Structural concepts for metallic LH2 tank designs life enhancement

Cu so: 2024-2025
Di ec o /Di ec o a: He e o Villalib e, Saioa
Es udian e: A ana A e xaga, And ea
STRUCTURAL CONCEPTS FOR
METALLIC LH2 TANK DESIGNS LIFE
ENHANCEMENT
MÁSTER UNIVERSITARIO EN INGENIERÍA MECÁNICA
TRABAJO FIN DE MÁSTER
Fecha: Bilbao, 24, sep iemb e, 2025
Supe isado y di igido en des ino po :
Ioannis Giannopoulos
CRANFIELD UNIVERSITY
SCHOOL OF AEROSPACE, TRANSPORT AND
MANUFACTURING
TRABAJO FIN DE MÁSTER
REALIZADO EN MOVILIDAD
Resumen
El hid ógeno se es á posicionando como una solución cla e pa a desca boniza la a iación,
o eciendo una al e na i a limpia y sos enible pa a educi las emisiones con aminan es en un sec o
que con ibuye signi ica i amen e al cambio climá ico. Es a esis p esen a un análisis de a iga de
diseños p elimina es pa a anques de almacenamien o de hid ógeno líquido (LH2) ab icados con
aleación de aluminio AA2219-T87 y soldadu a po icción-agi ación (FSW). Se ha desa ollado un
modelo global de elemen os ini os (MEF) pa a cap u a las dis ibuciones de es ue zo bajo
condiciones c iogénicas, apoyado po un submodelo e inado pa a un análisis p eciso de la
p opagación de g ie as. Se han examinado dos en oques: la es imación clásica de ida a a iga
basada en la iniciación de g ie as usando da os S–N y la e aluación de ole ancia al daño median e
mecánica de ac u a de c ecimien o de g ie as a empe a u as c iogénicas. Los esul ados indican
una sob ees imación de la ida a a iga du an e la iniciación, p incipalmen e debido a suposiciones
y la limi ada e idencia expe imen al, mien as que la p opagación de la g ie a es signi ica i amen e
más ápida y ue emen e in luenciada po las condiciones ambien ales y el espeso educido de las
pa edes del anque. Es os hallazgos esal an la impo ancia de complemen a los análisis a escala
es uc u al con e aluaciones localizadas de ac u a. El abajo u u o se cen a á en la alidación
expe imen al y écnicas a anzadas de moni o ización pa a mejo a la segu idad y iabilidad de los
anques de hid ógeno líquido.
Palab as cla e: MEF, G ie a, Fa iga, FSW, KI, Aluminio
Abs ac
Hyd ogen is posi ioning i sel as a key solu ion o deca bonise a ia ion, o e ing a clean and
sus ainable al e na i e o educe pollu an emissions in a sec o ha signi ican ly con ibu es o
clima e change. This hesis p esen s a a igue analysis o p elimina y designs o liquid hyd ogen
(LH2) s o age anks manu ac u ed om AA2219-T87 aluminium alloy wi h ic ion s i welding
(FSW). A global ini e elemen me hod (FEM) model has been de eloped o cap u e s ess
dis ibu ions unde c yogenic condi ions, suppo ed by a e ined submodel o p ecise c ack
p opaga ion analysis. Two app oaches ha e been examined: classical a igue li e es ima ion based
on c ack ini ia ion using S–N da a, and damage ole ance assessmen h ough ac u e mechanics o
c ack g ow h a c yogenic empe a u es. The esul s indica e an o e es ima ion o a igue li e du ing
ini ia ion, mainly due o assump ions and limi ed expe imen al e idence, while c ack p opaga ion is
signi ican ly as e and s ongly in luenced by en i onmen al condi ions and he educed hickness
o he ank walls. These indings highligh he impo ance o complemen ing s uc u al-scale
analyses wi h localised ac u e assessmen s. Fu u e wo k will ocus on expe imen al alida ion and
ad anced moni o ing echniques o imp o e he sa e y and eliabili y o liquid hyd ogen anks.
Keywo ds: FEM, C ack, Fa igue, FSW, KI, Aluminium
Labu pena
Hid ogenoa i is en a i da hegazkina en deska bonizazio ako soluzio gako bezala, ku sadu a en
emisioak mu iz eko al e na iba ga bia e a jasanga ia eskainiz, klima aldake a en e agile
nagusie ako ba den sek o ea. Tesi honek hid ogenozko anke ba en neke analisia au kez en du.
AA2219-T87 aluminio aleazioko e a ma uskadu a-agi azioko (FSW) soldadu a ekin ab ika u ako
hid ogeno likidoko (LH2) bil egi a ze- anken diseinu aldake a hasibe iak az e uz. Elemen u
ini oen me odo o oko (EFM) e edua ga a u da k io- enpe a u ako baldin ze an en sio banake ak
jaso zeko, e a azpisis ema ba ekin haus u a-p opagazioa en az e ke a zeha za egi eko lagundu da. Bi
ikuspegi az e u di a: haus u a hasie ako e a nekea en i aupena en es imazio klasikoa S-N da ue a ik
abia u a, e a haus u a-p opagazioa en kal e- ole an zia az e ke a k io- enpe a u an. Emai zek neke
i aupena en gehiegizko es imazioa e akus en du e, ba ez e e hipo esiak e a ogagin za muga ua en
ondo ioz; haus u a en p opagazioa askoz azka agoa da e a ingu uneko baldin zak e a ankea en
ho ma en lodie a xikia di ela e a e agin handia du. Au kikun zak egi u a-mailako az e ke ak
haus u a lokaliza ua ekin osa zea ga an zi sua dela azpima a zen du e. E o kizuneko lana izango
da ogak egi eko espe imen uak e a au e a u ako ja aipen- eknikak e abiliz hid ogeno likidoko
ankeak segu asun e a idaga i asunez hobe ze a bide a zea.
Gako-hi zak: EFM, Haus u a, Nekea, FSW, KI, Aluminioa

And ea A ana
S uc u al concep s o me allic LH2 ank designs li e enhancemen
Facul y o Enginee ing and Applied Science
Ae ospace Vehicle Design
MSc in Ae ospace Vehicle Design
Academic Yea : 2024-2025
Supe iso : Ioannis Giannopoulos
Da e 25/08/2025
Facul y o Enginee ing and Applied Science
Ae ospace Vehicle Design
MSc in Ae ospace Vehicle Design
Academic Yea : 2024-2025
And ea A ana
S uc u al concep s o me allic LH2 ank designs li e enhancemen
Supe iso : Ioannis Giannopoulos
Augus 2025
This hesis is submi ed in pa ial ul ilmen o he equi emen s o he deg ee o MSc.
©C an ield Uni e si y 2025. All igh s ese ed. No pa o his publica ion may be ep oduced
wi hou pe mission.
Academic In eg i y Decla a ion
I decla e ha :
•The hesis submi ed has been w i en by me alone.
•The hesis submi ed has no been p e iously submi ed o his uni e si y
o any o he .
•All con en , including p ima y and/o seconda y da a, is ue o he bes o
my knowledge.
•All quo a ions and e e ences ha e been duly acknowledged acco ding o
he equi emen s o academic esea ch.
I unde s and ha o knowingly submi wo k in iola ion o he abo e
s a emen will be conside ed by examine s as academic misconduc .
S uc u al concep s o me allic
LH2 ank designs li e enhancemen
And ea A ana
Abs ac
This hesis p esen s a a igue analysis o p elimina y designs o liquid hyd ogen (LH2) s o -
age anks manu ac u ed om AA2219-T87 aluminium alloy wi h ic ion s i welded join s. A
global ini e elemen model (FEM) was de eloped o cap u e s ess dis ibu ions unde c yo-
genic condi ions, suppo ed by a e ined submodel o accu a e c ack p opaga ion analysis.
Two app oaches a e examined: classical a igue li e es ima ion based on c ack ini ia ion us-
ing S–N da a, and damage ole ance assessmen h ough ac u e mechanics o c ack g ow h
a c yogenic empe a u es. Resul s indica e an o e es ima ion o a igue li e du ing ini ia ion,
mainly due o assump ions and limi ed expe imen al e idence, while c ack p opaga ion is sig-
ni ican ly as e and s ongly in luenced by en i onmen al condi ions and he hin ank walls.
These indings highligh he impo ance o complemen ing s uc u al-scale analyses wi h lo-
calised ac u e assessmen s. Fu u e wo k will ocus on expe imen al alida ion and ad anced
moni o ing echniques o imp o e he sa e y and eliabili y o LH2 anks.
Keywo ds: FEM, C ack, Fa igue, FSW, KI, Aluminium
8
2.1.4 Insula ion Technologies and The mal Managemen
E ec i e he mal insula ion is c i ical o minimising boil-o losses and main aining ope a-
ional e iciency. Mul i-laye insula ion (MLI) sys ems p o ide he highes he mal pe o -
mance, achie ing e ec i e he mal conduc i i ies as low as 0.135mW/m−Kunde high
acuum condi ions(23). Howe e , MLI sys ems equi e complex double-wall cons uc ion
wi h acuum main enance sys ems, adding signi ican weigh and complexi y o he o e all
s o age sys em.(24,25). Boil-o occu s no only du ing g ound s o age bu also con inuously
du ing ligh and e ueling ope a ions, necessi a ing ca e ul managemen o p e en uel loss
and main ain ank p essu e wi hin sa e limi s(12). Sp ay-on oam insula ion (SOFI) o e s a
simple , ligh e al e na i e bu has lowe he mal pe o mance and deg ades unde he mal
cycling. Ad anced closed-cell polyu e hane oams ha e shown p omise in ae ospace, hough
long- e m du abili y unde epea ed c yogenic cycles is s ill being s udied(25,26).
2.1.5 Manu ac u ing Technologies and P ocesses
The ab ica ion p ocess in ol es me al o ming echniques o c ea e ine-g ained o nanoc ys-
alline aluminum alloys ha imp o e hyd ogen apping and esis emb i lemen . Con olled
milling op imises pa icle and g ain sizes o be e hyd ogen abso p ion and elease, while
mic os uc u al ad ances such as dual-p ecipi a e alloys enhance s eng h and du abili y(27).
