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Eindhoven University of Technology MASTER Het breukgedrag van duktiele materialen Reijntjes, H.C.E. Award date: 1982 Disclaimer This document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Student theses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the document as presented in the repository. The required complexity or quality of research of student theses may vary by program, and the required minimum study period may vary in duration. General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain Take down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Download date: 04. May. 2018

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Eindhoven University of Technology

MASTER

Het breukgedrag van duktiele materialen

Reijntjes, H.C.E.

Award date:1982

DisclaimerThis document contains a student thesis (bachelor's or master's), as authored by a student at Eindhoven University of Technology. Studenttheses are made available in the TU/e repository upon obtaining the required degree. The grade received is not published on the documentas presented in the repository. The required complexity or quality of research of student theses may vary by program, and the requiredminimum study period may vary in duration.

General rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.

• Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain

Take down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.

Download date: 04. May. 2018

ArSTUDFERVERSlA6

HET BREYl<GEORRG

OlU<TIE"LE MRTERIAlfN

PT. 0522

b~: pt"O{:l~ ";lA.G. l<Q\S.

ol~. it: 'l H. '[)Q""tZfM W~ •

. ......--

EINDSTUDIEOPDRACHT.

voor

H.C.E. Reijntjes id.nr. 119751.

De opdracht houdt globaal de voortzetting in van onderzoek naar het

initiale breukgedrag van ductiele metalen. De algemene doelstelling

is een verdere stap te zetten in de richting van de kwantitatieve

voorspelbaarheid van de grenzen van de omvormbaarheid. In aansluiting

op de activiteiten van o.a. H. v.d •. Avoort en G.B. Huiskens dienen

de volgende deelopdrachten te worden uitgevoerd:

Nauwkeurige controle van de belangrijkste voorgaande studies in hun

onderlinge samenhang.

Verbetering van de krachtberekening in het beschikbare berekenings­

model en van de bijbehorende procedure. Speciale aandacht is hierbij

te geven aan het optimaliseringsgedeelte.

- Opstellen van gebruikershandleiding.

- Herberekening van de materiaalkarakteristieken v~~r aIle beschikbare

meetgegevens volgens de aangepaste procedure.

- Opstellen (zo mogelijk) van een scheurhypothese op fysische grondslag

die in principe geschikt is als objectieve materiaalqualificatie bij

de kwantitatieve analyse van omvormprocessen.

- Uitvoering van een volledige meet- en rekencyclus inclusief evaluatie

op een nader te bepalen materiaal .

24, november, 1981.

Prof.ir. J.A.G. Kals.

nit tQ~port be.vct.t eel"\ over-u..clAt VOYt de ~'ZQa""­

h~elt\l die gedaaYt 't.C1" in ket koder VOtri het: ond~ f"lQClr

he;! bcetAkC3«:fA:.':lC3 \.an clvtk.iie.1e NV\ct:\:e,t'"l.G\I0fl. 1)H ot"derz.azk

~rctt ~ah:tv\ .op de T~vt·,soLte t--I~I {e fi...d~ bq

de sekite OIWt\JOt"nlvt~r1olaje \JCt~ de u::tk:Jroey., '"Prod.uct;e\e~­

If\~ie.

A\fereetSt ~rd0.tl de C3roY"dsbqe.n can de ovd:vViLdA.gi~

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~ieproc.e':).

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zoek.

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-" -

j", cU.t hoo{oIsil.o(k v.:x:>c"ct*- het ~ooIe.t bet:>proLcew

WlClCUAN'Iee I 'M.:tgaarde \.Otl I\.a- lAVli{ofwYI2 olefof"~;e" cAi~t.e

'3n::>ot~ '11'\ de lcJe\.tisl.e oloor-st1€c:;L.Q vCI'" cAe i.re1csOOto'f ~f'cI~

bEu-e~ol.

'De qe~vens ucx>r de bere'-'e.,., i rvaeVt \NO( olev"'> yeA" Lc.t'~e¥I

ck:Jor he:!: ~\IOe'i'en \DV\ -ttekpr~ tIY'Iet ~.. ~erfd(!. Qf'\

orqeLc..erfde ~. Ttjcle..1s cAe ire.kp"oe[ ~t"deNl ole t.rekktaekt,

I="~ en de. ~et':e \JQ1'\ de ldeit1sle ~nede. OL/p., Cfl­

tmeWtl t ttcaWM" «2.-l) .

2,a.

r o./~ (_)

~ (-) ... 1

I'9u.w" Q." \lerOtV\dQl"lJ'\q va", ~e kerlq-eoMf\e.:h·;e itj.

d€V's de defotlWtalie vat1 cAe Proe1l1lQa f.

'2eals reeds qe-zegd ~ de. lW\o:Ae vVC\Q.;'lr"\ V'ue..t­

tAr\i(orMl1e. de{orMl\C1tte. e>ptreedl" i(\ he! /'tI'\ocle1 VOIS~elegd. ola?t"

de ~(et- c.t~l~orM.Mfe.ttsparal\Mete(", y, cl,e ~l-tOlt1l<erqk h. IJOY!

de ~et,.ie. vaf1 de. \,c.erf ~ ~'t'lS ..... oe(lY1~.

'De defoflWla.:tie VOY1 de veksw( ~~ct.:t vc:tY\Olf HeX

bec:3\Y1 VClt'l de r"I.e.i - tAni{ot"~ de.(o(~ie ~a.cselooot:;t iW\et ~p

vavt de ,>kps~~ze de~~jetMetkode. H,erbij 1.Al!O~ o.o."qe­

ytOM1~ dcc.-t de f).ei* tAnl ImtVWE de(<<h"IIN\a;i;e ',,, de 'StctQ( baj\4.

'ZocUct de mraal ~ R, \)Q.-"\ ole ker'( 01 i.t1S11oet'L~~ k.lettler \ ~

darn -tco IWl \.JtMl\e:ter.

("'\MAr 2.2: VOOj"!,tellit'1~ van de ::.bp~w~~ de~()r(\lV1G\.­

'b~et k.ode.

- b -

'De 'SbpS~(?A)~2e defoftlN\a.:t,eQlY\ethcde. ~'-Ac.lt' iI1 dctt

ole to~le de{o,~ie, dIe "Kit Y(liforlWl i~. ",n eeVl oavd-a.\ stapf0"'1

\70'" '3€(qke ~c(l\IYIofie-'arootfe ~ vetd.eetol. va \JerLu-i.j~

we oCcx>r de tolQle diq t'Meter - ver"""","",Iloleri~<j \JCItrl de. trek si:aa.t

"'0\ lAe{- kIeq',t') va.., ,..,ref -Ul1if0fl..fe detol'MAa..:t.ie. l.e verole.l.eK 'vl

I'J 1) '3eJg ke :;:.tappeV\.:

I = i.2, ... II N D. a~ 2.'1).

Vereb- worcU ole oiraai \JClrl ole klei .. rude. clClC)l'Sr'JEde

b~ ket btzca;11 \,/Q,.., nlef-c..(,..,qorlWte oIe(~ vercieetd. iVl

AS 1"1. r"Olc:Ua..1!e pos;nes:

( 2. '1) 3" .. 0, ~lt ••• , ~S-

H.e(~e. verdelE4;\; we de klei.t'lst.e otcorsnede "In A ~ Q)eWlet\­

tew (f~UA.U" 2.3).

:;., he! vlak VQt"l ole LdeLnste c::b:>rsnede ~o..a..t

eEM .,odlo1..t posl.he l,,"~~ door rio .. .. 1)e 'l"'IC.iex i. 'os --_. -0-11--- .tJ

kel fCh",9t1A.fMM€r va"'- 04-'2 de{orANt.a.f.eshp en de ,r\dex j i.s

ke:A: Ir1A.AHf-ie." ~lt"I de r~ positie.

( 2.3)

1)2 ~(oO"He vq~ E'eI'\ "'~crMl\.ccl.eslo..p ~(J.) u.~t vac;,t r:J.cor ~

Aa..; ve(I'W'\-'r'\det,!"9 \lQYI ole '$t~l \JQrt de kte\(\$1e clcdt's~de per clefcrtWKdiesil:::\p.

do ~ sir",," ~V1 ole. t.c.letrtste. c.(OI';>t"svte::k \0',; het bcq'IVl \1(;(,... ruet-uo-.{ortme oIeforMAO:tie <.. ket'f- of ir'l':."OI2'i,~':.straCl.t... t< <. "'00 i)!.1M\. ).

~t ro.Q.1 VO'" de I..c..le.insle oloo rSl'1Ed~ by b-eMW:.. t(: f .. "d\04c-e.).

- '=I -

\lefdetifl<] 1Ic::rt1 de l.Je.insfe dOOrsn«:(fil it1

A~ ... i ro\c::U.Gdt po~i t,e'S .

1)e ~rooHe va", de slrCAcd. \0.-"\ de kJei.fl~te doors.(lEde

V\o. ettu2 clefcriMQ.t,e.S\ap} ""4. , lu:w\ als ~t bereue.-1d wordeVI-:

i.,= ~. 2 •...• ND.

\/00(" t2lke d~rtWICl;;beS'~ j,(a", IlI.t. de. 1cWe <2Uecfielle

rek \X)~s "Br'~IWIat'l1 iai., C .... "ifoiMA C)ver d<2 ~Ie door:s~EtJle) \.OO~ bet'ek~:

( Q.s)

Q.."" ~ stracU UQr'I de. ~orltMeercle trElutaaf

Clo : st~ \1QN\.. de I.t.Ieinste ckx>f'St1ECle bij ~W\ \JaI"\ Vleet -Ull'lt~OrM1e de{0,.n.w;r.:.Le.

- 8-

:]'(\ oI.eze relcvt.e sietl de eerste lerl'YV\ aCe qetqklWl.O\.klqe

rek va'" de -tte.ksta:{ voor erf'\ de t~ede {erNVl cIe re.k i,.,

de k(eVi'Sf.e doo.-sn.eole ~ f'lCld.cd de. t"IJ2i - \At\i{erlW\e c:.tefo~le

bajor\net1 \ 5.

t 0.;(1.. {-)

def. stap ~

I I 0 I I I I

e, (-) ---... £Bf

hd ver100p lIa~

ole kert¥oMetrie

T~d&lS ole trekprael vvordt

keA: \Je'I'"loop ~el\Nleie¥l va""

de. kerfqeowteb-le.,. Q/Q., als

ft,tW'\cl.1e van cE de.fO~IW1a.t;e..

tMt<3ec;(.n.c1A.t it"l de ut\; rorM'te

-f{e:-f.,e,\Ie- rek.. ,.

'Da- cae~evt ~loop

.Non.::« ~d docr ~­

oIet vow, linea..ife re:rfes.sie

door one (!)peertyo~de tmeet­

plAt'\~et-\.. Met b~uJ(J von ctU

benOldet-de \lerba..a {cASw;\..

0./ R EW\. is kCh" c4e ket"f'leo­

lWIetri.e. "'~ <Zlke de.{or~ie­

sbp, Q.i./Rt bepaa1cL worclew

(7-le fiq\MA.r 2. ~)..

'De (G\ctia1L posi~.eS en de kletr1sie cloors(tecfe ~t1 de

SbGlf bg he;( beqitl1 \JaN1.., HAit -unifDrCWIe deto(~,e ku",V'lEWt

cds vo(qt beteke.vtd wofdev\.. ~

(Cl.6) j.:. 0,", ... , ~s . ..

the~e Llg~ a He ~::> lklVl cAe sktal . b~ he*

beqM \la., vue-i- UN\ifOtN\1€ de{C(~f.e. vasi.

- 9 -

l4et snetheiolsveW(. bcMA:ert de tUeinsie. ~,.,de. .... 'Q..,

de. siact{ et1 hd vOMI-'Ce vet .... het l\'V\a.te...too..l, dcU. Vl,e{ uni(oflW)

cfe{o(IMaerl: zljt'l ot1beL<el'1d. Hd- ~od€l ka~ obarC)l..f n.ef ~t-'JZ werU:t

v.,X)rdecA.- cCc::lor ~('...u.k ie. WII"IClI,.c.ev. .)0 ..... trce* bovevt'3revls~~eorel'l/lt1«.

