XII In e na ional Con e ence on Compu a ional Plas ici y. Fundamen als and Applica ions
COMPLAS XII
E. Oña e, D.R.J. Owen, D. Pe ic and B. Suá ez (Eds)
STEPWISE ADVANCING STRATEGY FOR THE SIMULATION OF
FATIGUE PROBLEMS
L. G. BARBU*,S. OLLER†, X. MARTINEZ†AND A. BARBAT†
*,†In e na ional Cen e o Nume ical Me hods in Enginee ing (CIMNE)
Uni e sidad Poli écnica de Ca aluña
Campus No e UPC, 08034 Ba celona, Spain
e-mail: lg a [email protected]; se g[email p o ec ed]; x.m[email p o ec ed]; alex.ba ba @upc.edu
Key wo ds: High cycle a igue, Con inuum damage mechanics, Time-ad ance s a egy,
cyclical load combina ion.
Abs ac .A ime ad ance s a egy o cyclic loading will be p esen ed, applied o he a igue
o mula ion i s p oposed by [1]. The coupling o bo h o mula ions p o ides a
comp ehensi e app oach o simula e high cycle a igue p oblems accu a ely and wi h an
impo an compu a ional cos educ ion. The capabili ies o he p oposed p ocedu e a e shown
in a nume ical example.
1INTRODUCTION
Fa igue is a phenomenon gene ally unde s ood as an al e a ion in ma e ial p ope ies
leading o ailu e unde cyclic loads below i s elas ic h eshold. Habi ually, he numbe o
cycles equi ed o he o al ac u e o he mechanical pa was ound o be in he ange o 104
– 107cycles o mo e.
Howe e , i has been obse ed ha when ei he he en i e load o some cycles o i , induce
s esses supe io o he elas ic limi o he ma e ial, an al e a ion o ma e ial p ope ies s ill
occu s, no only due o he inelas ic na u e o he load bu also due o i s cyclic applica ion. In
his case he numbe o cycles equi ed o up u e is ound o be d as ically educed and is
gene ally below 103-104cycles. Based on hese obse a ions, a igue p ocesses can be
di e en ia ed in o high cycle, low cycle and ul a-low-cycle a igue, as u he inqui y in o
mechanical beha iou showed undamen al di e ences be ween hem.
Rega ding he high cycle a igue phenomenon, i has been documen ed ha he ype o
ac u e in ol ed a mac oscale le el is a b i le ype. The e o e, high –cycle a igue (HCF)
does no in oduce mac oscopic plas ic s ain. When looking a he same phenomena om he
mic oscale, howe e , i can be seen ha a la ge pa o he ma e ial’s in e nal ene gy is spen
in a ea angemen o i s in e nal s uc u e o accommoda e be e he elas ic cyclical load,
ollowed by he gliding o he in e a omic planes phase. The e o e, me al g ains su e plas ic
slip and non-linea beha iou [2], and hese i e e sible p ocesses a e esponsible o c ack
ini ia ion unde cyclic loading.
The model he eby p oposed is based on he classical con inuum damage o mula ion made
sensible o a igue e ec s by inco po a ing he numbe o cycles as a new in e nal a iable.
High cycle a igue expe imen s habi ually exhibi a a igue li e in he o de o millions o
S epwise ad ancing s a egy o he simula ion o a igue p oblems
1153
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
2
dozens o millions o loading cycles. I a single loading cycle is desc ibed by nloading s eps,
hen he numbe o loading s eps equi ed o comple e a HCF analysis would be in he o de
o 107xn. Fu he mo e, i he mechanical piece has a complex geome y and a high le el o
disc e iza ion is equi ed a ini e elemen le el, hen a each o he 107xnload s eps a la ge
numbe o cons i u i e ope a ions need o be compu ed o each in eg a ion poin .
The abo e se e as a clea example o why ime-ad ance s a egies a e o he u mos
impo ance in HCF simula ions. The s a egy p esen ed in his pape is based on he model
de ined in [1], u ilizing, howe e , he s ages o he algo i hm in a wide display o si ua ions,
as will be p esen ed la e on.