Fo he cylind ical pa s o he anks, backwa d ex usion is a common me hod due o i s
abili y o p oduce seamless, high-in eg i y s uc u es wi h excellen mechanical p ope ies(28).
In con as , he domes a e ypically o med using hyd o o ming o spinning p ocesses, which
allow o p ecise shaping and hinning o he ma e ial while p ese ing s eng h and duc-
ili y(29,30). These combined manu ac u ing app oaches ensu e he s uc u al eliabili y and
pe o mance necessa y o demanding c yogenic hyd ogen s o age applica ions.
The join be ween he domes and he cylind ical sec ion in aluminum hyd ogen s o age
anks is ypically achie ed using ic ion s i welding (FSW), a solid-s a e joining p ocess
ha has demons a ed supe io pe o mance compa ed o adi ional usion welding me hods.
FSW employs a o a ing ool ha gene a es ic ional hea o so en, bu no mel , he ma e ial,
allowing plas ic de o ma ion and mixing o he me al a he join in e ace. This p ocess yields
welds wi h mechanical e iciencies anging om 70% o nea ly 100%, while e ec i ely elim-
ina ing common de ec s such as po osi y, c acking, and hea -a ec ed zone deg ada ion. The
esul ing welds a e ully sealed, s uc u ally obus , and capable o main aining in eg i y unde
he demanding p essu e and empe a u e condi ions cha ac e is ic o hyd ogen s o age(28,31).
Figu e 5: Schema ic Diag am o F ic ion S i Welding P ocess(32)

9
2.1.6 Sa e y Analysis and Load Case Conside a ions
Liquid hyd ogen s o age sys ems mus wi hs and a complex a ay o ope a ional and eme -
gency loading condi ions while main aining s uc u al in eg i y and pe o mance. P ima y
load cases include in e nal p essu isa ion ( ypically 1-1.5 ba ope a ional p essu e), hyd o-
s a ic loads om uel sloshing du ing ligh manoeu e s, and he mal s esses om c yogenic
empe a u e di e en ials(33,34). Ai c a -le el loading condi ions, including ul ima e loads o
9g and c ash scena ios, mus be accommoda ed wi hou comp omising ank in eg i y(35,3).
Hyd ogen-speci ic haza ds p esen unique challenges equi ing specialised sa e y mea-
su es. Hyd ogen’s wide lammabili y ange (4-75% in ai ) and ex emely low igni ion en-
e gy c ea e signi ican i e and explosion isks ha mus be add essed h ough comp ehensi e
leak de ec ion, en ila ion, and igni ion sou ce con ol. Hyd ogen emb i lemen e ec s on
s uc u al ma e ials equi e ca e ul ma e ial selec ion and long- e m su eillance p og ams o
ensu e con inued s uc u al in eg i y. P essu e elie sys ems mus be designed o he speci ic
cha ac e is ics o hyd ogen se ice, including apid p essu e ise a es and he po en ial o
in isible hyd ogen lames(36,37).
2.2 Fa igue in C yogenic En i onmen
2.2.1 Classical Fa igue and Damage Tole ance App oaches
Fa igue damage in me allic s uc u es is adi ionally unde s ood as a p og essi e p ocess ha
ul ima ely leads o ailu e unde cyclic loading. The classical a igue app oach di ides he
a igue li e in o wo dis inc phases: c ack ini ia ion and c ack p opaga ion. The c ack ini ia-
ion phase e e s o he pe iod du ing which mic os uc u al damage accumula es wi hou he
p esence o a mac oscopically de ec able c ack. This phase can ep esen a signi ican po ion
o he o al a igue li e, o en es ima ed o ange be ween 70% and 90% o a ious me al-
lic alloys and welded join s(38). Classical a igue analysis elies hea ily on s ess-li e (S-N)
cu es, which co ela e cyclic s ess ampli ude o he numbe o cycles leading o ailu e. The
Mine ’s linea damage ule is commonly applied o accoun o a iable ampli ude loading,
enabling a cumula i e damage calcula ion om di e en s ess le els(39).
Wi hin his adi ional amewo k, he in eg i y o he s uc u e is assumed in ac du ing
he ini ia ion phase, wi h no p e-exis ing laws ha comp omise i s load-ca ying capaci y.
This assump ion is alid o many enginee ing applica ions whe e ca e ul manu ac u ing and
inspec ion p ocesses minimise ini ial de ec s. Howe e , he mic os uc u al na u e o a igue
damage means ha c ack ini ia ion can be di icul o de ec and p edic p ecisely, especially
in complex welded join s and ha sh en i onmen s.
In con as , he damage ole ance me hodology adop s a mo e conse a i e and ealis ic
p emise. Damage ole ance assumes he p esence o small c acks o manu ac u ing de ec s
om he ou se and ocuses on p edic ing he a e o c ack g ow h unde cyclic s esses. This
app oach u ilises ac u e mechanics p inciples and expe imen ally de i ed c ack g ow h laws,
such as Pa is’ law, o es ima e he emaining se ice li e based on he p opaga ion o hese
laws o a c i ical size. Damage ole ance hus emphasises inspec ion, moni o ing, and main-
enance o de ec and manage c acks be o e hey each a c i ical leng h ha could cause ca as-
ophic ailu e(39).
10
A he academic le el, in eg a ing classical a igue app oaches wi h damage ole ance
me hodology is essen ial o a mo e comp ehensi e and p o ound unde s anding o s uc-
u al beha iou unde cyclic loading. While classical a igue s udies ocus on he ime o
c ack ini ia ion, damage ole ance p o ides he pe spec i e o c ack g ow h and p opaga ion,
emphasising s uc u al in eg i y in he p esence o de ec s. The e o e, his complemen a y
app oach s eng hens lea ning, suppo s applied esea ch, and p o ides a be e unde s anding
o a igue li e.
2.2.2 C ack ini ia ion and p opaga ion unde C yogenic Tempe a u es
When conside ing a igue c ack ini ia ion mechanisms a c yogenic empe a u es nea 20 K,
ma e ials such as he 2219-T87 aluminum alloy exhibi al e ed mechanical esponses ha in-
luence a igue beha iou . Speci ically, ensile es ing e eals a signi ican inc ease in yield
s eng h and ul ima e ensile s eng h a c yogenic empe a u es compa ed o oom empe a-
u e (Fig. 6), while he ma e ial e ains adequa e oughness. This inc ease in s eng h may
a ec he ini ia ion and ea ly p opaga ion s ages o a igue c acks by modi ying he local
s ess and s ain ields a ound de ec s, unde sco ing he impo ance o unde s anding a igue
mechanisms in c yogenic en i onmen s o ae ospace s uc u al applica ions(19,40).
Figu e 6: Low Tempe a u e Yield S eng h o A2219-T87(40)
Impo an ly, he a igue c ack g ow h h eshold (∆K h) inc eases by app oxima ely 20–30%
a 20 K ela i e o ambien condi ions, e lec ing enhanced esis ance o c ack ini ia ion un-
de cyclic loading a c yogenic empe a u es. This imp o emen in he h eshold in ensi y
ac o signi ican ly con ibu es o he alloy’s du abili y in low- empe a u e se ice en i on-
men s(19,41).
In con en ional se ice en i onmen s, he Pa is Law pa ame e s Cand ma e ega ded
as ma e ial-dependen cons an s ha emain ela i ely s able wi hin a gi en mic os uc u e.
These pa ame e s acili a e he p edic ion o a igue c ack g ow h a es as a powe -law unc-
ion o he s ess in ensi y ac o ange (∆K), hus o ming a co ne s one o s uc u al li e p e-
dic ion models(39). Howe e , unde c yogenic condi ions, shi s in mic os uc u al beha iou
and ac u e mechanics induce signi ican a ia ions in hese pa ame e s. Changes in disloca-
ion mobili y, c ack ip plas ici y, and o he low- empe a u e-speci ic mechanical phenomena
al e bo h Cand m, as well as he h eshold ∆K h (19,42).
11
Speci ically o aluminium alloys, he Pa is exponen m ypically alls be ween 3.5 and 4
and emains ela i ely s able despi e empe a u e a ia ions. Con e sely, he Pa is cons an
Cdemons a es app eciable sensi i i y o empe a u e, dec easing a c yogenic empe a u es
a ound 28% o 6061-T62(43), which co esponds o educed a igue c ack g ow h a es o
a gi en ∆K. The accompanying inc ease in a igue h esholds ein o ces esis ance o bo h
c ack ini ia ion and p opaga ion a low empe a u es. This beha iou aligns wi h analogous
obse a ions in a a ie y o me allic sys ems, whe e lowe empe a u es ele a e h eshold
s ess in ensi y anges and supp ess c ack g ow h a es, he eby educing Cwi hou ma kedly
a ec ing m(39,19).
O e all, hese empe a u e-dependen a ia ions in Pa is Law pa ame e s unde sco e he
c i ical need o a igue li e models o inco po a e en i onmen al and empe a u e in luences,
pa icula ly when p edic ing he pe o mance o ae ospace s uc u al ma e ials such as 2219-
T87 aluminum alloy ope a ing in c yogenic se ings.
2.2.3 Hyd ogen Emb i lemen
Hyd ogen emb i lemen (HE) is a deg ada ion p ocess in which me als lose duc ili y and ac-
u e oughness due o he abso p ion o a omic hyd ogen, po en ially leading o ca as ophic
ailu e o en wi hou isible wa ning(44). A omic hyd ogen pe mea es me allic s uc u es
h ough se e al pa hways, including co osion eac ions, di ec exposu e o high-p essu e
hyd ogen a mosphe es in s o age anks and pipelines, and manu ac u ing p ocesses such as
welding o o ging(45). Once abso bed, hyd ogen a oms di use h ough he me al’s c ys al
la ice and p e e en ially accumula e a mic os uc u al apping si es such as disloca ions,
g ain bounda ies, and p ecipi a es. This di usion is accele a ed by s ess g adien s, especially
in egions wi h high iaxial s ess, which concen a e hyd ogen a ulne able si es and p o-
mo e emb i lemen mechanisms. The se e i y o HE depends on ac o s including ma e ial
composi ion, hyd ogen concen a ion, applied s ess, and en i onmen al condi ions(46). In
hyd ogen s o age and anspo sys ems, hese p ocesses lead o subc i ical c ack g ow h and
mechanical weakening, posing a signi ican eliabili y isk(45,47).
