Fracture Mechanics, Damage and Fatigue Safe-Life Design
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- Kerry Cameron
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1 Univriy of Lièg Aroac & Mchanical Enginring Fracur Mchanic, Damag and Faigu Saf-Lif Dign Ludovic Nol Comuaional & Mulical Mchanic of Marial CM3 h:// Chmin d Chvruil 1, B4 Lièg L.Nol@ulg.ac.b Fracur Mchanic Saf Lif Dign
2 Dign wih r lowr han Elaic limi ( ) or Inroducion o af-lif dign Tnil rngh ( TS ) ~186 : Wöhlr Tchnologi in h Grman railroad ym Sudid h failur of railcar axl Afr variou im in rvic A load conidrably lowr han xcd w/2 w/2 1 cycl = 2 rvral w/2 w/2 Failur du o cyclic loading/unloading Fracur Mchanic Saf Lif Dign 2
3 Emirical aroach Inroducion o af-lif dign max 1 cycl = D = max - min a = D/2 D 2 rvral m m D min Lif of a rucur dnd on Minimal & maximal r: min & max & man r: m =( max + min )/2 Amliud: a = D/2 = ( max - min )/2 Plaic incrmn D Load Raio: R = min / max S lcur on crack roagaion Undr aricular nvironmnal condiion (humidiy, high mraur, ): Frquncy of cycl Sha of cycl (in,, ) cr D Fracur Mchanic Saf Lif Dign 3
4 Inroducion o af-lif dign Saf-lif dign No crack bfor a drmind numbr of cycl: lif of h rucur A h nd of h xcd lif h comonn i changd vn if no failur ha occurrd Emhai on rvnion of crack iniiaion Aroach horical in naur Aum iniial crack fr rucur Comonn of roaing rucur vibraing wih h flow cycl (blad) Onc crack form, h rmaining lif i vry hor du o h high frquncy of loading Fracur Mchanic Saf Lif Dign 4
5 How o ima h im-lif? Bad on mirical aroach Macrocoic marial ron (faigu ) Do no dircly comu h Rquir microrucur voluion Accura knowldg of ron fild Sr Sr concnraion» Facor K Plaic rain Tmraur Accouning for non-linar marial bhavior U of curiy facor A low a oibl Inroducion o af-lif dign Fracur Mchanic Saf Lif Dign 5
6 Inroducion o af-lif dign Inaccura imaion of laic rain Low-cycl faigu of a blad from ag 1 of h high-rur urbin Cracking a r concnraion in h inrnal cooling aag Blad faild and imacd ohr blad, which arad from laform Sourc: Auralian Tranor Safy, Engin Failur, Boing Co 717-2, VH-VQA, Nar Mlbourn, Vicoria, Ror Final, h:// Fracur Mchanic Saf Lif Dign 6
7 Balanc of body B Momna balanc Linar Angular Boundary condiion Numann Dirichl Marial bhavior T Small dformaion wih linar laic, homognou & ioroic marial n b (Small) Srain nor, or Hook law, or wih Invr law l = K - 2m/3 2m wih Fracur Mchanic Saf Lif Dign 7
8 Marial bhavior (Tru) Elao-laiciy (mall dformaion) Byond a hrhold h marial xrinc irrvribl dformaion Tyical bhavior a low mraur Curv - indndn of im Examl INCONEL 718 (u o 6 C) IN 1 (u o 75 C) Alicaion Yild urfac Plaic flow Comror of urbo-ngin f < : laic rgion f = : laiciy Aumion: dformaion can b addd Normal laic flow Pah dndncy (incrmnal quaion in d ) TS E (Tru) Fracur Mchanic Saf Lif Dign 8
9 Dilocaion moion ( rviou lcur) Mallic bond Marial bhavior: Elao-laiciy a low T FCC or BCC abov DBTT A dilocaion i characrizd by Th Burgr vcor Dilocaion lin (lin along which h diorion i h larg) Sli lan (lan whr h dilocaion moion occur) DoITPoMS, Univriy of Cambridg b Dilocaion lin Burgr vcor b b Fracur Mchanic Saf Lif Dign 9
