6-6 Linear-Elastic Fracture Mechanics Method. Stress Life Testing: R. R. Moore Machine

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1 6-6 Linr-Elstic Frctur Mchnics Mthod tg I Initition o micro-crck du to cyclic plstic dormtion tg II Progrsss to mcrocrck tht rptdly opns nd closs, crting nds clld ch mrks tg III Crck hs propgtd r nough tht rmining mtril is insuicint to crry th lod, nd ils y simpl ultimt ilur 6-6 Linr-Elstic Frctur Mchnics Mthod Crck growth in Rgion II is pproximtd y th Pris qution ΔK I β( σ mx σ min ) π βδσ π Pris Lw d m C( ΔK I ) dn N 1 d N dn 0 m C i ( βδσ π) m 1 d Δσ N m C i β π Δσ ( ) ( N ) constnt Propgtion o this clss o crcks lso ollows th -N digrm s unctionl orm. trss Li Tsting: R. R. Moor Mchin Quntiying Ftigu Filur: trss-li Mthod or Zro Mn trss (uitl or Elstic trss nd High Litims -N digrms ) Motivtion: Trin Axl Low Cycl Ftigu: 1 N High Cycl Ftigu: N> R. R. Moor spcimn (mtril point on th osid) R.R. Moor spcimn (in inchs) [Filur o mtrils in mchnicl dsign: nlysis, prdiction, prvntion, y Jck A. Collins, Wily, 199, p. 189] 1

2 Dormtion o R. R. Moor pcimn R. R. Moor Exggrtd Considr Zro Mn trss First lod rvrsls ( rvrsls 1 cycl) mximum strss, σ mx trss t A strss mplitud, σ t mid-rng strss, σ m 0 minimum strss, σ min [Modiid rom Filur o mtrils in mchnicl dsign: nlysis, prdiction, prvntion, y Jck A. Collins, Wily, 199, p. 189] Follow mtril point A on th or ir 6- trss-li Mthod Exprimntl Corrltions o Ftigu: -N Digrms R.R. Moor mchin tigu tst spcimn (in inchs). Fig. 6-. Ftigu digrm or (chromoly) stl, zro mn strss Th tigu strngth (or ndurnc strngth) is th strss mplitud σ corrsponding to th numr o cycls to ilur I strss mplitud σ is low nough, th spcimn lsts orvr in cyclic loding -N nds or luminum lloy Log-log plots tht corrlt strss mplitud to numr o cycls to ilur r clld -N digrms (to ilur)

3 Ftigu trngth nd Endurnc Limit, (R. R. Moor ) 6-7 Corrltion or th Endurnc Limit x This lowr limit o σ low which li is gurntd is clld th ndurnc limit Ductil Mrtnsit Th tigu strngth (or ndurnc strngth) is th strss mplitud σ corrsponding to th numr o cycls to ilur Th ndurnc limit o n R. R. Moor spcimn (i.., crully l-controlld) is dnotd y ' (to ilur) R.R. Moor spcimn (in inchs) For tls, kpsi(0MP) ' 0kpsi > 00kpsi 700MP > 0MP ( Eq. 6-8 nd Tl A-) 6-8 Estimting th -N Digrm High cycl ( N 6 ): N log log N + log Know two points ( ), ( ) 6 : (Us rom Fig or ( ) ) olv or nd : ( ) 1 log (Vlid or N 6 ) ( ) (lo-cycl oundry ssumd) ( ) 6 ʹ -N Digrm (us corrltion) 6 (hi-cycl oundry ssumd) N Givn 50 HR stl ( 90 ksi (Tl A-1)), stimt: () () (c) Th (R. R. Moor) rotting-m ndurnc limit t 6 cycl Th tigu strngth o polishd rotting-m spcimn corrsponding to cycls to ilur Th xpctd li o polishd rotting-m spcimn undr compltly rvrsd strss o 55kpsi. E.g. 1. (Exmpl 6-) () () ' 90ksi 0.5(90) 5kpsi 0.86 (Figur6 18) ( ) ( ) 5 1 log 1.1N (c) σ 1.1 N ilur log ( ) 6.6kpsi 1/ 55ksi ( )cycls