Hyd ogen emb i lemen signi ican ly deg ades mechanical p ope ies, especially duc ili y,
causing comme cial aluminum alloys o lose up o 40% o elonga ion and educ ion in a ea,
wi h a shi om duc ile o b i le ac u e modes(48). Al hough aluminum alloys gene ally
esis emb i lemen be e han s eels, some high-s eng h a ian s emain ulne able(49). The
AA2219 alloy in T87 empe shows ela i ely low suscep ibili y due o i s mode a e s eng h
compa ed o mo e emb i lemen -p one 7xxx-se ies alloys(50,51). Yield s eng h is mos ly un-
a ec ed, bu sudden ailu es below yield s ess can occu due o localised mechanisms(44),
posing c i ical isks o hyd ogen-exposed componen s like s o age anks(47).
Hyd ogen pene a es me allic s uc u es in bo h gaseous and aqueous o ms, di using
h ough mic os uc u al de ec s such as disloca ions, acancies, inclusions, and g ain bound-
a ies. Once abso bed, hyd ogen exis s in a omic, molecula , o mixed s a es, p omo ing lo-
calised s ess concen a ion ha leads o c ack nuclea ion and p opaga ion. These ac u e
p ocesses can ini ia e e en unde s esses below he ma e ial’s yield s eng h, as hyd ogen-
induced de ec s se e as c i ical weakening si es, causing ca as ophic b i le ailu es(44).
12
2.2.4 C ack p opaga ion in FSW join s
FSW is widely ega ded as one o he mos eliable solid-s a e joining echnologies, enabling
he ab ica ion o join s wi h excellen mechanical pe o mance in alloys adi ionally consid-
e ed di icul o weld by usion echniques(52). Fo his eason, i has been b oadly applied
in c i ical sec o s such as ae ospace, au omo i e, and hyd ogen s o age. Despi e hese ad an-
ages, main aining s uc u al in eg i y emains a key challenge, since e en mic oscopic laws
can ac as p ecu so s o ailu e h ough c ack ini ia ion and p opaga ion(53).
The weld mic os uc u e gene a ed by FSW is highly he e ogeneous, shaped by he com-
plex he mal and mechanical cycles o he p ocess. The nuclea ion zone (NZ) unde goes
subs an ial plas ic de o ma ion a ele a ed bu sub-solidus empe a u es, leading o dynamic
ec ys allisa ion and he o ma ion o ine g ains. This g ain e inemen enhances duc ili y
and ac u e oughness bu may educe ha dness due o p ecipi a e dissolu ion, especially in
p ecipi a ion-s eng hened alloys(54). Adjacen o i , he he momechanically a ec ed zone
(TMAZ) expe iences bo h s ain and empe a u e bu lacks comple e ec ys allisa ion, esul -
ing in elonga ed g ains and educed ha dness due o p ecipi a e coa sening. Finally, hea
a ec ed zone (HAZ) is in luenced solely by he he mal cycle, whe e o e -aging and p ecipi-
a e coa sening lead o he lowes ha dness and s eng h wi hin he weld(55). These di e ences
explain why ac u e and a igue ailu es o en localise in he TMAZ and HAZ, which consis-
en ly ac as he weakes links in he welded join .
The a igue and ac u e beha io o FSW join s is he e o e con olled by his mic os uc-
u al he e ogenei y. C acks equen ly ini ia e in he so ened HAZ o TMAZ, al hough hey
may also nuclea e a local s ess concen a o s such as oids, inclusions, o su ace i egu-
la i ies le by he ool shoulde (56,57). A e ini ia ion, p opaga ion ollows he pa h o leas
esis ance. The highly e ined and duc ile SZ may acili a e ela i ely as c ack g ow h unde
cyclic loading, while p opaga ion h ough he TMAZ and HAZ can be slowe and mo e o u-
ous due o plas ic incompa ibili y and esidual s ess e ec s(58,59). Expe imen al s udies ha e
shown ha he h eshold s ess in ensi y and c ack g ow h cons an s a y signi ican ly among
he SZ, TMAZ, and base ma e ial, indica ing ha mic os uc u al zones al e bo h ini ia ion
esis ance and g ow h kine ics (Fig. 7).
Figu e 7: Fa igue c ack g ow h da a o base ma e ial, TMAZ, and s i zone samples(59)
13
3.0 Me hodology
This s udy adop ed a sequen ial enginee ing design and analysis me hodology, beginning wi h
a comp ehensi e li e a u e e iew o es ablish he heo e ical amewo k and guide he p elim-
ina y con igu a ion o he ank. The ini ial phase encompassed decisions ega ding geome y,
in eg a ion wi h and a achmen o he uselage, ma e ial selec ion, and he mal insula ion.
S uc u al pe o mance was subsequen ly assessed h ough a wo-s age FEM app oach: i s ,
a global model was de eloped o e alua e o e all s uc u al beha iou , ollowed by a de ailed
submodel ocusing on c i ical egions. S ess da a ob ained om he submodel was hen used
in a ac u e mechanics analysis o es ima e c ack p opaga ion cycles and p edic a igue li e.
The esul ing indings enabled he iden i ica ion o a igue-c i ical a eas, p o ided an e alu-
a ion o s uc u al du abili y, and suppo ed he p oposal o design imp o emen s aimed a
u u e op imisa ion.
Figu e 8: Flowcha illus a ing he key phases o he p ojec me hodology
3.1 P elimina y design
Du ing he p elimina y design phase, a comp ehensi e compa a i e assessmen was con-
duc ed, encompassing ma e ial selec ion, manu ac u ing easibili y, in eg a ion s a egies, and
insula ion concep s, g ounded in indings om ele an ae ospace li e a u e. To his end,
se e al decision ma ices we e de eloped o e alua e he possible al e na i es, he de ails o
which a e p o ided in Appendix B, he eby enabling a sys ema ic compa ison o design op-
ions. The ou come o his mul i-c i e ia e alua ion, as summa ised in Table 1, acili a ed he
iden i ica ion o he op imal con igu a ion o he in ended applica ion.
Table 1: O e iew o P elimina y Design Selec ions
Fea u e Design Decision
Tank Ma e ial Aluminum Alloy AA2219-T87
In eg a ion Non-in eg al, bol ed ames
Insula ion MLI
Manu ac u ing Cylind ical: Deep d awing, Domes: Hyd o o ming,
Join s: F ic ion S i Welding (FSW)
Based on hese design decisions, he ank dimensions we e es ablished acco ding o con-
s ain s imposed by he uselage en elope and in o med by he selec ed pa ame e s. Fo he
design, i will be assumed ha he ank is in eg a ed in o an A320 uselage, which se s he
cons ain s o design pa ame e s and in o ms o he equi emen s. The maximum ank di-
ame e is limi ed o 3 me e s, cons ained by he A320 uselage diame e o ensu e p ope
clea ance and s uc u al compa ibili y(60). Following he li e a u e, a diame e - o-leng h a io
o app oxima ely 0.66(61) was adop ed o de ine he ank leng h acco dingly.

14
Fu he mo e, an analysis o he impac s on ai c a ange and passenge capaci y was con-
duc ed, as de ailed in Appendix C, compa ing hyd ogen ank in eg a ion wi h con en ional
ke osene- ueled con igu a ions. The esul s o his analysis a e p esen ed in Table 2.
Table 2: Key Dimensions and Capaci ies o he Hyd ogen Tank
Fea u e Value Uni s
Leng h 5000 mm
Volume 28.27 (60% o A320) m3
Range 1879 km
Passenge s 126 u
3.1.1 Minimum Thickness Calcula ion
Based on in e nal p essu isa ion as he go e ning load case, he minimum equi ed hickness
o he ank wall is calcula ed ollowing he o mula ion p esc ibed by p essu e essel design
codes(62). This app oach e ines he classical hin-walled p essu e essel equa ion by inco -
po a ing ac o s such as he ma e ial allowable s ess, join e iciency, and an accoun ing e m
o p essu e co ec ion, ensu ing compliance wi h sa e y and ope a ional s anda ds.
The go e ning equa ion o minimum hickness is:
min =P·
S·E−0.6·P
(62) (1)
Whe e:
•Pis he design in e nal p essu e, accoun ing o sa e y ac o s,
• is he in e nal adius o he ank,
•Sis he allowable ensile wo king s ess o he ma e ial a ope a ing empe a u e,
•Eis he join e iciency ac o ela ed o he quali y o welds and inspec ions.
Fo liquid hyd ogen anks in ai c a , ypical ope a ional p essu es ange be ween 1 and
1.5 ba absolu e. Howe e , ansien scena ios such as en ing o apid empe a u e luc ua-
ions can empo a ily inc ease his p essu e beyond nominal le els. To conse a i ely accoun
o hese e en uali ies and ensu e s uc u al sa e y, an ul ima e sa e y ac o o 3 is applied in
acco dance wi h CS25 s anda ds(3) o low-p essu e essels. This esul s in a design p essu e
gi en by:
Pdesign =1.5 ba ×3=4.5 ba =0.45 MPa (2)
The ma e ial selec ed o he ank (A2219-T87) exhibi s a yield s eng h o app oxima ely
393 MPa (57 ksi) a oom empe a u e (27◦C) (Fig. 6). To add ess unce ain ies such as hy-
d ogen emb i lemen , a educ ion ac o o 0.8 is applied o he allowable ma e ial s eng h,
as ecommended in he li e a u e ega ding hyd ogen se ice and ma e ial pe o mance ac-
o s(19).
15
Addi ionally, a conse a i e sa e y ac o o 1.15 is applied o he ma e ial s eng h, leading
o a design allowable ensile s ess o app oxima ely:
σp=0.8×393 MPa
1.15 ≈341.8 MPa (3)
As s udies ha e shown, F ic ion S i Welding o aluminum alloys such as AA2219 yields
welds wi h mechanical e iciencies anging om app oxima ely 70% o nea ly 100% depend-
ing on welding pa ame e s and p ocess con ol(28). The mic os uc u al e inemen and e-
duced de ec s compa ed o usion welding ansla e in o join e iciencies ypically in he
ange o 0.85 o 0.95(63).
