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buEnhohetforthecircrewhassme KE

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bodasshomsituAnexathedefpla

H

he intern materi

. N. Jameshool of Marineepartment of Mames@plymou

. Newby hool of Marineskom Research

BSTRACT. Tht which is a

ngineering cmogeneous terogeneousrm of a genue differing cumstances eep, environhere weldingsociated withetallurgical fa

EYWORDS. Cacture; enviro

NTRODUCTIO

istoricanalysof unc

dies) have besessments fomogeneous, uations arise. nalytical compample, the ine presence oformation) anasticity and f

H

rface beial perfo

s e Science & E

Mechanical Enguth.ac.uk

e Science & Eh and Innovati

his paper coa determinincomponents

and geners and often nuine interfacphilosophiewhere envir

nmentally-assg is used to jh cracking aactors in me

Continuum onment.

ON

cally, the educsing the behacracked bodieeen very power engineeringisotropic co

plexity is alsocrease in rigo

of a crack. nd hydrostatfracture are f

etween mormance

Engineering, Ungineering, Nel

Engineering, Uion Centre, Ro

nsiders an imng factor in m

and structrally continunon-continuce between mes of desigronmental insisted crackioin compon

and uses caseechanical per

mechanics;

cation of mecaviour of strues subject to eerful in advang artefacts.

ontinuum, an

o introduced aour necessitat

Three dimetic (which refundamentall

M. N. James e

metallue

University of Plylson Mandela

University of Plyosherville, Joha

mportant topmany aspecttures must, uum aspectsuum reality omaterial and

gn have to nfluences haing, or corronents, or whe study examrformance o

non-continu

chanical enginuctures and mexternal load ncing our abil The key a

nd considerab

as the appliedted by a movensional stresesist plastic dly controlled

et alii, Frattura e

urgy and

lymouth, PlymMetropolitan

lymouth, Plymannesburg, Sou

pic, and onets of the ser

of necessis of appliedof material sd environme

be mergedave a key roosion), wherehere tribologymples drawnof materials.

uum materia

neers has hadmaterials. In p

or deformatility to calcula

assumptions ble complexi

d loading or dve from unidiss states candeformation

by inhomog

ed Integrità Strut

d mecha

mouth (UK) University, P

mouth (UK) uth Africa

e that is oftervice performity, provide d load andstructure anent, e.g. at a d. The inole in determe performany plays a rol

n from engin

als; metallur

d a strong foparticular, soion fields) anate internal stin solid meity is introd

deformation irectional loa

n be resolvedand promotegeneous, non

tturale, 14 (2010

anics

Port Elizabeth

n poorly undmance of m

a bridge bd displacemed behavioursurface, or

nterface has mining perfonce is dominle. The papeneering prac

rgical param

cus on continolid mechanicd fracture meresses and str

echanics are uced into an

field becomeading to triaxid into deviae fracture) sn-isotropic a

0) 5-16; DOI: 10

(South Africa

derstood or metals (and o

between theent, and thr. This bridcan be a virparticular

ormance chanated by fatier focuses o

ctice to illust

meters; case

nuum mechancs (dealing wiechanics (dealrains and to musually that

nalysis when

es more realisial constraintatoric (whichtress compo

and non-cont

0.3221/IGF-ESIS.

a)

misinterpreother materie macrosco

he microscodge can take rtual one whimportance

aracteristics (igue or fracton the probletrate the role

studies; fatig

nics as a toolith the behavling with cracmake realistict the body n more com

stic; consider,t which occurh promote shnents. As btinuum mate

14.01

5

eted, als).

opic, opic,

the here e in (e.g. ture, ems e of

gue;

l for viour cked c life is a plex

, for rs in hear both erials

M.N

6

behSevprostreproAnplasimscadismetheThpreAssguiof Ththedefsurof serThtemmeamcreto oncpos CR

fatimotheIt condurfraccraproof Thin twaelemK’ spe

T

N. James et alii,

haviour it miveral factors ocess in whichess concentraomote 3D strnother importasticity is verymplified. Wheale yielding, mtribution and

echanics, disloe concepts of he fundamentedicting fractsessment of idance for ena component

