize he s esses a all p e ious s ages and a e subjec o con ol [22].
Unde ce ain condi ions, a each s age he e ec i e ol ages can exceed he cu en
pe missible alues. I de e mines he need o con ol bo h he esidual s esses (poin D),
and he cu en s esses a design poin s A, B and C [47].
In o de o de e mine he s ess–s ain beha iou o he s uc u e wi h he cha ac e is-
ics changing in he cu ing p ocess, a ising s esses a e de e mined as a sum o s esses on
he ce ain a eas, wi hin which [19]:
•
The mal and sh inkage s esses a e caused by co esponding inc ease in he empe a-
u e and sh inkage
∆Ti=Ti+1−Ti;∆ξi=ξi+1−ξi; (4)
•Elas ic modulus o he binde is aken o be cons an and equal o
Ei
b=1
i+1− iZ i+1
i
E( )d ; (5)
•The binde linea he mal expansion coe icien is aken o be cons an and equal o
αi
b=1
Ti+1−TiZTi+1
Ti
α(T)dT. (6)
The numbe o a eas o di ision is de e mined by he equi ed compu a ional accu acy.
The basis o op imiza ion o he s uc u e epai using PCM is he analysis o he
in luence o indi idual pa ame e s o he epai pa ch cu ing p ocess. They can be oughly
di ided in o wo g oups:
•Cu ing p ocess pa ame e s;
Polyme s 2021,13, 4342 8 o 20
•Repai p ocess pa ame e s.
Among he pa ame e s o he moulding mode, signi ican e ec on he s ess–s ain
beha iou is exe ed, i s o all, by cu ing empe a u e (
Tc
), hea ing a e (
V1
) and cooling
a e (
V2
) o he s uc u e unde epai . Holding ime a
Tc
de e mines he deg ee o cu ing o
he epai pa ch and a ec s no so much he s ess–s ain beha iou , bu physico-mechanical
cha ac e is ics o he PCM.
The second g oup o pa ame e s should include he condi ions o he s uc u e
ixa ion du ing he epai p ocess, me hod o implemen ing he empe a u e– ime egime,
and p esence o addi ional ex e nal loads.
Le ’s in es iga e he s ess–s ain beha iou o he la ec angula panel (Figu e 4)
made o he aluminium alloy 2024T3, o he pa ame e s below:
•Cu ing empe a u e Tc;
•Hea ing a e V1;
•Condi ions o he s uc u e ixa ion in he epai p ocess;
•Hea ing me hod.
Polyme s 2021, 13, x FOR PEER REVIEW 8 o 22
The basis o op imiza ion o he s uc u e epai using PCM is he analysis o he
in luence o indi idual pa ame e s o he epai pa ch cu ing p ocess. They can be oughly
di ided in o wo g oups:
• Cu ing p ocess pa ame e s;
• Repai p ocess pa ame e s.
Among he pa ame e s o he moulding mode, signi ican e ec on he s ess–s ain
beha iou is exe ed, i s o all, by cu ing empe a u e (), hea ing a e () and cooling
a e () o he s uc u e unde epai . Holding ime a  de e mines he deg ee o cu ing
o he epai pa ch and a ec s no so much he s ess–s ain beha iou , bu physico-
mechanical cha ac e is ics o he PCM.
The second g oup o pa ame e s should include he condi ions o he s uc u e
ixa ion du ing he epai p ocess, me hod o implemen ing he empe a u e– ime
egime, and p esence o addi ional ex e nal loads.
Le ’s in es iga e he s ess–s ain beha iou o he la ec angula panel (Figu e 4)
made o he aluminium alloy 2024T3, o he pa ame e s below:
• Cu ing empe a u e ;
• Hea ing a e ;
• Condi ions o he s uc u e ixa ion in he epai p ocess;
• Hea ing me hod.
Figu e 4. Geome ic pa ame e s o he in es iga ed s uc u e unde epai
Repai o he s uc u e unde s udy is ca ied ou by ins alling a ec angula ca bon
ib e composi e pla e. Physico-mechanical cha ac e is ics o he ini ial PCM componen s
a e gi en in Table 1 [49].