We prO~EW\. c.tw:J e::M op(o~~t~ 'be ",it'\devt i.., cIe ('icLAlY1j' \X)(t'\

~e* or'lCier'3n?N1sH'lEt:::lf'"0w1Gt." ~b<:1 op de eersfe pbcd.s vc/.c::Iaall\

~ ~t1 otClV'l ~i~ OCt .... "f)p:x .... t'ilfl'3e.v1. We M-to.kevt oIoIar­

b~ ~rcM.k \OV'I de ~wicLdsveor~e, -z.oa.ls die. doot"

1?,("ct:J0MCU'l ~~ o~'St!lcL. vcor cAe ~t'\snoerzcSne -\er pbo.kse

\Xl"" d~ kleiv1ste doorsne::ie [ .... 'Bgbse A]. 'Ue"2.e. Q.VelI1"",icLd;s­

vE)()('v..>aa.rcAe IJIlClOrd.:t." \.4"':':{':joal'1de IJQ~ 1'1..et-u.nl~~e cle,fot"Nl"'IOl-

1:ie., wtF('(A.kt Om een reia1:.e tYto1et ~ ot'lbekevu:;4e opa"u'\l~,

Gw., dO()(' ~br~k -te. tWt~ VOn de Lev"j -'-'Ot""l Hisef' ver­

~9tM.vl~ ell'l de. v(oeivoor~ole. VOln VOI'l f..-tises.

De s.rte~veraell"q if') de. k.1eit"ls~e oloonne.ae. vet..,

de irek.'bl~ :

a. ,.·'f'lh ( n. r,,!~ ) CA..r :: slr\h( ~i.) C'L.. ,

l'l.7) u.~ = 0 )

iA.,., \A, I IAz : verpl"cdsit1Cj~sre(Wcd<Zr1 ,VI rCtctA:oJe I \Q~qevtHClIe (f!:Sp aJUdJe r icktU'~.

0. : " mcUd\e. snel~~1"\ VIet opper-vb'" J", c::le Ldeiri$le oIc:ot-sfl<2de.

1)e nroo{heol~ Gt,' evt (',~ ° -,) t. "-.J tA..u""EWl berckev(c( v.J~

~+ ofe. (eeo(s loet<.evu:::I~ q,-oothedE.Y\ vet." ole vor~crz.

defor~,esta.p" t-1:

(2.8) a.."" Cl.\.-i -.6a.:1

- ~o-

a; \.

~~QGUf\de vee.., he* ~~eV\ snelke.i.ds'\Jeld. evt \Xl'"

lokct1e volMlWtetn~ie k,u""EWl ~r eI~ c:te4c:r~,es!c:t.p. l"

evt elke .. ~ poslfle. j , de reks,.,eLhe:;l~ betek.0J1ol \AJorol~.

\A.,tf cle rekSl'1~ ~~ cle -fledte.ve reksr1eUtei.ct ~L,j kerelca1d

wo~ ( "B~laqe C ).

I ci I "[,.j = '*''"tr.) · V Cf ((" •• j • a.i. • r.) I .

\)oor ",V\\eqrt:cl.ie peA"' de~OitWIa..tlesto..p vet«at hler ..

~t: de e{ fed,e,.,e. (eU cds ~0!9 van deiOOW\a.l.le"St:ct,o \. op

pb.cds j" .1 £.i"j :

~t

i:l '£" ::: J A £: . "'J "j

OI."·i

:: J sii"~(li.)· V If ( lid" a;. • rL) l do.. Q" ..

- 11 -

'De 1&aJe e4fec.b0Je. cek op pla.ais j t'\tA de l. -de

~~r~esbp is~ykQQ~

(~!l'2 )

WQaf"b\:4 -e- . de io{oJe. d~f()("~e op ~cc1.s \ 'Voor'Ste.li J l.--f'J ~ I-·~..J

a(s qevo{<a \IOn de voor~soIA.ledeV\iS van het lWlcJ.e.r~o.a..l op

ct~ ~S. H\~der- verst~V\ we :

• \foorde.f0t"CW\oX.ie von het l\fV\oierLQ.ct-l, £:0 ,

• 9.c2.li.jktwtct1:i¥ rek \loor kef ~l'" IICb'l de V\.e-f-

u",,~ortYV\e olefort1NLGl.i:;.e~

• de ~.redleve rek -ler'\ ¥"~ \,JOt'\ voor<aaa."de

cle.lortWlO..iresi:o..pfEW" b~ "lei- \Ani~ortW1e: ckfol'.wIcx.i,e.

'Dc>or ~eb~ ie (YV\~ VOW\. W CW'lCt1e.r~ou:dM10-

d£.t \X)NL No.cA.o.:i. kat'\ I'\A..\ ole effecke.ve O(.Xl'nlf\·Ir1~ b;ueLc.ec"o(

word~:

- C l- t'\ 6-· = £,. •. ) "tj '-,),

'\AIQJ.l£bij de spt"e"t\eke tJp::;t" .. il"'~, C} er"I de. ver-s:le.vi<;} i""'3sexpO~ ,

tI\,. ~toa.l<jfcot-ka:fevL ~n_

Hd be,h",lp \101M.- de ~~JM:VI~e4A VOlin lev~ - vo,""

t-tl~ ) welke aQ..vI... diL \I(oeivc::A?r~ u:::&N\ von J..tise.s IIO~

~u"nnef\ de de.vicdorisclne. IJpclV\'" i fl9~ 'I t'l ole n::dAale,. -\ctlf\ qQ.v\ -

-tict1L 9V\. ~ ~ivt~ be4~ v.lOrd~:

- ~2 -

'Doc::>r de olevicUort~e 'S;pc::tn~',t'1~ ie ')~s.tih.te"evt

"tn de ~tct.ds(elcdie, 'l.O~ ctU. ct.Icaeleld. ~C( d<:X.)r- 'Bdd~­

lVV'GW\, 'V'I'td€M. .we ~ EWli-a r~k. de \ld'3~ diHe­

r~'cxa..L~~k..i.t1~ !

do_ = Ga (x) - 6;(?C' _ }{6~(<<' ,} +" 2 ~ (' " (} '" +' 'X~ 'X C

t- ~.a br(9C..) - 6 Z ('JC) J .

rccndvoor'\ilJOa(de! ""-1. : 6""" = S; ,

f· . '-'l - ,

Q..\.

'Door tlWWlerreke 'I~ ro1ie luIJI\~evt ~ """'" de ...antde

vaftl ole. ·\SO.stG\~·ISCIAe ~"'..iI"'i-!)(.OMI\p~ 6-''-oj bef"eke..-teva..

:1r\1eqn:ttle votr\ "l;.t = ri..i-'" tot "'vt+ ... = rt.j €evet-t 1W1et: k>e..-ClC..i. "' Q.i,.

pac:.·.fltlCj va" de in:lpeUu4(~ef. :

(9..16) OIM c.,j': G"", ()t" ...... ) =

:. 61W\ lx",) - 6~ ("'''+1) .... 6; (-x,,) .... t( ?Con .. , -x",){t("n.tI)T f(?C,,)),

-1:3 -

'De i,...fe«3ra.:t.ie loopt \let..,

tW\ef. a.to rQ;1civoorrNOCU'ole :

"IX:or SO'V"t~e \k.tr'\ de '1''5.0 stod: isc.\.Ae- ~c,,"..,i 1"I'l •

GIWl .... j ef'l de de1lic:::doriscl.e 5p='''''i~ \1inclev\ v:e de ?pan­

Ylit1~ ',,, de k.leV1sw c::J.a:,r-sna;le cp pIaaA~ J t"lQ d~C),.~ i:

6 " a f' '-.j

, Go,. i~' +- 61Wl -",j ,

?pctt"l\lr()~ , 6%, bekevd. is kart \/00(" e!ke deJ0,.JVVIC1-\..e~·l

t.te trekkmcLd, ~., "'n de ldeir1ste doofsrtEde be,.eke.t1ot v:>or­

deAN t,ie. ~eCl~ 1;)).

We ~eb~ f(A.;(. de a~ Lc.mcL..*., r-~, Olr't!> tc.Anc!ie ,

va", de U~tfor~s~eb-, Yt, ¥-vot"d~

_ ~c.., _

lM..tC3aaftde ~n Viet ~er<3l0'lstheoC'0WtGt. kan ole ~ti.~

<.)pan~s vetd.eLi¥t~ rtM. ~~ev&- ""-"Ofdevr.. ~ c4e l.c.rclc1.U

in cJe kJeUJste c::fc.x:>r~e {e IW\QJC. Vwt~ev\,.

~ 2.5: Het verloor' \leh' ole kf-C4clU ~\'S. ~..-d.ie

vC}.V\ de nl,*-IAI1I~orMM.{ei;tsp::u-OltW\eAer..

jndaen we voor eet'I defortn1Q.·be'StQp l. de opHtW1Cl1e

,,0- tAr1'4ot"N1M.-\:el:(:>patt:lM'leier.., rtept, ~evClr"'lcl~ nehbevt., \leAHEM..

we. cl~ tV\. cte voorqQarode V2N'~~~~ ;vt, VolClCU"iWlee de

ept~ ~n:xn.hEdeM., if'! de Ldeirtste dcorsvwa::k Jnt'l de. otoal

vosil i99ew.

VOO( keA u.-tt\loe(ecA.., Vdn de2c2 bet'eLc.e.M."'3etA- 'lijt1

co'Wtpv.:.teH'pr09,clf''''''''''S O\ONlw.e-u.q. ~ ~rou..(1-'tO.. (A 4UCX::(4)

v(x)(' bereke.M..rtjeN\.. actV1 o~ker(de ev'l ~VI (Al.4UCX:>s)

VCOf bereketM..nqevt- Clan ¥kerfck ~Clvev1 [6].

- .'5' -

;jt'l de (oop der i:~cl~ i~ er vee{ ~e ... -wek ~111

V\QCtr he! optf"~ \XlI"") breu.k i.., ee.,.. /Wla.:tQri.o.c:Ll.

'Bij het ~yt1S& VOlI'1 breMk tW\oe:f.ea.,. v.>e I2cLder

t""C2e "ZCt~ qoEd. O~~~e«I\,' nOMlt eti.f k. :

- ~i~ van bret.Ak

- w.{q"~ tot toble lo}e....tk.

Ee~ breuk be«aitVt. cwte* het ~s-ba"" \XlV\ 02V\. sc .... eur

ot L..ot\e's i.., een ~\.oa..l. OnN\ tokde breuk, te veFOO('-

'ZGCUC2M.- tVYIoet- er ~ de voorwOtQACl.L, voIdocxV\ -cijl'\, ola.t de'Z€

s~eu(' of Lt.ofte!> u.c.~ k.unt'1eV\ "'"-t brWf2M... 'j" de lWlee~te

~IIEW\ j~ hel tMoet\qk ~eid ie ~~ i.,",,':)~

{"ef. ~'fl \JaV'l breuU J de vor~ VOV\ ee.vt kolte 0( eevt

~eu...r <W\..- ~ \A.t1:<J~ ~l'\ tot toted" breuk.. 1)\t

lwMt ~ oIeze "ersc~Y'\SeleV\ dl.rect i'\0l QlkC(Qf c!)(l­

tredev\-, 'B'j c:U.t o~er7.Qek u.:Jord.:f: ac\"'~CMe- dct.:t he!

-\~d~FIP \ot:If'l he-t bcajl., vQt'\ breuLc. ~"c.H· lWIet Wfc:tle bt'eUk. ,

'Ue va:r~E?N\. Or CD",cL.\.tae.S ~\l00f" b..-evtk '1111

~ ~~a.t o..,;b~, vJOrden \JQ~~eid ',.., EeV\ brE'AAk­

l.Lr"o\eitM...... HeA br~f\'\er"""l"'1 ~.-ctt opqesiek:( QcU't de ~

VClvt O\ClnVIQr..te¥\.. i de ~If\, worc:.fes,v OMI\ het btetAk~~ te

bescL\t·"c:jV'ev\. .

'By ~e{ Mtwe.rkevt. vaVl \'€A bre<ALtkr~f:erlIAM "",crott

€EM b(~kfCMtot,e. ~orMMJ.~. roe b(~{<Avdle is eetA {fAt1die

\.IOW\ .. 'i:?eM- a.( CVV\ee.I' ~~, elfe (n~ he~ ofJ he*

brecA.~ vat'! E?eY\. ~\o.c::xi. He* bretAk(a,:\erLWIN\ is ole

.• ,

9reYI~waaAoe va", ole. bre.vtk{uV'ctie e.., ~ deze ~'f"EWlSv.XXlr­

de ~et.u:t ~ctt, <:a I de oalW1~~ ~n ~ ~ef"~C\q,.(

verlof"ev\. ~0CMfl. ~~ b(etALt1u~-\erUAI--t kct~ alOOf"MAiddel u::tvl

pr~ "os~ tAJOrdevt.., ;,., QeV\ c.ons-taV\.4:e C2~ \JQ~ het

CW\ cder'-ot.ctl C\f~C'MAkeU:1ke vXJ.CV\d.Il..