Conside ing he igo ous inspec ion and quali ica ion s anda ds in ae ospace manu ac u -
ing, an ini ial join e iciency alue o E=0.85 is assumed o his s udy as a conse a i e ye
ealis ic pa ame e o s uc u al calcula ions.
Applying he calcula ed alues o Equa ion (1):
min =0.45 MPa ×1500 mm
341.8 MPa ×0.85 −0.6×0.45 MPa ≈675
290.53 −0.27 =675
290.26 ≈2.33 mm (4)
This heo e ical minimum hickness is inc eased o a conse a i e ini ial wall hickness
o 3.5 mm. This choice accoun s o unce ain ies in manu ac u ing ole ances, ex ended
ope a ional loads, and he inac i e sa e y ma gins commonly adop ed in ae ospace c yogenic
s o age designs. Addi ionally, he decision was in o med by compa isons wi h simila designs
in p e ious p ojec s(35,64,65), which suppo he selec ed hickness as bo h sa e and p ac ical.
Wi h a wall hickness o 3.5 mm, he hoop s ess unde in e nal p essu isa ion is app oxi-
ma ely 192 MPa, which aligns wi h s anda d ae ospace p ac ice o c yogenic hyd ogen s o -
age and p o ides an addi ional sa e y ma gin o manage ma e ial beha iou unce ain ies and
load a ia ions. Since expe imen al alida ion lies ou side he scope o his hesis, his con-
se a i e hickness se es as a obus ini ial baseline o he subsequen de ailed s uc u al
e i ica ion ia ini e elemen analysis.
16
3.2 Load Cases De ini ion
The s uc u al e i ica ion o he liquid hyd ogen (LH2) s o age ank equi es conside a ion
o he ull spec um o mechanical solici a ions expec ed du ing a 25-yea se ice li e. In ac-
co dance wi h he me hodology(66), a ep esen a i e en elope o load ypes has been de ined,
encompassing bo h ope a ional cycles and ce i ica ion-d i en ex emes. Table 3 summa ises
hese load ca ego ies in e ms o cycle equency, s ess a ia ion, and s ess a io.
Table 3: Loading Types o LH2S o age Tanks in Regional A ia ion(66)
Loading Type Cycle F equency S ess Va ia ion S ess Ra io (R)
S o age p essu isa ion Low La ge 0
P essu e con ol sys em High Small 0.9
G ound manoeu ing and gus s High Small–medium 0.2
Ex eme manoeu ing Ve y low Ve y la ge 0
Cycle Quan i ica ion wi hin he Ope a ional En elope
In all cases, o ensu e he s uc u al in eg i y o he componen h oughou i s se ice li e, a
conse a i e app oach is adop ed by conside ing he mos c i ical scena io wi hin he ope a-
ional en elope. This means ha he maximum numbe o cycles and he mos se e e s ess
a io Ra e assumed o each load case, ensu ing ha he design accoun s o he highes
possible a igue demand.
P essu isa ion cycles (R=0) co espond o e ills om ambien p essu e o 1.5 ba p io
o ligh . Fo a egional ai c a ope a ing h ee sec o s daily wi hou uel anke ing, wo ull
e ills pe day a e assumed, leading o:
2×365 ×25 =18,250 cycles .
Val e en ing due o he mal boil-o and ambien p essu e a ia ions occu s in e mi en ly
du ing ligh . Li e a u e epo s a ypical equency o one o wo e en s pe day(67,68), yield-
ing:
2×3×365 ×25 ≈54,750 cycles ,
wi h R≈0.9 gi en he na ow s ess luc ua ion.
Gus and manoeu e esponses con ibu e addi ional s ess a ia ions in he ange R=
0.2–0.3. Assuming 3–5 signi ican e en s pe sec o (69), one ob ains:
5×3×365 ×25 ≈136,875 cycles .
Finally, ex eme manoeu es unde combined ine ial loads (R=0) a e a e, expec ed
once o wice o e he li e ime o he ai ame(70). These scena ios, al hough excep ional, a e
p esc ibed by ce i ica ion amewo ks such as CS-25(3) and mus be conside ed o ul ima e
load e i ica ion.
17
Selec ion o Load Cases o Analysis
Al hough h ee p incipal load cases we e modelled in de ail using ini e elemen me hods,
addi ional ope a ional loads we e accoun ed o using simpli ied analy ical calcula ions, li e -
a u e da a, and conse a i e scaling based on FEM esul s. This hyb id app oach allowed he
inco po a ion o se ice condi ion a iabili y while emaining compu a ionally manageable.
Using Mine ’s ule o accumula e a igue damage, bo h de ailed and es ima ed s ess cycles
we e in eg a ed o p o ide a comp ehensi e p edic ion o he componen ’s a igue li e.
Baseline p essu isa ion
The e e ence load case consis s o s eady in e nal ank p essu isa ion, ep esen ing he
nominal ope a ing condi ion ac oss all ligh al i udes. Va ia ions due o he p essu e con ol
sys em a e conse a i ely modelled as 1.1 imes he nominal s ess.
P essu isa ion wi h se e e ine ial loads
These cases assess he in e ac ion o in e nal p essu e wi h ine ial accele a ions ep esen-
a i e o ealis ic manoeu es. The loads examined co espond o 2.5g e ical, 1.5glongi-
udinal, and 3gla e al, combined indi idually wi h nominal p essu isa ion. This app oach
pa allels CS-25 ce i ica ion p ac ice(3), whe e p essu isa ion and ine ia may be applied in
combina ion.
P essu isa ion wi h ex eme ine ial en elopes
Selec ed ul ima e load scena ios a e included o e i y obus ness unde a ely expe ienced,
excep ionally se e e condi ions. The combina ions analysed a e:
•P essu isa ion +9glongi udinal +3gla e al: simula es an ex eme decele a ion e en like
a ha d eme gency landing o sudden s op wi h la e al gus s, ep esen ing a a e bu se e e
ine ial load he ank mus wi hs and.
•P essu isa ion +6g e ical downwa d +3gla e al: eplica es se e e downwa d e ical
accele a ion combined wi h la e al loading, simula ing u bulence o apid descen and
imposing comp essi e and shea s esses.
•P essu isa ion +2.5g e ical upwa d +1.5glongi udinal: ep esen s signi ican upwa d
and o wa d accele a ion du ing s eep climbs o pull-ups unde p essu ised condi ions,
es ing s uc u al in eg i y du ing dynamic ascen .
Summa y o Load Cases Analysed
The selec ed load cases add essed in he nume ical wo k a e summa ised in Table 4:
Table 4: Summa y o Load Cases Conside ed in he Analysis
Case Desc ip ion Loads Applied
1 S o age p essu isa ion P essu isa ion only
2a Se e e manoeu e ( e ical) P ess. +2.5 g e ical
2b Se e e manoeu e (longi udinal) P ess. +1.5 g longi udinal
2c Se e e manoeu e (la e al) P ess. +3 g la e al
3a Ex eme man. (long. +la .) P ess. +9 g long. +3 g la .
3b Ex eme man. ( e . down +la .) P ess. +6 g e . down +3 g la .
3c Ex eme man. ( e . up +long.) P ess. +2.5 g e . up +1.5 g long.
24
a) Weld Zones b) C ack F on
Figu e 16: 3D Submodel Pa i ioning:
The c ack i sel was modelled wi h a semi-ellip ical geome y. The Mode I s ess in en-
si y ac o , KI, was calcula ed using he con ou in eg al me hod, commonly known as he
J-in eg al, applied along se e al con ou s closely su ounding he c ack ip. This app oach
p o ides a pa h-independen and eliable e alua ion o KI, which is c i ical o ac u e anal-
ysis.
A me iculous meshing s a egy was employed, in ol ing p og essi ely ine mesh elemen s
concen a ed a ound he c ack ip o achie e nume ical con e gence while managing compu-
a ional cos s. Nea he c ack on , special singula o ocused elemen s we e likely used o
cap u e s ess g adien s wi h high accu acy.
Se ice loads consis en wi h he global FEM esul s we e applied. A he in e ace be-
ween he submodel and he global model, bounda y condi ions we e imposed o cons ain
displacemen s as necessa y, ensu ing con inui y be ween he e ined egion and he o e all
s uc u e. Along he c ack su ace, mo emen pe pendicula o he c ack plane was es ic ed
o ealis ically simula e c ack ace beha iou unde loading.
Figu e 17: Submodel: Bounda y Con idions
Finally, mul iple ex ac ion poin s we e placed along he c ack on o eco d he spa ial
dis ibu ion o KI. Fo each c ack size, all compu ed KI alues we e collec ed and documen ed
(wi h ull da ase s a ailable in Appendix E). The maximum KI alue along he c ack on was
selec ed as he ep esen a i e pa ame e o ac u e assessmen , ypically occu ing nea he
in e sec ion o he c ack wi h he ee su ace.

25
Analysis P ocedu e and Ou pu P ocessing
The desc ibed p ocedu e was applied o all eigh modelled c ack sizes, main aining con-
sis en bounda y condi ions, mesh e inemen , and ma e ial p ope y assignmen s o ensu e
accu a e and compa able esul s. Fo each con igu a ion, he maximum Mode I s ess in en-
si y ac o along he c ack on was ex ac ed om he nume ical ou pu . These maximum
KI alues we e hen co ela ed wi h hei espec i e c ack leng hs o cons uc he KI e sus a
(c ack leng h) ela ionship. This ela ionship se es as he undamen al inpu o a igue c ack
g ow h assessmen and is illus a ed in Fig. 18.
Figu e 18: Rela ion be ween Mode I s ess in ensi y ac o , KI, and c ack leng h, a(mm).
Wi hin his con ex , ailu e is de ined as occu ing ei he when he s ess in ensi y ac o KI
eaches he ma e ial’s ac u e oughness KIC, o when he c ack leng h exceeds he ma e ial
hickness. The la e case is c i ical because h ough- hickness c ack pene a ion can cause
leakage.
