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New way o quan i a i e c ack closu e decomposi ion and
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de ini ion o less sca e ed ma e ial- ele an h eshold ΔK h
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Tomáš Voj eka*, Pa el Poko nýa, Radek Kubíčeka, Michal Jambo a, Pa el Hu ařa
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a Ins i u e o Physics o Ma e ials, Czech Academy o Sciences, Žižko a 513/22, 616 00 B no, Czech Republic
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* Co esponding au ho : oj [email protected]
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Abs ac
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The a icle p esen s new me hodology o ob ain c ack closu e alues based on a igue c ack g ow h
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a es, which is in con as o o he me hods, such as c ack closu e measu emen o nume ical modelling.
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The ad an age is ha he ue load a io e ec in di e en ma e ials is espec ed. Mo eo e , quan i a i e
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decomposi ion o plas ici y-induced c ack closu e, oughness-induced c ack closu e and oxide-induced
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c ack closu e (OICC) componen s ac i e in he nea - h eshold egime is possible. I is emphasized ha
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h esholds measu ed in humid ai using he s anda d load shedding me hod a e a ec ed and non-
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conse a i e. I is sugges ed ha he h eshold ΔK h should be measu ed in d y ai in s eels and ha in his
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way i is less sca e ed, conse a i e and mo e ele an as a ma e ial pa ame e , since i does no depend
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on in luencing ac o s o he es . A simple expe imen al se up o ob ain h esholds in d y ai is p esen ed.
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On he o he hand, he e alua ed OICC componen is esponsible o la ge sca e and dependence o
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h eshold on a ious es ing condi ions. C ack g ow h a e da a and ac u e su ace images a e p esen ed
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o i e di e en s eel g ades and he new me hodology is demons a ed on hese da a. Su p isingly, he
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in luence o OICC in s ainless s eels is as signi ican as in co oding s eels. Unde s anding o he
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mechanisms and imp o emen o he h eshold eliabili y and conse a i eness con ibu ed o he
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p og ess o he long- e m discussed p oblem o applicabili y o he h eshold pa ame e o esidual a igue
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li e es ima ions.
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Key wo ds
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a igue c ack g ow h h eshold, c ack closu e, load shedding, ai humidi y, s eels
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1 In oduc ion
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1.1 Fa igue c ack g ow h h eshold
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The a igue c ack g ow h h eshold ΔK h, ep esen ing he limi o cyclic loading below which he
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long c ack does no p opaga e, is he c ucial ma e ial pa ame e necessa y o esidual a igue li e (RFL)
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es ima ion o cyclically loaded enginee ing componen s [1,2]. This is especially impo an in applica ions
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wi h high demands on long- e m sa e ope a ion, whe e he damage- ole ance design is used. Apa om
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he dis inc ion be ween he cases o g owing and non-g owing c ack and he de ini ion o damaging and
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non-damaging cycles o he loading spec um, i is also essen ial o know his pa ame e accu a ely o
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eliable p edic ion o a igue c ack beha iou [3,4]. While mos o he ma e ial esea ch ocuses on as e
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c ack p opaga ion in he Pa is egime, he e a e many se ious concep ual ques ions u gen ly needed o be
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answe ed abou he nea - h eshold egime [2,5,6]. Du ing he las decades, s udies conce ning he
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h eshold we e done bu no signi ican p og ess in he opic o he sca e o he h eshold as a ma e ial
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pa ame e was made. Since only small di e ences o he h eshold alue may esul in d as ically la ge
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changes o he o al calcula ed RFL, he desc ip ion o a igue c ack g ow h (FCG) a e in he nea -
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h eshold egime should be imp o ed signi ican ly.
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I should be emphasized ha enginee ing componen s a e usually designed o be du able o a long
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ime, which means ha he as majo i y o ope a ional loading cycles lies below o sligh ly abo e he
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a igue limi . This means ha he ini ia ed a igue c acks will be ei he non-p opaga ing o p opaga ing in
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he nea - h eshold egime [1,3]. The e o e, o achie e easonable accu acies o RFL es ima ions, he FCG
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a e da a in he nea - h eshold egime should be de e mined as p ecisely as possible. Un o una ely, many
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ma e ial cha ac e isa ion s udies do no ake ca e o his, pe haps due o expe imen al and heo e ical
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di icul ies associa ed wi h he h eshold de e mina ion. One o he issues is ha e y slow c ack g ow h
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demands much expe imen al ime. Ano he issue is ha he e a e many un esol ed ques ions abou he
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in luencing ac o s on h eshold and he ela ed mechanisms, which b ings con usion in o he opic o
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h eshold measu emen echniques [7-9]. The esul s ob ained using jus one h eshold measu emen
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canno p o ide su icien in o ma ion abou he sca e band, in which he ob ained alue lies. Such
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p ocedu es may be dange ously non-conse a i e. Nume ous expe imen al h eshold alues p oduced by
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esea ches may seem un us wo hy o he communi y in applica ions. Addi ionally, inco ec h eshold
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alues may also a ec componen es ing, since he h eshold alue de e mines which loading ampli udes
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can be omi ed om he spec um as non-damaging. Mo e de ails abou he opic o he omission-le el
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loading cycles can be ound in [9].
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The u gency o he need o an imp o emen o he si ua ion makes he opic o h eshold highly up-
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o-da e, which is documen ed by in e es in he opic by di e en esea ch g oups [7,10,11] and i is also
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by conclusions o he special scien i ic wo kshop dedica ed o he p oblems o h eshold and i s
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applica ions, which we e published in he o e iew a icle [2]. F om his a icle (and in ag eemen wi h
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o he sou ces), he ollowing poin s can be deduced: (i) I was known o a long ime ha he s anda d
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expe imen al me hods o h eshold de e mina ion o en esul ed in a oo la ge sca e o he esul s, which
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we e some imes non-conse a i e. (ii) I was known ha he a ia ion was ela ed o c ack closu e
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mechanisms, such as plas ici y-induced c ack closu e (PICC), oughness-induced c ack closu e (RICC)
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and oxide-induced c ack closu e (OICC), see also [1,12-14]. (iii) No eliable me hodology o
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quan i a i e conside a ion o hese componen s was p esen ed, ei he o expe imen al s udies o o
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nume ical simula ions ha would be usable o RFL es ima ions. The e o e, he de elopmen o a new
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app oach is equi ed, which is he aim o he p esen wo k.