"Bij h"'* (!)pS{el~ I..QV\ bravdltu-\.tet-U:t. Li:jn versclA.il-

\eM- -te s"3noUef"eV\.. op PQS1S \oOV\ de ctClnl'\QMel'1 oi (V'V\ooIef~. olA2. E'-("QCXV\ ;eVl <3n:mc;(sbq &.q q.(W\; .

Gfobacr1 n.Ajn de tJO~de M-\ode(levl. ~e o."oIet"sclAei-

- 01 i s Ioa:::t:-l',e.. - (W\ odel )

hoH:e-~roo.. - /\'II\odeL,

- spaVlrl\"9" - CWlode1. ev\

- eN' et' ~ Ie - NV1:a::leL .

\leet onclerz.cek V\c~cU" Viet Ot'\ts~ \Xlt\ brE!AAk.

op bas,~ VOl." v.et oli.slo:a..t~cdd. wetd. ~<ae:lcu:::t.N\.. door

o. 0.. .......F.' Hott lio1 > S\:t-oh e~ Lotte-en (~-\<:15"+). '"jn cU! tWloct.ei

\A)ordi bretA.ti'It1lficdie verkl~ot olco,.. het verpla.a;(sen tCM

opkopeN'- \o.v\ dtslo::c:vlie s. 'Dc:::c,.. kraclA.ie.tt. ... aile ~ EeV\ vO{)('v.;2rP

""",-t~~ wordeAv .. cwUe¥\ ~ ;111 ~~ ~er~Q.t ?pat1l1t~

Drtt~aaw. O.,ck-r invloeol va'" ~ec:e SfXU",...i~etIl 'U.-f1/eNt ofiS'OC'~­

'hes t dt~ cdf:yol ir'l eecA lW\c;t{erU:xc::d OlC(rl~ ~V\, ~ck

verplc:c~. fr'ti1n 111 ~ CW1cd.eri.ctcd eck~er h.r1dernissevt

(Xtfltwe:u,q , ~oot.r s b~voorbeelot korrel<3fe¥rZEW\-', die ~et ver-der

'o~ van de aisloccdie.s verhlnaereV1. 1)e oti'61occct.kt

s

VlOpet" .uclA obar MV\ op &t\ \A!>rtWteV\ eev\ ?cM€AA..t'" "'111

- f1 -

~ecAr\lO"'~'3 dcor \Ae.t ophop0A

voW'\ 04isloccti..k IS

Mclint.ock" Tt""c.e;j, Rice (2.1'\ T~ [19J ortb.o\kkel~

4tModellet'\,ol.e als crzlW\~~Etql.te fad.or de c:c:lA~heioL

\I:l" ~ at Nrt~cA(ue hoMe's otl$ hastS tJOOr het Mtoolel haddet'l.

?j \.1ef'~st~ c*d It'l ieole.- tvV\~~ k;l{e'~ aClt'\~9

""1" OIls ~o~ """" ... ~{c~ eI'\ insl~tse{s. O"det'iY\uloed

VOl" de lM..i~~ belasti"'~ '301C1f'\ deoz.e "-otf.:e.:s v,,,,:t'3~

en er o,d-"Stoc:::i een gcheu,.. 'Z.O<k0l lW'esrciere hot\:e s iVl

efkoa.,. Otlef"<j'G'IIt'.'¥~. 'De \J€fsclM.IleM. it'l de. ~ode'b. ttljn ~'e­

~" ., n de VO("/WI. \.Q~ de no K:e 3 el't oCe. wCj 2e WQCtAL:J(l oIe2.e

\M.i9roei.ew. 1=lqWAJ S.2. 'tQ,CA.t ket eiEtWW2.fA.,t ~o,., T~o~­

~V\ ,~,.., fWtOcId ~~. Hg f1a1lM OQI't 0(0)( olE· ",",oKe's b1

Q.lkClCU' OI/lU ~OlQr'\ cioorctvf de ~~le b~~ i~ i-~

0+ -+~ o

o

-18 -

~.L -I2b t-2. 0 0 T 0]

fiqWM S.~: Voorstelli1l3 ~r'\ h~ eJe'W\~t WtllOti0t'J

ThOM'\Ol~ ~n lV'noole{ ,,"00'" "'e! breuk­

kr~ ter~tA.M bo\seerde.

Hu "erifietev\ VctY'\ de breuk,kriierLGt 1 die <3eht1~

'lA:jn of) de twee ~stc.ctY'tde Mflode.(J~;~ f"Ifei: CV\'\oqeL:j k

tMet de relcc..te.{ eer1vofActige ~ .. oe"''''9StWtethode'::'.>, dIe toe~­

pgsl:. ...,.vc.,. .. det;t. 'll'l de ONY\.vo"I\N\.~Y\olCICJle. 1)e'2Q ~rdEW\ etf\I..Ce(

uercmetcL, ~(' 'f'" de ~det"e. bescko~~en oc(d~~

~cd~.

Ii I~ oIeroe CGdeqot"ie k.ct1J1eVl we. de ~aerla.

onde.r~~, dfe qeb:lS6efct ~" 0(.) bepaa.kle co"""pot"ev\~

\la" ole I)fX:mni"9s'\oe~ in Iftet ~er~oo1, cite hef ¥volg

~ (\ \XI'" ~ iAAt ~ be1a.-:t i"~" H'~n/ch1 "Zljn de ~sie.·o

k.rae:.f'lU~ Var1 de k.(tH~e 1"\0000<MOal.~YI\~

kri\0"UAM \lar\ de k.ra;s~e ·,::.o'S~iscke "'fXl""'~"l~ ..

- 19 -

I-tet eersCe kt"i.1erL~1W\ nOfAcU- i.... c::*:d breuk i.., het

tW\a.:tertaa...l qe-lnHleetd. ..«>rctA: ~nt1eer de rlortW'laalspaYllli .... S'

pba;tsefyk eeV"l k.ri.tiscL.e Qt"I Mf\~lQal.c:4'hOlt'\~ke pesti:Jelie

.w~rde ~~"'4cU..

breAAkfc..tf'lciie : { = 6 n

bf"e.tAkk.t"i. ~,.i..UM: f .$ tkr = G"'f'

t-Iel at\dere k..riierivcl-1 s1e..lt clod bt'euk be~i~ it"\cItevJ

cAe -fSO~e. O~'~S~Ot1~ l.Ql'\ de tJPat"l"'II\'Y'~.,d, dee pfacd.setqi<. .,.., \1~ 4w,,:uertOOL.-l OQM~u..q is, ee~ kd !1seL,e.l

tm~t.act!a.fkQ"'kel\jke posHleve. wo:~e berei.L<.:t_

bt"e.ukfunclie : t "" 61W\

bret.A.k kri.terWMl\ : f - f kr = 0Ml\ f .

Als "lercle ~.., de b(etAkklt\et-~ ~~d) cite Cf'­

~ cU1t'l (!)P C2t1E'rCJiepr~t'\cipe~.

G .. lIetwlO"l ~telde clcd ~ ~t" ~ .... ts1:Qa.:t, ind,e"

ole plastlscke eYlen:Jie C2evl tu-i'lisc1e vJCtarcle be.re4..\Lt, dfe. vat')

he! lWlCdu~ ~ha"kel'1k is. [1J

c - n+"I

Hle.rb~ d.eMt eckier we! 0pCjeM;\erU te vo..')OtdE!.v\. da:t

~e. breA.Ak(W1ctie. 'Jeh::tseercL ,:;, op a:?v1 expor1t?('fbeeL versfeviqe.t'Jd

Ml\o.1e1"iaa.t (Nada,.-i). GiliellMo1 eckfer berloderde de

- 2.0 -

plastisc.t.e ~je c(oor L-le:t: lOp~\lb.k: 'ie ~ ~ de

k..£ot...f .... e jn ~et ~m~ vall') ole v.)Clf'e n(Xl'V\V\\"'~ Qlf'\ cAe v.:nre

rek. H~ sielde h,ervoOf"" {Of'MM.A.Ie.'s op. dre e<avl .Je'¥lC:~.der4

<3e~ voor dLt q;¥>ervfak.

- 21 -

Hoofds.tLtk lJ : Hell"Herw4Nt va'" de (.Lri:Hscf"e spec."'ffeCLe elasHscfAe,

. ex\e("g,e.

'jt')d.~ <2eVl llckcolWl befast WCIfd.;t, cia", ~ da.t ecdAGlOtIWl

ven/O.f"~. Als de bc2Io.ShflQ ~r«7l q&"IOEtj ',s. "2.c:t1 cle \JU"\IOr~~

dIe. optreatt, \/Glf'l blijvevde QcttVl ~n ~ dc:t:t wit ~~ ~e:t.

ltdAOIaNVl '2.a.l tU1W'l oorsprot'\Ltel~ke VcrNV\ va.ef lW\4!'er ao."r1eM~.

\lX.tt'u'leer- ole belc:vltit'l~ wEtJ~ ...oorct:t: ~et lickoolWt l S

f(Q~f~ \NU1JC)f'iWCA. 'B~ he! opvoen?vt \.A:I'" de belasti"'~ a::U.

op eEW\ ~ 'WlON'Vl0A.t <2en sc!-teA..U" i...., l-Jl.f tW\cderic::u:d

ottlsiaavl, waarnnee de:' '3re"'S va .... de Cttl1l1Of"""", ~~

\1001'" Viet <Wlcderta~ berelk+ is.

VO()(' cAe \IOf'~ va., 'U)'r') t)c1tetAr' is e€V\ ~~­

he\ct enet"G3;e t\c:diq" 'D<:or de v...iiWE?N1~ belc:v.iti~ \AX)roVf;

~;e ~ h~ ~\.ru::t.t ~rol. '"De €\"let'C3I€, d;e

~oIeAIIS e~ OW'\vorCWIproce~ word.-t ~d. kLtv .. '\fW\.. we o...d&'

.,c.k1e(d€4l\. in

- plasf\~e QA/\et"<3"le

- e1astls.dAe eYlerq"ie

1.}e' plasHsc.lA.e e¥I~je c::)oai \X.?rlot"evt.. ~ de de­

forlWdlie \fa.., L-tet lWUXieriatd ev'\ ~ C;3rotevtdQQ.ls ~

itA ~1:e. He! re&tat"li: \/0'" de p1GlSusoL.e ~ie U30rctt c(oo,.

~e! ~iacJ1 "P~ et'l \.rQM.:t iof- tM:tdn..d.t.~ ifl biJv«.>t'­

\oeeld.. ~ tQeCf\CNY\II€ ~ de kc::ud.ke4d.. \,DVl l-u2t ~k:t.c:tl"

<D~ e1a::.t,soIne enetl3~e blq{t lfl ~et ~erL.ocd Qal't­

weuC3 eVl ~ "rg \AXlKrleer de belastir1Cj \..QV\ lAd 'icL.OQ<'IN'\

W€qqenotw\BV\, ~. 'Door ket <1?pvoer€N'l,- \JOVIA de bettWti~

ctNtlf.eM. ole hoe.veelh~ \10M. ptastisofAe en ebsHsot-e

- 2.2. -

~,e .,,, I.tet ~~ t:::e.fV2AM.eAA.

~e o"U\AJ031i1Cj€Vl 1eUltZA/\ ~ tot het opstC2lf€AA.

valli !/let k,i:..let'i.wwt \Jc:tV\ de l,u-i.t·,sc!Ae spec:..l{,eke elastisJ".(2·

eret'C3ce :

J", eeY\ ~ia.a1.. wora;t b'feuk

~r\·d:1eed. '"clie.-1 de spec~~Lle

e\a!>t isclAQ er'\erq~e. eeV\ kI"ti.'S~ €

QV\ valf\ \.tet CWlaieriqal of ha.,\(elyke

lAJ()Qrde DereLkt.