10 Kinmaic Hardning Ioroic Hardning Marial bhavior: Elao-laiciy a low T Hardning law Tnion-comrion ( ) Tnion-orion 3 12 f(, )= - E 11 - ( ) 3 12 f(, X)= X( ) X Fracur Mchanic Saf Lif Dign 1
11 Phnomnological xlanaion Ioroic hardning Marial bhavior: Elao-laiciy a low T Dilocaion craion du o laic dformaion Irrgularii a h grain boundari (Poly-cryallin marial) Irrgular cryal urfac (mono-cryallin marial) Incra of h dilocaion dniy Obruc dilocaion moion ( ) - - ( ) Long rang laic forc bwn dilocaion of am ign Macrocoic yild r incra E Fracur Mchanic Saf Lif Dign 11
12 Marial bhavior: Elao-laiciy a low T Phnomnological xlanaion (2) Kinmaic hardning Polycryallin mal 2 oibl ourc Dilocaion accumula (il-u) a barrir (grain boundari, rciiaion)» Thy can mov aily in backward dircion» Yild i rducd in rvr dircion Whn rain ar rvrd, dilocaion ourc roduc dilocaion of ooi ign» Annihilaion of dilocaion» Rduc h rngh (a yild i roorional o dilocaion dniy) X( ) Fracur Mchanic Saf Lif Dign 12
13 Marial bhavior: Elao-laiciy a low T Von Mi ioroic hardning (J2-laiciy) Yild urfac Dviaoric r f < : laic rgion f = : laiciy Plaic flow Aumion: dformaion can b addd ( ) - - ( ) E Normal laic flow Normaliy: inc Thn h laic flow bcom Fracur Mchanic Saf Lif Dign 13
14 Marial bhavior: Elao-laiciy a low T Von Mi ioroic hardning (2) Yild urfac f < : laic rgion f = : laiciy f< 3 d* * f(, +d )= df= Plaic flow Hardning law 1 f(*, )= 2 During laic flow h rrnaiv r a rmain on h yild urfac Fr nrgy Can b dfind a wih Fracur Mchanic Saf Lif Dign 14
15 Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning Yild urfac f < : laic rgion f = : laiciy Dviaoric ar of h r nor X( ) X i dviaoric by naur A nw yild urfac i dfind Examl: laic flow during nil Fracur Mchanic Saf Lif Dign 15
16 Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning (2) Yild urfac Plaic flow Aumion: dformaion can b addd X( ) Normal laic flow Normaliy: inc W alo hav Fracur Mchanic Saf Lif Dign 16
17 Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning (3) Yild urfac Plaic flow (2) 1 3 f< X d* * dx f(*, a)= 2 f(, a+da)= df= A X i a r, an aociad rain i dfind in h fr nrgy funcion wih During laic flow h rrnaiv r a rmain on h yild urfac Wha i miing i h law govrning h voluion of X: hardning law Fracur Mchanic Saf Lif Dign 17
18 Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning (4) Pragr linar hardning flow A any im, in 1D: = X( ) ± 3 X( ) f< X Fracur Mchanic Saf Lif Dign 18
19 Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning (5) Armrong-Frdrick non linar hardning law Hardning Dynamic rcovry 1D monoonic nil A any im, in 1D: = X( ) ± 3 Limi urfac X( ) C/g X 1 f< Fracur Mchanic Saf Lif Dign 19
20 Marial bhavior: Elao-laiciy a low T Gnral formulaion Rcour o N inrnal variabl V k Yild urfac Plaic flow f < : laiciy f = : laic flow Th rrnaiv r a rmain on yild urfac 1 3 f(, V k +dv k )= d* f< * df= f(*, V k )= 2 Paricular ca Inrnal variabl Aociad r Ioroic hardning Kinmaic hardning a X Fracur Mchanic Saf Lif Dign 2
21 Marial bhavior: Elao-laiciy a low T Examl: Combinaion of ioroic and kinmaic hardning Yild urfac 3 Fr nrgy funcion X 1 f< 2 Plaic flow Fracur Mchanic Saf Lif Dign 21