2DAMAGE MODEL
2.1 Mechanical o mula ion
The ee Helmhol z ene gy is o mula ed in he e e ence con igu a ion o elas ic G een
s ains, 𝐸𝐸𝑖𝑖𝑖𝑖 =𝐸𝐸𝑖𝑖𝑖𝑖
𝑒𝑒, as [3][4]
𝛹𝛹= 𝛹𝛹�𝐸𝐸𝑖𝑖𝑖𝑖,𝑑𝑑�=(1−𝑑𝑑) 1
2𝑚𝑚0�𝐸𝐸𝑖𝑖𝑖𝑖 𝑪𝑪𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
0𝐸𝐸𝑖𝑖𝑖𝑖�
(1)
Conside ing he second he modynamic law (Clausius-Duhem inequali y – [5] [6] [7]), he
mechanical dissipa ion can be ob ained as [3]
𝚵𝚵=−𝜕𝜕𝛹𝛹
𝜕𝜕𝑑𝑑 𝑑𝑑󰇗≥0
(2)
The accomplishmen o his dissipa ion condi ion (Equa ion 2) demands ha he exp ession
o he s ess should be de ined as (Coleman me hod; see [7])
𝑆𝑆𝑖𝑖𝑖𝑖 =𝑚𝑚0𝜕𝜕𝛹𝛹
𝜕𝜕𝐸𝐸𝑖𝑖𝑖𝑖 = (1 −𝑑𝑑)𝑪𝑪𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
0𝐸𝐸𝑖𝑖𝑖𝑖
(3a)
Also, om he las exp essions, he secan cons i u i e enso can be ob ained as:
𝑪𝑪𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
𝑠𝑠(𝑑𝑑)=𝜕𝜕𝑆𝑆𝑖𝑖𝑖𝑖
𝜕𝜕𝐸𝐸𝑖𝑖𝑖𝑖 =𝑚𝑚0𝜕𝜕2𝛹𝛹
𝜕𝜕𝐸𝐸𝑖𝑖𝑖𝑖𝜕𝜕𝐸𝐸𝑖𝑖𝑖𝑖 = (1 −𝑑𝑑)𝑪𝑪𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
0
(3b)
whe e 𝑚𝑚0is he ma e ial densi y, 𝐸𝐸𝑖𝑖𝑖𝑖 =𝐸𝐸𝑖𝑖𝑖𝑖
𝑒𝑒is he o al s ain enso s, 𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖 ≤𝑑𝑑≤1is he
in e nal damage a iable enclosed be ween i s ini ial alue 𝑑𝑑𝑖𝑖𝑖𝑖𝑖𝑖 and i s maximum alue 1,
𝑪𝑪𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
0and 𝑪𝑪𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖
𝑠𝑠a e he o iginal and secan cons i u i e enso s and 𝑆𝑆𝑖𝑖𝑖𝑖 is he s ess enso o
a single ma e ial poin .
2.2 Th eshold damage unc ion o ien ed o a igue analysis. Mac oscopic app oach
The e ec s caused by applying an inc easing numbe o loading cycles a e aken in o
accoun by means o a p oposed 𝑓𝑓𝑟𝑟𝑒𝑒𝑟𝑟(𝑁𝑁,𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚,𝑅𝑅) unc ion. This unc ion is in oduced in he
abo e o mula ion in he exp ession o he discon inui y h eshold p oposed by [7], [8] and
[9], 𝐹𝐹𝐷𝐷�𝑆𝑆𝑖𝑖𝑖𝑖,𝑑𝑑�. The numbe o cycles can hen be inco po a ed as a s a e alue.
This enables he classical cons i u i e damage o mula ion o accoun o a igue
phenomena by ansla ing he accumula ion o numbe o cycles in o a eadjus men and/o
mo emen o he damage h eshold unc ion.