hus, in conside fact that thefect populatiorface conditiothe applied

rvice crackinghis paper willmperature. Aechanical engi

mbient tempereep mechanismbe properly sce a critical csition that is d

RACK TIP STR

he first crack grin many

igue crack grore accurate Ke elastic modewas noted bnsiderations, ring crack grocture (with a

acking of struovides the begthe 20th centu

hese stress andthe 1950’s ons governed bment from thwith fracture

ecimen. The

T

Frattura ed Inte

ight be anticserve to mitigh Poisson’s ration factors ress states andtant factor is y extensive there plasticity metallurgical d size; heat trocation mech

f uncertainty, tal role of plature using a the Integrity

ngineering critt or structure

dering the beheir macroscopon), the environ (roughnessfield (e.g. pr

g in materials l focus on thAlthough noineering pracratures is oftems is time-descheduled. Scrack size is difficult to in

RESS FIELD

issue worth rowth by the y circumstancrowth. An inK-solutions oel for crack tipby Griffith [4and that fracowth. This a

a magnitude euctures becauginning of a sury was the and energy strann crack tip strby the first tehe crack tip. e occurring ae stress inten

egrità Strutturale

cipated that pgate these peratio is 0.5 an

that arises frd increase plathe relative s

he design criteis limited fracfactors (e.g.

reatment and hanics and plstatistics and

asticity in cracFailure Ana

of Structurestical assessmeto fracture an

haviour of mpic behaviourronment in ws, chemical croportional ois truly a cutt

he metallurgin-metallic m

ctice is conceren experienceependent andSub-critical crreached (whi

nspect) fast fra

S IN THE PR

briefing conpresence of a

ces but underncreasing em

or improved fp stresses can4] in a classicture occurredapproach explequal to the vuse of the cosound undersnalysis of cracnds were broress fields [7]rm in a serieThis led to dat a critical msity factor is

e, 14 (2010) 5-1

prediction oferturbations; od this tends t

from plastic fastic constrainsize of criticaerion is likely cture will domcrystal struchardness; su

lasticity theorreliability hav

cking of metalysis Diagras containing ent of defectsnd to plastic aterials underr reflects their

which they opomposition,

or non-propoting edge intecal-mechanic

materials are brned with theed as a suddend the damageracks may groich may be eacture occurs

RESENCE OF

nsidering cona plastic enclarpin the cont

mphasis on mfatigue life prn be improvedic paper thatd when the elicitly links crvalue of the complexity in standing of thck tip stress f

ought togethe. He recogni

es expansion, defining the nmaterial consused in situa

16; DOI: 10.3221/

f structural bone is the facto promote 2flow. Howevnt (the move fal defects at fto be plastic

minate and mcture; slip beurface conditiry. Many anave to be factotallic alloys haam (FAD), wDefects [1], s [e.g. 2]. Thcollapse and r applied loadr microscopicerate (temperresidual stres

ortional multirface between

cs interface inboth intereste behaviour on and unfore can often beow very sloweither relatives in metals at

F PLASTICIT

cerns the peave surroundtinuing contr

multi-parameterediction modd to include it the phenomnergy releaserack size, appcritical strain quantifying

he driving forfields performer to lay the fised that the ithrough a 1/

numerator in stant value Kations where

/IGF-ESIS.14.01

behaviour woct that plasticD stress statever, increase from plane st

fracture compcollapse of th

material behavehaviour; graiion; residual alytical and nored into the as led to the which was dand has been

he FAD approplots this statd or deformac compositionrature, chemiss state) as weiaxial loadingn metallurgy, n relation toting and impof metals. It eseen phenome monitored

wly via fatigueely small in tespeeds which

TY

rturbations imding the crackroversy surroer characterisdels, brings ininfluences arimenon of rued by crack explied stress an

energy releaand measurin

rce for crackinmed by Inglis foundations ointensity of th/√r dependenthis first stre

KC appropriat the overall

ould generallc deformationes, whilst a sein compone

tress to planepared with zohe structure a

viour will reflein and phasestress state).