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The h eshold ΔK h and he c ack ip shielding e ec s should no be o e looked in ma e ial p ope ies
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esea ch. I is usually belie ed ha he ma e ial a igue damage mechanisms and he ela ed esis ance o
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a igue c ack p opaga ion a e he same as in he case o la ge c ack g ow h a es o e en mono onic
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loading. I is usually belie ed ha he phenomena ela ed o ma e ial s eng h a e he same as hose
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in ol ed in he esis ance o a igue c ack p opaga ion and ha he only p oblem is ha hey occu a a
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much smalle scale nea he c ack ip. This is w ong o wo easons. Fi s , he pa o he h eshold
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ela ed o he ue ma e ial esis ance o c acking in on o he c ack ip (e ec i e h eshold) does no
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depend on classical ma e ial p ope ies, such as he yield s ess o he ul ima e ensile s eng h. The
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e ec i e h eshold depends only on he Young modulus and he Bu ge s ec o leng h [15-19]. The e o e,
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i is easily p edic able in mos me als and i canno sol e he p oblems ela ed o he obse ed sca e o
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he measu ed h esholds ΔK h. Second, due o he small c ack opening displacemen s ypically occu ing
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in he nea - h eshold egime, he c ack ip shielding e ec s become dominan wi hin he o al ΔK h alue.
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These e ec s a e also esponsible o he obse ed sca e and he s ong dependency o h eshold on
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many expe imen al in luencing ac o s [1,2], while hey ha e no hing o do wi h ma e ial s eng h.
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The e o e, in o de o imp o e he si ua ion, he ele an mechanisms and p ope ies should be s udied. In
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pa icula , he c ack ip shielding e ec s, such as c ack b anching o ac u e su ace con ac , should be
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cha ac e ized as p ecisely as possible, which has he po en ial o imp o ing RFL simula ion esul s
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signi ican ly.
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1.2 Majo p oblem o cu en app oaches #1 – measu emen echniques
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I may seem ha c ack closu e has al eady been s udied su icien ly long ime in he las decades bu
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i u ns ou ha a wo king eliable quan i a i e ool is s ill awai ed o be es ablished. The mos commonly
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used app oaches o he load a io e ec desc ip ion, such as he NASGRO me hod [20,21], conside PICC
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as he only mechanism o closu e. In he nea - h eshold egime, i is equi ed o ake RICC and OICC in o
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accoun oo. Recen s udies indica e ha OICC ep esen s a signi ican componen o ΔK h in co oding
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s eels and ha i depends on such "exo ic" ac o s as ai humidi y o loading equency [5,22], which a e
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ac o s ypically di e ing e y much among di e en es ing acili ies, as well as in applica ions, while
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hey a e seldom moni o ed o con olled. The e o e, applica ion o ΔK h is no s aigh o wa d and
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a numbe o se ious challenges should be esol ed in o de o ob ain ealis ic RFL es ima ions.
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One o he p oblems is ha he h eshold measu emen is essen ially an unna u al p ocedu e o he
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a igue c ack o eme ge, in ol ing applica ion o pa icula loading his o y designed o he es , which is
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e y di e en om ac ual loading in ope a ion. Thus, i is necessa y o unde s and he mechanisms and
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he ela ed in luencing ac o s o imp o e he us wo hiness o he measu ed da a and hei
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ans e abili y o componen s. Fu he mo e, i should be iden i ied which o he ac o s a e he mos
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ele an and i should be de e mined wha is he ange o possible a ia ion o he esul ing da a in o de
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o assess hei conse a i eness.
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Newman [23] poin ed ou ha h esholds measu ed by he mos widely used s anda d load shedding
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me hod acco ding o he ASTM 647 [24] a e a ec ed and non-conse a i e, suppo ing his conclusion by
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bo h expe imen s and modelling o he PICC e ec . Consequen ly, he sugges ed using al e na i e
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expe imen al p ocedu es o ob aining conse a i e h esholds, aking ad an age o he cyclic
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comp ession p ec acking echnique [25,26]. This echnique was de eloped o a oid he p oblems wi h
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c ack closu e e ec s du ing es ing. In pa icula , he comp ession p ec ack load educ ion (CPLR)
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me hod ollowed by he comp ession p ec ack cons an ampli ude (CPCA) p ocedu e seem o be
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a p omising al e na i e. The p ec ack p oduced by cyclic comp ession-comp ession loading ensu es
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educ ion o he PICC o e load e ec , which in u n also educes he OICC e ec on h eshold du ing
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load educ ion. Ano he possibili y is o apply he p ocedu e o cons an Kmax wi h inc easing Kmin o
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ob ain conse a i e h esholds [2,27]. In his case, he inc easing R a io leads o ob aining alues close o
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he e ec i e h eshold. The h esholds o loading wi h low load a ios need o be ob ained by a di e en
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s a egy. This can be o e come by he use o a mul iple Kmax modi ica ion epo ed in [28]. Some a gue
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ha high-R closu e can also be p esen when applying hese s a egies [29].
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The p esen wo k emphasizes ha he e ec o OICC causes signi ican loading his o y e ec s and
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ha hey should be conside ed in any analysis conce ning in he nea - h eshold egime in s eels. Using
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unsui able me hods o ma e ials suscep ible o he oxide deb is e ec can lead o dange ously high
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h esholds, which may esul in ex emely long p edic ed RFLs, while in eal ope a ion he si ua ion may
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be di e en . The p esen app oach has been de eloped o a oid such e o s and o b ing cla i y in o he
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opic o quan i a i e in luence o indi idual c ack closu e componen s.
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1.3 Majo p oblem o cu en app oaches #2 – nume ical modelling
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An app op ia e quan i a i e desc ip ion o PICC is a necessa y condi ion o s udying and e alua ing
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RICC and OICC. I was epo ed ha he up- o-da e models o PICC ha e limi ed p edic abili y and ha
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hei abili y o ep oduce he load a io e ec eliably in di e en ma e ials is limi ed [30]. The mos
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common p edic ion is ha he PICC e ec is nea ly he same in all ma e ials, independen ly o hei
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cyclic p ope ies, which canno be co ec heo e ically, and which does no ag ee wi h expe imen s
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ei he .
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Typically, he s udies ely on he idea ha PICC o igina es om he plas ic s e ch o ma e ial in he
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c ack ip plas ic zone du ing c ack p opaga ion. This is only pa ially ue because only he mono onic
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loading ma e ial p ope ies a e conside ed. In eali y, he e e sed (cyclic) plas ic zone gene a ed unde
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a igue loading is also essen ial o unde s anding PICC. Du ing unloading, he e e sed plas ici y
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diminishes he posi i e plas ic s e ch o he ma e ial. The cyclic plas ic ma e ial p ope ies de e mine he
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ex en o he educ ion o he plas ic s e ch o med du ing loading, in o he wo ds, i akes back some o
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he de o ma ion gene a ed in ension. The heo y o PICC should be co ec ed in his sense [31]. I is he
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di e ence be ween he plas ic s e ch p oduced du ing loading and he comp essi e ebound ealized
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du ing unloading, wha de e mines he le el o PICC. Ine i ably, he amoun o he ebound in
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comp ession depends on ma e ial cyclic beha iou . This explains why he models based only on
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mono onic ma e ial p ope ies ha e limi ed abili y o ep oduce he ue beha iou . In gene al, he model
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should be able o conside one ma e ial model o gene a ing he mono onic plas ic zone and a di e en
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ma e ial model o gene a e he cyclic plas ic zone. Al hough his may be ep oduced in some
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sophis ica ed ini e elemen models, he esul s depend on many pa ame e s, which need o be uned o
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ma ch he expe imen . Besides, only a small numbe o cycles can be modelled, which makes his
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app oach bo h non-p edic i e and ine ec i e ( oo much compu a ional powe needed o insu icien
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numbe o loading cycles).