22 Marial bhavior: Elao-laiciy a low T Examl: Combinaion of ioroic and kinmaic hardning (2) From yild urfac, during laic flow & f< 1 During laic flow h rrnaiv r 3 X 2 a rmain on yild urfac Hardning law Ioroic Kinmaic Fracur Mchanic Saf Lif Dign 22
23 Marial bhavior: Elao-laiciy a low T Bauchingr ffc Du o kinmaic hardning Linar kinmaic hardning modl Exrimn Cyclic loading D 1 cycl = 2 rvral m D D Fracur Mchanic Saf Lif Dign 23
24 Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning Th Hyric loo i no alway dircly abilizd D Rul from chang in marial rucur Inniy of chang dcra wih cycl numbr m D Th marial can xhibi Faigu hardning D Faigu ofning Fracur Mchanic Saf Lif Dign 24
25 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D Fracur Mchanic Saf Lif Dign 25
26 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D Fracur Mchanic Saf Lif Dign 26
27 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D Fracur Mchanic Saf Lif Dign 27
28 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D D Fracur Mchanic Saf Lif Dign 28
29 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D D Fracur Mchanic Saf Lif Dign 29
30 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D Fracur Mchanic Saf Lif Dign 3
31 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D D Fracur Mchanic Saf Lif Dign 31
32 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D D Fracur Mchanic Saf Lif Dign 32
33 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D D D * Fracur Mchanic Saf Lif Dign 33
34 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D D D D * Fracur Mchanic Saf Lif Dign 34
35 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D D D D * Fracur Mchanic Saf Lif Dign 35
36 Conrolld D = c Conrolld D = c Marial bhavior: Elao-laiciy a low T Faigu hardning/ofning wih accommodaion Cyclic ofning Cyclic hardning D * D * D D D D D * D * Fracur Mchanic Saf Lif Dign 36
37 Marial bhavior: Elao-laiciy a low T Faigu Hardning Uually whn iniially low dilocaion dniy (annald marial) Examl: oly-cryallin iron a low amliud cyclic loading cycl 2 cycl 2 cycl Dilocaion dniy incra unil auraion Sauraion obaind afr a fw hundrd cycl and no furhr dcabl chang r Mirko Klnil,Pr Lukáš «Faigu of mallic marial», Elvir, 1992 N Fracur Mchanic Saf Lif Dign 37
38 Marial bhavior: Elao-laiciy a low T Faigu ofning Uually whn iniially high dilocaion dniy (cold workd marial) Examl: oly-cryallin iron a high amliud cyclic loading 1 cycl 1 cycl 1 cycl Dilocaion localiz o form cll (hardning roc) If incra of amliud (a conan D dformaion) Cll brak down o form rin li band (PSB) Localizaion of li in PSB Sofning Origin of crack Fracur Mchanic Saf Lif Dign 38
39 Marial bhavior: Elao-laiciy a low T Faigu ofning (2) High amliud cyclic loading Cyclic Sofning Cyclic Hardning Cyclically Hardnd marial D/2 D /2 =1% D /2 =.5% PSB D /2 =.25% D /2 =.3% N Fracur Mchanic Saf Lif Dign 39
40 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading Primary loading Scondary loading D m Examl Prur vl Ga urbin Whr D can b du o» Flow flucuaion» Dilaaion r Sabilizd a? Fracur Mchanic Saf Lif Dign 4