Table 1. Physico-mechanical cha ac e is ics o ini ial PCM componen s
Ini ial
Componen s Binde EA9396 Ca bon
Fib e
Cha ac e is ics
Elas ic modulus, MPa 2750 290,000
Poisson’s a io 0.35 0.07
Linea he mal expansion coe icien
α·10−6, 1/C
85 a T ≤ 65 °C$$75 a 65 °C
< T ≤ 95 °C$$70 a 95 °C < T
≤ 105 °C$$65 a 105 °C < T ≤
125 °C$$50 a T > 125 °C
−0.64
Volume ic con en in PCM 0.45 0.55
Fo he modes p esen ed in Table 2, s ess–s ain beha iou occu ing du ing epai
o he analysed s uc u e in a ee s a e has been de e mined. In his case, he bounda y
condi ions co esponded o he hinge moun o he panel a he cen al poin , ensu ing i s
un es ic ed de o ma ion in he moulding p ocess. The uni o m empe a u e se ing o e
he en i e s uc u e a ea modelled he pa ch cu ing in he o en. Non-uni o mi y o
Figu e 4. Geome ic pa ame e s o he in es iga ed s uc u e unde epai .
Repai o he s uc u e unde s udy is ca ied ou by ins alling a ec angula ca bon
ib e composi e pla e. Physico-mechanical cha ac e is ics o he ini ial PCM componen s
a e gi en in Table 1[49].
Table 1. Physico-mechanical cha ac e is ics o ini ial PCM componen s.
Cha ac e is ics
Ini ial Componen s Binde EA9396 Ca bon Fib e
Elas ic modulus, MPa 2750 290,000
Poisson’s a io 0.35 0.07
Linea he mal expansion coe icien α·10−6,
1/C
85 a T≤65 ◦C
75 a 65 ◦C < T≤95 ◦C
70 a 95 ◦C < T≤105 ◦C
65 a 105
◦
C < T
≤
125
◦
C
50 a T> 125 ◦C
−0.64
Volume ic con en in PCM 0.45 0.55
Fo he modes p esen ed in Table 2, s ess–s ain beha iou occu ing du ing epai
o he analysed s uc u e in a ee s a e has been de e mined. In his case, he bounda y
condi ions co esponded o he hinge moun o he panel a he cen al poin , ensu ing
i s un es ic ed de o ma ion in he moulding p ocess. The uni o m empe a u e se ing
o e he en i e s uc u e a ea modelled he pa ch cu ing in he o en. Non-uni o mi y o
empe a u e o e he hickness was no aken in o accoun because o he small hickness
o pa s and he p esence o a wo-way hea supply.
Polyme s 2021,13, 4342 9 o 20
Table 2. Pa ame e s o analysed cu ing modes.
Numbe o Regime Hea ing Ra e
V,◦C/min
Cu ing
Tempe a u e Tc,◦C
Cu ing
Time c,◦min No e
1 – 25 7200 S anda d mode ecommended
by he manu ac u e [49]
2 1 90 60 Mode No.1 + addi ional
hea ea men
3 1 66 60 Accele a ed mode, ecommended by he
manu ac u e
4 1 70 60 –
5 1 90 60 –
6 1 120 60 –
7 1 150 – –
8 0.5 90 60 –
9 3 90 60 –
10 5 90 60 –
Da a ob ained as a esul o calcula ions a e p esen ed in he o m o :
•
Pic u es o s ess dis ibu ion in he panel and pa ch a he s age o empe a u e
holding and a e cooling o he s uc u e (Figu e 5);
•
Diag ams o maximum s esses in he s uc u e du ing moulding a di e en empe a-
u es (Figu e 6);
•
Diag ams o maximum s esses in he s uc u e du ing moulding a di e en hea ing
a es (Figu e 7).
Polyme s 2021, 13, x FOR PEER REVIEW 9 o 22
empe a u e o e he hickness was no aken in o accoun because o he small hickness
o pa s and he p esence o a wo-way hea supply.
Table 2. Pa ame e s o analysed cu ing modes.
Numbe o Regime Hea ing Ra e
$$V, °C/min
Cu ing
$$Tempe a u e Tc,
°C
Cu ing $$Time
c, °min No e
1 – 25 7200
S anda d mode ecommended $$by he
manu ac u e [49]
2 1 90 60 Mode No.1 + addi ional$$hea ea men
3 1 66 60
Accele a ed mode, ecommended by he
manu ac u e
4 1 70 60 –
5 1 90 60 –
6 1 120 60 –
7 1 150 – –
8 0.5 90 60 –
9 3 90 60 –
10 5 90 60 –
Da a ob ained as a esul o calcula ions a e p esen ed in he o m o :
• Pic u es o s ess dis ibu ion in he panel and pa ch a he s age o empe a u e
holding and a e cooling o he s uc u e (Figu e 5);
• Diag ams o maximum s esses in he s uc u e du ing moulding a di e en
empe a u es (Figu e 6);
• Diag ams o maximum s esses in he s uc u e du ing moulding a di e en hea ing
a es (Figu e 7).