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As a consequence, he p esen ed app oach sugges s ha no modelled PICC alue should be imposed
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on he eal ma e ial beha iou du ing i ing o he FCG a e da a. Ins ead, he ue load a io e ec
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exhibi ed by he ma e ial should be de i ed om expe imen al da a ob ained a di e en load a ios. I
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was shown ha he nea ly cons an p edic ed PICC alue o all ma e ials o e es ima ed he load a io
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e ec in ma e ials wi h cyclic so ening and ha i unde es ima ed he load a io e ec in ma e ials wi h
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cyclic ha dening o wi h supplemen a y b i le mic o ac u e mechanism [30]. Fo hese easons, he
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newly de eloped me hodology is equi ed o enable conside a ion o he eal obse ed ma e ial
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beha iou , ins ead o elying on nume ical p edic ions. This conce ns (quasi-)cons an ampli ude loading.
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Fo a iable ampli ude loading, nume ical modelling becomes p ima y, aking he newly de ined ma e ial
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pa ame e s as inpu s.
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Using he esul s o he s ip-yield model [32,33] has been a success ul way o es ima e PICC. In he
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ame o his model, limi ed in luence o he PICC alue was possible o adap a ion o he ma e ial
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di e ences. The cons ain ac o α could be used o a ia ion o he esul s, since i is he only pa ame e
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in luencing hem o a su icien ex en . In he p esen app oach, his is a he a oided due o he de ined
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physical meaning o he α ac o . I should co espond o he ue cons ain condi ions, such as he
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specimen and c ack geome y, he maximum applied s ess and he ma e ial yield s ess. Mo eo e , as
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shown in [30], in o de o ep oduce he la ge obse ed di e ences be ween ma e ials, he cons ain
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ac o α would ha e o be a ied oo much up o nonsensical alues. The e o e, he p e e ed way is o
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ind some o he pa ame e in he s ip-yield model o a ia ion o he PICC esul s. In he p esen wo k,
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he c ack closu e pa ame e = Kcl / Kmax, desc ibing he PICC e ec , is simply de e mined om he
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expe imen ally obse ed load a io e ec in he in es iga ed ma e ials.
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1.4 Oxide-induced c ack closu e and i s signi icance
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Al hough he oxide-induced c ack closu e was s udied al eady long ime ago, e.g. [34,35], no
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p ac ically useable quan i a i e desc ip ion was p o ided. The si ua ion changed ew yea s ago when i
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was e ealed ha he h esholds in s eels dec ease signi ican ly in d y ai due o he elimina ion o oxide
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deb is p oduc ion on ac u e su aces, which allowed s udying o he quan i a i e signi icance o he
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OICC e ec [13,22]. The mechanism o OICC is ha he oxide laye on ac u e su aces is dis up ed by
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high comp ession con ac wi h e y high numbe o epe i ions, which is he same mechanism as e ing,
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and whe e mic oscale ic ion is essen ially in ol ed du ing he high p essu e con ac . The deb is o oxide
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and me allic su ace is accumula ed in he c ack wake, wi h he laye hicknesses g owing o he o de o
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hund eds o nanome es. Due o he speci ic olume o he e ous oxide being la ge han ha o me allic
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i on, he c ack wake is illed in by ex a ma e ial. The laye hickness is compa able o he c ack opening
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displacemen in he nea - h eshold egime, which means ha he e ec i e ΔK can be educed
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signi ican ly. The subsequen c ack b anching educe he e ec i e ΔK as well. This is why OICC
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ep esen s such a signi ican cons i uen o he applied h eshold and, he e o e, o he ma e ial a igue
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s eng h. The condi ions o he eme gence o no able OICC a e as ollows: a e y slow c ack g ow h
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(<10–6 mm/cycle) and he p esence o ano he c ack closu e mechanism, such as PICC o RICC. A high
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load a io whe e c ack closu e is missing, he oxide deb is is no gene a ed a any c ack g ow h a es.
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Some es ima ions o c ack closu e componen s we e done o he ailway axle s eel EA4T [13,22].
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The p esen app oach abandons he in en ion o es ima ion o he RICC componen heo e ically. Ins ead,
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i uses a new way and he OICC e ec is s udied on mo e ma e ials o exclude he possibili y o he la ge
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OICC in luence being an anomaly o he EA4T ma e ial. O he s udies ela ed o OICC we e also
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published, whe e mo e de ails abou he speci ic p oblems nea h eshold can be ound. Fo ins ance, in
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[8], he di e ence be ween h esholds ob ained a 10–7 mm/cycle and a 10–8 mm/cycle was poin ed ou .
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In he wo ks [9,14] i was emphasized ha OICC gene a ed du ing non-damaging loading cycles cause
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signi ican e a da ion o he subsequen c ack g ow h, which leads o e o s in RFL es ima ions i hese
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cycles a e no conside ed in simula ions. I was epo ed in [5] ha using low loading equency, such as
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5 Hz, signi ican ly educes he h eshold alue due o he absence o OICC. This ep esen s an issue o
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es ing, since such a low equency would make es ing imp ac ically long, while la ge equencies
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would lead o non-conse a i e esul s. As a consequence, he p esen wo k o e s a solu ion o his
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p oblem by educing he OICC, while s ill keeping he es a high equency.
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1.5 Pu pose and aims
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As men ioned abo e, i is impo an o know he ange, in which he h eshold ΔK h can a y in bo h
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expe imen al measu emen s and in applica ions. Only small changes cause signi ican di e ences in RFL,
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while he h esholds ob ained by he s anda d expe imen al measu emen echniques can di e
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signi ican ly.
35
His o ically, an impo an s ep o analyse ΔK h was i s di ision in o he in insic and he ex insic
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esis ance o a igue c ack p opaga ion, in o he wo ds, he dis inguishing be ween c ack ip shielding,
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mos ly ealized by c ack closu e e ec s, and he e ec i e h eshold ΔK h,e . A u he di ision o he
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ex insic pa in o indi idual c ack closu e mechanisms is he key poin o be ocused on in o de o make
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a p og ess in his opic. Unde s anding o he mechanisms and hei quan i a i e signi icance is essen ial
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o he judgemen o he in luencing ac o s occu ing du ing es ing and du ing applica ions. Such a
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p og ess is necessa y o imp o emen o he RFL p edic i e ools, since he ele an pa ame e s should
42
be aken in o accoun in hei de elopmen . The e o e, i is equi ed o p o ide an easily applicable
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me hodology o quan i y he cons i uen s o ΔK h ega ding he mechanisms. In pa icula , he pu pose o
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his wo k is o p o ide he answe s o hese ou ques ions:
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(1) Wha is he composi ion o he ΔK h alue om he poin o iew o mechanisms and which o
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hem is he la ges sou ce o he expe imen al sca e and disag eemen ? Which quan i a i e
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componen s o ΔK h e lec p ope ies o he ma e ial and which e lec pa ame e s o he es ?
