Influence of Mean Stress

Transcription

1 Influence of Men tress Discussion hs been liited to copletely reversible stress thus fr. Mening = 0 However, there re ny instnces of dynic loding when en stress is nonzero.

2 Men tresses Incresing en stress in the tensile direction results in reducing ftigue life (for constnt stress plitude). A constnt life digr ( versus ) or stress life digr ( x versus N f t different levels of R), etc. cn be used to understnd the influence of non-zero en stresses.

3 Constnt Life digr

4 tress life digr

5 Endurnce Liit Endurnce liit (Ftigue liit): hould be obtined by testing cn use the following e e = 0.5 ut = 740MP ut ut 1460MP > 1460MP e Endurnce Liit Rtio, s e / s ut 5

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7 Modifying Fctors for Metl Ftigue A nuber of vribles cn hve significnt ipct on ftigue, such s: ize; Lrger coponents re ore likely to hve ftigue crcks initite, due to lrger volues of teril subject to high stresses, nd due to greter chnce of residul stresses (inherent processing difficulty). Effects inly seen t very long lives. Type of loding; Endurnce liits vry by loding condition (xil, bending, torsion) urfce finish; crtches, pits nd chining rks dd stress concentrtions. Fine grined terils (high strength steel) re ore ffected. Lrge effect, correction fctors usully presented grphiclly Teperture; Endurnce liits increse t low teperture (but frcture toughness decreses significntly) Endurnce liits dispper t high teperture 7

8 Modifying Fctors for Metl Ftigue urfce tretents. Ftigue crcks initite t free surfce, tretents cn be significnt Plting, therl or echnicl; ens to induce residul stress Copressive residul stresses re beneficil, tension is detrientl (reson why shot peening is benificil) The sensitivity of the surfce is ore higher for high strength terils Environent. Corrosion hs coplex interctive effect with ftigue (ttcks surfce nd cretes brittle oxide fil, which crcks nd pits to cuse stress concentrtions) Often in prctice, odifying fctors for the bove re plied to the eqution for the endurnce liit. 8

9 Clculting Endurnce liit using odifying fctors Endurnce liit odifying fctors = k k k k k k e b c d e f e k = urfce fctor k b = ize fctor k c = Lod odifiction fctor k d = Teperture fctor k e = Relibility fctor k f = Miscellneous effects fctor 9

10 urfce Fctor Ground k = 1.58 ut Mchined or cold rolled k 0.65 = 4.51 ut higley, Mechnicl Engineering Design, 1 st etric ed Hot rolled k As-forged = 57.7 ut k = ut Note: ut is in GP 10

11 ize Fctor For bending nd torsion (round brs) d.79 < d 51 k b = d 51 < d < 54 Equivlent dieter for nonrotting squre d = 0.808( hb) 1/ For xil loding: k b =1 11

12 Lod nd Teperture The endurnce liit differ if tests re crried out using rotting be, xil (push pull) nd torsion loding 1.00 Bending k c = 0.85 Axil 0.59 Torsion Use k c =1 for cobined loding Teperture effects Tepertures below roo teperture - brittle filure At high tepertures there is no ftigue liit. 1

13 Modifying Fctors Relibility fctor (bsed on 8% stndrd devition) Relibility % Relibility Fctor k e higley, Mechnicl Engineering Design, 7 th ed 13

14 Miscellneous Fctor Corrosion (k f ) Benh & Wrnock, Mechnics of olids nd tructures,

15 tress concentrtions At sudden chnges in section the stress distribution cn no longer be clculted by the stndrd equtions for stress This phenoenon is known s stress concentrtion, nd the chnge in section is referred to s stress riser tress concentrtion fctor, K t, is defined s the increse in stress over the noinl stress = K x t 0 Where K t is the theoreticl stress concentrtion fctor 15

16 Notch ensitivity oe terils not fully sensitive for the presence of notches A reduced vlue of K t cn be used for these terils The xiu stress in these terils is: x = K f 0 x fs 0 This fctor, K f. is clled ftigue stress concentrtion fctor τ = K τ K f = t 1+ q( K 1) Where q is clled the notch sensitivity, 16

17 Notch ensitivity For steels nd 04 Aluiniu lloys in reversed bending: Fig 7-0:higley, Mechnicl Engineering Design, 7 th ed 17