41 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl Fracur Mchanic Saf Lif Dign 41
42 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl Fracur Mchanic Saf Lif Dign 42
43 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl Fracur Mchanic Saf Lif Dign 43
44 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl Fracur Mchanic Saf Lif Dign 44
45 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl m >2 D 1 X Fracur Mchanic Saf Lif Dign 45
46 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl m >2 1 D X 1 X Fracur Mchanic Saf Lif Dign 46
47 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl m >2 2 2 >2 1 D X Fracur Mchanic Saf Lif Dign 47
48 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl m >2 2 2 >2 1 D X 2 X Fracur Mchanic Saf Lif Dign 48
49 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld Elaic adaaion For rducd D Ioroic or/and linar kinmaic hardning Adaaion in 1 cycl D m 2 For lighly highr D Ioroic and (linar) kinmaic hardning Adaaion afr a fw cycl m D N X N N Fracur Mchanic Saf Lif Dign 49
50 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (2) Accommodaion Larg D Can b modld by linar kinmaic hardning (accommodaion afr 1 cycl) m 1 D X 1 D X 1 m Fracur Mchanic Saf Lif Dign 5
51 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (2) Accommodaion Larg D Can b modld by linar kinmaic hardning (accommodaion afr 1 cycl) 1 D X 1 m 2 X 1 1 D m X 1 2 X Fracur Mchanic Saf Lif Dign 51
52 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (2) Accommodaion Larg D Can b modld by linar kinmaic hardning (accommodaion afr 1 cycl) m 1 2 D X X 2 1 D m X 2 2 X Fracur Mchanic Saf Lif Dign 52
53 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (2) Accommodaion Larg D Can b modld by linar kinmaic hardning (accommodaion afr 1 cycl) 1 2 D X 2 m 2 X D m X 2 2 X Fracur Mchanic Saf Lif Dign 53
54 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (2) Accommodaion Larg D Can b modld by linar kinmaic hardning (accommodaion afr 1 cycl) m D X min 2 X Max D * D m X Max 2 X min D * Fracur Mchanic Saf Lif Dign 54
55 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (3) Raching (or Roch) Larg D & m Thran lif Non-linar kinmaic hardning lad o raching m 1 D X 1 If X min X Max curv of back-r ar no rvribl X 1 m Fracur Mchanic Saf Lif Dign 55
56 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (3) Raching (or Roch) Larg D & m Thran lif Non-linar kinmaic hardning lad o raching m 1 D X 1 X 1 If X min X Max curv of back-r ar no rvribl 1 X 1 m X Fracur Mchanic Saf Lif Dign 56
57 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (3) Raching (or Roch) Larg D & m Thran lif Non-linar kinmaic hardning lad o raching m d 1 2 D X 2 X 1 If X min X max curv of back-r 1 d ar no rvribl X 2 m X Fracur Mchanic Saf Lif Dign 57
58 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (3) Raching (or Roch) Larg D & m Thran lif Non-linar kinmaic hardning lad o raching m d 1 2 D X 2 X 2 If X min X max curv of back-r 1 2 d ar no rvribl X 2 m X Fracur Mchanic Saf Lif Dign 58