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(2) How o ge back o he o iginal meaning o ΔK h as a ma e ial pa ame e ha could be used in
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simula ions, ee om oo many p oblema ic in luences?
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(3) How should ΔK h be expe imen ally measu ed o be p edominan ly conse a i e and sa e o
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esidual a igue li e p edic ions, while no being oo much conse a i e, as is he case o ΔKe , h?
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(4) How signi ican is he e ec o oxide deb is accumula ion in di e en co oding and non-
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co oding s eels?
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To answe hese ques ions, an ad anced expe imen al p og am was designed o se e al ma e ials. All
10
ma e ials a e used in impo an applica ions wi h he equi emen o long- e m eliable ope a ion. Because
11
co osion is a c ucial ac o o p oduc ion o oxide pa icles, s eels wi h di e en co osion esis ance
12
we e selec ed o e eal he ole o he OICC e ec in hem.
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2 New me hodology o c ack g ow h a e da a p ocessing o
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sepa a e c ack closu e mechanisms and o ind he ma e ial-
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ele an h eshold ΔK h
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A new me hodology is p esen ed wi h he pu pose o a oiding he p oblems ela ed o unce ain ies o
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c ack closu e de e mina ion, especially in he nea - h eshold egime. Apa om he imp o emen o he
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accu acy o RFL es ima ions, he me hodology aims o p o ide be e unde s anding o mechanisms,
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iden i ica ion o ele an ma e ial p ope ies and o he in luencing ac o s.
21
2.1 Acquisi ion o c ack g ow h a e da a
22
The p ocedu es o c ack g ow h a e da a de e mina ion acco ding o s anda ds a e o en used, e.g.
23
ASTM E647 [24] o ISO 12108 [36]. Se e al da/dN s. ΔK da a se s should be ob ained o a ious load
24
a ios R in o de o ha e su icien basis o RFL de e mina ion.
25
The NASGRO equa ion [20,21] i s he expe imen al c ack g ow h a e da a wi h a p e-de ined c ack
26
closu e pa ame e , which has wo disad an ages. Fi s , only he plas ici y-induced c ack closu e
27
mechanism is conside ed, which esul s in inaccu a e ideas abou c ack closu e in he nea - h eshold
28
egime. Second, e y simila alues a e p edic ed o all ma e ials, which is incon enien o s udying o
29
di e en ma e ial p ope ies. Fo example, i was epo ed ha o a 3D-p in ed 304L s eel, he
30
pa ame e ailed o desc ibe he dependence o c ack g ow h a es on he load a io [30]. In he p esen
31
s udy, i is sugges ed ha he alues a e de e mined di ec ly om he c ack g ow h a es, which
32
cha ac e izes he ma e ial accu a ely. I is compu ed based on he c ack g ow h a es measu ed a wo
33
di e en load a ios, ypically R = 0.1 and R = 0.8. In he p esen ed analysis, i is su icien o wo k wi h
34
only hese wo load a ios. Fo mo e complex s udies, whe e should be exp essed o any desi ed R, he
35
use o he alues p edic ed by NASGRO is cu en ly he only p ac ical and e icien way o do i . The
36
disc epancies be ween he eal ma e ial beha iou and he p edic ed can be o e come by de e mining he
37
using he s ip-yield model simula ions wi h an addi ional a iable, as sugges ed in [30].
38
7
In he i s s ep o he desc ibed me hodology, he ollowing h ee da/dN s. ΔK da a measu emen s
1
we e done: (i) a R = 0.1 in ai wi h no mal ela i e humidi y a oom empe a u e, (ii) a R = 0.1 in ai
2
wi h ela i e humidi y less han 10% a oom empe a u e (absolu e humidi y less han 2 g/m3) and (iii) a
3
R = 0.8, whe e ai humidi y does no ma e , howe e , i is easie o conduc he es in no mal (humid)
4
ai . The da a including he h eshold we e ob ained in his wo k using he s anda d ASTM load shedding
5
me hod, see Sec ion 3.2 o de ails. A e ha , he da a we e i ed using a special p ocedu e desc ibed in
6
he nex sec ion.
7
2.2 E alua ion o he plas ici y-induced c ack closu e e ec
8
2.2.1 Modi ied i ing p ocedu e
9
The p esen app oach is based on he idea ha i is no pu pose ul o sea ch o he pa ame e by
10
means o nume ical simula ions o compliance change measu emen echniques. Reliabili y o he esul s
11
o hese app oaches is ques ionable [37,38], he e a e oo many in luences and he p edic ed alues need
12
o be e i ied expe imen ally anyway. He e, ins ead, he ue expe imen ally obse ed load a io e ec is
13
ex ac ed om he c ack g ow h a e da a and he pa ame e is e alua ed acco dingly. I exp esses he
14
load a io e ec di ec ly as he desi ed alue, ega dless o he mechanisms in ol ed o hei complexi y.
15
This me hod is applied o he Pa is egime da a o a oid addi ional c ack closu e mechanisms ha a e
16
ac i e nea h eshold.
17
The NASGRO Equa ion (1) was used in o de o ensu e compa ibili y o he app oach wi h he mos
18
commonly used me hodologies o RFL es ima ion.
19
d𝑎
d𝑁 =𝐶[(1−𝑓
1−𝑅)∆𝐾]𝑛(1−∆𝐾 h
∆𝐾 )𝑝 (1)
20
He e, a is he c ack leng h, N is he numbe o applied loading cycles, C, n, p and ΔK h a e i ing
21
pa ame e s, = Kcl/Kmax is he c ack closu e pa ame e (no e ha only PICC is included in ), R = Kmin/Kmax
22
is he load a io and ΔK is he applied s ess in ensi y ac o ange. The e m associa ed wi h he inal
23
ac u e in he o iginal NASGRO equa ion is omi ed in his wo k, since i co esponds o insigni ican
24
numbe o loading cycles and since he loading is usually associa ed wi h la ge-scale yielding, making he
25
K pa ame e in alid.
26
In he newly p oposed p ocedu e, he i s s ep is ha he h ee desc ibed expe imen ally ob ained
27
FCG a e cu es a e i ed sepa a ely using a simpli ied o m o he equa ion, whe e Δ𝐾e is eplaced by
28
∆𝐾. In his way, he e m con aining and R is emo ed, which allows ob aining o wo di e en C
29
coe icien s, one o he high load a io, ypically R = 0.8, which is deno ed as Ce , and one o he low
30
load a io, R = 0.1 in his wo k, which is deno ed CR=0.1.