Fo he Hea A ec ed Zone, he calcula ed s ess in ensi y ac o a he poin o ull hick-
ness pene a ion is
KI=25.13 MPa √mm,
while he ac u e oughness o he ma e ial is
KIC =27.5 MPa √mm.
Since KI<KIC, ailu e in his case is go e ned by c ack pene a ion h ough he hickness
a he han by exceeding he ma e ial’s ac u e oughness.
3.4 Classical Fa igue Li e Calcula ion and Damage Tole ance
The a igue li e o me allic s uc u es is gene ally di ided in o wo p incipal phases: c ack ini-
ia ion and c ack p opaga ion. The ini ia ion phase in ol es he accumula ion o mic os uc-
u al damage unde cyclic loading un il a c ack becomes de ec able, whe eas he p opaga ion
phase desc ibes he g ow h o his c ack un il ailu e(39). Fo aluminium alloys and welded
join s, ini ia ion is o en he dominan po ion, ep esen ing up o 70–90% o o al a igue
li e(38).
26
In his s udy, a conse a i e 50% o he o al a igue li e (N ) is alloca ed o c ack ini ia ion,
e lec ing bo h me hodological assump ions and he limi ed ele an expe imen al da a unde
c yogenic se ice condi ions. A damage ole ance app oach assumes an ini ial mic oscopic
law o 0.02 mm wi hin he c i ical weld egion, consis en wi h enginee ing s anda ds and
ypical nondes uc i e inspec ion capabili ies(78).
The adop ed a igue li e assessmen me hodology ollows he dual-phase wo k low p e-
sen ed in Fig.19, combining classical a igue li e es ima ion o c ack ini ia ion using S-N da a,
and ac u e mechanics-based c ack p opaga ion analysis u ilising Pa is law pa ame e s spe-
ci ic o ic ion s i welded aluminium alloys a c yogenic empe a u es. This complemen a y
app oach enables a ho ough e alua ion o s uc u al du abili y.
Figu e 19: Wo k low Diag am o Dual-phase Fa igue Li e Assessmen Me hodology
3.4.1 Classical Fa igue Li e Calcula ion
C ack ini ia ion modelling o he AA2219-T87 aluminium alloy was unde aken using S-N
da a sou ced om he li e a u e(79) (see Fig. 20), which co ela es he applied se ice s ess
ampli ude o he co esponding a igue li e in cycles,N .
Figu e 20: S-N da a o 2219-T87 welded unde c yogenic empe a u e condi ions S ess
Range (ksi) s Numbe o Cycles (N)(79).
27
The a ailable S-N da ase o c yogenic es ing was ob ained om expe imen s con-
duc ed on TIG welded join s unde a load a io o R=−1, ep esen ing ully e e sed en-
sion–comp ession loading. Al hough he p esen s udy ocuses on ic ion s i welded (FSW)
join s, he use o TIG-based S-N da a in oduces a deg ee o conse a ism. FSW join s ha e
been demons a ed o ou pe o m TIG welds in a igue pe o mance owing o hei ine mi-
c os uc u e and absence o solidi ica ion de ec s(31). The e o e, TIG a igue da a p o ide a
sa e lowe bound o a igue li e es ima ion in he absence o di ec c yogenic es da a o
FSW join s.
Fu he mo e, he applica ion o S-N da a ob ained a a load a io o R=−1 o p edic
a igue li e unde ension– ension loading condi ions wi h R alues anging om 0 o 0.9 is an
accep ed enginee ing app oxima ion. Fo he same maximum s ess magni ude, ully e e sed
loading esul s in a la ge cyclic s ess ange compa ed o ension– ension loading, e ec i ely
doubling he s ess ampli ude, hus leading o sho e a igue li es. Since a posi i e mean
ensile s ess (R>0) gene ally educes c ack opening and delays c ack ini ia ion, basing li e
p edic ions on R=−1 da a p o ides a conse a i e es ima e(38). This conse a i e app oach
conside ing bo h he weld ype and loading a io ensu es he inclusion o sa e y ma gins o
accoun o po en ial unce ain ies.
The S-N da a we e digi ised using WebPlo Digi ize ( e sion 5.2) and subsequen ly plo ed
on loga i hmic scales o linea ise he powe -law ela ionship be ween s ess ampli ude and
a igue li e. A linea eg ession analysis was pe o med on he ans o med da ase , i ing a
s aigh line o he o m:
log(N)=−mlog(S)+log(C∗),(6)
whe e Nis he numbe o cycles o c ack ini ia ion, Sis he applied s ess ampli ude, and
C∗=Cm o con enience in he i ing p ocess. The eg ession yields he slope and in e cep
o he bes - i line, om which he a igue s eng h exponen mis ob ained as he nega i e o
he slope, and he a igue s eng h coe icien Cis calcula ed by:
C=10in e cep
m.(7)
These pa ame e s cha ac e ise he ma e ial’s a igue beha iou unde cyclic loading. The
esul ing Basquin equa ion hen allows calcula ion o he a igue li e N o any applied s ess
ampli ude Sas:
N=C
Sm
.(8)
Table 7: Load cases wi h co esponding s ess le els and numbe o cycles.
Load case S ess [MPa] Numbe o cycles
P essu isa ion 172 755,424
P essu isa ion o e p essu e 174 683,353
Se e e manoeu e 195 254,365
Ex eme manoeu e 270 15,125
28
To assess cumula i e a igue damage unde a iable ampli ude loading, Mine ’s linea dam-
age ule was applied by conside ing he cha ac e is ic numbe o in-se ice cycles niexpe i-
enced a each s ess le el i. The damage ac ion Dis calcula ed as:
D=X
i
ni
Ni
=n1
N1
+n2
N2
+··· +nk
Nk
,(9)
whe e Niis he numbe o cycles o c ack ini ia ion a s ess le el iob ained om he
Basquin equa ion.
Mine ’s ule assumes linea damage accumula ion and does no accoun o load sequence
e ec s, in e ac ion be ween di e en s ess le els, o po en ial ma e ial memo y e ec s. De-
spi e hese limi a ions, i emains widely accep ed in enginee ing p ac ice due o i s simplici y
and gene ally conse a i e na u e, especially when combined wi h adequa e sa e y ac o s.
Using he speci ic load spec um and cycle coun s de ailed in Table 19, he damage ac ion
was calcula ed as D=0.64, indica ing ha app oxima ely 64% o he c i ical a igue damage
has al eady accumula ed. Conside ing a o al o 1,708,269 applied load cycles in he analysed
spec um, he es ima ed o al a igue li e is ob ained by di iding his numbe by he damage
ac ion D, yielding:
N o al =Nspec a
D=1,708,269
0,642 ≈2,658,725 cycles.(10)
Thus, he s uc u e is expec ed o endu e app oxima ely 2.66 million cycles be o e eaching
he c i ical a igue damage h eshold.
While he classical a igue li e calcula ion and Mine ’s ule p o ide a use ul es ima e o
accumula ed damage and emaining li e be o e c ack ini ia ion, hey inhe en ly assume ha
he s uc u e emains ee o de ec able c acks up o ha poin . Gi en he c i ical na u e o
hyd ogen s o age anks, whe e small de ec s may al eady exis o ini ia e ea lie , i is essen ial
o complemen his analysis wi h a ac u e mechanics-based assessmen o c ack p opaga ion
and i s impac on s uc u al in eg i y.
3.4.2 Damage Tole ance
Unlike classical a igue li e calcula ions ha ocus on c ack ini ia ion, he damage ole ance
app oach di ec ly add esses he g ow h o exis ing c acks unde cyclic loading, p o iding
essen ial insigh s in o esidual li e and s uc u al sa e y. This sec ion ou lines he me hodology
and key inpu s equi ed o model c ack p opaga ion.
C ack p opaga ion analysis equi es he ollowing c i ical inpu s:
1. The a ia ion o he Mode I s ess in ensi y ac o KIwi h c ack size a( he KI–a ela ion-
ship), p e iously ob ained om a e ined ini e elemen submodel.
2. The a igue c ack g ow h a e pa ame e s o he ma e ial, namely Cand m, aken om he
li e a u e(59) .
These inpu s a e hen used o implemen he Pa is–E dogan law:
da
dN =C·(∆K)m,(11)
whe e da
dN is he c ack g ow h a e pe cycle and ∆Kis he s ess in ensi y ac o ange.
29
Expe imen al s udies ha e shown signi ican a iabili y in a igue c ack g ow h a es ac oss
ic ion s i welded aluminum join s due o spa ial di e ences in g ain s uc u e, ha dness,
and esidual s esses(72,59). Acco dingly, dis inc Pa is law pa ame e s a e applied o each
weld zone: NZ, TMAZ, and HAZ.
C ack g ow h da a o c yogenic FSW aluminum join s we e digi ised om Fig. 7 using
WebPlo Digi ize ( e sion 5.2). Fo each weld zone, he da a we e linea ised on loga i h-
mic scales, and he Pa is pa ame e s mand Cwe e ob ained h ough eg ession analysis in
MATLAB (see Table 8).
To accoun o he c yogenic condi ion (−253◦C), adjus men ac o s om p e ious s udies
we e applied p opo ionally(64). The modi ied Pa is pa ame e s a e he ea e e e ed o as m′
o dis inguish hem om he baseline alues.
Table 8: Pa is law pa ame e s o FSW aluminium join s unde c yogenic condi ions
Zone mAdjus ed m′
NZ 3.30 3.84
TMAZ 3.08 3.58
HAZ 3.08 3.58
Zone-by-Zone P opaga ion Simula ion
U ilising he zone-speci ic Pa is law pa ame e s alongside he FEM-de i ed KI–acu e,
c ack g ow h was simula ed inc emen ally ac oss he weld, sequen ially p og essing om
he NZ h ough he TMAZ o he HAZ. Due o he absence o di ec expe imen al c ack
g ow h da a in he HAZ, and conside ing i s ypically highe c ack p opaga ion a es, he
Pa is pa ame e s o he TMAZ we e conse a i ely applied o he HAZ.
The o al numbe o a igue cycles N equi ed o c ack g ow h om an ini ial leng h ai
o a inal leng h a in each weld zone was calcula ed ia nume ical in eg a ion o Pa is’ law.