numerical appanalysis. adoption of

developed forn adopted in oach conjointte on a failureation, full conn and conditiical species, cell as the mog). The pred

materials scie cracking pr

portant, it reis also the c

menon, whilstin service allo

e or environmerms of the sh can reach ar

mposed on tk. These pertunding plastisation of cranto sharper fsing from plaupture in solxtension was nd the concepase rate GC), bng the work ng. Other im[5] and West

of fracture mehe applied strncy where r iess term (σ√a)te to the parstress-strain

ly be difficuln is largely a econd is the lent or structu strain situati

ones of local and the analyect interactione dimensions This is the r

proaches are

a two paramr the CEGBsimilar Britis

tly considers e locus diagransideration haion (heat trea

contact with ode, frequencydiction and uence and mecoblems in m

emains true tase that failut failure by coowing repair

mentally-assisscale of the sround Mach 0

the elastic strturbations areicity-induced ck tip stresse

focus the queasticity. lids was govequal to the

pt of a materibut was difficto fracture.

mportant worktergaard [6]. echanics in thress field neais the distanc) to be the ‘strticular state constitutive b

lt and imprecconstant volu

local reductioural size tendons). plasticity. W

ysis can be grens between sms; inclusion trealm of fracapproximate

meter approachB R6 documsh and Europthe susceptib

am. as to be givenatment, hardnother parts), ty and compleunderstandingchanics.

metals at ambthat the bulk

ure by crackinorrosion, weaand replacemted cracking, structure, or 0.4 [3].

ress field drive relatively mshielding du

es, to give eiestion of whe

verned by enenergy absorial’s resistanccult to extend Nonetheles

k in the early

he work by Irar the tip of cce of the stretress intensity fa

of stress in behaviour of

cise. ume

on in ds to

When eatly mall type, cture

and

h to ment, pean bility

n to ness, their exity g of

bient k of ng at ar or ment

but in a

ving minor uring ither ether

ergy rbed ce to d to ss, it part

rwin rack ssed

factor, the

f the

crastreas plaLinin ceve(vialevthegovof areinteExablSatwitwoplaplaconstredrivcradifT-sThthe

whpla

wh

whcrainteplacomCofun

Dis

acked body is ess concentrarecognised in

ane strain thisnear elastic frcracked and sents from thea the Irwin pl

vels should bee K concept verned by thethe applied st

ea of fatigue ensity approa

xtremely interle to providetisfactory ansth plasticity-inork on this isastic ‘inclusionasticity-inducenstant volumesses must exving crack gr

ack tip, and afference in pristress) or four

he stress variae Williams sol

Nf

h

here the two uane. The 4-te

Nf

h

here the four u

Nf

h

here the four uack growth Kensity acting

astic interfacemparable with

onsidering disnction is given

2 u

splacement fi

linear and elaation at the crn the case of s relationship racture mechastressed struce bulk appliedlastic zone coe a relatively to fatigue c

e stress intentress intensitycrack growth

aches. resting (and lae an adequatwers to thesenduced shieldssue [12-14] cn’ representined closure) a

me process wixist at the inrowth forwara shear-induceincipal stresser-term solutio

ant of the equlution. The W

2y x

unknown coerm solution i

2y x

unknowns are

2y x

unknowns arKF, T-stress, a

to retard crac (leading to ah photoelasticsplacement fin by:

iv z

ields can be s

astic, i.e. wherack tip). Crif plane stress becomes G =

anics and the ctures with and elastic field. orrection to alow fraction

crack growth nsity factor, thy, ΔK = Kmax h and life pre

argely ignoredte characterise questions wding of the crconsiders theng the plasticand compatibth Poisson’s

nterface. Therds KF, a retaed stress intees [14], usingons to the Weuation represeWilliams solut

1

2xyi Az

efficients are is:

xyi A z

e A, B, C and1

2xyi Az

re A, B, C anda crack flank ck growth KR

a KS term). Tc data. ields, both p

'z z z

ubstituted int

M. N. James e

ere there is a litical values oby the equat

= K2/(1 – ν2)Estress intens

n associated d Plasticity is

apparent crack(perhaps < 0rate on the

hen sub-critic– Kmin. With ediction und

d) questions sation of phewould seem lirack tip durine boundary cc enclave surrbility-inducedratio ν = 0.5

e CJP modelarding stress ensity KS. Ang full-field phoestergaard or enting the CJtion for 2-term