59 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (3) Raching (or Roch) Larg D & m Thran lif Non-linar kinmaic hardning lad o raching m D d If X min X max curv of back-r ar no rvribl X Max m d X min Fracur Mchanic Saf Lif Dign 59
60 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld (4) Br diagram For a givn marial D/2 A Non-linar kinmaic hardning 2 alway rdic raching (if m ) Linar kinmaic hardning nvr rdic raching Law hould b nhancd 1 Thrhold Chaboch (1991) 1 m / Fracur Mchanic Saf Lif Dign 6
61 Marial bhavior: Elao-laiciy a low T Combinaion of rucural and cyclic loading undr conrolld No man r rlaxaion Man r rlaxaion (Accommodaion) (Raching) D D 2 2 m D * 1 m 2 m N m D * Fracur Mchanic Saf Lif Dign 61
62 Marial bhavior: Thrmal ffc Cr Examl: IN1 & T = 1 C undr diffrn conan nil r Primary cr Low rain ( < 1 ) (%). Iniially high bu dcra 239 MPa 4 R x fracur wih hardning c 3 25 MPa MPa. c 137 MPa 1 1 R (hur) Fracur Mchanic Saf Lif Dign 62
63 Marial bhavior: Thrmal ffc Cr Examl: IN1 & T = 1 C undr diffrn conan nil r Primary cr Low rain ( < 1 ) (%). Iniially high bu dcra 239 MPa 4 R x fracur wih hardning c Scondary cr For 1 < < 2. Nar conan Balanc bwn hardning and hrmal ofning Dilocaion li & climb ( nx lid) MPa 171 MPa c MPa 1 1 R (hur) Fracur Mchanic Saf Lif Dign 63
64 Marial bhavior: Thrmal ffc Cr Examl: IN1 & T = 1 C undr diffrn conan nil r Primary cr Low rain ( < 1 ) (%). Iniially high bu dcra 239 MPa 4 R x fracur wih hardning c Scondary cr For 1 < < 2. Nar conan Balanc bwn hardning and hrmal ofning Dilocaion li & climb ( nx lid) Triary cr For > 2. Incra of Bgin of damag Grain-boundary liding Void formaion MPa 171 MPa. c 137 MPa 1 1 R (hur) Fracur Mchanic Saf Lif Dign 64
65 Marial bhavior: Thrmal ffc Dilocaion li and climb During rimary cr Dilocaion accumula (il-u) a barrir (grain boundari, rciiaion) During condary cr If aom Hav nough nrgy (Tmraur and rain nrgy) In clo ackd laic Thy will lf-diffu and fill vacanci Thi corrond for a blockd dilocaion To climb normal o i li lan by aom lf-diffuion To li on an unobrucd li lan Slf diffuion To mov and o annihila wih a dilocaion of ooi ign Sli lan Fracur Mchanic Saf Lif Dign 65
66 Marial bhavior: Thrmal ffc Triary cr Grain boundary liding i acivad Formaion of void undr haring Nimonic 8A, 123 K and 154 MPa Fracur Mchanic Saf Lif Dign 66
67 Marial bhavior: Thrmal ffc Rcovry: rain drivn Qunchd AU4G alloy A 2 C 3 (Ma) 2 c 1 c () Fracur Mchanic Saf Lif Dign 67
68 Scondary cr Conan Noron law. Marial bhavior: Thrmal ffc n (Noron) 2 1 INCO 8 IN 1 Lmaîr law 5 1 T ( C) n m K (MPa. 1/n ) n m K 2 1 T ( C) Fracur Mchanic Saf Lif Dign 68
69 Marial bhavior: Thrmal ffc Effc of cr during cyclic loading undr conan D IN 1 Sur alloy, fir cycl wih holding im, 9 C (Ma) (Ma) 4 cr D Cr dnd on Holding im Tmraur Frquncy Fracur Mchanic Saf Lif Dign 69
70 Marial bhavior: Thrmal ffc Examl of cr during cyclic loading undr conan D HP urbin blad Long working ha a high mraur (axial loading) Long r ha a room T Inr-cryallin fracur mod and void Fracur Mchanic Saf Lif Dign 7
71 Marial bhavior: Thrmal ffc Effc of cr during cyclic loading undr conan D IN 1 Sur alloy, fir cycl wih holding im, 9 C Rlaxaion: dcra of D Rlaxaion dnd on Holding im Tmraur Frquncy Cr and rlaxaion can b modld by conidring Kinmaic hardning Vico-laiciy Fracur Mchanic Saf Lif Dign 71