1154
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
3
The non-lineal beha iou caused by a igue is in oduced in his p ocedu e implici ly, by
inco po a ing a a igue s a e a iable ha is i e e sible and depends on he numbe o cycles,
he ampli ude and he maximum alue o he s esses in he ma e ial, and on he ac o o
e e sion o he load. This s a e a iable a ec s he esidual s eng h o he ma e ial by
modi ying he damage h eshold ei he on he s eng h h eshold (le e m) o on he
equi alen s ess unc ion ( igh e m)[1].
𝐹𝐹𝐷𝐷�𝑆𝑆𝑖𝑖𝑖𝑖,𝑑𝑑,𝑁𝑁�=𝑓𝑓𝐷𝐷�𝑆𝑆𝑖𝑖𝑖𝑖�−𝐾𝐾𝐷𝐷�𝑆𝑆𝑖𝑖𝑖𝑖,𝑑𝑑�∙𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟(𝑁𝑁,𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚,𝑅𝑅)
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
�
𝐾𝐾𝐷𝐷�𝑆𝑆𝑖𝑖𝑖𝑖,𝑟𝑟,𝑁𝑁� = 0
(4)
𝐹𝐹𝐷𝐷�𝑆𝑆
𝑖𝑖𝑖𝑖
,𝑑𝑑,𝑁𝑁�=�𝑓𝑓𝐷𝐷�𝑆𝑆𝑖𝑖𝑖𝑖�
𝑓𝑓
𝑟𝑟𝑟𝑟𝑟𝑟
(𝑁𝑁,𝑆𝑆
𝑚𝑚𝑚𝑚𝑚𝑚
,𝑅𝑅)�
�
�
�
�
�
�
�
�
�
�
�
�
�
𝑓𝑓𝐷𝐷′�𝑆𝑆𝑖𝑖𝑖𝑖,𝑁𝑁,𝑅𝑅� −𝐾𝐾𝐷𝐷�𝑆𝑆
𝑖𝑖𝑖𝑖
,𝑑𝑑�= 0
In Equa ion (4), N is he cu en numbe o cycles, 𝑅𝑅=𝑆𝑆𝑚𝑚𝑖𝑖𝑚𝑚
𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 is he s ess e e sion ac o ,
𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚 he maximum applied s ess (see Figu e 2) and 𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟(𝑁𝑁,𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚,𝑅𝑅)is he educ ion
unc ion in luenced by he numbe o he cycles N. Fu he mo e, in he abo e,𝑓𝑓𝐷𝐷′ =𝑓𝑓𝐷𝐷𝑓𝑓𝑁𝑁
⁄,
is he equi alen s ess unc ion in he undamaged space, 𝐾𝐾𝐷𝐷(𝑆𝑆𝑖𝑖𝑖𝑖,𝑑𝑑,𝑁𝑁)is he damage s eng h
h eshold, and 𝑑𝑑=∫𝑑𝑑
󰇗𝑑𝑑𝑑𝑑
𝑡𝑡
0 he damage in e nal a iable. The e olu ion o he damage
a iable is de ined as,
𝑑𝑑󰇗=𝜇𝜇󰇗𝜕𝜕𝐹𝐹𝐷𝐷
𝜕𝜕𝑓𝑓𝐷𝐷
(5)
being µ he consis ency damage ac o , which is equi alen o he consis ency plas ic ac o
de ined in [3]. Consequen ly, o he iso opic damage case,
𝑑𝑑󰇗=𝜇𝜇󰇗
𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟
(6)
The educ ion unc ion 𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟(𝑁𝑁,𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚,𝑅𝑅)makes he damage model dependen on he
phenomenon o a igue.