3

2Bz z C

A (A+B = 0

1 3

2 2z z z

d D, while the1 3

2 2Bz z

d D and D+Econtact stre

R) and a compThis provides

perpendicular

' z

to Eq. 4 to gi

et alii, Frattura e

limited extentof stress intention G = K2/E. sity approach decoupling ofprimarily conk length), stre0.6) of the yie

basis that ifcal crack grow

the developmer cyclic load

remain as toenomena thaikely to assistg fatigue crac

conditions tharounding the d stresses at 5, whilst in ell [12, 14] forintensity KR

nalysis of its otoelastic datWilliams [15]P model is gims, K and T-

0Cz

0) and C and

1 1

2 2(B z z

e CJP model i1

0 2Cz Dz l

E = 0. This mess with a 1/patibility-indufringe pattern

and parallel

ive:

ed Integrità Strut

t of crack tip nsity factor an/E where E

have provenf local crack tnsidered throuess state and eld strength of critical cracwth under cycment of fractuding has beco

why, and hoat explicitly at in resolvingck growth [10at would be crack. Thesthe elastic-pllastic deformr crack tip str

which captucapability in

ta, indicate a l] equations. iven below alstress is:

z is the coo

102 )z Cz D

is given as: 3

2lnz Ez zln

model allows√r distributio

uced shear strns for differe

to the crack

tturale, 14 (2010

plasticity (whnd strain eneris the elastic

n very useful itip microstruugh its influethrough the sof the alloy. ck growth unclic loading mure mechanicome the prim

ow, an elasticarise from plg a number o0, 11]. The eximposed on e arise from lastic interfac

mation ν ≈ 0.3resses leads t

ures wake concharacterisin

lower fitting

long with 2-t

rdinate of a s

( )D z z

nz

for calculatioon behind thress as a bounence in princi

k face, the M

0) 5-16; DOI: 10

hich arises frorgy release ramodulus of

in characteriscture and plances on specistipulation thParis [8] ext

nder monotomay be govercs into a matume applicatio

c approach tolastic deform

of controversixplanation adthe applied crack wake cce. Plastic d3 and plasticito a modifiedntact influenc

ng near-tip frierror than eit

erm and 4-te

stressed poin

on of a stresshe crack tip (ndary conditiipal stresses w

Muskhelishvil

0.3221/IGF-ESIS.

om the high lte are equivalthe material.

sing critical stasticity controimen complia

hat nominal stended the usonic loading ned by the raure discipline,on area for st

o crack growtmation proces

ies [9] associdvanced in reelastic field b

contact (so-cadeformation ity-induced shd stress intences ahead of

ringe patternsther two- (K

erm equations

(1)

nt in the com

(2)

(3)

s intensity driv(leading to stion at the elawhich are dire

li complex st

(4)

14.01

7

local lent, . In

tates olled ance tress se of

was ange , the tress

th is sses. ated cent by a alled is a hear nsity f the s for plus

s for

plex

ving tress stic-ectly

tress

M.N

8

wh u,v

z A, CasexaKS,fou

It ipla

N. James et alii,

2 u

z

Az

here:

,z z

B, C, D, E, Fsting the CJPample, using , KR and the Tund as compo

Figure 1:full-fiel

l

l

l

I r

Sr

R r

X

y

K

K

K

T

T

is not yet cleaasticity-induce

Frattura ed Inte

iv

2B E z

1/2 1/2Dz ln

= s = f = h

= a

= cF = uP model in thdigital imageT-stress as foonents Tx in x

Displacementld fitting betwe

a crack 29.3

0

0

0

im 2

lim 2

lim 2

r

r

r

r

r

r

C

F

ar whether theed growth rat

egrità Strutturale

2 2B E z

1/2 1/2Ez ln

1/22nz Dz

shear modulufunction of Pohorizontal and

auxiliary funct

complex coorunknown coehese terms allo correlation t

ollows (note tx-direction an

t field around aeen model andmm long und

3

2

2

y

xy

y

Eln r

e CJP model,te perturbatio

e, 14 (2010) 5-1

1 1

2 24z Ez

4

C Fnz

2

C Fz

us, MPa oisson’s ratiod vertical disp

tions in Musk

rdinate in the fficients and ows direct cotechniques (Fthat when usind Ty in y-dire