'By ~et bep::tl~ UlV\ de speci.i,.eke <2.1cv:stiscLte

EW"ert:J.e wordevL de vol~e "e .. o~det"SieU~~ ~;

• tVWliet'wa1 e"Po~tieel \1e,.ste,,~0OOl

• ehsHa:.t.ei1s~odM..llAs. E .. is C:Olf\stcu1t

WO!AV\eU eelf\ tre\Lst-aa.(, d'e. plast,~ \Ylr\JCJl"fWId.... is

ot"der 'IOvloect \1CU\ ole belas.t:i~" ontlast ~otd.t I '2ct..l ole~

elasii.scLt 1B"cAc3 V€fe&;\ • ~E! C2la:;>-tisd.te erte f"'<3ie. I olie. op~bs2n

is 'l(\ ""e;t ~er\ota.l ~ d:x:lroH v~\c.onM~.

Als de-zel fde bebstl.n~ v:>eer op ate stc::.v::4 ou:::vtCJ2brackt

wot'Clt 1lAA1~ 0r e",lAet etcv.Jtisof.,e VenJ~)f·~c:levt. op tr~ .

TIe ~ueel\-teicl eIQsti~e. 0Aetqie, dte. daa."bi1 ~vc:erd. vuord.t­

.. 'So ')elqk oQl'\ de <2~ie I Ole V#"9 kW<l1W\ b~ het OvltlaSfevt

Veb'\ de otaa{ etl\ Lcalll QeY\volA~ bere~ V\lo,.ae....v.

Voor eell\ vclA...tNvte -e~EM-\:~ 'I~ de. ~t~f kccr'l de

snu.atre uerc:tuAdelglct worcJ.Bv\. CWle* ~p \.OYl he*

r 6

- 23 -

~ratW\ UCtIl\ ole ef{.ecbe\e rek. eV'\ de e{ fed: le"e S~"'Y) il)~ .

Als ole Qfaa.{ be1ast is, Lu..tf"lVlev\. I.A>€ de sHuaxi'e u::tVl

het- ele'lN\evtt}e ~erqev0'\. door pc.AV\t A op de l.u-ow'\lWIe.

r (ldien . .de ~t~ { VUA or\.tlast vX>rd:t·, d()Or-loopt fflet vci .. ,vWle­

e\e/WleV\.tie- de si.~ie '?DCtIs ~<2is1: ok;or de sHppellqf'l

(fi..qtu.Lr 1I.i. to.)). Wanneer de skxa{ ~ ~st wodt. 'WLl IneA:: vd.u­

t'VY\e-e'~)e eer-st ebsHscL.. vet"VO,.()'Vl~ tot Qan pCAV\.t A

eIIl cloa.rna. pk~stiscl,. vetder delDfllM€revt. l fi<3w.AT ~.1. (b)).

lOl)

I

-£.

I I

/

I I

I , I

..

f I ,

I I

I I

I I I I

I

( b) (c)

riqUM.( '-'.1: C;cl1elW\c:d;iscL.Je. voorstelnt'l9 \lOt'} de sl,h .. -

Ott.e VQYl <i!eI'\ volcA.wte ~\:)e if'l €01

tnak'S\aa~ .

'jY'\ ~)<.tr€IWIUM kaY! de -t:r€ks~af betas-{- vJotdevl -lot COn

het ptAlI\t, W~.- VlOCj net "jle'l\ brevtk Ot1s-tacct it") net ~ri.Cta.(

vco~~e{ol door PtAYd "B op c:le "Sf"U1n,~s- rek ~e. ( fi'jWAr '4.1 (b).

- 2.~ -

HlervlQ. worat c;te s~ oV\itlc:;\st.

Ris we de steal jM.A.. OPJ1.e.w.v ~laslen ·u .. dleJ1 cle. \Je("­

VO~~,.,~ elQstls~ z'j'" \:ot CfJ lr\et ","OIM'1e.wt v.JQ.CUo(J ole b,.ec,.c.l.c. be-­

':jiM- ((iq\A.Ul' «.4 .. f (,)).

'De ~peci..f,Ed.te elasi:isCke ene~le lean r\M. bere"'evad.

vUOfclew. H,e.,.loij beperlt~ we o,.,s ~t\N\ClkshCt\ue tot sIe sift.tc:d.e

i.-l ck hoorctriclAiir1~ [a]. W'C2 "itl~ obrl VOO,. ole 'Specif.eke

ela:)~ .... scLte enerqie. ~ lNse :

(4.2.)

(~. 3)

VoortS NV'OltfM we ~br~ \.0,., ole el{ed:,eve C)(JOrJrl iJ1'19

uo{get1s VOfl Hises:

- 25 -

Dcot: i rt de (da..tle V<:JV'I ole speci.f ;eke e.last:is~e eYlef"­

gie, (4.1), de t"ekkeV\ te elitwline.-eII\. door ~elg'dYl~ (4.2)

~e "\Abst:i.ta...e~ verl4r'::j<]&' we 1'WJe* beklAlp \/01'" ver9".lQ-

k(flg (\4.3) eVi (\4 ..... ) nO!. enitj r~k ole. ~ck reb-

-tie \o'Q:)r de speciiieke ebs!is~e eret"9 le 0.

(4. 'S) w. . I r ~(1+11) -'1 '3 { 1-2V) 2] .::_- 6+ G-.. S.. - 2 3 C:: E -.- • .

~ rela:.tie 1.uAt1l'1ev\ ~ vetder \JCi!t'ee¥'\vou~ cIcot­

~ vol~de elas~isck <3rClOtt,~ ',.., te ~)

(u. ":I)

(If.S) ~E=

"J.-. deze rebtie's is Y (Spfeek vc.At:nu.) de dWOrsCOVl­

troctle.~f~ van tpo·~n.

""jn dE kow\pu.-\et"'proc;)fQM-1N110'S v.x:>tt:it \A.it'3aal'\de

VQf(\ ole lWleet<J~S de s~ffelA.e Glasti:sc::l..e ~ie ep

elk€. p(cicds 'f" de klei.tlste d(X)('SflEde vee.., de.. treL<staof bete­

kevtd [6.].

- 2.& -

~ het cf'ldenoek. -u;x:tls va'" de.... A voOrt cAM op-zetle.

worclt de \,AJOCtf"de \X:4('1 de isosb:::U:.is.c:&e ?pantlit"lCjsCOAN\ponev-t-,

G""",) be.i.r1vloed door ket'vevt in de stao.f CCC*Y1 te Ioren~e¥\. ~

v.x.n:« h,c.t"door verh:x:qol. 'De ~cvu::I(2 VQift de i~is~e

')p:1t1.,; f'l~pO~ ~f'I edder verl..c;.lo ~ u,>o,..detA. cl(X)("

treU.p"'oev~ u..it (e vc:er~ onde1' ~ ~os.\:c.t.t iscke

dn.ALt.uew.

s-~ beJOtl-:3 f LjUe rol in cUf ,-,oort oYlderu:ek wercL

~pee!ol door H Lf. l>. '"PuCO h. ~ze Ot'l"t::.....,cerp ~ ar~-,

1M%lr~ trekpr~ ~A:t~ ~d~ ~evt or'lde ...

ho¥ kodrostcd:lscL-..e d.f(A~ tof: 1'2. '200 Gt.~CW\. (~ -t. '3 kN/IMtWt'\1)

['3]. 1)e reqisVcd.e \XlIV' ole treL<k.faclA.t ef'l cAe qeDtWlet..-ie

\A:lf'l ~ kIei"sie dO?fStJEde \lOin cIe '*oaf ~Ieal ~ behulp

varl rota's, dee tgolens ole tcekp~ va.., de sbclJ ~tW\a:au.t

wordEM. ( f '9\MA.( 5.1).

'De voorde(eY\ \.On c.ti+ ctpp"roa.:t iert ~1.e. \XlI')

de appa.raio-t, die al aerder ~ ~, ~ t~IECt.i9'

Ie., ee"s~ is ck tWlel;~ \)''''1 de trekLu-~ or ole rroe1 Q\~ beirouwb:lctr ~ er ~cl ctoU'\9efoo,nC( ~ de at~gk...t~€o'l

ook Joij "09€ ol,.~k!.tevt .sIeck:l.s ~ri.""C3 ~".

- 9.'1 -

Ten tweede 6..., de ~tYVIetf',e \Jar') de. 'Insr1oer,-Yl~

"an de sbaf bepc.::u:t!ol v..:»ot"cfeN\. J -v::>VlC'1er cia.:( de trekprai ie1-

~ of1de-r-brO~ d.e",t ie \Alor~.

fi<](,UA..r '5".1 Rec:Jist..-ccke \1OY'I de tf'ekk.tQclAt eVl de

¥OtW\etf';e ~t1 de k.feit1:s{e doorsv'lE'Cfe

\;QV\ de otaa.f ~. b. v. Ioto s.

~ H. Le. D. P"'9i.t J ~oar oOk door CI~ ot'"Clev-­

tcekef"s werdeM.- vOOf' dillerse 1Wl~~ vekproov0v\.

.~~o'. b'1 \Jersclttil/€Y1de olt"(..(kuevl.

- 28 -

~ c{e bere~~ va." ole fe,)uLf..aievt. wet"~

de "ol~ otat1V1atW1e1A. ~td (VVlet bei,.ekk:.i.n~ tot de

drcio~e en de sp"n"i~verdeiil1';r

a) de(orfW\a..:t:ie: 1)e defo,,~a.:t.e i~ Ut1iforNV\. Ujclevl'S de

~e ir<2kproe{· el1 deze woldt uadqeleqd door de

af\ai(..(.AA.r(gke reIL.. E.

Ao: begi"docrsl"1ede '-0" ~ Q-bctt, A : tW'o~()e Wei.n<ste doc:>rsne­

de vaYl de ()iaa.(.

Af : k.tetnsle doorst'lE"de lJCli'\ de ?factI h9 bretAk.

b) '::>pctt1""'?3s~elU\~: 'De :spal"l"'U1'3sede~ is c.4l"1ilot'"llNt.)

Oat wil "2t2q~ cor1statd 0Jer de ~ele ~ ,

{ot o~ ~e* ~ttM0A.t v..>cccuofl ole fJb~· beq,r1t il1

{e ~V'oet"etIL. \loot"' cAe de '.nst"loer'Z2>t1e ~ qe­

b"c..AA..k ¥tWtoctk.i va", de t)pa"t1i4 svetdelc:."'9 I

(s.s)

-2CJ -

IT .... ['+1 .. (12+20R_,2)]

I t\ ad

1_---t---4--

£""'""1' S. '2: SPl't\nii'l9s\lerde~ in de If''\ snoef"ZO tle

\,1Q'" eetl\ trekstAc~T "Iqs. 'B('\~Nl'\dt').

6" (1 .. tn («- +:: -r-) J + P

G,. = Gf

S 6., { t. (+::-r")J .. f'

6 2 ,6 r ,orr ~ ~ootd~~('\"tV3 \'" c:uda.\e, ~cUale resp. \af'1C3€V'\t\ale ricktt"'~,

6" : vloett')plr'lt\'V1<;1 VQt'\ \1et tWtc:deJ'~,

a.., Q. : ~OMtel(ie. \lQI"\ de ·,()sn<::.letifJ,S,

r : (odAa.le (.Qdrcl..UlaGct' ~

p ~ o(u.;~.e uekspat1v\" t'\C.f., Q.k or de "3tt.4c.c.f worclt t..U.1~oe{&ill voor dr(Ak i~ p V\&q~).

- 30-

'De wQorde VCh,\ cte ·,'SC)slOl..\.i.sdAe. ~1'1.1"I'I"l<3S(.O\N\rOo'1a4. ..

G_ , 'I~ 'J2'~k. OIQI"'\ !

( q? +2aR - 1"1)}

= (C,V {!... ~ :t.aR + p

en aeze h ~cuc."",,ou:::d. i." he*. hCllrt \J0l'" ~ :!t~. "'De ~G\.rcle

\,Qt't 6M1\ ,.,e~ af b'j ~etW\eI'lde. oIrwk; p tWWtet" twe~.{.

~ ctoel va" ole pr~ ~ he! bepalEM ~.., ole

~rek, f-l' als f"""'cLe. \XlI.., de ¥f'Cs\Q.tiscLe olrc.A.lc J -p.

fM:i: het Ot'ldet-aoeLc. bleelc. cb.:l ~t;'l9 ~ de k.~C$~~e

dt-f.A.k br~o.. ~Lt1:.1 cAcd wit "ZE\':jqevt QeV\ 1.:::ena~

\.0'" de ~rek uet"~c:t.u.t.

SO 100 .zoo 100 t,()O 500 600 '1t:IO 8co (N/Mt /)l11 )

5 500

! , 4<0

- ~ ~II J

! 'i

1t15na

1Uhn·SI.IIVED ';:"_$IUM CAST _

10 10 30 40 iiO I>Q 70 60 ~ 100 110 "0"0'

P 1I'I'CIIOST4nc N_ - "I."