31
(𝑑𝑎
𝑑𝑁)𝑅=0.8 =𝐶e (∆𝐾)𝑛(1−∆𝐾 h
∆𝐾 )𝑝 (2)
32
(𝑑𝑎
𝑑𝑁)𝑅=0.1 =𝐶R=0.1(∆𝐾)𝑛(1−∆𝐾 h
∆𝐾 )𝑝 (3)
33
The coe icien CR=0.1 is kep equal o he humid ai da a and o he d y ai da a. The h eshold alues a e
34
i ed as di e en o all h ee cu es, while he exponen s n and p a e kep equal o all h ee cu es.
35
8
2.2.2 Finding o
1
The shi o he da a in he Pa is egime due o he load a io e ec can be cap u ed by he alues o
2
Ce and CR=0.1. In Eq. (2), ∆𝐾 co esponds o Δ𝐾e , hence he Ce alue has he same ole as he
3
undis inguished C alue in he o iginal NASGRO equa ion. The p esence o PICC a R = 0.1 ha can be
4
desc ibed by he alue is supposed o shi he da a in such a way ha hey a e desc ibed by Eq. (3).
5
The e o e, Eq. (3) can also be w i en in he second o m ha enables he coe icien CR=0.1 o be
6
ma hema ically exp essed as ollows:
7
(𝑑𝑎
𝑑𝑁)𝑅=0.1 =𝐶R=0.1(∆𝐾)𝑛(1−∆𝐾 h
∆𝐾 )𝑝=𝐶e [∆𝐾(1−𝑓
1−𝑅)]𝑛(1−∆𝐾 h
∆𝐾 )𝑝 (4)
8
𝐶R=0.1 =𝐶e (1−𝑓
1−𝑅)𝑛 (5)
9
Then, he sea ched alue can be de i ed as:
10
𝑓 =1−(1−𝑅)(𝐶R=0.1
𝐶e )1
𝑛 (6)
11
Finding o his alue enables he u he desc ibed comple e quan i a i e decomposi ion o ∆𝐾 in o
12
indi idual c ack closu e mechanisms.
13
2.2.3 Cla i ica ion o quan i a i e PICC exp ession
14
In o de o co ec ly desc ibe he PICC e ec quan i a i ely, a special sepa a ion has o be i s
15
in oduced. The pa o PICC lying inside o he ange o he applied ΔK should be de ined. The
16
componen o PICC lying below Kmin should be sub ac ed, since any hing lying ou side o ΔK = Kmax –
17
Kmin is non-exis en and hus i ele an . The e o e, he o al alue o PICC co esponding o he pa ame e
18
, which is KPICC = ·Kmax, should be di ided in o wo pa s. The i s pa is equal o he PICC e ec
19
deno ed he e as ΔKPICC, lying inside o he loading ange ΔK. The second pa is simply equal o Kmin o in
20
he case o nega i e load a ios R i is equal o 0. This is one op ion which is adop ed in he p esen wo k
21
o he sake o cla i y and no o call he nega i e pa o he loading cycle as PICC. Technically, he
22
second pa could always be equal o Kmin including he nega i e load a ios and only he i s line o
23
Eq. (7) could be used. This would simpli y he compu a ion o o he closu e componen s o nega i e R,
24
since ΔK would no ha e o be ans o med in o Kmax o ob ain he co ec summing, see also Sec ion
25
4.3.4.
26
The pa o PICC lying inside ΔK is hen:
27
Δ𝐾PICC ={𝑓𝐾max −𝐾min ……… o 0≤𝑅 <1
𝑓𝐾max ……… o 𝑅 <0 . (7)
28
Conside ing Kmax = ΔK (1 – R), he exp ession akes his o m:
29
Δ𝐾PICC = Δ𝐾(𝑓−𝑅+
1−𝑅 ) , (8)
30
whe e R+ = R o 0 ≤ R < 1 and R+ = 0 o R < 0. Such de e mined alue is hen supposed o be alid o
31
he whole c ack g ow h a e cu e.
32
33
9
2.3 E alua ion o he oughness-induced c ack closu e componen
1
The RICC componen is he emaining closu e pa , which canno be e alua ed by any o he way han
2
by sub ac ion o all o he componen s om ΔK. Al hough i is called RICC, in eali y i is he componen
3
simply co esponding o he es o he di e ence be ween ΔK and ΔKe , a e PICC and OICC a e
4
sub ac ed, ega dless o he ue physical mechanism. Based on he da a measu ed in d y ai , he
5
decomposi ion o ΔK is as ollows:
6
Δ𝐾 =Δ𝐾e +Δ𝐾PICC +Δ𝐾RICC (9)
7
and using he exp ession (8) o ΔKPICC, he e m ΔKRICC can be de i ed as:
8
Δ𝐾RICC =Δ𝐾−Δ𝐾PICC −Δ𝐾e (10)
9
Δ𝐾RICC =Δ𝐾[1−(𝑓−𝑅+
1−𝑅 )]−Δ𝐾e . (11)
10
This alue can be used o e alua ion o he RICC e ec o any desi ed da/dN and a h eshold.
11
In o de o g aphically exp ess he ΔK componen sepa a ion, an ex a line was de ined in he c ack
12
g ow h a e diag ams. I was plo ed as he dashed blue line in he schema ic Fig. 1 and in he esul s in
13
Sec ion 3.3. Fo e e y c ack g ow h a e da/dN he quan i ies ΔK and ΔKe ob ained om he
14
expe imen al i s a e used o p oduce a new alue on he ho izon al axis. The ela ionship be ween his
15
new alue and ΔK and ΔKe is de i ed om Eq. (9), whe e ΔKPICC and ΔKe a e g ouped oge he on one
16
side, see Eq. (12), keeping in mind ha he sums a e o d y ai , hence no OICC componen is included
17
ye .
18
Δ𝐾e +Δ𝐾PICC =Δ𝐾−Δ𝐾RICC (12)
19
Bo h sides o Eq. (12) de ine he bo de line be ween he a ea o PICC and he a ea o RICC in he
20
diag am in Fig. 1. Thus, he g aphical sepa a ion o all ΔK componen s can be seen. The le -hand side is
21
mo e s aigh o wa d o exp ess, using Δ𝐾PICC acco ding o Eq. (8). No e ha ΔKPICC is no equal o
22
𝑓𝐾max. Thus, o e e y da/dN in he measu ed ange, he blue dashed line is c ea ed by he poin s
23
sa is ying he ho izon al axis alues de ined by Eq. (13).