Figu e 5. Dis ibu ion o no mal s esses σx in he aluminium panel (a,b) and epai pa ch (c,d) on comple ion o he
empe a u e holding a Tc and cooling.
Figu e 5.
Dis ibu ion o no mal s esses
σx
in he aluminium panel (
a
,
b
) and epai pa ch (
c
,
d
) on comple ion o he
empe a u e holding a Tcand cooling.
Polyme s 2021, 13, x FOR PEER REVIEW 10 o 22
Figu e 6. Maximum no mal s esses occu ing in he aluminium panel (a) and composi e pa ch (b) a di e en cu ing
empe a u es.
Figu e 7. Maximum no mal s esses occu ing in he aluminium panel (a) and composi e pa ch (b)
a di e en hea ing a es (V1).
Fo he mode No.5 (see Table 2) he s ess–s ain beha iou occu ing in he p ocess
o epai o he s uc u e unde s udy wi hou p elimina y disman ling wi h he use o
ine- ib e esis i e s uc u e in he hea ed ool was also calcula ed [19]. In his case,
bounda y condi ions co esponded o he hinge moun o he s uc u e along he con ou .
Se ing o he empe a u e on he su ace a ea being 15 mm la ge han he pa ch on each
side modelled he local hea ing using he he mal blanke [19]. Figu e 8 shows he quali y
pic u e o he dis ibu ion o no mal s esses in he aluminium panel unde epai and
pa ch a he s age o hea ing and a e cooling o he s uc u e. Figu e 9 shows he
maximum alues o no mal s esses a ising in he s uc u e unde a ious epai
condi ions.
Figu e 6.
Maximum no mal s esses occu ing in he aluminium panel (
a
) and composi e pa ch (
b
) a di e en
cu ing empe a u es.
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Polyme s 2021, 13, x FOR PEER REVIEW 16 o 22
Figu e 15. Change in he empe a u e, deg ee o cu ing (a) and de o ma ions occu ing (b) in he
aluminium panel unde epai and composi e pa ch in he p ocess o cu ing acco ding o he mode
3 (Table 3).
(a)
(b)
Figu e 16. Change in he empe a u e, deg ee o cu ing (a) and de o ma ions occu ing (b) in he
aluminium panel unde epai and composi e pa ch in he p ocess o cu ing acco ding o he mode
4 (Table 3).
Nume ical alues o de o ma ions a con ol poin s C (holding comple ion o he
cooling a =) and D (comple ion o cooling s age) o all in es iga ed modes a e
summa ized and analysed in Table 4.
Table 4. Compa ison o esul s o heo e ical calcula ions and expe imen al s udies.
Poin
De o ma ions in Ca bon Fib e Composi e
Pa ch De o ma ions in Aluminium Panel
Shea
De o ma io
n
Exp. Analy ical E o , % Exp. Analy ical E o , % Analy ical
Cu ing mode 1
C −1.69 × 10−4 −1.60 × 10−4 5.79% 3.59 × 10−4 3.43 × 10−4 4.70% 5.31 × 10−5
D 5.05 × 10−5 1.89 × 10−4 — −7.55 × 10−4 −8.53 × 10−4 12.29% −6.21 × 10−5
Cu ing mode 2
C −3.06 × 10−4 −2.85 × 10−4 7.07% 8.11 × 10−4 7.78 × 10−4 4.12% 1.10 × 10−4
D 2.63 × 10−5 1.61 × 10−4 — −7.19 × 10−4 −8.21 × 10−4 13.35% −5.47 × 10−5
Figu e 16.
Change in he empe a u e, deg ee o cu ing (
a
) and de o ma ions occu ing (
b
) in he
aluminium panel unde epai and composi e pa ch in he p ocess o cu ing acco ding o he mode 4
(Table 3).
Inc ease in he di e ence be ween he expe imen al and heo e ical alues a he
cooling s age is explained by he p esence o elaxa ion p ocesses, which we e no aken
in o accoun in he heo e ical calcula ions because o lack o heological cha ac e is ics
o he ma e ials used. Taking hese p ocesses in o accoun will imp o e he calcula ion
accu acy, as well as p o ide an addi ional oppo uni y o op imize he cooling mode
(selec ion o empe a u e holdings) and o u he educe he le el o esidual s esses.
The pe missible le el o esidual s esses in he epai ed s uc u e is no a gua an ee o
high-quali y epai , since he cu en s esses can signi ican ly exceed he esidual s esses
and lead o appea ance o hidden de ec s (c acks, delamina ion) o e en he ailu e o he
epai join al eady in he cu ing p ocess (as in expe imen No. 2 Figu e 14).