~\.\L4r S. 3 '. Grafisck VCX)t".5teJliI)~ \Or') clQ hrec..tk rek.

fr als Iu"ct;e VCb'l ole h~;~e.

otr,-"k, {>, vO\'3e.1S 'P«.t<jh [S] .. Re5\A.~ vo~s ~~5 [9]

- '31 -

H. 5.3. 13e::erekUJ:;r van de r~ita.:te¥\ van de t.rekpf"oe.JeYl

o11del' h~ d __ lAk.

'De resvlHa..:l0'\ va..., de proeve.Y\ o",ol~ h.~ olruk k..ytl­

n~., .. i.., ole vorlYlA wac:Uu., -ze C)€f'"e.sEWl\eetd 't.Cjt'\ .. (lIef ~,.~kt

we>rd0A- voor It\et of"ldet"~ .. 'tOCt1s d.a.i op de TI-I. ~qevDrC?i'cl.

worat. E"r kalfl sla:~s ~~~d wordev'l- dcU de. t.e.vdet1s~dai

de breuk('ek .. £:r, ~ ~~ de 'i~i~e q~r7l:JS­

c<')MAPOt'letAt, 6""", ' • .., he! tlNlC.l.Aeri:.acd aft'l~" v..At beide.. Otl­

c::fer-z..oeke4A- naar t/orevl kowl.-t .

13eide onaeM.OtZ\.c..e.., he.~ sleci&is -\:v:>ee" p-1ntEWl"

~Q?M, , waru- tWl~ ole r~~ voor ~ be(:na..«d twtaIe­

rtaa1 ."Met <2.lka<1r kal'1 vet9eUjk.ev\. 1)lt \S -\en e~.fste de bf'&.·d .. <­

flelc. vaVl eev... on~e imk~, t.M.t~ on:::ler cd/WI.os­

~ec',s~e dfuk. 01\- ~t~~ \.QYl lAni{ortWte det01'lWlatie -f'j­

~ kQ.i trekprca2s. T eYI twea::le .~ he! CW\~Qlij k ONV\ ... ""'-.t­

~aavt.cle. ~ ole rt£Sul~ \JO.VJ beide onolerwekevvlO rAe

~cU \Ic:W\.- olQ.. ·asostatisc!e opott,..i~qs~poneva;t.~, II ..

{e berel.t.eM.evt, waar"Q:)r brosse 1::re.cAk Op 1.£)(.4. ir.edEWv. +-lIbbY

oerstaall\. we oJ'\Cfe.-- bt-osse breuk:. obA Qr brecAk op1r~ 'W~er

clctA kel tlM.aJ.ec-iaal pl"stiscl-t \Jervot"lV'V1Q\.

J..feA is ~d. dct::t ~'" ole ~et.f"ie \Klrt ole in­

St'lOU'i"CJ 1tjc.leNts de irekpttl€~ ~t \IN>tc:J2legc:i. l'tIV\Qa.r hebc.ts

tt.i:1 (\ deze ~.e~ nlet ',tl Ot'lS be'l..H:. No. eeY1 kJeine

W~'I"'3 "v\ itJei progra..."..o. 0""" ole. vVOatde \,CU'1 de lrt~drosfq­

tiscke olrCAk l(\ re~"n~ ~e bcen<3evt. "ZOL.(cI~ ole-ze ~3

verwe.-tU- k.u ... vt~ wordevv. Hlerotoor '2.0'-'\ heA b~k va.., . ~e breA.,k\,y.Vlci.e's O(cu'I't.'eVlly k tM+¥brei.d \NOrdevv.

-32 -

1

"£ (-)

f'9<.AAAr $.4: tMt ~r~ llat'l het b0-ei.k. votV'! de

b<~kft.All'lotie door het ..M.t~ vct;')

t<ekpt"OeVeV\. o~er h0C3€ oIrLA.k.

fr karl ecLt.ter .",et \1ef"wo.clt.t v.JC)rd~ dak cjoor

he! bet:nSSev1. VClI1 ho'3€ h'1drost.a.:.ti~ drukkeVl de isosta­

tiSck€ t')pan"·1w:J8C.OM1~ in de insY\oe.t"t~ '-'011'1 cAe trelt:~

neqa;b~ (<3root ) vOOrcLt. Uit ONV\da.t door de hcc3e d,-w k. de.

s~ct{ uetder 'tll -zal sn~. "ei~ <2eII'\. ~"""e UOIII'I ole

·.sosto.i:i~e ?pa"'''' iYlqs c.olWlPO~ 'lot ~vol9 heelt.

- '33 -

By ottuene N1"aleri..aJe,.". bk:ild er e0'\.. UvtecM.. ... ver­

bonol {e be:.-iaQV'\ tAs:3eJV\. de h'jol,.o~tctkisoLte dn ..... k c.n de nQ­

h.uA.dqke f'ek ~ bt-euk. (~ie ~~~ 5.S).

t1. 'Bra~ steld.e Eevt tWleU,c::de UODt" OI\N\. ~t'jQQnole

VQ't'l de-ze lirJlE:!:l.lre "t)er bt::a1det.... de .. bros:se -brewk -stertde" :> Ro )

\e bepaleV\ [11]. 'De "bro.:sse - bre«.Ak - s~e .. \.c!e II ~,.ctt hler-

b~ c:JEdeflVllee .... ol cals "I'.ij~e ole lcriHscL.e ~role V<:C.VI de

V\on~.cdspa..,~i,,'3 ~ die hrec:AU \XM he! tl"'\a.ter~ ~3OIQ.Ltt

ZOIt'cler dc:tt- plasHsot...e ver\A::)~g op~{teclEW\ is.

;J"..d,e,., E'en ah.lj~ tceW.sfUl'I",i~'l """-tqeoele..d. ..,.,otdX

f!)P aall'\ tfek'5iao.\ do", -zed de ....,aa,.oI.e VOCIfl ole h.o:s.to.t:bcL.te

?fOJ1."it'19SCOlW\p~ ,,., de ;n:st10erL"'~ ~Ifl de st,Qa.{ loe­

"etW1e.A. ~et P (<3roter c::lc::t,. 0) tot ~

( 6.1)

'De de,,\cUor·,~e t')ponnU'\~" welke vetaW'\.;'woardQ{~ k ~.,

Voor plast'ls~e "ervo(,l\M.in~ # "Z,..c..cl~ VlII2t 1JBI"CV'Idef'eva. Qb <3e­

\lol~ van de2e al-r.gge 1:re.USfXlnn'1f'l~ .

..... ~' 20

f to "

~ ::l--:o,'r-~--:rJl.c!-;-1-0:t;;'6-o.:t;;8--='=I'O-~\~' ~ i', iJ

-30 ~ -40

fi~V\M( 6. ~: 'B~(Xllli"~ vQt'\ de ~htf~ e tfek/J~"ni"'~

,,{)Or bross.e bfeuk. d.H.\!. l2.XtfClpolo..tle.

- 3"1 -

13rOloole.s no"",", 0lQ.tft oUxA het ViU"oonoi ~t .. l(p} ~­

cUr bl.i.f(t \A)Qrh1eef" Eevi Cfhij~e tt'ekspcaV.I1in9 op de O+o.a.l

word.l ~5I.A.perpotiEStd... 'Door ex:irCApo(a..tle \lain de '9" ~(.c I (p)

noar de 01.5 1 waarvoor de bre...tkrek:l tf' ~ k QO.Ift l"\.IlA.l is ~

~l'\ de ~de. \A:l1>1 ate alUid..i.qe ireklJpo.JWlit19. po, ve,.k~ lJOO('deM.. I.AJCIOlrllt:JOr EeV\ ttekl)ba.{ VOIn CI.1EW\ of..c.A.klle.l (W\~eri.ota.l:l

i,. CC)lWtbinai.e. 91'l& d.e eenQs:s~e treks~lI\in~ • 6Q., bros

breeJ<..t (fUjuur b. ~ ).

De 3pq"nin'33\1et"~ in de d.oorsneole \lC#\ de

I")tc.a{ , ileA uoor-c*:Lt breu.k optfeectt, uef er oCan ales vo'9t

t.U..t :

l Co. 2)

(6.3)

H\e,.b~ ;5 ~ de QJelo..le t')rnrU'lifltj Itl de. dcor.sne­

ole ., de Wzl- ~DI'j is \Xl1>1 de i:.relduClCkt:l d.€ op ~ .7taa( w.t'5eoe(eMd.. '-'lOfdt. 'i)e'l:€ 'I~ in l1el tjf~'3~ ~9k. octtll

de vloei.spalftVli~9 VC1~ ~f t\McdeK~al.

'De trelc.sterfde \loor bros.se IotetAk J f<o" \Jan ~

olM.td~l ~erlaal is clus ~ety k Ci\QM. :

(b.y)

- 31 -

13mrlde:; berekevtofe OF> dez€ ~ ze ,,00'" vet"sctu:lleAA­

ole IW\cd.erta..l~ ole bro3X - breuk - oterk.te l tabel 6.1.).

Chemical Material composition, %

and thermal treatment

Steel C 1·0 LH-15 MnO'S

Cr 1'4 Annealed

Armco C 0-03 iron Annealed

Steel-20 C 0·22 Annealed

Copper Cu 99·5 Annealed

!abel b. f

Mechanical properties at atmospheric pressure Po Ro= Reference

Po + R. Re Rm

kgcm -2 kgcm-2 Z% kgcm- 2 kgcm- 2

4000 6350 62·0 9200 13200 35

1850 3250 73-3 3610 5460 47

3410 4850 68'4 7490 10900 38

-500 2310 84·3 4100 ,..,4600 38 .,

Re: vloeispat1r1il?<3.

RIM: trekst~dde ,

Qt1rtEQ \eGi : %ctCkt qeqloeid.

'i3ros~ - btevtk -s-led,de vOO" et\\.ce1e.

~e.-i.Q.'0t\. •

f)c~lt\N\ervteel -roud~ we ole bro$~- bfeA.Ak- sie,..L4e

lu.c"'t)eV\ bepal&\ ciOOi' ee.t\ tfekstC\"'-f CI x.icxa.( {e belc:tslen. 1W\eA:

~tM. 0l1C.\a1e <)fX't1t1t~ ioiotM re:t ~ vw opireedi. e:-o

et\ otaart\C'. eet'\ OlJ-z1j~e {C'ek'fX't1n;~, p, op de ~ Q(i\~

"e bf~.€AA- et'\ {e ver~ tot de WOCI-rcJe. po) ~r b~

cle siaa( breewt.

-36 -

Hoo{cfsiuk f.: tproe\l~.

In de bajiVlfase \JOn ole sif"lCish4d,e .......:IIi!f'cle".., "'fer

trek.proe\lS4l\ 1Ai.-\~cL Anet I.lf.fs s8. Hat- doe( h.er\JQ~ \AXla

t~Ied."3.

Ten eersle d.ende het a's ~ eot'\lrS Ie '"'oot' de f'e­

pc-c;d.c.AcQad:nari1eict ~~ de ~etVqev1.· jt1 €eY\ ~('der stoc:::t4.u ....

weroleltl rJQlW\e(\jk exl P(O~ lM:t-~ I\""\et kHs s8 ~

A. Lo..llr":j S'Sev\ [2].

Tef"\ ~e ~ote.., ole-ze p~ qec:tQo."'. oNV'. ver­

tt'"OrA.wct ie rc::c~ M1et ole M-1~"ocra:W.re Q¥\ het- ~('....cLk \JQII'\

de C,OtW\ pu.lerproqn::fq\l\/WtO rs.

'De (\'\I\ee:f.c:fq~s VGln deze pr~ "irxU: U i..-, de

~b(~hG\rd.~~ by ~e r~a::rMMa's (6J. ONV\ota;t e,...

slecfAt5 4 {rekp(oev~ t.M.~cl %~n., worden de re'!>L.tIta.b.

Vliet verwerLtt. 2e \NOrolev\ slecf..c.J.s i~e1tQc.;td. ttl ~ <3ra­

flelL tmet breuk{ \AY\cl.e~" "'toals G. 'B. Ht.U..siLe.ns d.e. op­

steIde (Bilacae 'B) .

"j", eelf\ lc:der stacl.UANVI t.Nerd. ~ k.otMplde

iW\eet~dc..4~ a/qewet'1A..t VOOt" A(\AfW'\ir'lifAM1.