4 Exrcis: Find sty Fctor ginst tigu ilur, R. R. Moor spcimn o E.g. 1, M mx 00 l-in 6-9 Endurnc Limit Modiying Fctors High-cycl Ftigu ( <N< 7 cycls) k k k k k k ʹ c d whr ndurnc limit undr idlizd condition k surc ctor k siz ctor k c lod modiiction ctor k d tmprtur ctor k rliility ctor k miscllnous ctor urc nd iz Fctor urc ctor: k iz ctor For Torsion nd Bnding k R.R. Moor spcimn 1 For Axil loding 1 k k 0.879d 0.91d 1.d 1.51d d in < d in.79 d 51mm 51< d 5mm iz ctor: Non-R.R.Moor Loding/Gomtry Ectiv dimnsion, d Equt th volum o mtril strssd t nd ov 95% o th mximum strss to th sm volum in th rottingm smpl A π d ( 0.95d ) 0. Bnding witho rottion: solid/hollow round A 0.95σ 0. 06d d 0. 70d Rctngulr sction [ ] 0766d 0.95σ d A 0. 05h 0.95σ h

5 Tl % trss Ars Loding nd Tmprtur ctors 1 Bnding Loding Fctor k c 0.85 Axil 0.59 Torsion Tmprtur ctor k d ( ) TF 0.115( ) ( 8 ) T 0.595( 1 ) T F RT F T F I th ndurnc limit t room tmprtur is known T k d Dt culld rom 1 cron nd lloy stls or whn tmprtur tsting is not vill (tndrd Hndook o Mchin Dsign, higly/mischk, nd d., McGrw Hill, 1996, p. 1.16) Rliility ctor Rliility is dind s th proility o no ilur. W sy, Th ctul vlu o th ndurnc limit is grtr thn k (R) with proility o R (lt-most column). ( lso 6-17) Miscllnous ctors Mnucturing history Rsidul strsss Corrosion Cotings Elctrolytic Plting Mtl prying Cyclic rquncy Frttg Corrosion 5

6 trss Concntrtion nd Notch nsitivity (Bnding & Axil) ttic strss concntrtion, K t, dpnds on gomtry (s Tl A-15): σ K σ mx t o trss Concntrtion & Notch nsitivity (Torsion) ttic strss concntrtion, K ts, dpnds on gomtry (s Tl A-15): τ K τ mx ts o Notch snsitivity ctor K 1 q K 1 For cst iron, q0. t Eqn 6-5 (xtnds Figur 6-0) q 1, 1+ r Ftigu strss concntrtion, K, dpnds on gomtry, mtril & loding Endurnc limit or K notchd spcimn Endurnc limit or notch- r spcimn 1+ ( K 1) q t r [in], [kpsi] Notch snsitivity ctor K s 1 qs K 1 ts For cst iron, q s 0. Eqn 6-5 (xtnds Figur 6-1) 1 qs, r Ftigu strss concntrtion, K s, dpnds on gomtry, mtril & loding Endurnc limit or K notchd spcimn s Endurnc limit or notch- r spcimn 1+ ( K 1) qs ts r [in], [kpsi] to o illt E.g.. N Digrm or Zro Mn trss ht A: hot-rolld stl K ts 1.6 t th -mm illt F 0.5 to 0.5 kn cycl 0 MP Find sty ctor ginst th init-li tigu ilur o sht A. T F d F 0.05 m 0.5kN F 0.5kN 5N m T 5N m Tc Tc T τ 6660 T J πc π( 0.01) 15.9 MP τ 15.9 MP ttic shr-strss concntrtion is K ts 1.6 t th to o th -mm illt: τ to K ts τ nom (95% strss r is th sm s R. R. Moor spcimn) (k c convrts tnsil ndurnc to shr ndurnc!) E.g.. Zro Mn trss Approximt idl ndurnc limit: ʹ ( 0) 160 MP Convrt idl to ctul ndurnc limit: k k k k k k ʹ s c d c k c 0.59 k k 1.( 0) k ( 0) (0.9)(0.59)(160) 77.9MP K Clcult th tigu concntrtion ctor with K ts 1.6 t th to o th -mm illt: K 1+ q ( K 1) or s s ts 1 + q ( K 1) ( 1.6 1) 1. 6 s s ts 1.6( 15.9) τ.mp τ to to 1.6(15.9).MP 0 MP too low to rgistr on Fig Us Eqn. (6-5) trss mplitud: ty ctor:.1 (.1) τ.1 strngth n srvic strss τ s Th dimtr o sht A provs to ovrly consrvtiv. Exrcis: How much do w hv to rduc th dimtr to gt dsign ctor o 1.75? 6