72 Marial bhavior: Thrmal ffc Modl of cr during cyclic loading Sabilizd cycl During holding im incra (o ). dcra (o v ) a incra. v ( ) ( ) X. v ( ) ( ) Modl rquir (Ioroic) Kinmaic hardning Vico-laiciy Lmaîr & Chaboch U a diiaion onial If <, hr hould no b a laic flow If >: < > =, if no < > = Fracur Mchanic Saf Lif Dign 72
73 Marial bhavior: Thrmal ffc Vico-laiciy modl Plaic flow dircion & amliud? 3 W*> Normaliy L X dx W= v W/ 1 2 A Fracur Mchanic Saf Lif Dign 73
74 Marial bhavior: Thrmal ffc Vico-laiciy modl (2) Examl of onial W k h hardning law (could b drivd from a mor comlx form of W) W*> 3 Paramr ar mraur dndn Normaliy X dx W= v W/ Rlaion vicou r rain ra? Fracur Mchanic Saf Lif Dign 74 v
75 Inroducion o damag Tru Failur mchanim of ducil marial Plaic dformaion rior o (macrocoic) failur of h cimn Dilocaion moion void nuclaion around incluion micro caviy coalcnc crack growh Griffih cririon hould b rlacd by TS Tru Fracur Mchanic Saf Lif Dign 75
76 Fracur mchanic Inroducion o damag Failur mchanim of faigu Crack nuclaion a rin li band Sag I crack growh Along li lan Sag II crack growh Acro vral grain Along a li lan in ach grain, Sraigh ahad macrocoically Sriaion of h failur urfac: corrond o h cycl Prfc cryal Fracur Mchanic Saf Lif Dign 76
77 Failur mchanim of cr Inr-granular void formaion Inroducion o damag Fracur Mchanic Saf Lif Dign 77
78 Inroducion o damag Inracion bwn damag ourc High mraur; vico-laic dformaion; inr-granular void CREEP DAMAGE DUCTILITY Larg laic dformaion; low mraur; void nuclaion and growh inracion FATIGUE Bauchingr ffc, crack growh Saf-lif dign: valuaion of a ruling damag Fracur Mchanic Saf Lif Dign 78
79 Inroducion o damag Modl (1D) A hr ar void in h marial, only a rducd urfac i balancing h racion Virgin cion S Damag of h urfac i dfind a F F So h ffciv (or damagd) urfac i acually And o h ffciv r i Ruling dformaion Aarn macrocoic r Hook law i ill valid if i u h ffciv r So vryhing i haning a if Hook law wa mulilid by (1-D) Ioroic 3D linar laiciy Failur cririon: D=D C, wih < D C <1 Bu how o valua D in af-lif dign, and how do i volv? Fracur Mchanic Saf Lif Dign 79
80 Emirical aroach: Toal lif Toal lif aroach max 1 cycl = D = max - min a = D/2 D 2 rvral m m D min Lif of a rucur dnd on Minimal & maximal r: min & max & man r: m =( max + min )/2 Amliud: a = D/2 = ( max - min )/2 Plaic incrmn D Load Raio: R = min / max S lcur on crack roagaion Undr aricular nvironmnal condiion (humidiy, high mraur, ): Frquncy of cycl Sha of cycl (in,, ) cr D Fracur Mchanic Saf Lif Dign 8
81 Toal lif aroach Fir kind of oal lif aroach: «r lif» aroach For high cycl faigu Srucur xrincing (nially) laic dformaion Lif > 1 4 cycl Faigu limi For a < (nduranc limi): infini lif (>1 7 cycl) For a >, fini lif a = D/2 Marial wih faigu limi Mild/low rngh l Ti-Al-Mg alloy N f Wih ~ [.35 ;.5] TS Marial wihou faigu limi Al alloy Mg alloy High rngh l Non-frro alloy Fracur Mchanic Saf Lif Dign 81