18 Notch ensitivity Estition of q by Peterson q 1 = 1 +α r α [] ut [MP] Eq 4.4 Bnnntine 1990 For steel only α = 0.5 for norlized or nneled steels BHN 170 α = for quench nd tepered steels BHN 360 α = 0.05 for highly hrdened steels BHN 600 Modified Neuber q = 1+ 1 iplified nd odified Neuber epiricl fits to experientl dt for reltively ild notches shows tht, q, is relted to: Mteril Notch size / r Eq 6-34 :higley 008 Feture Trnsverse hole houlder Groove 174/ ut 139/ ut 104/ ut [] ut [MP] 18

19 Fluctuting stresses higley 008 : 6.11 Fluctuting stress re frequently not coplete stress reversls. N Curve only for coplete stress reversl (or stndrdized cses) hpe of wve not iportnt in periodic ptterns Only the peks (xiu nd iniu) re iportnt 19

20 in =iniu stress x =xiu stress =en stress =stress plitude r =stress rnge x = in x + = in 0

21 Ftigue trength under Fluctuting tress Copressive Men tress Filure occur t = e or x = yc 7-11 higley 005 1

22 Men tress Goodn + e u oderberg + Gerber n = 1 e n + ( n 1 e AME elliptic n n ( ) + ( e y = u n ) y = ) 1 = 1 higley nd Mischke, Mechnicl Engineering Design, 7 th ed 7-11 higley 005

23 Men tresses Goodn eqution: e + = 1 ut e is the endurnce strength. Conservtive nd sfe choice for design of ductile terils, for tensile en stresses. oewht non-conservtive (overly conservtive) for copressive en stresses. One possible pproch for copressive en stresses is to copletely disregrd the en stresses.

24 Men tresses If the su of norlized nd is less thn 1, then the prt hs infinite life. (norlised stresses: / e nd / ut ) However, if the su is ore thn 1, then the prt hs finite life. Goodn criteri is ost coonly used since it is esy to use nd slightly conservtive.

25 Gerber eqution: Men tresses e is the endurnce strength. Provides good fit for ductile terils, for tensile en stresses. Cnnot be used for copressive en stresses since it predicts hrful effect due to copressive stresses (which is never true in prctice, nd overly conservtive) e + = 1 ut

26 Morrow eqution: Men tresses + = 1 e f e is the endurnce strength. Provides good fit for brittle terils (such s cst iron), for tensile en stresses. Generlly results in good fit for copressive en stresses s well. ' f is often equl to the frcture strength.

27 Cobintion of Loding Modes Indentify the principl stresses Deterine the en nd lternting coponents x in τ = x τ τ in = τ x + τ x + τ = in in = Cobine the coponents for using either: Von Mises = + ( K f ) 3( K fsτ ) = + ( K f ) 3( K fsτ higley 008 : 6-14 ) Tresc = K ) + 4( K ( f fs τ ) = + τ ( K f ) 4( K fs ) 7

28 Cobined Loding (hfts) Alternting bending nd constnt torsion oents: My x = I 3M 3 πd = xy = 3 von Mises tress AME Elliptic = K = 3 K τ f x fs xy Tr 16T τ = J πd n ( e n + ( Tresc - oderberg = ) y ) = 1 x = τ xy n e n + y =1 8

29 Coputing Ftigue Life Re-writing Goodn criteri: e + = ut = For infinite life with N N = FO e ut Fro -N curve 1 + = For finite life with N N ut N = FO

30 Coputing Ftigue Life elect n plitude-en odel Goodn criteri ost coonly used. elect FO, if needed. Deterine if life is infinite. If not, use the FO nd the criteri to deterine the equivlent stress plitude for zero en stress, N.

31 Coputing Ftigue Life Use the en stress odel to copute equivlent stress plitude. N = 1 Use the -N curve nd N to copute ftigue life. ut N = AN B f

32 Finite Life Region N Infinite Life Region e ut

33 Typicl exple For n un-notched sple de of AII 4340 steel subject to cyclic stress with = 00 MP nd = 450 MP, deterine the nuber of cycles to filure using Goodn criteri, Gerber criteri nd Morrow criteri. Copre results nd coent on the estited life. Following dt is given: ut = 117 MP, A = 1643 MP, B = , ' f = 1758 MP