a crack tip mead experimental er a load of 12

3

2

2

3

r

A B

D E

, based on theons, or lead to

16; DOI: 10.3221/

1

22C

Ez lnz

o ν placements

khelishvili‘s m

plane z=x+iyD+E = 0

omparison wiFig. 1). Expring displacemection):

asured using Ddata. A 2 mm

20 N. The mea

3 8A B E

e plastic incluo a reconciliat

/IGF-ESIS.14.01

4

C Fz

model

y

ith full field cressions can bment data rath

DIC techniquesm thick aluminiasurement regi

E

usion concepttion of conflic

crack tip dispbe directly obher than stres

s. The pattern ium specimen iion is 17.7 mm

t, will providecting views o

placement fielbtained from ss data, the T

of points is usis used which c

m by 13.2 mm.

e a means of cf plasticity-in

(5)

lds measured,Eq. 5 giving

T-stress has to

sed for the contains

characterisingnduced crack t

, for g KF, o be

g tip

shifitt IN

depdisstruthrThsam

Thand[19asycangrosusAnof allolighincborfatimelevincIn par

I

ielding. It doting error whe

NTERGRANU

ntergranulaalloys, e.g. consequen

pendent on tlocations, whucture of a ½ree 1/6[1 1 1] his leads to slme as that req

Figurperiod

he motion of sd {1 1 2} slip9] and ultra-loymmetry given then form aowth along exsceptible alloyn interesting e

bcc steels usoys have to bht weight andcreased formaron and nitroigue loading,echanism outlvels of P and creased P andthe case of IFrticularly duri

I

es, however, en compared

ULAR FATIGU

ar faceting ducertain α-iron

nce of crystaltemperature, hich are less

½[111] screw fractional dislip asymmetryquired to mov

re 2: Core of a dically repeating

The arrows ar

screw dislocap planes. Intow interstitials rise to shapalong grain bxtended crackys subjected texample of thsed in the au

balance severad are likely toability and deeogen, typically, however, llined above. Mn in solid

d lower interstF steels, desping crack init

capture influwith photoel

UE

uring fatigue ns and ultra-ll structure astrain rate anmobile thandislocation inlocations whiy whereby thve it in the op

½[111] screw g the three (11re the relative (

ations hence dterstitial atoml atom contenpe changes ofboundaries wk paths plastito fully revershis phenomenutomotive indal conflicting o be subject tep-drawing cy 10-200 wt plow interstitia IG crackingsolution. Su

titial C, B or Nite plastic deftiation and lo

M. N. James e

uences of plaslastic full-field

is a second low carbon stand dislocationd interstitial

n non-screw n a bcc alloy ich also sprea

he shear strespposite directi

dislocation pa1) layers (distin(screw) displac

depends on stms present in nt (e.g. C, B, Nf bcc grains u

which favours ic deformatiosed loading innon occurs industry for forrequirements

to reversed cyapability are a

ppm (0.001 wal content (

g may also beusceptibility tN [16]. formation beiong life fatig

et alii, Frattura e

ticity that havd fringe data.

plasticity-indteels with a bon movemenl atom contedislocations is non-planar

ad asymmetriss to move a ion on the sa

arallel to the plnguished by dicements of neig

tress-assistedthe cores of N) would theundergoing futhe nucleatio

on may be strn high cycle fan interstitial-frrming thin gas, i.e. deep-dryclic loading assisted by ve

wt % to 0.02 w< 40 ppm) e promoted wto brittle frac

ing strongly lgue, the fatigu

ed Integrità Strut

ve, up to now

duced phenomody-centred c

nt [16]. Slipent and are gand which mr, lying in thrically on threedislocation i

ame plane.

ane of the figuifferent colourghbouring atom

d thermally acf screw dislocerefore promully reversed on of intergrrongly localisatigue where lree (IF) steelsauge sheet brawing capabiin service. Tery low amouwt %). At thpromotes IG

with high strecture has bee

localised at grue performan

tturale, 14 (2010

w, largely been

menon that ocubic (bcc) crp mechanismgoverned by make cross-slree {1 1 1} pe {1 1 2} planin one directi

ure. The atomiced atoms) alonms along the disl

tivated genercations appare

mote slip asymcyclic deform

ranular fatigused within gralevels of plas

s which constody panels. ility, fatigue r

The conflict inunts of intersthe small plastG cracking ength IF steeen shown to

rain boundarince is little d

0) 5-16; DOI: 10

n ignored and

occurs infrequrystal structur

ms in bcc allthe behavioulip more difflanes (Fig. 2)nes in the twiion on a slip

c block is formng the dislocatilocation line [17]

ration of kinkently make th

mmetry in bccmation. Strese cracks. Duain boundarietic strain rangtitute one of tIn performa

resistance, tenn requirementitial elementstic strains typthrough the

el grades conbe higher in

ies, which leadifferent to o

0.3221/IGF-ESIS.