C ack g ow h in he nugge zone was conside ed om he minimum de ec able c ack leng h
up o he ansi ion in o he TMAZ. In u n, he TMAZ was modelled om i s onse un il he
beginning o he HAZ, and inally, he HAZ was analysed om i s s a un il he c ack eached
he ull pla e hickness.
N=Za
ai
1
C[∆K(a)]mda,(12)
whe e Ndeno es he o al numbe o cycles equi ed o c ack g ow h be ween he ini ial
leng h ai(onse o a igue c ack g ow h) and he inal leng h a (c i ical c ack leng h a ail-
u e). The pa ame e s Cand ma e he Pa is coe icien s co esponding o each weld zone,
while ∆K(a) ep esen s he s ess in ensi y ac o ange as a unc ion o c ack leng h.
This in eg a ion was implemen ed in MATLAB, employing he zone-speci ic Pa is pa am-
e e s, FEM-de i ed KIda a, and p esc ibed c ack leng h inc emen s.
The o al c ack p opaga ion li e Npwas ob ained by summing he calcula ed cycles o
c ack g ow h h ough each weld zone:
Np=NNZ +NTMAZ +NHAZ.(13)
The esul s o his c ack p opaga ion simula ion a e p esen ed and discussed in 3.3 Damage
Tole ance Analysis sec ion, p o iding c i ical insigh in o he damage ole ance beha iou .

30
4.0 Resul s and discusion
4.1 Valida ion o Fini e Elemen Model
The ini e elemen model de eloped o he LH2 ank was alida ed agains hand calcula-
ions pe o med o he p essu isa ion load case. These hand calcula ions, based on classical
p essu e essel heo y, p o ided analy ical es ima es o he maximum hoop and longi udinal
s esses.
The compa ison ocused on he poin s o maximum ension iden i ied in he FEM esul s
unde he p essu isa ion load. Good ag eemen was obse ed, wi h a de ia ion o app oxi-
ma ely 11% (see Table 9). This di e ence is a ibu ed o he FEM’s abili y o accoun o
local s ess concen a ions, which a e no cap u ed by he simpli ied analy ical app oach.
Table 9: Compa ison o s ess esul s om hand calcula ion and FEM analysis
Analysis ype S ess (MPa)
Hand calcula ion 192.9
FEM analysis 172.1
De ia ion 11%
Fu he mo e, he ini e elemen model no only con i med he analy ical s ess le els bu
also p o ided a de ailed pic u e o he s ess dis ibu ion ac oss he ank s uc u e, which
is essen ial o p edic ing po en ial c ack ini ia ion a eas. Unlike he uni o m s ess ields
assumed in classical p essu e essel heo y , he FEM allowed he iden i ica ion o local ensile
and comp essi e egions, he eby highligh ing c i ical zones whe e s ess concen a ions may
a o damage onse (71).
4.2 Classical Fa igue Li e Calcula ion
The classical a igue li e es ima ion, based on he applied load spec um and Mine ’s cumula-
i e damage ule, yielded a o al a igue li e o app oxima ely 2.66 million cycles.
Figu e 21: Damage ac ion ( ni
NI) accumula ed unde each load case.
31
Se e e manoeu es, al hough less equen han en ing p essu iza ion o p essu iza ion
cycles, induce highe s ess ampli udes ha cause g ea e cumula i e damage. Load cases
associa ed wi h hese highes s ess ampli udes, such as se e e manoeu es, exe he g ea -
es in luence on Mine ’s damage accumula ion, despi e hei lowe equency compa ed o
p essu es gene a ed du ing en ing. This e ec is illus a ed in Fig. 21, which displays he
con ibu ion o each load case o he o e all damage ac ion.
O e all, he classical a igue app oach sugges s ha c ack ini ia ion unde he speci ied op-
e a ional spec um would equi e a la ge numbe o cycles, con i ming he inhe en du abili y
o he AA2219-T87 alloy unde c yogenic condi ions and he conse a i e assump ions em-
ployed in his analysis. I c ack ini ia ion is assumed o cons i u e 50% o he o al a igue
li e, he ini ia ion phase would las app oxima ely 1.33 million cycles. The subsequen c ack
p opaga ion phase is analysed using a damage ole ance app oach in he ollowing sec ion.
4.3 Damage Tole ance Analysis
In s iking con as , he damage ole ance app oach p edic s a a igue c ack p opaga ion li e
o app oxima ely 12,000 cycles, s a ing om an ini ial mic oscopic law o 0.02 mm up o
c i ical ailu e, assumed when he c ack eached he ank hickness, which occu s be o e he
s ess in ensi y ac o eaches KIC.
A de ailed examina ion o c ack p opaga ion li e imes calcula ed using he baseline expo-
nen mand i s adjus ed coun e pa m′ e eals ha inco po a ing c yogenic e ec s dec eases
li e es ima es by app oxima ely 57%, unde lining he c ucial need o conside en i onmen al
in luences in damage ole ance assessmen s as shown in Fig. 22.
Figu e 22: C ack g ow h (a s N) - Compa ison be ween m and m′
32
The c ack p opaga es mo e apidly in he TMAZ and HAZ despi e ha ing a lowe Pa is
law exponen m compa ed o he NZ. This accele a ed p opaga ion occu s because he s ess
in ensi y ac o KI eaches highe alues due o he la ge c ack size in hese zones, which
compensa es o he educed ma e ial sensi i i y o c ack g ow h. This beha iou is clea ly
illus a ed in Fig. 23.
Fu he mo e, an impo an obse a ion eme ges when analysing he blue do ed line, which
ep esen s he c ack p opaga ion beha iou conside ing only he NZ pa ame e s h oughou
he en i e specimen. This idealized scena io p edic s a lowe o al numbe o cycles o ail-
u e compa ed o he ealis ic case ha inco po a es he speci ic Pa is law pa ame e s o each
zone (TMAZ and HAZ). This compa ison unde sco es he c i ical impo ance o implemen -
ing zone-speci ic ma e ial pa ame e s ha accoun o mic os uc u al he e ogenei y in welded
join s. Neglec ing hese a ia ions would lead o non-conse a i e p edic ions ha unde es i-
ma e c ack p opaga ion a es and o e es ima e he a igue li e o he componen .
Figu e 23: C ack g ow h (a s N) - Compa ison be ween FSW Di e en Zones (NZ, TMAZ
and HAZ) o Cons an NZ
These esul s complemen he classical a igue li e es ima ion p esen ed ea lie , which o-
cused on c ack ini ia ion. Toge he , hey p o ide a comp ehensi e unde s anding o he o al
a igue li e o he LH2 ank weld join s, b idging he gap be ween a igue ini ia ion and g ow h
phases unde ealis ic c yogenic se ice en i onmen s.
33
4.4 Discussion on Fa igue Li e Pe spec i es
The esul s clea ly unde sco e he dual and complemen a y na u e o a igue li e assessmen
me hods. F om an academic pe spec i e, hese indings align wi h ex ensi e li e a u e epo -
ing ha AA2219-T87 aluminium alloy exhibi s a no ably low a igue h eshold ∆K h (41). This
low h eshold explains why he c ack ini ia ion phase can encompass a subs an ial po ion o
he o al a igue li e, o en spanning millions o loading cycles e en unde demanding se ice
condi ions.
Con e sely, once a c ack ini ia es, c ack p opaga ion p oceeds apidly, pa icula ly h ough
he he e ogeneous mic os uc u al zones o he weld. This accele a ed g ow h is ma kedly
exace ba ed by he combined e ec s o c yogenic empe a u es and exposu e o hyd ogen en-
i onmen s, bo h o which a e documen ed o deg ade a igue c ack g ow h esis ance signi -
ican ly(64). Such en i onmen al ac o s educe Pa is law pa ame e s and sho en p opaga ion
li e, as e idenced in he adjus ed pa ame e s and educed cycle coun s obse ed in his s udy.
Figu e 24: C ack g ow h (a s N) - Ini ia ion (99%) and P opaga ion(1%)
F om a p ac ical enginee ing s andpoin , gi en he c i icali y o he LH2s o age ank, ac-
u e con ol and damage ole ance p inciples should guide he a igue li e assessmen and
main enance s a egies. While classical a igue li e models emain aluable o unde s anding
ini ia ion beha iou , he b ie c ack p opaga ion li e manda es ha inspec ion and moni o -
ing p o ocols p io i ise ea ly de ec ion and managemen o c acks, as e en mino de ec s can
lead no only o s uc u al ailu e bu also o leakage o highly lammable LH2, posing se ious
sa e y and ope a ional isks.
Inco po a ing damage ole ance amewo ks as he basis o inspec ion in e als and s uc-
u al in eg i y e alua ions ensu es ha he accele a ed isk associa ed wi h c ack g ow h unde
c yogenic hyd ogen se ice is e ec i ely mi iga ed. This app oach aligns wi h bes p ac ice
in sa e y-c i ical componen s subjec ed o ha sh en i onmen s, p o iding a obus basis o
isk-in o med main enance and ope a ional planning.
40
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Appendices
18 June 2025
Dea And ea
Re e ence: CURES/25628/2025
P ojec ID: 29195
Ti le: S uc u al Concep s o Me allic LH2 Tank Designs
Thank you o you applica ion o he C an ield Uni e si y Resea ch E hics Sys em (CURES).
We a e pleased o in o m you you CURES applica ion, e e ence CURES/25628/2025 has
been e iewed. You may now p oceed wi h he esea ch ac i i ies you ha e sough
app o al o .
I you ha e any que ies, please con ac CURES Suppo .
We wish you e e y success wi h you p ojec .
Rega ds,
CURES Team

46
APPENDIX B: P elimina y Design
This appendix de ails he p elimina y design conside a ions o he liquid hyd ogen s o age
ank, emphasising ma e ial selec ion, in eg a ion s a egies, insula ion concep s, and manu-
ac u ing easibili y. The con en is g ounded on au ho i a i e ae ospace li e a u e and ecen
ad ances, wi h p oposed e inemen s o enhance cla i y, comple eness, and scien i ic igou .
Whe e app op ia e, ables summa ise decision c i e ia o acili a e comp ehension and u u e
e e ence.