Figu e 1a:S ess e olu ion a a single poin Figu e 1b: S-N (Wöhle ’s) Cu es
1155
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
4
2.3 Func ion o esidual s eng h educ ion o a igue –Wöhle cu e de ini ion
Wöhle o “S ess-Num. o cycles” (S-N) cu es a e expe imen ally ob ained by subjec ing
iden ical smoo h specimens o cyclic ha monic s esses and es ablishing hei li e span
measu ed in numbe o cycles. The cu es depend on he le el o he maximum applied s ess
and he a io be ween he lowes and he highes s esses (R=Smin/Smax). Usually, S-N cu es
a e ob ained o ully e e sed s ess (R=Smin/Smax=-1) by o a ing bending a igue es s.
S-N cu es a e, he e o e, a igue li e es ima o s o a ma e ial poin wi h a ixed maximum
s ess and a gi en a io R. I , a e a numbe o cycles lowe han he cycles o ailu e, he
cyclic load s ops, a change in he ma e ial’s elas ic h eshold is expec ed due o accumula ion
o a igue cycles. Fu he mo e, i he numbe o cycles exceeds N , being N he a igue li e as
esul ing om Figu e 2, he ma e ial will ail wi h he consequen educ ion o s eng h and
s i ness. Thechange in s eng h is quan i ied by he s eng h educ ion unc ion
𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟(𝑁𝑁,𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚,𝑅𝑅).
Figu e 2:E olu ion o he esidual s eng h wi h he applied load and numbe o cycles
In he case o a cyclic load wi h cons an maximum alue and e e sion ac o h oughou
he en i e li e o a ma e ial, he S-N cu e is su icien o de e mining a igue li e. Howe e ,
when dealing wi h di e en load in e ac ions he main ocus esides on he esidual s eng h
cu e. The cu e quan i ies he loss o s eng h in he ma e ial as he numbe o cycles
accumula es and as load cha ac e is ics change.
All a igue nume ical simula ions a e based on expe imen ally ob ained Wöhle cu es.
These cu es a e desc ibed in an analy ical o m wi h he help o ma e ial pa ame e s. Thei
exp ession, as well as he analy ical de ini ion o he s eng h educ ion unc ion, is connec ed
o he expe imen al cu e and, he e o e, subjec ed o change i he ma e ial changes.
The analy ical exp ession o he cu es used in his pape can be ound in [1]. Di e en
analy ical de ini ions can also be ound in [10], [11] and [12].
1156
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
5
3 STEPWISE TIME ADVANCEMENT STRATEGY
3.1 In oduc ion
The s epwise ime-ad ancing s a egy p oposed in his pape is based on he o mula ion
p esen ed in [1] and consis s o wo di e en s ages. The i s one is de ined by ime-ad ance
being conduc ed by small ime inc emen s wi h he consequen load a ia ion ollowing a
cyclic pa h. The second s age is cha ac e ized by ime-ad ance being done wi h la ge
inc emen s o numbe o cycles.
3.2 Load- acking s age
The i s s age is cha ac e ized by he load being applied in small inc emen s. The pu pose
o his s age is o de e mine and sa e he cha ac e is ics o he cyclical load. A e ha ing
de ec ed he maximum and he minimum s ess, a each in eg a ion poin , he e e sion ac o
is compu ed, R=Smin/Smax. Se e al mo e cycles a e hen desc ibed by small inc emen s. A e
each one o hem, a s abiliza ion no m quan i ying he sum o he no malized a ia ion o he
e e sion ac o , compa ed o i s p e ious cycle alue, is e alua ed as shown below in
equa ion 7.
0
1
1
→
−
=η ∑
+
+
GP i
GP
i
GP
i
GP
R
RR
(7)
When his no m is below a gi en ole ance i can be said ha he e e sion ac o has a
s able alue h oughou he solid.
This s age is necessa y a he beginning o each di e en cyclical load in o de o
de e mine he pa ame e s ha de ine he cyclic beha io a each Gauss poin o he s uc u e
(R and Smax). In case o modi ying he cyclic load, a new ac i a ion o his s age is necessa y
in o de o ecalcula e hese pa ame e s.The low cha o his s age is p esen ed on he le
side o Figu e 3.
In his s age he a iable is he le el o he load.