Ma:f:erlaal9€9ev~s·. AIWW1l"'llAM k.~laei.t 2 S,

~q.o ~ qg.\.(q % H', McderiacUnr. 3. 0'20'5"' "

'DiN "'1-4"1 / NeN 6031.

Noda.t de proe("bafF \Jei"vaaA'cWJet wa.rew. ~€V\ "2e Cj.edu(evtel€ 2 ~ (A.M.( ~Ioe'ol b~ eEM ~~a..tc..c..u.1"

van :t:3 bo • C i..., een \IO.C(..(\"(f.i O\lev\...

- 37 -

De tW\ee~vens VC\'" de trekpraweva virdl tA i.,

bjk:t'¥ ~.

T~d01S de elt"lCistuolie '!>{ui.t{e 'Ik ook op QE?lI'\ n:xpport

va'" H. T. r. leeYlCkr~ (f2 J. HErin"tCj Vl ~~s o~­

n()'W\ev\. va.., i.rekpn:::e\Je&.1, aarl o"'~"lde ob.ve&;t.

'De (W'leet<3eq€\J3V)s van de proe.VEM- lWlet c: .... $ ~I?M

iWlet het c.oNVtpvJerprC".'9rQIWtIW'lGl vervJcUld. "De re:.uHal€vl hler­

van wo,..devw ver~e.laa"" CW\et de rescAt~ vet., de trek­

~ valft G. 'B. Hl.A.is~s.

-:;8 -

G. 'B. HuIsk.EwJs ovttw.erp t~ c:..OnMP~Pf0<3(aHt--Q:'

v..xx:u-~e. VlA:tcaaot'\cle tXt.., de ~~S ""'.., de trekp~,

d,v~se qrClG'lhrcclel<1 "In ole? Ldell1S'le c:fc:x;r~ va .... de -(rekS'~

~ k.oI'l~ ~et-\, ot,) bexsb \10\"1 cae ~ze de(c.,.~ ~letVV\ethoole "

~n OeZL pn:~rol"'HQ" ~n Q4t\kele. ~~~il1~ aWl­

~n:;.ccWt 1Wlek- be:tre.~,.,'3 tot!

• te lc.rodAf bere~'r19 ;11 cIe klei",sfe. olco-&~ \.bn

de 'S{a~.

• ~ kec-rektie va'" ole kerf~eL-,e ~ CAI«, \XIY'I

"'e* Icu:xis\e ~pveJl\t .

• He;{ q'-)t~soc.:.t:,e - prOCe.3 ~ot~-z. het ~","~ise'fl9.Y\ .

vOY\ cJi2 k.rcxM otis i'-«nc*ie vem ok? yt~ - UVl'.fC)("~-

4.el.i $p:1lrc;t....e-ler I F' = F(¥).

• Oe ~ek..e.a-t~ VOl"" ote .. ~.e.f.<e pbstiscLte ~'e .

• Dz· be~ir1~ \,Qn de ~.eke ~e ~e.

• He;{ ~~ va" de loerekevlOle 'l"1~s.

\k.tder is _fW" ook Ee¥\ qzlof~ershot..-dIeicU..If)<::J b'j de'2e pro-

~rocNfo.iCf'S ~t'eNeV\ [6].

HeA: de ~~afe progfQMMGt S ~~ cAe ~Eet­

c;,~s ~ekevtd.. va"" de l.rek~ 1YW'Ie:t de 1Jd~­

oe ~er~aJ~ ~

C 45

E"lec\-ro''dti5~ looper

e. lfS

(6. 'B. H~\.skevJS [3]) I

(G.B. HyiskevJ$ [3]},

( rl. T. T. 1.eender5 [1'1]),

l-<Ms 5& (HC.E. f<ei3flt.,e.S (b 1), ('B'1IQ~e F).

'De Mt:Voer \JCV" ole"2e bereken'I""~ i.:. ¥bytl"\defol

i(l E'eVl k.b.pper I v.JE.Ike ir'l het be-z.H is va" if'. ~f\.6. llcJ~.

Lu..t- ote M\ee;t~S \JC4J1"\ -trekp~ a.Clr'l de 0"'­

¥k.erfcle ~ uX)('~ de vol~ole. t\M~gf'Oothe­

d€Al\. ber~ol: KQrdkter't'Stiei.ce spann'It1Cj, C!.,

VU$-\;ev'~"'<.;5e.ltporeKt.l '(\;'

voorde{or~.e, Eo ('B~\Q<3e E).

'De ~rcc:*le "a.n cAe (2.bs.Hci.{e.ti.SMI\odJ.Alu~, E en de. owoY"Sco,",,-

trac.!.ec.o~ f;c.ieM.t \A.Jl2t"cleM. ~t de hoc"C:Ux~.~ qct"'OMBIN.

H\.4ls!.tens ~'S

C= f:1&2 ca01 - (N/tmfWlt. )

n= 0.21 0 ... 8 (-) - ( - ) £Os 0 0

E : 21 ill> IO~ t'" 1,,~2) V : 0.3 ( -)

C= ,",00 ( N/IW\IW\'l.)

n: O.S l- )

~= 0 l- ) t: 1~. 5' .,.. 10"4 ( N I M\/Wl't )

v: 0.3"" (- )

-1.{0 -

AluMoit~M C= -4'2.0 (NI""",tW\1. )

f\::. a"f (- )

- (- ) Eo= 0.1

E" .. r *'0'" (N/tWttIMt)

v= 0. 3'-' (- )

'De v..)Cl.Clt('* de. \JCIOt"' de voorde~ot"~ie .l.o, van

r:\\\..4tWlin1lAM veri~e eevt '3"ote ~,~.

jn l:l(C((,ef" 1. -6j1"l <31"C1Of.~~ ~ttseuet dIe ket breuk-

~dm9 \101"" een CW\a.Ae...~l bEpale4k. Er i:s. ~-zen \.1OOt" de {~e

\Ian GidkaOlf' OY'l~hQtftLte(gke., 04ill'Vler\<SIElcze ~ n::x:*heole.-, CS-/c:. eVJ

iI/~, dee cp he* M'tolWtevvt \lOt'" de brecA.k 0I0l1l\~ 'lljn 6p

dte pbo..t" if) de Lcle\riste ~nede va.., de t:nQct.( ~r o4e sp!!"­

ci(leke gfa~e et1erg;e (W\QJt It'W\a.a1. °as •.

Q,k. "IS er Q0'\ ~~Ie.\c ~ ~'" """""Ie en

! \/IJordev\. w.;\~e~et. "De '3rQt lelt€N\.. v;>Of"detA- ~a.kt ",~f"

de "ol~e ~eri.aJ&,.. '.

C4"S'~

e-le~tr·ol'jHsck ltopef.

A hANV\l1"\\'-"M

',.'"

1 0.15

,. 1&

1C

0.50

0.15

GrcaFt.k 1 ~ B re u k f uncti e '~

kri\"chc ~peci'ieke elG!.h:r.c~, efl8NJ'.e,

@ e>

e

j.

tp 11

• @ .11 ,. •

1.0 us

" • • • •

1. so

6/C (-) ~

)C. C -'5

e Hr.droh.,t-iSch \coper

I .t" .....

1.15

- 42. -

Als breukkr',terU4"""" v.X)t'd..t cAe ~~elcIe ~OQr­

de ~O\N1e""" va", de. ~)C..\twta.le t)~,eke gbs.\.~~Q ~e

per tre\.t.sb::u::..f. 1)e f'l2'.Sutto.te.,.., \JOI.I"l de .v:lr~~ proe.l.Ie£A -c.j..,

kle.-bij nl~ lYVl~OWI64A.- (1l:;e. H. tj : 1)is\c.yss·,e.). "let te>t.4l­

tQQ.t ,-"o,.ctt ~vevr C41s !

'}2Hiddelde 2: 2 ~ sbn::lco .... cb(~~~ {B9kl.¥ EJ

De k.rtHscL-e '!S pe:i{ .eke elasliscL..e e~le~ Wse in 'J/lWttWt' •

<:~S ( t4",is-kevrs ) t -3 kr = 2.7"10 :t 0.3 .,.. 10-3

<:. '" '5 l+ leeYl~) lkt' 6 -3 =~. '''0 ~ 0.'5"'" 10.3

~IEd:,ol~~i Sc:h ~,. ~&q- :: o-'!S" 10 10-3 -:t 015 ill \0-3

~t..A-W\'VliuM flU = 0."'1 .. 10-3- .t 0.0\( tIr 10.3

~ot1du 'iof~ev\ de andere bre.uk:k,.~terQ., '2<:::lQls de "o,~ vt.i:t

de bere~'3evt, ~

'De k.riHsoLte '(loC"~p:t,.,V1~~ .. 6!:l . rtf 'IW\-.'l : 'I')

("'-IS fkl" • .. 150 .t. 160

Elech-"'y HsclA. Lwper t \cor = 550 .t '5""5

A1UMA'MlA<\N'\ flu :: 2.00 ± 30

'i.).e k(itis~e isosia;tisotte l)p;1n"'i.-)~, GM-\ . N/C'M'W\1.. : . ")

<: .... 5 fk.f' .: sliP.t 200

e lai:rol\}" i Set,., koper fl« .. .2qo .t 4O

A tu (\i\I\\n..U.c1lN\ fkf' = "10 t. 30

'De lc..riH~e see:eif ieke pbsi'1dJe e~'1e ir'l 'J/i'WttWI3 :.

eLlS' 'Kf' z 0.80 .t o.2S

E lectro(<j Hse!... koper ~kr :: abo ± 0.45

Al\.4t)t1;t'\lu'W\ lkr ,. 0.32. .! 0..10

"~g Hi~j IX'I~ de (e'SuLtcden VOIn he*. ~

cb.:t kaer 0(.) de T.~. ~V\ v.X>n:Lt eV\ VOV\ de r:>~ o..oe.r

koc.fl f..t~s.tce.:t isolte dn...ckkeM-" die ......ttqe.ooe.n::(. ...uudeM- da!>r

'Pu~h CW\ 'f,rarlcles leverde 0(;) (}'If\et ba.tre~ tot :

- Bret..fkrek. (~;t9 QQtf\de van tAnl { Of"1Y\f\€ rek over de hete

dc::x:,c-snede \On de i:re~ ) "a~ i((2.k.pfOe.ll~

onder oc..tlVl"\OS~er ,scLte dry k. : ,

.~: "P> t'Cl r"tOIes £2>- 1."#8

Hui:s~s is. 1.49

• Af'IVII\(..() : 'i;randes la- -t.31

v.d. flvcort l.s= i. q'2.

• FtluHlnluM: "Pugh i.s • 0.3'2.

R~Vlii"S i!:-= 2..'2.0

- Hech:lr,,~e 3«"oot l-tedeM...

(l'MOdel-) v\oel<3 reve tneksterk.te.

( N / f'f'IWVa?) (NI""""",,"t)

• koper ~f"Q.,de5 "1'3.1 2~b.6

f-tuiskens 34.1 "l.O~.S'

• Ftr~o ~n:::..,de~ 18'l5" 318.8

v.d. A"arl $8.0 'l6'"t. "

- "" -

'::1", Hooid~\..(k b helobEwt v..)e ~Zfen da..t t--t. 'Bralll-

des Ge!Vl tYY\e!koc.;ie bedacl.t.t C'.WV\ de brosse. - breuk- s\erk.t:e." (20,

~e be(ek~eA;\- I ~b'3 h~ qelor~ cww::nkt \JQr\ de teSu{b::..jE?Nt

\JQVl de. ire.kprOEWeV\ ~de,. ~ clr""k. Het- bek.vt1p \lOt.., de

r~I{a.:f:e&i\. d~VOl'" \AXIS he! Mfloqe19k. de k'jdrosta.tisoL.e

<;)~"" nCjsc.o<l\N\po~., G""", \Coot" bro.sse bteA.Ak -le bepc:LJeAN.

"oor /c..opet-" vi~ we cb.n het vo'qevtde teSulb:lo.t ~

G_= f~ "po

: 1500 +""00 :. "'I'2Ei1 (k9/e.'Vft1"Z)

(tQbel 5.1).

'De woo,..cJe va.., de isasta..tlsd".e ':>fO.., .... i..,~ voor br06Se breuk

~n oak. here kevu::l. wc::wde..v door ~c.AA..k. ie (\N\Q.ket".. va",

~~ Iu-tienMM \,QfI\ de ~,e.Lce elaS+isc!te. eJl\erqie. lM.t a42. res(.tlia.t~ IoOVl de ire.kpr~ NV\e* koper. Vtnc:::.l0IA.. we

dan ..