Tank Ma e ial
Selec ing a sui able ma e ial o LH2s o age anks en ails balancing ex eme c yogenic pe -
o mance wi h mechanical, he mal, and manu ac u ing p ope ies. Among con en ional and
eme ging ma e ials, he leading candida es a e aus eni ic s ainless s eels, aluminium alloys,
and composi e ma e ials. Aus eni ic s ainless s eels (e.g., AISI 304L, 316L) o e obus -
ness a c yogenic empe a u es wi h excellen duc ili y and esis ance o hyd ogen emb i le-
men . Thei lowe he mal conduc i i y aids insula ion, bu hei densi y imposes a weigh
penal y de imen al o mobile ae ospace applica ions. Aluminium alloys, no ably AA2219-
T87, combine low densi y wi h adequa e mechanical s eng h and c yogenic oughness, main-
aining ensile in eg i y e en a 20 K and exhibi ing minimal hyd ogen-induced deg ada ion.
Aluminium’s highe he mal conduc i i y challenges insula ion bu can be compensa ed by
ad anced mul ilaye sys ems. Composi e anks, using CFRP o glass ib e lamina es wi h
me allic o polyme line s, p omo e weigh educ ion and a igue esis ance, ye in oduce
conce ns o e mic oc acking and pe mea ion unde he mal cycling, making hei indus ial
eadiness less ma u e.
Table 10: Compa ison ma ix o ma e ial selecc ion
C i e ion /P ope y S eel Aluminum
(AA2219-T87) Composi es Weigh
(%)
Sco e
S eel
Weigh ed
S eel
Sco e
Aluminum
Weigh ed
Aluminum
Sco e
Composi es
Weigh ed
Composi es
S eng h and Toughness a 20K High Good High 25 4 1.00 4 1.00 5 1.25
Weigh E iciency Low High Ve y High 25 2 0.50 4 1.00 5 1.25
Resis ance o Hyd ogen Emb i lemen Good Good Mode a e 15 4 0.60 5 0.75 3 0.45
The mal Conduc i i y Low Highe Low o mode a e 10 4 0.40 2 0.20 3 0.30
Manu ac u abili y Mode a e High Mode a e o Low 15 3 0.45 4 0.60 2 0.30
Cos Low Mode a e High 10 4 0.40 3 0.30 1 0.10
To al Sco e — — — 100 — 3.35 —3.85 —3.65
Based on his e alua ion and li e a u e e idence, AA2219-T87 aluminium alloy is selec ed
o he ank o op imise s uc u al in eg i y, manu ac u abili y, and weigh pe o mance in he
c yogenic en i onmen .
Tank In eg a ion
Tank geome y and placemen s ongly in luence ai c a pe o mance and main enance.
LH2 anks a e ypically classi ied as in eg al o non-in eg al ela i e o he ai ame.
In eg al anks se e dual oles as bo h hyd ogen s o age and s uc u al membe s, o e ing
supe io mass e iciency and load ans e op imisa ion, pa icula ly sui ed o u u e blended
wing body (BWB) ai c a wi h high in e nal olume u ilisa ion. Howe e , hey pose chal-
lenges in access, inspec ion, and equi e bespoke design adap a ions o each ai c a con ig-
u a ion.
47
Non-in eg al anks a e modula uni s isola ed om p ima y s uc u e, o e ing main enance
ease, e o i lexibili y, and s anda dised designs. The ade-o includes inc eased s uc u al
pa asi ism and educed olume ic and ae odynamic op imisa ion, especially o ad anced
ai ames like BWB.
Table 11: Compa ison ma ix o ank in eg a ion selec ion
C i e ion In eg al Tank Non-In eg al Tank
Weigh (%)
Sco e In eg al
Weigh ed In eg al
Sco e Non-In eg al
Weigh ed Non-In eg al
Main enance Access and Down ime Challenging Easy; modula and eplaceable 25 1 0.25 5 1.25
Load Isola ion and S uc u al Con ibu ion Di ec load-bea ing; highly e icien S uc u ally isola ed; pa asi ic weigh 25 5 1.25 2 0.50
Mass E iciency Highes ; in eg a ed s uc u e educes weigh Lowe ; ex a suppo s add weigh 15 5 1.00 3 0.60
In eg a ion wi h Cu en Ai c a Requi es edesign; less e sa ile Easily e o i ed; lexible 20 2 0.40 5 1.00
Sui abili y o Fu u e Con igu a ions (BWB) Op imal olume ic and ae odynamic syne gy Limi ed op imiza ion due o modula cons ain s 15 4 0.60 2 0.30
To al Sco e — — 100 — 3.00 —3.65
Conside ing ope a ional lexibili y and scope, he ank design adop s a non-in eg al con ig-
u a ion wi h bol ed a achmen s o uselage I- ype ames. These a ach poin s will be concep-
ual only, wi h ame sizing and bol con igu a ion based on analogous designs alida ed ia
FEM.
Insula ion Concep s
Insula ion c i ically go e ns boil-o a es and sa e y. The wo main app oaches a e: Mul-
ilaye Insula ion (MLI): Vacuum-based, consis ing o many e lec i e oil laye s sepa a ed
by space s inside a double-wall s uc u e main aining acuum below 1 Pa, MLI minimizes
conduc i e/ adia i e hea ans e , achie ing hea leaks as low as 0.9 W/m2and boil-o nea
0.20%. Howe e , acuum in eg i y isk necessi a es obus s uc u es and backup oam lay-
e s o main ain insula ion i acuum is los . Sp ay-On Foam Insula ion (SOFI): Polyu e hane
oam applied on su aces o e s ease and weigh bene i s bu is p one o mic oc acks on he -
mal cycling, has highe he mal conduc i i y, and esul s in abou 43 W/m2hea leak and
12% daily boil-o , less sui ed o a ia ion LH2s o age.
Table 12: Compa ison ma ix o insula ion sys ems
C i e ion Value MLI Value SOFI
Weigh (%)
Sco e MLI
Weigh ed MLI
Sco e SOFI
Weigh ed SOFI
The mal Conduc i i y /Hea Leak (W/m2) 0.9 43 30 5 1.50 2 0.60
Daily Boil-o (%) 0.20 12 30 5 1.50 2 0.60
Vacuum Dependency High None 15 2 0.30 5 0.75
Weigh Penal y Mode a e (double-wall) Low 10 3 0.30 4 0.40
Ope a ional Sa e y (Boil-o /P essu e Con ol) High (minimal boil-o ) Medium (highe boil-o ) 10 5 0.50 3 0.30
Du abili y Unde The mal Cycling High; s able wi h acuum Low; p one o mic oc acking 5 4 0.20 2 0.10
Main enance Complexi y Medium; acuum main enance Low; easie inspec ion 5 3 0.15 4 0.20
To al Weigh ed Sco e — — 100 — 4.45 — 2.95
48
Gi en he c i ical equi emen o minimise boil-o and maximise ope a ional sa e y, MLI
is selec ed as he p ima y insula ion me hod. Seconda y oam laye s will be conside ed o
acuum b each mi iga ion.
Manu ac u ing Feasibili y
Manu ac u ing echniques di ec ly impac ank pe o mance ia ma e ial p ope ies and
s uc u al in eg i y.
Cylind ical Zone: Deep d awing is employed o o m seamless cylind ical shells wi h uni-
o m wall hickness, c ucial o a igue esis ance. The p ocess induces s ain ha dening,
enhancing yield s eng h bu equi ing pos - o ming hea ea men o elie e esidual s esses
and p e en a igue c ack ini ia ion. Fo e y la ge anks, olling pla es in o cylind ical shells
ollowed by high-in eg i y welding is an op ion, hough i in oduces aniso opy and ensile
esidual s esses i no con olled.
Table 13: Compa ison ma ix o cylind ical zone manu ac u ing
C i e ion Weigh (%) Sco e – Rolling Weigh ed – Rolling Sco e – Deep D awing Weigh ed – Deep D awing
Residual S ess Con ol 25 2 0.50 4 1.00
G ain Re inemen Quali y 20 3 0.60 4 0.80
Fa igue Li e Po en ial 25 3 0.75 4 1.00
Manu ac u abili y 15 3 0.45 5 0.75
Sui abili y o LH Cylinde s 15 3 0.45 5 0.75
To al Sco e 100 — 2.75 — 4.30
Dome Ends: Spin o ming (spinning) allows symme ic, obus dome p oduc ion, wi h ho
spinning p e e ed o hicke domes o maximise de o ma ion wi hou c acking. Hyd o o m-
ing o e s supe io p ecision and uni o m hickness wi h lowe esidual s esses, bene icial o
complex dome geome ies and specially alloys, enhancing a igue li e.
Table 14: Compa ison ma ix o dome ends manu ac u ing
C i e ion Weigh (%) Sco e – Spinning Weigh ed – Spinning Sco e – Hyd o o ming Weigh ed – Hyd o o ming
Residual S ess Con ol 25 4 1.00 5 1.25
G ain Re inemen Quali y 20 4 0.80 5 1.00
Fa igue Li e Po en ial 25 4 1.00 5 1.25
Manu ac u abili y 15 4 0.60 4 0.60
Sui abili y o LH Domes 15 4 0.60 5 0.75
To al Sco e 100 — 4.00 — 4.85
A achmen be ween Sec ions: F ic ion S i Welding (FSW) is selec ed o join s due o
i s solid-s a e na u e, esul ing in e ined mic os uc u e, high ensile s eng h, and supe io
a igue esis ance wi h minimal de ec s. While Tungs en Ine Gas (TIG) welding is common,
i is mo e p one o de ec s and induces coa se g ain zones and esidual s esses, which may
limi a igue pe o mance.