82 Toal lif aroach Fir kind of oal lif aroach: «r lif» aroach (2) Lif of rucur Aumion m = & N f idnical cycl bfor failur For a < (nduranc limi): infini lif (>1 7 cycl) For a >, fini lif Wih ~ [.35 ;.5 ] TS 191, Baquin Law a = D/2 N f f faigu cofficin (mild l T amb : ~ [1; 3] GPa) b faigu xonn (mild l T amb : ~ [-.1; -.6]) Paramr ruling from xrimnal If nduranc limi xi: u N f =1 7 and a = in Baquin Law Fracur Mchanic Saf Lif Dign 82
83 Toal lif aroach Fir kind of oal lif aroach: «r lif» aroach (3) Effc of man r Wöhlr curv TS max (ki) 12 - A A R = R = -.5 R = -1 R =.2 R = R = -.5 R = N F For m and N f idnical cycl, h maximal amliud i corrcd Sodrbrg conrvaiv Goodman Grbr only for alloy undr nion Fracur Mchanic Saf Lif Dign 83
84 Toal lif aroach Fir kind of oal lif aroach: «r lif» aroach (4) Effc of varying amliud load a ( m =) a1 ( m =) a1, m1 a2, m2 a2 ( m =) N f1 N f2 N f n 1 n n i cycl of conan amliud lad o a damag 1945, Minr-Palmgrn law A fracur: Do no accoun for h qunc in which h cycl ar alid Only if low variaion in cycl Only if ur faigu damag Fracur Mchanic Saf Lif Dign 84
85 Toal lif aroach Scond kind of oal lif aroach: «rain lif» aroach For low cycl faigu Srucur xrincing (nially) Larg laic dformaion Sr concnraion (High mraur) For N f idnical cycl bfor failur m D D 1954, Manon-Coffin D f : faigu duciliy cofficin ~ ru fracur duciliy (mal) c : faigu duciliy cofficin xonn ~ [-.7, -.5] (mal) laic rain incrmn during h loading cycl Fracur Mchanic Saf Lif Dign 85
86 Toal lif aroach Gnral rlaion Uing Goodman D /2 (log cal) c b 1 1 LCF HCF 2N f (log cal) Fracur Mchanic Saf Lif Dign 86
87 Inroducion o damag aroach Exrimn Damagd aml Equivaln homognizd aml 1 Exrimnal D D 1 Damag (in 1D) Faigu.5 1 N N F Duciliy Marial, mraur dndn, aramr obaind from 1D xrimn Cr (Kachanov-Rabonov) Fracur Mchanic Saf Lif Dign 87
88 Inroducion o damag aroach Advanag Wri Diiaion onial W and Fr nrgy in rm of h ffciv r inad of h micro-r Non-linar inracion of damag from diffrn naur Examl: Cr and faigu Fracur Mchanic Saf Lif Dign 88
89 Dign uing oal lif aroach 1952, D Havilland 16 Com 1, UK (1) Fir jlinr, 36 angr, rurizd cabin 1954, January, fligh BOAC 781 Rom-Hahrow Plan G-ALYP diingrad abov h a Afr 13 fligh Toal lif aroach faild Fulag faild wll bfor h dign limi of 1 cycl Fracur Mchanic Saf Lif Dign 89
90 1952, D Havilland 16 Com 1, UK (2) 1954, Augu, rriv from h of h ALYP roof Origin of failur a h communicaion window U of quar rivd window Punchd riving inad of drill riving Prnc of iniial dfc Th oal lif aroach accoun for crack iniiaion in mooh cimn bu do no accoun for inhrn dfc Th iniial dfc of h fulag d again faigu could hav hardnd afr h iniial aic load, which wa no h ca wih h roducion lan Lif im can b imrovd by Dign uing oal lif aroach Sho-ning : urfac bombardd by mall hrical mdia Ridual r of comrion in h urfac layr Prvn crack iniiaion Surfac olihing (o rmov crack) Fracur Mchanic Saf Lif Dign 9
91 Economically infficin PW F1 (F15 & F16) Uing oal lif aroach again LCF All dik rlacd whn aiically 1 dik had a faigu crack (a<.75 mm) Sudi indica ha a la 8% of ar rlacd hav a la a full ordr of magniud of rmaining faigu lif Dign uing oal lif aroach Exra co for US Air forc: > $5 /yar h:// h://ocw.mi.du/cour/marial-cinc-and-nginring/3-35-fracur-and-faigu-fall-23/lcur-no/faigu_crack_growh.df (Subra Surh) Fracur Mchanic Saf Lif Dign 91