1.25' J( ,oS' - __ .0.'3'$ 1- '!Z -0.3'1

.. Hd b .. euk~rauiuH ~~,ee:rd. op de spcc.i(.e.tce ebsHsc.t.e

eNer<;pe lever(: ~ rela:tle. op 1....t'SSek de ~ \Xl~ ele "''1.

cko.5tnHscLe SfX1"t1;n~. 6""", e" IIeu\ de ~tedleve t)por",.,ir')~. (; •

'De2e fela:tI~7 de b"'eMkrc.4~ie k~ i.....,ee \t.QrQ\derlsiiSlee <jE.\1o\\en:

.. .. - z(..five-r br0<3Soe bt"e..u k 6-0

- Z\.4;\Jer "toet.i.e II b.-etAk. 6~:o

HMutmee kQ" cli.+ krC1eru...M qezk." ""O ... ~ als eeYl

soor( cOWlbVJo1.,e va", kef kf'"t.1eftu ..... \Xl,., de k.ri~scLe "''1dtOS­

fa;.(;~e. tlf'ai1'1il1tJ evt he! "-ri~erU-tM VCln de kriHscL.e pbsiiscLe

~31e. (Gillel\1Aoi).

ria l(.t't~WM \JQlY\ de k.ribscl.e k'idf'Ostcdf~e sfX"rrr'JincJ s-

co~ Icertrt ~ '3,enslAJQa.Ilde ~ ~ver " t c:o.ie." breuk.

Hel kan • s\edA.A. s" '1~d V'X)rd(?IA. vr::::>Or prcressevt lW\et reb. ~

be.( \LleiAe pb~;scLe ~o,~~ vtX>f"da.t brecAk op{reedJ..

~ ILri..ferUAM \011 ole k.rifisoL.e (JlasliscLte e~;e

\even ~ ~(ens~ V'CX)r ~ver bt'osse bt'et.tk. ~,., ~.

heid is ~ -tot- proce5SeVl. ~bg fe.b-tle( ~e ~cU"

\)Qf(\ cIe k~rostc.&iscLe Sp::u1r')it1CJSCOMPO~ O{l,teclf!AA,. \Iud&- kef ...

"O~ vUIW\e.kl \.AX>,.deM.-, dcf.t (~cfews eevr defoftWlC1:lt~raes de pbsfisclte

~,,(e ~ cyzdi~sipeercL INOfdt, vJaCAAby dete koo{d1.CllteLiji.< iVl

war,.,ue wort::M o~et. kMqoal'\de !XlY\ he! idee &::d er Ee'v1 k.ce­

veetl.1eLd. (iW\~(ie ~ is 01M ~ ~eu.r i" ~ ~er"aai.. ic

vor~, ~ we C¥rr1ttQMevt. cJ.ct* &a pbsHsclte &1eI"~je daarvcor

"'let ',,, OCU'\ lW\eddVlCj ko..a. 'De efa&ilsoL,e evterg',e b ''111 ec.td.e,. vri.j

iV') keA IVVlctlerio.oi <~cu1~9 (2,.(1 ~r'\ dus weJ.. " q.e.bru.U<.t

- lib-

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word eM. \Joor he* VOnYYleva,. vOl,... eev1 SCJ\'\ev'-r. Oller he:t ~t9E-

,...neevl i~ he*. '0 dcU. e'e>'\ toeYlOlVVie \,X:1Vl de pashscL-.e Q.Vlerc;3le cOle

eev\ tceroM€ ~Y1 de efastisck !2V!er:J;e tot ~~ heeft. E"r besia£:t..,t

d",,!> E.'EM kwa,/,.Hfc:t:t,e! vet' band ~V\. Ittd bere.i.keMA. vet.., de

krHiscLte v.JCX'lrde VCX)('" de plaslisotte ~~~ elfl e#astisci.e enel'~le.

* ""et b.-ec...tk luliericAM ~sElefcl op cAe spec.ibeue. QJersiiscLte

~i.e is EeV1 krHer(..uM C¥l M1a(.rc.:sc...opi set. I'\tve:tU.. W~ proev€v1.

\lQd(,.rg~ we de ~e, lUCQrvcor breL.<k ~acd it1 0b1 1Vl"a.-

1eri.~ . vX\o:,ri"" rces.iet-lou.1ew J i~hels ev't t.<.orreLgte4lt'1ev\ volo(>

oav\~!tL9 UJrl. Or> ~UC$COpisdt "iv<2a.U v,eej'l b(evfk tx>t qevd9 ob.t

t\Alee I'\GtkHA.A"iCf dE1eL'lp va" elkaar verv.Jqd6YCl. tflQ,.cleM..

tiqcA;U.r Q.1 ~ Voorsiell i..,':1 Vd~ de. pofevttie If!. EWler~fe vc¥ Yt

hA}I2E. deettp. otIs. ~r1c*le VCb1 de a/"fal1ct {i.A3Se4A de d.ee{tf-"f>.

- 41 -

VO\'3(W1S de tke",,.;e ~V\ Mle eVl .Grutleisen [1'~1 j ~

daa ... eEWt hoe.veeti1etcl ~Ie IJClOr n~. 1:eze kcevee1l-teiq is

~l9k a01V1 de ~cdJeve ~rr:Je. vcr" dl2 billcUn<3~~ie ,

-Wf:>. -W~it'\ <Ji«3\A..AA.t" ~ ... ).

'De k.t-cA.dM. die n~ ·IS. 0tV\'\ -tw.ee deeltj ~ 01" GeY\ ~­

~o€ r 1IQN\ eUmaA'" 'Ie k.o\A~ ;~ ~~ OI?IN\- ole p:utleie aJ­~Ieide vowv de pO{eW'\~iele ~~

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f"9lMA.r <3. '2 ~ "De k.raclA.t F, ~ no:::U.~ i:> OIW\ tvJ4iE' c:fGEftf 5

op E!EW\- aJn~and. r te ~daN.

'De k.,ctc1A1 de rl~ is OW\. twee cleeltfS --z.£>\JeIr \Xlt1 alkoa-r te ..JE'A"­

w~detreM.. olotf tt,Q ~ i"lulad ~ ~ elkoo.r- tM.;fo~.fet'tQt\. is

~~ Gt""""- F /MaX (fi~\MA-r q. 2.). TeC"c..(.9ker ecAct <rJfJ l:\fVlaCf"osc..opiscL YlIl/eaM. t<.Wt1t1eY\. we

de IuHiScite. ~.el«z. ebsfi!>c.L.e QN\e41jie als eq ~i va.1~

- 48 -

I::e.:.cltOI.AW~ \lCUl de St"Ierqie -vJ1!. _ d,e rtcx:U.g i So. CMA. i-wee

deet,e.s \Ion cl kaat" ie \J2.rw'~~. "J:)e fc.riHsd..te -rrof"iI\IV\O.a.l­

")p:-n.rtinca IA.CU\ als eq..M..~ bes~ot.A,.CA)ol ....:>orole..tA. vCln.

de {reWt~. ~)C, die do.a.rvoor t'\o~ is:.

Tf,erCA.A.t tVV1GlC3 blcjkeM- c::.toLt or eEWl ku.:>c&.iicz.;l.e.( ver­

baV\~ besh ... a.k. t'-'4.:':E.v\· he! krl~iutW\ VOl'" ole spe04,e.k.e

eb5fiscL.e. CW\erg,e ert ole. krlfisclte i\orNVtaa.!SfO-r1ni I'\~ J eec.-..

vec-~ ol~ Dp V\el ~ ~u~t hele IW\~ .,\lei QCl~-

~ ~k.A: ie ttA.j1't •

.,.. er WMrJlfeVl. ecMer ock ei\Lc.ele QOlVIm-terLc.iI"l~ Cje-

. t'M0laA..d:-" wor~ op heA: k..ri4er'-ut-t \lcut ole k.rlHs~e speei.­

f.e.lte ebAtlscLe &\~ie. .

. We. ~,er"l d.ot1 de bretAk(unc:t,e ( \of.8)

( q.?)

lw: ~\MA.1" ~.?> bf,1« olcd ~e. ~ vQM. de et .. fed.e.-ve ,)~rJ.-\·'Vl~, 6 y steeds mMYder- SVleJ. ~c:::e~t 01$ CIte

waOA.CJ.t \10M.. <:b- ~drosla.Jl sct.e ()poU't.-\ i~ l.d£V1er worcU: . U it hj k t i,., \eqevtsprctak ~e* ole ('e<\tA..( WeM. VC4.n de pt""~

~ ko~ drlA.k. ~vv\.i t:tjlc..t ctcvt o4e wou;lV\cU ~

~ .-~ (-)

6k (-) ... --

....

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tW\£e~{ aJeNVtEM.tetA.t'e tJOf'MN.

H~rb9 l«x"" e::W12.(, wei. oJZ.rl'Meld. word6iN C(c<.1 Qevt,. s,1ertce \oe­

v\OMe. VOW1, cJ..t. eJfec.t.eve. 'l€lc. ~E , flCef vtcx:d«lkelyLt e~ S1er-

1Ae. ~e IIC4M- ole e.I f ectlEVe Spaf1y\W1g I 6J ~t ~or<3 ~f.

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W" het bovew>taaHdL blyk-t oIcd he{ lui~~t\M.. ~Vlole

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'sos-b.{isd.te <lfX1n";~~ ter diSC(A.$le Oj~1:eIol. kc..M,

WOtd~. +-1« tu,-b~u'VV\ verI/est ectder <tijl'1 qe{cttiJheicl ~r pro­

c.es~ vJOUAIlb9 t'l~re.\1e WOl~ tJ<X)f" 6f'1<V\ OfiredetN. O~M

de"J2 ')p:;tf1V'infj ~a..ti~ ,,(X:)("Lw~ tVl de br~k~r1ct,e

-50 -

lcc:::t" 001£ VCOf"'" ~eve ~etA.. tJOV\ 6 ........ oOt'l ke* Iore..uk­

lu-aerilMM. \JOIdOlQ..V\... v.x::>rdevv. L.u:+- cle pf'CClLfgk ,~ ectvter b!­

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by "O~ f'V2qa:.t.e.ve· i~tscLe. l")f'C1n"it'1g€n i.1 kek IW\aAe-rLOto.l

opilledevv.

E"~ cfe «Wleesw ~ bre,c...dcfuLier'-o.... ve-rhest c:.xJk

oUt lu-i.iei..s.A1-{ MJo'l ~ kei.ol voor P"'c.x:~ ~b9 ~a;f;le­

ve isosW,sot.e ~t1J'l~ opfredeM-.

f' 13~ h€'l pot1efetl\.. van n~ krHerUANV\ \.XlC",. ole «)peci/,e­

~e gbs{isot..e e¥10tl3~ V:X>rC:U Olat1~t10t--Cevt. dcM- bfeLAk ck:Jor~­

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de belaLtecM.ngevl bl~ Lc da1 &t.t CWlQX: ~ en ellA S c:::lCk I-tet ha:Ji.-l vaVl 1o~ \tan optredevt Of' efke vOille~iqe. f~ ;1'\ de kfe:t"l­

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oncJer-zo.e.Lc. ~.edaoY\ (lQar de fIQc:tk~

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trekpro~ ~e! AlullMittAMH blgtvt he)­

bc-euk..vlak als • doultM- {..A.fp It hreuk ~_ C"

peercL -ie la..cflrtelA ~. 1)eze ~I.u1orM

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vutW\\"9 lA:(vt e&f. kolt-e ',1'1 k~ ~ \XlVl·

cle sbat. w'f ~~ EC~ bt~£d .

£j~""Yr 9.'-1 :

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dat de.. '5peciJ,elA.e ekcsti;sc.ke e.vref''jie tW\Q,cLMc\Gt ( ~ar\

b~i~ytt \/QY\ cle. siataf (po5. j...:> i 'Bg\oqe e).

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:& 'loals we ~'Z.fel"l hebbevt ~111 ~ de ~ lJCIn de

bretA.kk.riJeria. de (e/.)CA./~ 1lQY'I de ~riYl3pr~ ~ ..... L. 'Darks

~e q~. 'Di+ 0M1dcd: oIez~ E:eV1 veel f~e. VI:xxude

t,JCJ(X de krlterta. ('!)P~ obr'\ cAe trek~. Oak de

breuk~r'lC!ie's t.oQlls. G. H(.(islc.ev"ls d.e O(->'l\efoIe !)uqqere£~ cta..t de re~ict1EWl. \/Ctr1 de writ1jp,.oet "{e ~ If ~Vl ('Bi1IQ..'¥ 'B).

