Some History. Over the Next Several Days. Three Stages of Fatigue Failure. Identifying Fatigue Fractures. Three Approaches. Low vs.

Transcription

1 Over the Next everl Dys Wht is Ftigue? Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis oe History Ril The cr xles ll-iportnt icrocrck Role of stress concentns ¾oet irplnes ¾ Unixil Fully Reversed ¾ Unixil Fluctuting ¾ Multixil ¾ rck Growth Three tges of Ftigue Filure rck rck Initition Propgtion Identifying Ftigue Frctures bechrks ¾oscillting stress crck grows, stops growing, grows, stops growing with crck growth due to tensile stresses Frcture ¾sudden, brittle-like filure Three Approches Low vs. High ycle >03 cycles, high cycle ftigue tress-life stress-bsed, for high-cycle ftigue, is to prevent crck initition trin-life useful when yielding begins (i.e., during crck initition), for low-cycle ftigue LEFM (Frcture Mechnics) best odel of crck propgtion, for lowcycle ftigue cr crnk shft ~.5 E8 Rev/05 iles nufcturing 00 rp.5 E8 Rev/yer <03 cycles, low cycle ftigue ships, plnes, vehicle chssis

2 Updte Wht is ftigue? Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis Fully Reversed x Repeted x + Fluctuting stress A R ¾ Unixil Fully Reversed ¾ Unixil Fluctuting ¾ Multixil ¾ rck Growth x Testing Ftigue Properties Rotting Fully Reversed Epiricl Dt An -N urve (tress-life) Be ost dt is fro this type Axil ¾lower or higher? Why? ntilever Torsion Wrought teel Fully Reversed Epiricl Dt Endurnce Liit e A stress level below which teril cn be cycled infinitely without filure Mny terils hve n endurnce liit: low-strength crbon nd lloy steels, soe stinless steels, irons, olybdenu lloys, titniu lloys, nd soe polyers Mny other terils DO NOT hve n endurnce liit: luu, gnesiu, copper, nickel lloys, soe stinless steels, high-strength crbon nd lloy steels Aluu f for these, we use FATIGUE TRENGTH defined for certin nuber of cycles (5E8 is typicl)

3 Updte Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis Unixil Fully Reversed Multixil rck Growth Fully Reversed Repeted Fluctuting x x + stress A R x Getting Ftigue Dt Estiting e Fro ttic Dt ) Test prototype ) Test the exct teril used 3) Published ftigue dt 4) Use sttic dt to estite steels irons luus see pge 34 in your book e 0.5ut e 00ksi e 0.4ut e 4 ksi f 5E8 ut f 9 5E8 for ut 00 ksi for ut 00 ksi for ut 60 ksi for ut 60 ksi for ut 40 ksi for ut 40 ksi BUT, these re ll for highly polished, circulr rotting bes of certin size orrection Fctors onstructing Estited -N urves e f lod lod size size surf surf tep tep pges 36+ in your book relib relib e f The teril strength t 0 3 cycles, : 0.9 ut for bending 0.75 ut for xil loding The line fro to e or f, n N b or log n log + blogn 3

4 Ftigue tress oncentn K f +q(k t -) q notch sensitivity function of teril, ut, Neuber constnt, notch rdius, r q + r Updte Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis Unixil Fully Reversed Multixil rck Growth Unixil Multixil 0 0 Unixil, Fully Reversed trtegy Loding & tress Hlf N (uber of cycles) Fluctuting Lod (F ) Tenttive Mteril Tenttive Design Fully Reversed Repeted Fluctuting x x + stress A R x K t K f,, 3 (principl) (von Mises) (nol) Unixil, Fully Reversed trtegy Ftigue Hlf Unixil Fully Reversed trtegy N (uber of cycles) Fluctuting Lod (F ) lod surf size tep relib e or f e or f Estited -N urve Tenttive Mteril K t K f Tenttive Design,, 3 (principl) (von Mises) (nol) lod surf size tep relib e or f e or f Estited -N urve N f n N f ftigue sfety fctor; n Ftigue strength t n cycles; lrgest von Mises stress 4

5 Updte Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis Unixil Fully Reversed Multixil rck Growth Unixil Multixil 0 0 Fully Reversed Repeted Fluctuting x x + stress A R x Does Men tress Mtter? The Dt Trnsfor -N --> - Fluctuting tress Filure Plot constructed for given nuber of cycles N y Yield Filure e or f odified-goodn fety oderberg Gerber y ut 5

6 Definitions Fctors of fety Four cses ) constnt, vries ) vries, constnt 3) nd increse t constnt 4) nd increse independently If you know how the stress cn vry, only use one of four cses If stress cn vry in ny nner, se 4 should be used (the ost conservtive) Four ses (Use Ruler!) Augented Modified- Goodn Plot y + y y + yc yc f e or f + ut f yc y ut von Mises clculted for nd for seprtely Unixil Fluctuting trtegy tress & Loding N (uber of cycles) Fluctuting Lod (F ) Unixil Fluctuting trtegy Ftigue Aspects Tenttive Mteril K t K f Tenttive Design (no) (no) lod surf size tep relib e or f e or f K f Modified-Goodn Digr,, 3 ;,, 3 (principl), (von Mises) 6

7 Unixil Fluctuting trtegy N (uber of cycles) Fluctuting Lod (F ) Tenttive Mteril Tenttive Design trtegy Find nd with pproprite stress concentn fctors K t (no) (no) K f K f,, 3 ;,, 3 (principl) lod surf size tep relib e or f e or f Find e Plot odified-goodn digr Find fctor of sfety, (von Mises) Modified-Goodn Digr N f Updte Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis Unixil Fully Reversed Multixil rck Growth Unixil Multixil 0 0 Fully Reversed Repeted Fluctuting x x + stress A R x Multixil Ftigue siple ultixil stress periodic, synchronous, in-phse coplex ultixil stress everything else ssug synchronicity nd being inphse is usully conservtive Fully Reversed Multixil Find von Mises equivlent stress for lod iplictions ( ) + ( ) + ( ) 3 3 y N f 7

8 Tie Fluctuting Multixil ines Method Von Mises Method ( ) + ( ) + ( ) 3 3 ( ) + ( 3 ) + ( 3 ) Modified-Goodn Digr Updte Epiricl Dt Estiting Endurnce/Ftigue trength trtegies for Anlysis Unixil Fully Reversed Multixil rck Growth Unixil Multixil 0 0 lculte: Which Follows rck Growth Experients tressmesure vs. cycles K β Then plot d dn ( ) π A ( K ) n d ln dn n ln( K ) d ln dn Kc β π c rck Growth Anlysis ln( K ) lculte: K β π Kc c πβ n Fro N f A 0 N f A N f A d dn A ( K ) n d ( ) ( n dn K ) d n A( K ) A n A n ( ) ( ) ( ) ( ) c n c K d β π d ( ) ( ) ( ) n n n + + β π 0 ( ) ( ) ( ) n n n n ( ) ( ) β π c 0 c 0 Overll trtegy 8