5. Discussion
The e o e, he new me hod o de e mina ion o echnological s esses occu ing in
he s uc u e unde epai in he p ocess o he composi e pa ch cu ing has been de eloped.
This me hod is based on he analy ical model p e iously de eloped in [
47
] o de e mine he
s ess–s ain beha iou o he panel o s ep- a iable hickness. The esea ch demons a ed
he signi ican in luence o he empe a u e– ime egime o cu ing and me hods o i s
implemen a ion on he bea ing capaci y o he s uc u e unde epai . Resul s o he
esea ch allowed o he conside able imp o emen o he model o he mo- eac i e binde

Polyme s 2021,13, 4342 17 o 20
cu ing ob ained ea lie in [
23
,
25
,
26
]. Consequen ly, i is now possible o ob ain a mo e
comple e pic u e o he changes conce ned and o de e mine he cu en and esidual
s ess–s ain beha iou o he s uc u e unde epai .
Ou s udies, which con i m he indings o [
24
–
27
], p o e ha a , he ime o gela ion,
he deg ee o binde cu ing is a cons an cha ac e is ic o he polyme no depending on he
cu ing mode. Fo he epoxy binde Hysol EA9396 (Henkel) [
48
] unde s udy, he deg ee o
i s cu ing is 52%.
When analysing he esul s, i is necessa y o no e he signi ica e ise in s esses and
mo e une en s ess dis ibu ion in he p ocess o epai o he panel wi hou p elimina y
disman ling, as p oposed in [
19
]. The e o e, owing o he high equi emen s o he bea ing
capaci y o he s uc u e being epai ed, he pe o mance o epai s ha wo k in his way
equi es mo e ca e ul choice o he cu ing mode pa ame e s; in ex eme cases, i may no
be accep able a all.
The ob ained expe imen al g aph o o al de o ma ion o he composi e pa ch allowed
he esea che s o clea ly de e mine he momen o s ess occu ence in he s uc u e unde
epai . This momen ma ches qui e exac ly (wi h he disc epancy no exceeding 5 min)
he gel poin de e mined analy ically based on dependence o he deg ee o cu ing on he
moulding mode. I con i ms he alidi y o he hypo hesis accep ed based on [
26
,
27
,
29
,
49
]
on he occu ence o echnological s esses in he s uc u e a e gela ion only.
The de eloped me hod allows o inc easing he epai e iciency [
7
,
12
,
47
] by aking
in o accoun he empe a u e– ime egime o cu ing and me hods o i s implemen a ion.
The ad anced comp ehensi e algo i hm o choosing he e ec i e pa ame e s o he dam-
aged panel epai p ocess can be ep esen ed as ollows.
1.
In o de o ensu e he minimum down ime o he s uc u e, and aking in o accoun
high complexi y o disman ling ope a ions, a he i s s age he epai wi hou p e-
limina y disman ling is chosen.
2.
Taking in o accoun he limi a ions ela ed o he quali y o su ace being epai ed,
he me hod o he epai pa ch ins alla ion is chosen.
3.
The choice o ma e ials o be used o epai s should, i s o all, be guided by hei
physico-mechanical cha ac e is ics, a ailabili y and abundance. Much a en ion is
also paid o he op imal combina ion o he mechanical and s eng h cha ac e is ics o
he s uc u e being epai ed, he pa ch and adhesi e used.
4.
Wi h he use o he cu en me hods, geome ic pa ame e s o he epai pa ch, which
ensu e he es o a ion o ini ial bea ing capaci y o he s uc u e, a e de e mined.
5.
Fo he esul ing epai pa ch geome y, pa ame e s o he cu ing mode gi ing ise o
occu ence o he minimum esidual echnological s esses a e de ined wi h he use
o he de eloped model. A his ime, con ol o he cu en s esses in he s uc u e
unde epai o p e en he ailu e o adhesi e join a he s age o epai is manda o y.
6.
The impac o esidual echnological s esses on he bea ing capaci y o he epai ed
s uc u e unde he ac ion o ope a ional loads is assessed. I he o al alue o
ope a ional and echnological s esses exceeds he pe missible le el, he ollowing
s eps o adjus he epai pa ch geome ic pa ame e s a e aken:
•
I he p esence o he esidual echnological s esses leads o he ailu e o adhe-
si e laye , plan dimensions o he pa ch should be inc eased and/o be elling o
edges is used o educe he ope a ional shea s esses;
•
When he bea ing capaci y o he s uc u e unde epai dec eases in gene al,
hickness o he epai pa ch should be inc eased. I con ibu es o he edis ibu-
ion o s esses and he educ ion o he load pe cei ed by he panel. In his case,
i can also be necessa y o inc ease plan dimensions o he pa ch o sa is y he
condi ions o adhesi e laye s eng h;
•
Simila ac ions a e o be aken in case o he iola ion o he condi ions o epai
pa ch s eng h as well.