3.3 La ge inc emen s acking s age
A e he s ess pa ame e s, R and Smax, s abilize h oughou he solid he e is no need o
keep applying small inc emen s as he e will be no change in he s ess s a e unless ei he he
elas ic h eshold is eached o he applied cyclical load changes. The e o e, he load le el can
be main ained a i s maximum alue and la ge numbe o cycles inc emen s can be applied.
In his s age he a iable is no he le el o he load, kep cons an , bu he numbe o
cycles.
A low cha is p esen ed below in Figu e 3 o each o he wo s ages. The algo i hm o
he la ge inc emen s s age is p esen ed on he igh side o he igu e. The pass om one s age
o he o he is indica ed by ed a ows.
Akey poin o he abo e o mula ion is he s eng h educ ion unc ion, 𝑓𝑓𝑟𝑟𝑟𝑟𝑟𝑟(𝑁𝑁,𝑆𝑆𝑚𝑚𝑚𝑚𝑚𝑚,𝑅𝑅).
I s exp ession depends on he a io be ween he maximum s ess and he elas ic h eshold and
on he a igue li e gi en by he Wöhle cu e, as can be seen in [1]. These wo pa ame e s a e
1157

Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
6
de e mined a he beginning o he analysis a each Gauss poin and hey a e cons an unless
in e nal o ces change.
Figu e 3: Flow cha o he wo s ages o he ime-ad ance algo i hm
1158
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
7
This in insic s ep can p edic he exac numbe o cycles a which damage ini ia es. A e
e alua ing he Wöhle ’s N (see Figu e 2) co esponding o each s ess le el a he beginning
o he analysis, a sea ch is made o ind he minimum a igue li e h oughou he solid. The
esul ing numbe o cycles is conside ed o be he i s s ep o he la ge inc emen s s age
ensu ing ha he en i e span o numbe o cycles be o e he damage p ocess ini ia es is done
in one s ep. The nonlinea p ocesses occu ing pas he poin damage ini ia es in he i s
Gauss poin will be simula ed wi h a use -de ined Ncs ep.
3.4 Au oma ic load- acking s age ac i a ion
The abo e men ioned s a egy has he ollowing implica ions:
When applying a single cyclical load, ime ad ance will be done by passing once h u he
load- acking s age and hen ad ancing by numbe o cycles inc emen s bo h be o e and a e
eaching he elas ic h eshold. Howe e , when inside he cons i u i e model a Gauss poin
su passes i s elas ic h eshold, he in e nal o ces o he s uc u e a e modi ied in o de o
achie e a new equilib ium con igu a ion.
This si ua ion leads o a a ia ion o he e e sion ac o and, he e o e, o he s ess s a e a
in eg a ion poin le el.A his poin , he load- acking s age i au oma ically ac i a ed.
Fu he mo e, i will be ac i a ed a each s ep whe e damage accumula es (𝑑𝑑󰇗> 0).
In he case o applying di e en cyclic loads, damage can appea ei he due o a igue o
due o a new load applied ha leads o s ess alues o e he elas ic h eshold. In bo h cases
he model will jump au oma ically om la ge inc emen s acking s age o load- acking
s age.
4 NUMERICAL EXAMPLES
4.1 Tes case geome y and ma e ial
In o de o alida e he p oposed cons i u i e model a es case analysis o one linea
hexahed al elemen wi h 8 in eg a ion poin s was pe o med. Geome y dimensions we e
1x1x1cm. The ma e ial used has he ollowing cha ac e is ics: Young modulus =
2.01 𝑥𝑥 105 𝑀𝑀𝑀𝑀𝑀𝑀; Poisson a io = 0.1 ; S a ic elas ic h eshold is 𝑆𝑆𝑢𝑢=838.9 𝑀𝑀𝑀𝑀𝑀𝑀and he
ma e ial ac u e ene gy has a alue o 𝐺𝐺𝑡𝑡=𝐺𝐺𝑐𝑐=10 𝑘𝑘𝑘𝑘 𝑚𝑚
⁄. The damage model used has
exponen ial so ening and a Von Mises ailu e su ace.