24
Δ𝐾e +Δ𝐾(𝑓−𝑅+
1−𝑅 ) (ho izon al axis alues o he blue dashed line) (13)
25
26
16
3.2 Measu emen o a igue c ack g ow h a es
1
In his wo k, he c ack closu e e ec s a e e alua ed o m he expe imen ally ob ained a igue c ack
2
g ow h a e cu es. The cu e measu ed a R = 0.8 is p esumed o p o ide ΔKe da a. The cu es o
3
R = 0.1 measu ed in d y and humid ai se e o e eal he basic e ec o load a io and oxide deb is. The
4
a igue c ack g ow h a es da/dN we e measu ed using he middle-c ack ension M(T) specimens wi h he
5
wid h 2W = 60 mm and he hickness B = 5 mm o he s eels X20C 13, GX4C Ni13-4, EA1N and EA4T.
6
In he case o he s eel P265GH, he compac ension C(T) specimens wi h he pa ame e W = 30 mm and
7
he hickness B = 6 mm we e used. Geome y o he specimens is schema ically depic ed in Fig. 3.
8
A sha p no ch was p oduced by elec ic discha ge machining wi h he wi e diame e o 0.25 mm. The
9
expe imen s wi h he M(T) specimens we e pe o med using a esonan es ing machine Schenck PVQ
10
wi h he o ce capaci y o 60 kN. The expe imen s wi h he C(T) specimens we e pe o med using a linea
11
mo o es ing machine Ins on elec opulse 10000 wi h he o ce capaci y o 10 kN. All expe imen s we e
12
es ed a equencies in he ange om 40 o 80 Hz.
13
The empe a u e and humidi y was con olled in he labo a o y. The empe a u e was se o 23 °C and
14
he absolu e humidi y was se o 10 g ams o wa e molecules pe cubic me e , which co esponds
15
app oxima ely o 50% o ela i e humidi y a 23 °C. The specimens es ed in humid ai we e exposed
16
di ec ly o he con olled labo a o y ai . The specimens es ed in d y ai we e su ounded by a special
17
chambe o educ ion o humidi y. The amoun o wa e apou inside he chambe was educed by he
18
p esence o silica gel pa icles. The absolu e humidi y was kep below 2 g ams o wa e molecules pe
19
cubic me e , which co esponds o ela i e humidi y lowe han 10% a 23 °C. The chambe s we e
20
o iginally designed by au ho s, one o he M(T) specimens, see Fig. 4(a), and one o he C(T)
21
specimens, see Fig. 4(b). The chambe o he M(T) specimens had no mechanical e ec on he specimen,
22
which was es ed and epo ed in [13], whe e mo e de ails abou he usage o his chambe can also be
23
ound. Due o much smalle s i ness and loading o ce, he chambe o he C(T) specimens had o be
24
mechanically isola ed, see he scheme in Fig. 4(b). Rela i e humidi y inside he chambe was moni o ed
25
using wo senso s o he ype HIH4000-003 (accu acy o ± 3.5%) and he empe a u e inside he chambe
26
was measu ed using he empe a u e senso SMT 160-30.
27
28
29
17
1
Fig. 3. Geome y o he M(T) specimen (le ) and C(T) specimen ( igh ) used o he
2
expe imen s.
3
4
5
Fig. 4. Sealed chambe su ounding he specimen du ing silica expe imen s in d y ai , (a) he
6
M(T) specimen, (b) he C(T) specimen wi h dynamic isola ion. Silica gel pa icles we e
7
loca ed inside he chambe o pump ou ai mois u e.
8
9
10
18
The p ec acks in he M(T) specimens we e ini ia ed a he no ch oo using he o ce ampli ude
1
Fa = 23 kN a he load a io R = –1, which esul ed in he ini ial maximum SIFs in he ange om 10 o
2
14 MPa·m0.5 depending on he no ch leng h. No e ha he whole cycle ange a R = –1 con ibu es o
3
c ack ini ia ion in he no ch. The e o e, ela i ely small maximum SIF could be used, which is good o
4
educe he e ec o o e load and no o use oo la ge loading o ce o he es ing machine. On he o he
5
hand, he C(T) specimens can be loaded only a a posi i e load a io. This is why he maximum ini ial
6
SIFs we e in he ange om 15 o 16 MPa·m0.5. The p ec acks we e ini ia ed in he no ch oo using cyclic
7
o ce wi h he ampli ude Fa = 1.72 kN and he load a io R = 0.1.
8
Du ing he es , he c ack inc emen s we e measu ed op ically using digi al came as ixed o
9
a a elling able equipped wi h he mic o-posi ion measu emen sys em wi h he accu acy o 0.01 mm.
10
The c ack leng h was measu ed on bo h specimen su aces and he alues we e a e aged ( wo c ack
11
leng hs o he C(T) specimen, ou c ack leng hs o he M(T) specimen). This me hodology has been
12
success ully used o a long ime and p o ided eliable da a o many expe imen s. The ad an age o his
13
me hod is ha he c ack leng h is measu ed di ec ly, and i is no calcula ed om o he a iables, such as
14
changes in he elec ical esis i i y o he mechanical s i ness.
15
A e he c ack ini ia ed and eached 1 mm, he expe imen s a ed wi h a s ep-wise load shedding
16
(ΔK-dec easing) p ocedu e o de e mine he c ack g ow h h eshold. The load ampli ude educ ion
17
co esponded o he pa ame e C = –0.4 mm–1 de ined in he s anda d ASTM E647 [24]. A e he c ack
18
s opped a h eshold, he o ce ampli ude was inc eased and he c ack was e-p opaga ed wi h a g adually
19
inc easing ΔK un il he inal ac u e. The da/dN-ΔK da a we e p ocessed acco ding o he s anda d
20
ASTM E647 in o de o exclude in alid da a poin s (e.g. a oo la ge di e ence be ween he leng hs
21
measu ed on he wo sides).
22
23
3.3 P ocessed c ack g ow h a e cu es and ac u e su aces
24
Fo each ma e ial a se o h ee c ack g ow h a e cu es we e measu ed and p esen ed in Figs. 5 – 9:
25
(i) a R = 0.8 in humid ai – g een poin s and solid i ing line, (ii) a R = 0.1 in d y ai – blue poin s and
26
solid i ing line and (iii) a R = 0.1 in humid ai – ed poin s and solid i ing line. In addi ion, a blue
27
dashed line is plo ed as a bo de be ween PICC and RICC, as explained in Sec ion 2.3. The expe imen al
28
poin s a da/dN = 10–9 mm/cycle we e plo ed o cases when no mo e c ack g ow h was de ec ed.
29
Based on obse a ion o he ac u e su aces, se e al s a emen s can be made. A R = 0.1 in humid
30
ai , an inc easingly signi ican oxide deb is laye was o med and isible op ically a he ac u e su aces
31
when app oaching he c ack a es a h eshold. A R = 0.1 in d y ai , he oxide laye was signi ican ly
32
elimina ed. A ull elimina ion o he oxide would equi e he ai o be ully d y, he wa e apou
33
comple ely pumped ou , which was no possible wi h he simple echnology o silica gel pa icles. E en
34
wi h he used echnology, he h eshold was no iceably smalle in d y ai . This was he case o all
35
in es iga ed s eels, including he s ainless s eels, which is qui e su p ising and ema kable. I e eals ha
36
he e ec o OICC is no limi ed o co oding s eels. Su ace oxida ion plays a signi ican ole in
37
co osion- esis an s eels, pe haps due o he epea ed mechanical dis up ion o he passi a ion laye .