92 Dign uing oal lif aroach Economically infficin (2) Air-forc ar uing Rirmn For Cau aroach in 1986 Priodic nondruciv valuaion o a h damag a of comonn Comonn wih no dcabl crack: rurnd o rvic Allow Par wih low lif Dcd and dicardd bfor hy can cau an incidn Par wih high lif Ud o hir full onial Baic o an RFC rogram Calculaion of crack-growh ra undr h xcd rvic load (mchanical and hrmal) Th rul ar ud o dfin af-u inrval bwn rquird (nondruciv) incion h:// h://ocw.mi.du/cour/marial-cinc-and-nginring/3-35-fracur-and-faigu-fall-23/lcur-no/faigu_crack_growh.df (Subra Surh) Fracur Mchanic Saf Lif Dign 92
93 Faigu dign a (cm) «Damag olran dign» Aum crack ar rn from h bginning of rvic Characriz h ignificanc of faigu crack on rucural rformanc Conrol iniial crack iz hrough manufacuring roc and (non-druciv) incion Eima crack growh ra during rvic (Pari-Erdogan) & lan conrvaiv incion inrval (.g. vry o many yar, numbr of fligh) Vrify crack growh during h incion Prdic nd of lif (a f ) Rmov old rucur from rvic bfor rdicd nd-of-lif (fracur) or imlmn rair-rhabiliaion ragy Non-druciv incion Oical X-ray Ulraonic (rflcion on crack urfac) a P P Srucur incion oibl (for DP 1 ) DP 2 > DP Fracur Mchanic Saf Lif Dign 93 DP 1 Raid crack growh Ruur N f (1 5 )
94 Exrcic 1 Effc of avrag r Circular rod Uniform cro-cional A = 2 cm 2 Subjcd o a man axial forc of 12 kn Marial Faigu rngh a = f = 25 MPa a 1 6 cycl of fully rvrd loading Tnil rngh TS = 5 MPa Yild r = 35 MPa Allowabl amliud of forc P for which h haf would b dignd o wihand a la on million faigu cycl? P 12 kn Fracur Mchanic Saf Lif Dign 94
95 Exrcic 2 Sho-nd mallic marial Prori bfor ho-ning Young modu E = 21 GPa HCF aramr f = 11 MPa, b = -.8 LCF aramr f = 1, c = -.63 Du o ho-ning Comriv ridual r of 25 MPa Tnil rngh TS = 5 Ma Wha i h lif imrovmn du o hoo-ning? Fracur Mchanic Saf Lif Dign 95
96 Rfrnc Rfrnc Mchanic of Solid Marial. Jan Lmaîr,Jan-Loui Chaboch, Cambridg Univriy r, 1994 Plaiciy and vicolaiciy undr cyclic loading. Jan-Loui Chaboch, ATHENS Cour MP March Fracur Mchanic Saf Lif Dign 96
97 Exrcic 1 Circular rod Du o P, hr i a cyclic loading P of amliud a Wihou axial forc Th rod can and 1 6 cycl a a ( m =) = 25 MPa Wih axial forc Avrag r m = 12 /.2 = 6 MPa For 1 6 cycl, h loading P hould induc a cyclic loading of amliud Sodrbrg 12 kn Goodman Grbr (Ok a nion) Fracur Mchanic Saf Lif Dign 97
98 Exrcic 2 Bfor ho ning Afr ho ning Ridual r ac lik a comriv man r Fracur Mchanic Saf Lif Dign 98
99 Exrcic 2 Comarion Original Wih ho-ning D/ N f f Imrov mainly h HCF rgim Fracur Mchanic Saf Lif Dign 99
100 Annx I: Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning: Tangn Pragr linar hardning flow 3 f< X d* * dx f(*,a)= f(,a+da)= df= 1 2 Tangn nor W can find back: Fracur Mchanic Saf Lif Dign 1
101 Annx I: Marial bhavior: Elao-laiciy a low T Von Mi kinmaic hardning: Tangn (2) Armrong-Frdrick non linar hardning law 3 f< X d* * dx f(*,a)= f(,a+da)= df= Fracur Mchanic Saf Lif Dign 11
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