d gives a lowe

uently in spere, and is a diloys are strour of long scficult. The c). It spreads inning sense plane is not

med by ion line. ].

k pairs on {1 his process eac alloys. Thisss concentratiuring subseques, particularlge are low. the major groance terms, thnsile strength nts arises becas such as carbical of high c

slip asymmntaining increan the presenc

ds to IG faceother compar

14.01

9

er

cific irect ngly crew core into [18]. t the

1 0} asier slip ions uent ly in

oups hese and

ause bon, cycle

metry ased e of

eting rable

M.N

10

alloIGto e RE

difthenumstreof wawel

ThstruparresperfatisucfroslipcycloaWeassto engsurof FroA s

R

N. James et alii,

oys which doG facets on a f

either critical

ESIDUAL STR

esidual consequof the y

fferent distancerefore also vmber of waysess and fatigustructural parke effects, lolding), mecha

Figure 3: IG

heir magnituductures produrticularly in thidual stress rformance thrigue ‘quality’ ch as the initiom interface cp processes. clic loading, tad. elding is the sessment for wpropose verygineering critrface measuremeasurementom the 1970ssynchrotron l

R

Frattura ed Inte

o not exhibit fracture surfaor sub-critica

RESSES AND

stresses arisuence of manyield or prooces over whic

varies with typs, including cue crack growrts. They als

ocal phase traanical propert

faceting near t

des can be higuced under nhe presence oprofiles durrough, for exof the comp

iation of fatigcoherency, e.g

Despite the there is still a

most commwelded jointsy conservativticality of defements, e.g. uts, alongside as onwards, thlight source i

egrità Strutturale

such IG faceace are usuallyal cracking w

D WELDS

e as a consenufacturing anof strength. ch the residupe, nature andchanges to lowth. These st

o occur as a ansformationties, microstru

the crack initiatand 0.

ghly variable;nominally simof stress concring service xample, peeniponent [23]. gue cracks andg. of intermetwidespread e

a lack of accu

monly used sts often has a ve ways of defects. A larg

using low eneran ‘innate’ coe available X-s a form of p

e, 14 (2010) 5-1

eting during cy an indicatio

would be lowe

equence of mnd fabricationThese regional stresses seld origin [20]. ad eccentricit

tresses often aconsequence

ns), and are pucture and ge

tion site in an .013Ti. The st

; both from pmilar condition

entrators suc[21]. Compng [22] or coType II stresd corrosion ptallic particlesexistence andurate 3D info

tructural joinideciding influ

ealing with rege contributiorgy X-ray sou

ontribution to-ray intensity

particle accele

16; DOI: 10.3221/

crack initiatioon that some ered. Fig. 3 sh

misfit between processes, wns of misfit clf-equilibrate. Type I mac

ty and failurearise from noe of the crackparticularly ineometry of th

IF steel contaiteel has a yield

place-to-placns. The exterh as weld toepressive residld-working tesses are intergprocesses. Tys and regions,d frequent usormation on t

ing process auence on the esidual stress on to this unurces, imprecio scatter fromy increased drerator in whic

/IGF-ESIS.14.01

n and growthform of embhows typical I

en various rewith magnitudcan occur wi. Their influerostresses cane stress durinon-uniform plk growth procnfluenced by he componen

ining 0.001C, 0strength of 17

e within the rnal applicatioes, defects anddual stressesechniques, whgranular in scype III stresse, and from die of residual the magnitud

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ss profiles at a

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m below the su

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CO

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RE [1]

[2]

[3] [4] [5] [6] [7] [8] [9]

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[14

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ONCLUSION

his papedominatplasticity

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CKNOWLEDG

he awarassistancDanie H

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