The elemen has one o i s aces subjec ed o a cyclical displacemen while he opposi e
ace has bounda y condi ions ha ix i s longi udinal displacemen , allowing ans e sal
expansion and con ac ion.
One o he model’s pa icula i ies is he s eng h al e a ion occu ing p e ious o he
damage ini ia ion momen . The p og essi e loss o esis ance leading o he ini ia ion o
damage is ep esen ed in he s eng h educ ion cu e. In o de o i o be clea ly
di e en ia ed om he Wöhle cu e,a di ec jump o he poin whe e damage ini ia es was
no done. Ra he , an app oxima ion o he damage ini ia ion poin was made by choosing a
sui able numbe o cycles as ime s ep.
Below, wo di e en cases a e p esen ed. In he i s case a cyclical load wi h a e e sion
ac o o 0.3, minimum displacemen o 0.0000114m and maximum displacemen o
0.000038m is applied. The load applied in he second case has a null e e sion ac o , a
1159
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
8
maximum displacemen o 0.000035m and a null minimum displacemen . The numbe o
cycles adop ed as a s ep o he la ge inc emen s s age in he i s case is 106cycles. The
second case was calcula ed wi h a s ep o 105cycles.
4.2 HCF1 load case
In he ollowing able he s esses gene a ed a in eg a ion poin le el by he imposed
maximum and minimum displacemen s a e displayed as well as he a igue li e esul ing om
he FEM model.
Table 1:Cha ac e iza ion o load HCF1
(no malized wi h h eshold limi )
Case code Re e sion
ac o
Max.
S ess PG
Min. S ess
PG
Med.
S ess PG
Nc a which
damage ini ia es
hc 1 0,3 0,91 0,273 0,59 4,90E+06
The s esses induced by he cyclic displacemen applied lead o a a igue li e, acco ding o
he ma e ial Wöhle cu e, o 4,9 x 106cycles. This numbe o cycles ma ks he beginning o
he nonlinea p ocess and, he e o e, o he ene gy dissipa ion in he olume associa ed o he
in eg a ion poin p esen ed.
Below, in Figu e 4, s eng h, Wöhle s ess and damage e olu ion a e p esen ed. I can be
seen ha , while he esidual s eng h cu e is abo e he Wohle a igue li e cu e, he e is no
s ess al e a ion o damage accumula ion. The ma e ial is conside ed o be in an elas ic s age.
Howe e , once he esidual s eng h cu e in e sec s he Wöhle a igue li e cu e a exac ly
he maximum s ess le el induced in he ma e ial olume analysed, damage accumula ion
s a s.
Figu e 4:Pa ame e s o in e es o he a igue analysis unde load HCF1
1160
Lucia G. Ba bu, Se gio Olle , Xa ie Ma inez and Alex Ba ba
9
F om ha poin o wa d, a e each la ge inc emen whe e 𝑑𝑑󰇗> 0, he load- acking s age is
au oma ically ac i a ed so ha damage e olu ion can be moni o ed om cycle o cycle. I ,
a e desc ibing se e al cycles wi h small inc emen s, he s ess s a e h oughou he solid has
s abilized, a new la ge inc emen will be applied. The p ocess hus au oma ically epea s un il
he ma e ial eaches a s a e o comple e deg ada ion.
Figu e 5:Pa ame e s o in e es o he a igue analysis unde load HCF1 in he nonlinea zone
The p ocess can be obse ed wi h mo e de ail in Figu e 5 abo e, whe e a zoom on he
a iables’ e olu ion in he nonlinea zone is p esen ed.Load- acking and la ge inc emen s
acking s ages a e indica ed.
Bo h Figu e 4 and Figu e 5 ha e a loga i hmical scale along he ho izon al axis.
Figu e 6:S ess-S ain a in eg a ion poin o load HCF1
1161