38
The obse ed clean ac u e su aces a R = 0.8 in humid ai con i med ha he enhanced oxide laye
39
was no o med and ha c ack closu e causing epea ed con ac p essu e is he necessa y condi ion o he
40
o ma ion o oxide deb is.
41
42
19
1
2
Fig. 5. (a) Expe imen al c ack g ow h a es and hei i ing lines o he X20C 13 s eel ob ained
3
a R = 0.8 in humid ai (g een diamonds), a R = 0.1 in d y ai (blue ci cles) and a R = 0.1
4
in humid ai ( ed c osses) accompanied by he blue dashed line sepa a ing he PICC and
5
RICC componen s o ΔK, as de ined in Sec ion 3.3. (b) – (d) ligh mic oscopy images o
6
he ac u e su aces o he co esponding specimens. The in es iga ed a ea o c ack
7
p opaga ion is ma ked by he whi e e ical a ow and he c ack a es a he measu ed
8
h eshold is unde lined by he whi e do ed line.
9
10
11
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1 2 4 8 16 32
da/dN[mm/cycle]
ΔK[MPa·m0.5]
R=0.8 humid ai R=0.1 humid ai R=0.1 d y ai
R=0.1 ΔKe + PICC
R = 0.1 d y ai
R = 0.1 humid ai
R = 0.8 humid ai
1 mm
(d)
1 mm
(c)
1 mm
(b)
X20C 13 R = 0.8 humid ai R = 0.1 humid ai
(a)
R = 0.1 d y ai R = 0.1 ΔKe + ΔKPICC
20
1
2
Fig. 6. (a) Expe imen al c ack g ow h a es and hei i ing lines o he GX4C Ni13-4 s eel
3
ob ained a R = 0.8 in humid ai (g een diamonds), a R = 0.1 in d y ai (blue ci cles) and
4
a R = 0.1 in humid ai ( ed c osses) accompanied by he blue dashed line sepa a ing he
5
PICC and RICC componen s o ΔK, as de ined in Sec ion 3.3. (b) – (d) ligh mic oscopy
6
images o he ac u e su aces o he co esponding specimens. The in es iga ed a ea o
7
c ack p opaga ion is ma ked by he whi e e ical a ow and he c ack a es a he
8
measu ed h eshold is unde lined by he whi e do ed line.
9
10
11
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1 2 4 8 16 32
da/dN[mm/cycle]
ΔK[MPa·m0.5]
R=0.8 humid ai R=0.1 humid ai R=0.1 d y ai
R=0.1 ΔKe + PICC
R = 0.1 d y ai
R = 0.1 humid ai
R = 0.8 humid ai
1 mm
(d)
1 mm
(c)
1 mm
(b)
GX4C Ni13-4 R = 0.8 humid ai R = 0.1 humid ai
(a)
R = 0.1 d y ai R = 0.1 ΔKe + ΔKPICC
21
1
2
Fig. 7. (a) Expe imen al c ack g ow h a es and hei i ing lines o he EA1N s eel ob ained a
3
R = 0.8 in humid ai (g een diamonds), a R = 0.1 in d y ai (blue ci cles) and a R = 0.1 in
4
humid ai ( ed c osses) accompanied by he blue dashed line sepa a ing he PICC and
5
RICC componen s o ΔK, as de ined in Sec ion 3.3. (b) – (d) ligh mic oscopy images o
6
he ac u e su aces o he co esponding specimens. The in es iga ed a ea o c ack
7
p opaga ion is ma ked by he whi e e ical a ow and he c ack a es a he measu ed
8
h eshold is unde lined by he whi e do ed line.
9
10
11
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1 2 4 8 16 32
da/dN[mm/cycle]
ΔK[MPa·m0.5]
R=0.8 humid ai R=0.1 humid ai R=0.1 d y ai
R=0.1 ΔKe + PICC
R = 0.1 d y ai
R = 0.1 humid ai
R = 0.8 humid ai
1 mm
(d)
1 mm
(c)
1 mm
(b)
EA1N R = 0.8 humid ai R = 0.1 humid ai
(a)
R = 0.1 d y ai R = 0.1 ΔKe + ΔKPICC
22
1
2
Fig. 8. (a) Expe imen al c ack g ow h a es and hei i ing lines o he EA4T s eel ob ained a
3
R = 0.8 in humid ai (g een diamonds), a R = 0.1 in d y ai (blue ci cles) and a R = 0.1 in
4
humid ai ( ed c osses) accompanied by he blue dashed line sepa a ing he PICC and
5
RICC componen s o ΔK, as de ined in Sec ion 3.3. (b) – (d) ligh mic oscopy images o
6
he ac u e su aces o he co esponding specimens. The in es iga ed a ea o c ack
7
p opaga ion is ma ked by he whi e e ical a ow and he c ack a es a he measu ed
8
h eshold is unde lined by he whi e do ed line.
9
10
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1 2 4 8 16 32
da/dN[mm/cycle]
ΔK[MPa·m0.5]
R=0.8 humid ai R=0.1 humid ai R=0.1 d y ai
R=0.1 ΔKe + PICC
R = 0.1 d y ai
R = 0.1 humid ai
R = 0.8 humid ai
1 mm
(d)
1 mm
(c)
1 mm
(b)
EA4T R = 0.8 humid ai R = 0.1 humid ai
(a)
R = 0.1 d y ai R = 0.1 ΔKe + ΔKPICC
23
1
2
Fig. 9. (a) Expe imen al c ack g ow h a es and hei i ing lines o he P265GH s eel ob ained
3
a R = 0.8 in humid ai (g een diamonds), a R = 0.1 in d y ai (blue ci cles) and a R = 0.1
4
in humid ai ( ed c osses) accompanied by he blue dashed line sepa a ing he PICC and
5
RICC componen s o ΔK, as de ined in Sec ion 3.3. (b) – (d) ligh mic oscopy images o
6
he ac u e su aces o he co esponding specimens. The in es iga ed a ea o c ack
7
p opaga ion is ma ked by he whi e e ical a ow and he c ack a es a he measu ed
8
h eshold is unde lined by he whi e do ed line.