•
As e idenced in p ac ice, he e is no need o epea edly op imize he cu ing mode
in case o sligh adjus men o he epai pa ch dimensions. The e o e, esidual
Polyme s 2021,13, 4342 18 o 20
echnological s esses occu ing in he s uc u e wi h he adjus ed geome y
du ing moulding a e de e mined in acco dance wi h pa ame e s o p. 5, and
hei accep abili y is assessed.
•
The sequence o ac ions desc ibed in p. 4–7 should be ollowed un il he se o
pa ame e s o he epai p ocess is de e mined ( epai pa ch geome y + cu ing
mode), which allows o sa is ying a condi ion o es o a ion o he s uc u e bea -
ing capaci y. I no such pa ame e s a e ound du ing he sea ch, i is
necessa y o
:
•
Re u n o p. 3 and choose he ma e ials (adhesi e and/o PCM) wi h he highe
s eng h cha ac e is ics, and hen con inue o sea ch o pa ame e s acco ding o
he desc ibed algo i hm;
•
When he o he ma e ials a e no a ailable, o he condi ion o es o a ion o
he bea ing capaci y s ill canno be sa is ied wi h he use o such ma e ials, i is
possible o choose he epai o disman led panel, i.e., o e u n o p. 1. Howe e ,
i is impo an o no e ha i is he leas e ec i e me hod in e ms o labou cos s
and ime equi ed;
•
I in he cou se o epai o he disman led panel he bea ing capaci y ails o
each he speci ied alue, he epai is conside ed inexpedien , and he damaged
s uc u e is eplaced by a new one.
Thus, he esea ch, oge he wi h he esul s p e iously ob ained [
19
,
47
], allows e-
sea che s o make an in eg a ed choice o geome ic pa ame e s o he epai composi e
pa ch and empe a u e– ime egime o i s cu ing in o de o ensu e he speci ied le el o
s eng h and s i ness o he s uc u e unde epai .
6. Conclusions and Fu he Resea ch
The me hod o de e mina ion o echnological s esses, which a ise in he s uc u e
unde epai in he p ocess o cu ing o he composi e pa ch, has been de eloped. This
me hod allows one o:
•
Take in o accoun he sh inkage, change in physico-mechanical cha ac e is ics and
heological p ocesses occu ing in he binde du ing he moulding p ocess;
•
De e mine he s esses in he s uc u e being epai ed a any ime, which allows
a oiding p ema u e ailu e o he adhesi e join a he epai s age;
•Take in o conside a ion he impac o he condi ions o epai wo ks.
Reliabili y o assump ions and de eloped me hod is con i med by compa ison wi h
he expe imen al da a.
Ou s udies demons a ed a signi ican e ec o he empe a u e– ime egime o cu ing
and he me hods o i s implemen a ion on he bea ing capaci y o he s uc u e being
epai ed. Ne e heless, in o de o inc ease he economic e iciency o he ope a ion o he
epai ed s uc u es o a ious applica ions, i is necessa y when choosing hese pa ame e s
o addi ionally ake in o accoun he ac o s o he cos o ma e ials and epai wo ks,
inc ease in ope a ing expenses as a esul o highe mass o he s uc u e and down ime.
Au ho Con ibu ions:
Concep ualiza ion, A.K. and V.P.; me hodology, M.S. and L.S.; alida ion,
A.F., P.K and A.P.; o mal analysis, V.P. and P.K.; in es iga ion, L.S. and M.S.; esou ces, A.F. and
L.S.; da a cu a ion V.P., M.S. and A.K.; w i ing—o iginal d a p epa a ion, L.S., A.F. and M.S.;
w i ing— e iew and edi ing V.P. and A.K.; isualiza ion, L.S. and A.F.; supe ision, M.S.; p ojec
adminis a ion, A.K. All au ho s ha e ead and ag eed o he published e sion o he manusc ip .
Funding:
The au ho s g a e ully acknowledge unding om he Speci ic esea ch on BUT FSI-S-20-6267.
Ins i u ional Re iew Boa d S a emen : No applicable.
In o med Consen S a emen : No applicable.
Da a A ailabili y S a emen : No applicable.
Acknowledgmen s: The au ho s hank B no Uni e si y o Technology o suppo .
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Polyme s 2021,13, 4342 19 o 20
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