E~ ~~~ h.ervoor ligt WOlarscL...ij""'9k 100 de

var""'9 proe.{ 'tel f : 'B~ c(e vJ( lYl9 proe.{ is he:t b~*~ ne! 'l.MJaQrst

be(Mi'e deal VOVl de proef~. Het i:> 'FSt eLl:f op~"fdk oIed

by de oer~it'lj VC\II\ c:k;? proe.(ljtcuJevt de llMees~e l/ervor-

1VY\\r1<j heett OI'lderCjOQ.V1. He! i5 otM.s ie .\lerwackl.eM. olaA de

wrir19Proe.( 1e l~ ""oc:z..rdetl VCDr de IIWvO(MA..!.:n:Jr heid 7a.1

oplevt1.etN ,

Hd probfeeM LeaK ondett/CCJ4q~ wo~ deer de wri.t1~-

5\CUJ~ -te cf.o~, WQ.QAc£a:>r cAe '1r1"{oec{ UNVI.. de ~k..i~

1€ net-~ \AJClrC«:. t.u.t prOEW€l1.A.. \.JOVV\.. L. ~k,:> blyM f~­

olcc.~ot o(o.,t d.cor ~ F~ de rek tot bre.u..IA: toe­

~ ([41, 'B~lc«j~ 9.1).

*S~ \I~\~\.c.M1q Wlr1 de fe':)(A .. f:l~ \.bV) ole tVV\a.AeriC¥t.l­

beproevi.-t"j or'lde.-r ~e dn"(k: evt de ~ ~ d,E. bg de

!)rZ\dI~ OMAVD(iW\~~;e ~ ~V\, Lc..ul1r1e",,- we ccr-d.u.d~

c:t::tA ctUe~ voar l<.q'Jer eni9~ getyk&A.i~~. Ook b~ IJet"ge­

r~\.<.4,1'j vOW\, ole ~Ielte tW\E?c.iA~s~e ~1"cot~ IolyLtk

ote qe.tqk~3 al~ \XXJr Lw~ ie ~baM. VercJ~ t.1€Y\ vJ€

c:kt:t oolt de becekeu.iVl9 \A?(Y\ de. is-05ta:HsdA.e :>pxr1r1i"~sc.o .... fX'~,

- 52-

~, ~ bros.se brevtk, et'lef'Ujos ~bCl9i?erot op ole QCtrlr'O,....ev1

vOt'" '5rcb"~, arde-Mijds ~b::v.,agJd. Dp net kri:fe.-~\A"" VOl'" de

I')peci.~,eke <2lov.7JiscJ....e (2T1e~;e, v;oord€.vl.. q:J~, die elkaar te­

defg k qoed i:eYladeA"evt..

Voor wa.A: ArnMco- ~,er be:ire.( t """oC3eJ\A....,.::Je QCtn­

V\€tW\ev' ... ala! er versck,iJ was in het (VV\~erL~ d..n.k ~fCtV\:

oles ~r...u.Lt!e.. etA, oIcvf: wClo ....... ee ",d.l'lifOOrt de proeuevt.. tM:t:­

vDefde.

Met la~ i" de fijn VQVI de vei-1AXlc1 ... :ii.v'\c:"evt '*'-* ~k "COr f\LY~M de f"e':)cAl~ \JOlVl PV.9'" ~ ~'te(r ':}<2€-v\ ovef"e~lwtwtst rt£)\Ac(~ opeve.r~. 0IN\dct;4: er 9e.b,...c..i.k

~ ',s. \JaV\ -h-uee ~~ee{ \JUscLU.llevcle f)CCdevt AtVV1Ml.M.-­

tJlNV\.

• lM,{ ole (&.l~ \)Olt'\ ~ iJ-ekpt"oeVevl.. 0IVle-t Alc..tnc.,.(.-

vvU-tM blijlAl ddt de kerf ifl de. itekstc:we&A. vrj ~ ;tf\",lcx:t;(

\t\ee{i 0(.) de waaAcU VCVV\.. de isosla...ti.scLte 1)p::tt1niYl9 j., lrtet

~e.rLGl.Cl.t ~a ~vt \le.rLUOOIld l;Vo£Ofe.,.t.. doDr Wlk feit da..t

ae ~ \)(~ sierk ·,flSVlOUeva". "be t)trcu::x.1 VOVVI ole il'\sncet'iyu:1

\lQV\ de o,,~eker-/CAe ()~eN\.. is OV)~ <3el9k Q~ de I)wQcd

\/O.{I\.. de scl"erpst: ~keftde ,.,ioaf· lMt c;(e C3rat.ek~ \ICCM. 'B~I~¥ A (A!I ev\ AI.4) "t.,~

we. o\ctk e.,- \/00f" Alu~M eev-t vrj <Jf"oie t')pt~ jr1 ole

~et)~evv optn2ectf. 'Di1 kaVl \Jef'lU..cc.cv'ot v..>Ord~ cloo,. ket flU-t clcU: W2.k ALuMi"iut4 s\erlA.e Ctt''1lsotrope ~ncita(.)(Jet4.. vedoovde

( 13tfClr;rf:).1)e"e, cU1isotfopie is {e verk1cuevt,ok;or ~e.t feit daA'

cfe {re!v)t~ WOU€,VL. verllCACU'~o(. lAAf €€v\.. diutu, pbat

- 5.3 -

et'1 j"., eefA plClce..t ",':, b-:1V1"'- otU:ijct aYlisctropie ctONt~~.

Tot <.)lo~ kaV\ Ylog \Je.(""iW\€1d wot'detA- ctal t'\tXCU'" C(l!e

v..x:xQ,rsckc1f1lgklriOCd he{ cjoo.(Jrocen t1let o(.ltilWtaal. ~(ope4ll is.

1)if kat1 ~£:nSE'tyOl ~€AA. 0(.) ~ fei.t c;b.k de vOOt'de4o('tWIa~ie.,

lo, !JOn "'e1- Ml\a1~ nle~ <jetgk OClVl !MA..I. is. 8V\ c::toVl c:I€

qrOte r)pretd.41~ ,,0lV\ de ~ ~~ \Ja.., de. "oorde­

rorlWCLtie. .

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k,e.v.. I C:£!e als \Ierl~')tc..(k var'\ cUt o~u;>eLc ~ rl~' bekel.ceY1

la..cnl"\ev\. \IVOt"deM-.

'De b("etA~",c-tje. qebocseer-d. op Of! opecii,eL<e ebst.~alte

E!J"Ierg;'e., i s, it'l dc2. vorlWl v.X:u: ... ·Lrl &-let V\o(.A.. 9~~d is, \JOn Ql!!!!I!U'"

a9V\VO\A.~ ac:u-cL" Er -z-y" ~uerbg C\C'l"t10(tW\St'\ '3EtknI"'l, \.AX2G\.f'"VOlr"\

~oL is d£d U! ",.it helel\N\G\o..l ~etk. Zo i~ b!j\loodoeebl

ole eb'ShcUeL~od..uL::.. C. mei c.o""sla..,t J NVlQQr E!'E'W'\ itAr1cl:ie

1lar1 de de(Ot''lM~ie:l e - e H:); e " He! is ;,,-\e("ressa!l\.t 0IW1

l'\Ol te ~r'\ q preci.sier~,,~ \.0'" de ki.ctA.~ nreukfUnc.*ie

201 eeA.cleA1.. 10t ~e ~.

'De proc.edJ,.ue. die MA. ~dqd. word1 b\j L-teA; ......a~

~.., de {(~ t:'> "leEU" i'jdro~. Uu-cIer ~ de tv\'1e-

. ~i~ aan de kerf a( if'lsnoer;'t1~ v.iJ::~ i" 01~{e ice­

sfa~. tkt ',::. ~"3 eeV' Nll\eAkoo'e -fe o..d""ild.t~, \.N~bij

de 'W\e.ht\~ coW'\.tUuA. ljdevts kef -f.re.kpn:x:G':> ~~ cMt~e­

VCtlKcL, .. i", - ptOCeS'5 • - tY\I\eA;i~" ~t «t.O\A ic:fa:Ao1 ¥ WC(Wleer

de lW\et~ "Zo ~~ol ~~ ~evv, ototl- ~"" Nl'\eet--

re..,<.A1.tcUeN\, otLted: ~i~ ~('ev.... voor "" .. U.,4a-,eke. ver-

~ ~

He+ j:) ',t11etre!>5CXvvt r\Ol {e Cja:::u1 ".1\ ~(e heX breuk­

w.~~~ 'J&'l~ j~ C!)'Wt lofec4k ie. \h:X)('t;)~ bij Pn:xe~,

- '5'5" -

r;J.i.L ~~t vOOrd~ ',,, cAre O'W'\VOt'M"\-\eckfl'\.Ol0C3e,

Fe.r. voor\oeek:l h.en.nYl 'I:> Irtet ~ 'J1:c..td~'" ~Yl

<!. 'Bt'Ot~.f-s. 1 ~"'" de. br-e.ukfu""c.t.iel

!!. ~ \..brt ~ Avoort clUz.. ~~ t-o.cLJO ~("~ v.X)rdeM.- OlW\ W

beqil'\ 00'" ocLr.eu.re.tA., by k..Vl: vlakota .... f"2'A -fe ~leu [1"1].

B(j ola onderzoek. '1$ de nadt'\Ak ~0:3ot op de..

vn:.u:.t~ onder ~ke. ,,~ac.vrof.e t.a.ev1 bteA,..c.k ~ io1J{ (2.v'1 vue.#­

~ ~ ~e\ke pba1s de2e do"" v.:xd. ~~c:::Vt. t.M..i de

a~lAM..-r tty t'\ Q.vlke.t.e.. \JOO('bEldQvl... bekev.ol ~(1("" b~ de

p~~ u:::I~ Ltek ~i'" \.O~ breu.k .,~ ~ele~.

5mm

b)

b~ i 1'1 vccn brevi k.kx:d (eclAt op de ri.cv..'­

-tiOS va" de. tr~k.r04cltt '1('\ ~ Y'eT btA..A\ev\.. "'€A

hctrt van de Stoetf. (-1-;] t~ &1.

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Cp de.. tre.\d(.~ [15 J .

14mm

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proef?t:uk. t "et' ()('jdet' l-1e;\ opperv(aL<. veu""

ote. ker f! [16].

lv..1- c\e'le ~1.Mev\. eV\. tM-t- de (~lA..H:cd:ecA. \ICW1 ole.

b-ekproeveA.A 'Wl~ RI~~M. (~k:tCA( b, 1 eng) bl~k.t ~ eer'\

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resulfcvleM. kat'l cp~.

j", ~e* CW\od~ vc:..n de .,,,ei -""",i{oc"l'Me del0oIMa:i:;e

~rcf;l OCt~DNVl~ ~ de ·lnsrlOef~~ circ.et~~ ·t~. Er

\to", Qa~5 protckisoLte et'l +~scLte vVE>~ ~ p~ 'YI~ ge -

obON\. CAlOrd~ eetA (Fs{ere?) bacchr~ vu.,9 \X;(Yl de

'J(\St1QeI'WlCJ -te ~ [i1].

Oak ltavt t1C('if~~ ~orcl~ of k~ l'W\ocfeL C\CtY\~$t

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~ ~r1l9k ~evv ~ door QaI'\~;r19 \.Ctll1..

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keAd?ve{bl eJ"l ole ~~e ~V1ede [i8].

+4e* brevckkr(tui..cAM "OVi de specif,eke eJQ~tiscL.e

ewz.t'"9te \lulce.st n~'" ~I\e vVOlo.,..scLt~ril~kheU:ll u:jtl'\ ~f..,etcX.

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b~ie J 't.Ooat oDk \XX)r d&U2.. p~ ~et ep1ra:>letA..

va" bre.rAk ~e4ol. ~ ~eAN.

L. lerClh..u.u" OVlU'tLcLvt .

[-1] \lafl cier f1voort. > H.,

'PfQs\:i~e sp\\jtbtetA.k. \l!Jtr'l Gtvtldiele CWIotfer~ .»

PT. ra.ppoti nr: 'PT 0'-1'-1\.1 , (-1'17-9) ~ T.H E.

t 2] Lc:",ri.jsSEWl., A. W. H.,

13( el,tl,(~&"ZO€k. b'::j Ol4A.Lc:he.\e lW\~eri.Q..\~ •

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