9
10
11
12
1.0E-09
1.0E-08
1.0E-07
1.0E-06
1.0E-05
1 2 4 8 16 32
da/dN[mm/cycle]
ΔK[MPa·m0.5]
R=0.8 humid ai R=0.1 humid ai R=0.1 d y ai
R=0.1 ΔKe + PICC
R = 0.1 d y ai
R = 0.1 humid ai
R = 0.8 humid ai
1 mm
(d)
1 mm
(b)
1 mm
(c)
P265GH R = 0.8 humid ai R = 0.1 humid ai
(a)
R = 0.1 d y ai R = 0.1 ΔKe + ΔKPICC
24
3.4 Ex ac ion o impo an pa ame e s and decomposi ion o ΔK h
1
As desc ibed in Sec ions 2.2, 2.3 and 2.4, he pa ame e s o he i ing Eqs. (2) and (3) p o ide use ul
2
in o ma ion abou he composi ion o ΔK in ela ion o d i ing o ce and closu e. Table 3 p esen s he
3
ob ained i ing pa ame e s. The alues hen enabled de e mina ion o he c ack closu e pa ame e
4
acco ding o Eq. (6) and he c ack closu e componen s o h eshold loading ΔKPICC, h, ΔKRICC, h and
5
ΔKOICC, h acco ding o Eqs. (8), (10) and (14), espec i ely. The esul s a e summa ized in Table 4.
6
The componen s ΔKe , h, ΔKPICC, h, ΔKRICC, h and ΔKOICC, h we e g aphically exp essed in Fig. 10 o
7
o e a much be e o e iew o hei signi icance and he co esponding esis ance o a igue c ack
8
g ow h. Owing o his diag am, he esponsible mechanisms o ming he o al h eshold can be clea ly
9
imagined. Al hough sligh shi s o some o he componen s can be subjec o discussion, such
10
decomposi ion is unp eceden ed and o e s a unique insigh in o he complex p oblem o a igue c ack
11
g ow h h eshold. The OICC componen enables assessmen o he ange, in which he adi ionally
12
de ined h eshold may a y due o expe imen al condi ions.
13
Table 3: Fi ing pa ame e s o he c ack g ow h a e Eqs. (2) and (3) ob ained based on he
14
expe imen al da a.
15
Ma e ial
Ce
[*]
CR=0.1
[*]
n
[*]
p
[–]
ΔKe , h
[MPa·m0.5]
ΔKR=0.1, h
(d y ai )
[MPa·m0.5]
ΔKR=0.1, h
(humid ai )
[MPa·m0.5]
X20C 13
7.0·10–9
3.3·10–9
3.2
0.65
2.8
4.8
5.7
GX4C Ni13-4
3.2·10–8
1.8·10–8
2.4
0.75
2.7
3.6
4.5
EA1N
1.7·10–8
1.3·10–8
2.8
0.60
3.0
4.6
5.2
EA4T
2.0·10–8
1.5·10–8
2.6
0.70
2.5
4.2
6.1
P265GH
1.3·10–8
1.0·10–8
2.8
0.70
3.0
5.0
7.0
*Uni s o C and n co espond o da/dN alues in [mm/cycle].
16
17
Table 4: C ack closu e pa ame e s calcula ed using Eqs. (6), (8), (11) and (14).
18
Ma e ial
=
KPICC/Kmax
ΔKPICC, h
[MPa·m0.5]
ΔKRICC, h
[MPa·m0.5]
ΔKOICC, h
[MPa·m0.5]
X20C 13
0.29
1.01
1.04
0.9
GX4C Ni13-4
0.29
0.77
0.13
0.9
EA1N
0.18
0.42
1.18
0.6
EA4T
0.19
0.44
1.26
1.9
P265GH
0.18
0.45
1.55
2.0
19
20
21
22
23
24
25
1
2
Fig. 10. G aphical summa y o he h eshold ΔK h decomposi ion wi h espec o he mechanisms
3
o he i e in es iga ed ma e ials. The e ec i e h eshold ΔKe , h, he plas ici y-induced
4
c ack closu e componen ΔKPICC, h, he oughness-induced c ack closu e componen
5
ΔKRICC, h and he oxide-induced c ack closu e componen ΔKOICC, h.
6
7
4 Discussion
8
4.1 Signi icance o he esul s and gene al discussion
9
Expe imen al echniques o c ack closu e measu emen , such as he back ace o c ack mou h opening
10
displacemen echniques a e no eliable and many discussions and ques ions a ise abou he ele ance o
11
he esul s. While hey s ill ep esen a way o ob ain he alues, especially unde a iable-ampli ude
12
loading, he p esen ed me hod o e s o ind he c ack closu e pa ame e s wi hou any p oblema ic
13
measu emen echniques. Mo eo e , he possibili y o sepa a ion o indi idual closu e componen s is
14
o e ed.
15
4.1.1 PICC e alua ed om c ack g ow h a es e sus nume ical modelling
16
One o he in e es ing indings o he p esen ed p ocedu e is ha he cha ac e is ic c ack closu e
17
pa ame e o he 5 in es iga ed ma e ials we e ob ained di ec ly om he c ack g ow h a es wi hou
18
any necessi y o measu emen o modelling o c ack closu e. These alues a e no a ec ed by any
19
p oblema ic aspec s o he c ack closu e heo y in he sense o he di ec con ac de e mina ion
20
echniques. Looking a he esul s in Table 4, wo g oups o ma e ials wi h simila numbe s we e o med,
21
one o he non-co oding s eels ( ≈ 0.3) and one o he co oding s eels ( ≈ 0.2). The eason can only be
22
a subjec o specula ion. I is clea , hough, ha wi hou he newly p oposed me hodology, his
23
in o ma ion abou he ma e ials would be los and he ue alues could no be compa ed in his way.
24
They would be compu ed as ≈ 0.25 o all ma e ials. The p esen ed me hodology no only sa es ime and
25
e o by a oiding c ack closu e measu emen bu i also emo es he need o ini e elemen modelling o
26
PICC. These nume ical models a e ypically oo complex wi h high demands on compu a ional ime wi h
27
insu icien abili y o p edic . Many pa ame e s o he simula ion need o be calib a ed, in which case he
28
expe imen al da a o he ma e ial need o be a ailable anyway. The eliabili y o c ack closu e
29
expe imen al measu emen has been subjec o deba e o a long ime wi h no consensus. The p esen
30
0
1
2
3
4
5
6
7
8
Composi ion o ΔK h [MPa·m0.5]
ΔK_OICC, h
ΔK_RICC, h
ΔK_PICC, h
ΔK_e , h
(R = 0.1)
ΔKOICC, h
ΔKRICC, h
ΔKPICC, h
ΔKe , h
32
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1
Kmax, h. In J Fa igue 2021;142:105911. h ps://doi.o g/10.1016/j.ij a igue.2020.105911
2
[12] Ri chie RO. Mechanisms o a igue-c ack p opaga ion in duc ile and b i le solids. In J
3
F ac u e 1999;100:55–83. h ps://doi.o g/10.1023/A:1018655917051
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5
p opaga ion in ailway axle s eel EA4T. Eng F ac Mech 2017;185:2–19.
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8
Induced C ack Closu e De elopmen in C -Mo Low-Alloy S eel. Ma e ials 2021;14:2530.
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