49
Table 15: Compa ison ma ix o aluminum joining
C i e ion Weigh (%) Sco e – FSW Weigh ed – FSW Sco e – TIG Weigh ed – TIG
Residual S ess Con ol 25 5 1.25 2 0.50
G ain Re inemen Quali y 20 5 1.00 2 0.40
Fa igue Li e Po en ial 25 5 1.25 2 0.50
Manu ac u abili y 15 4 0.60 3 0.45
Sui abili y o LH Join s 15 5 0.75 3 0.45
To al Sco e 100 — 4.85 — 2.30
A achmen o he Fuselage
As p e iously discussed, he cylind ical sec ion and he domes will be joined using ic ion
s i welding (FSW) in combina ion wi h I-sec ion ci cula beams. This join con igu a ion
p esen s some pa icula conside a ions. The uselage ames ha e a g ea e hickness han he
ank componen s (bo h he cylind ical shell and he domes). Since FSW equi es consis en
hickness a he welding in e ace o ensu e op imal join quali y, he ame geome y will
inco po a e a g adual hickness educ ion in he welding zone o ma ch he ank wall hickness.
Fu he mo e, he edge o he dome is s uc u ally c i ical due o he p esence o geome ic
discon inui ies, which can concen a e s esses and accele a e a igue damage. Welding he
ame di ec ly a he dome’s e mina ion would he e o e inc ease s ess concen a ions and
educe a igue li e. To mi iga e his e ec , he ames a e posi ioned sligh ly inwa d om he
dome edge, close o he cylind ical mid-sec ion, whe e s ess dis ibu ion is mo e uni o m.
These ames se e as he a achmen in e ace o he I-sec ion uselage ames. The con-
nec ion be ween he ank ames and uselage s uc u e will be ealised h ough bol ed join s
o ensu e s uc u al in eg i y unde ope a ional loads. The de ailed design o his bol ed a -
achmen lies ou side he scope o he p esen hesis bu is acknowledged as a c i ical s ep in
he in eg a ion p ocess.
Summa y o P elimina y Design Decisions:
Table 16: Summa y o P elimina y Design Decisions
Fea u e Design Decision
Tank Ma e ial Aluminum Alloy AA2219-T87
In eg a ion Non-in eg al, bol ed ames
Insula ion Mul ilaye Insula ion (MLI)
Manu ac u ing Cylind ical: Deep d awing
Domes: Hyd o o ming
Join s: F ic ion S i Welding (FSW)
56
Figu e 32: Analy ical ield de in ion o longi udinal 9g in e ial load
Figu e 33: Longi udinal 9g in e ial load applied
Figu e 34: Longi udinal 9g in e ial load: p essu e load (PDLOAD)

57
The men ioned cases a e analysed, and shown in he ollowing pic u es:
a) Max VM s ess: 172.10 MPa b) Max de o ma ion: 3.58 mm
Figu e 35: Resul s unde 1 load case
a) Max VM s ess: 191.6 MPa b) Max de o ma ion: 4.08 mm
Figu e 36: Resul s unde 2a load case
a) Max VM s ess: 195.5 MPa b) Max de o ma ion: 4.18 mm
Figu e 37: Resul s unde 2b load case
58
a) Max VM s ess: 184.8 MPa b) Max de o ma ion: 3.85 mm
Figu e 38: Resul s unde 2c load case
a) Max VM s ess: 270.8 MPa b) Max de o ma ion: 5.72 mm
Figu e 39: Resul s unde 3a load case
a) Max VM s ess: 233.8 MPa b) Max de o ma ion: 5.16 mm
Figu e 40: Resul s unde 3b load case
59
a) Max VM s ess: 204.2 MPa b) Max de o ma ion: 4.31 mm
Figu e 41: Resul s unde 3c load case
Resul s om hese analyses a e summa ised in he able below, showing maximum s ess
and de o ma ion alues pe load case, p o iding clea insigh s in o s uc u al pe o mance and
c i ical loading condi ions.
Table 19: Global FEM analysis esul s: Von Mises s ess, de o ma ion and sa e y ac o o
di e en load cases
Load case Maximum VM s ess (MPa) Maximum de o ma ion (mm) SF
1 172.1 3.58 1.98
2a 191.6 4.08 1.78
2b 195.5 4.18 1.74
2c 184.8 3.85 1.84
3a 270.8 5.72 1.26
3b 233.8 5.16 1.45
3c 204.2 4.31 1.67
As can be obse ed om he esul s, all calcula ed sa e y ac o s exceed uni y, which con-
i ms ha he ank s uc u e emains wi hin he allowable design limi s. This ou come indi-
ca es ha , unde he applied loading condi ions, he s esses expe ienced by he ank do no
su pass he pe missible ma e ial s eng h, he eby ensu ing s uc u al in eg i y and compliance
wi h he es ablished sa e y equi emen s.
60
APPENDIX E: De ailed FEM
This appendix p o ides a comp ehensi e desc ip ion o he de ailed ini e elemen analysis
conduc ed o in es iga e he beha iou o c acks in he welded join egions o he s uc u e.
This analysis builds upon he global model, na owing ocus o c i ical a eas whe e c acks
may ini ia e and p opaga e, wi h pa icula emphasis on he e alua ion o he S ess In ensi y
Fac o (SIF).
The de ailed model was de eloped as a submodel ex ac ed om he global Abaqus model,
speci ically a ge ing he welded join a ea. Submodelling is a echnique in Abaqus ha allows
he ex ac ion o de ailed s ess and s ain in o ma ion in a localised egion using bounda y
condi ions ans e ed om he global model, ensu ing consis ency be ween global and lo-
cal esponses while managing compu a ional cos e ec i ely. This me hod equi es ca e ul
alignmen o he submodel wi h he global geome y o ensu e accu a e in o ma ion ans e .
Figu e 42: Submodel om gene al model
The submodel geome y ocussed on he welded join , which was isola ed and con e ed
in o a h ee-dimensional solid model wi h a hickness o 3.5 mm, ma ching he shell hickness
used in he global model. This consis ency in hickness be ween he global shell model and
he de ailed 3D submodel p e en s e o s a he in e ace and ensu es compa ible bounda y
condi ions. The welded zone was subdi ided in o dis inc mic os uc u al egions known o
ha e di e en mechanical p ope ies, namely:
•Nugge Zone (NZ)
•The mo-Mechanically A ec ed Zone (TMAZ)
•Hea -A ec ed Zone (HAZ)
•Base Ma e ial (BM)
61
Figu e 43: Model pa i ion o di e en FSW zones
This subdi ision e lec s he eal a ia ions in mic os uc u e and ma e ial beha iou ob-
se ed in ic ion s i welded join s, allowing a mo e accu a e ac u e assessmen . To ep-
esen c acks, he c ack size was ini ially de ined by speci ying he c ack ace wi hin he
submodel. The c ack ip egion was meshed wi h an inc eased le el o de ail by gene a ing
con ou s a ound he c ack ip. The geome y nea he c ack ip was pa i ioned and meshed
using he sweep ool o acili a e a high-quali y, s uc u ed mesh ha is c i ical o accu a e
ac u e mechanics calcula ions.
Figu e 44: Di ision o c ack o acili a e he meshing
Ma e ial p ope ies we e assigned dis inc ly o each mic os uc u al zone, e lec ing hei
speci ic elas ic and plas ic beha iou s documen ed in he li e a u e o ic ion s i welded
join s.
Table 20: Mechanical p ope ies ac oss di e en weld zones
Zone E (GPa) Poisson (–) J (kJ/m2) Max P incipal S ess (MPa) Dis ance om cen e (mm)
NZ 70 0.33 28 295 2.75
TMAZ 70 0.33 22.5 250 5.25
HAZ 72 0.33 32 292.5 10.25
BM 72 0.33 40 477.5 —

62
In assembling he submodel, a local coo dina e sys em was de ined o ensu e p ope align-
men wi h he global ank model. This alignmen was con i med by placing he submodel
wi hin he global assembly, allowing he bounda y condi ions and load ans e o be co ec ly
applied.
Figu e 45: Submodel om gene al model
Hexahed al (hex) elemen s we e used o mos o he model, while he c ack ip and i s
immedia e icini y we e meshed wi h e ahed al elemen s o accu a ely cap u e singula i y
and s ess g adien s du ing con ou in eg al e alua ions in Abaqus. The su ounding egion
employed ee meshing o balance mesh quali y wi h compu a ional e iciency.
a) De ailed mesh o he c ack b) Global mesh o he model
Figu e 46: Submodel meshing
The c ack de ini ion wi hin Abaqus employed he con ou in eg al me hod, a obus ech-
nique o compu e s ess in ensi y ac o s ha le e ages a se o in eg al con ou s a ound he
c ack ip o cap u e he singula s ess ield wi hou equi ing ex apola ion. The c ack on
and p opaga ion di ec ion we e explici ly de ined o guide he calcula ion o KIand acili a e
po en ial c ack g ow h analyses.
63
Figu e 47: Con ou in eg al: c ack di ec ion de ini ion
Bounda y condi ions we e applied o e lec symme y and con inui y. The c ack ace ly-
ing on a symme y plane was cons ained in ansla ion pe pendicula o he plane, e lec ing
ealis ic s uc u al cons ain s and educing he compu a ional domain. A he in e aces con-
nec ing he submodel o he ank model ( he la e al and pa allel aces adjacen o he c ack),
submodel cons ain s we e imposed o es ic unwan ed igid body mo ions and ensu e dis-
placemen compa ibili y wi h he global model. The in e nal su ace o he model was sub-
jec ed o a uni o m in e nal p essu e o 0.45 MPa, consis en wi h he p essu isa ion load used
in he global analysis.
Figu e 48: Bounda y condi ions o submodel (yellow)
64
Figu e 49: Bounda y condi ions o submodel: submodel cons ain s
Resul s om he analysis e ealed ha he maximum KI alues coincided spa ially wi h he
loca ions o maximum s ess, alida ing he accu acy o he modelling app oach. The a ia-
ion o KIalong he c ack on was examined ac oss di e en con ou laye s, demons a ing
he expec ed s abili y and con e gence o he ac u e pa ame e .
Figu e 50: Submodel esul s: S ess (VM)
Figu e 51: KI alue along he c ack con ou and c ack leng h
65
The analysis was epea ed o se e al c ack leng hs, and he esul ing KI e sus c ack leng h
ela ionship was plo ed o p o ide insigh in o he ac u e beha iou unde inc easing c ack
sizes.
Figu e 52: Collec ed KI alues o ou di e en c acks
This is he inal g aph ha shows KI s. c ack leng h along he ank’s hickness.
Figu e 53: KI s a (c ack leng h) g aph