Lecture 9 Fatigue limit for multiaxial stress cycles Stress histories of marine diesel engine crankshaft (courtesy Wärtsilä)

Transcription

1 Lecture 9 Ftigue limit for multixil stress cycles Stress histories of mrine diesel engine crnkshft (courtesy ärtsilä) 1

2 Generl multixil stress histories Generl multixil stress histories τ τ x xy xz = τxy y τyz S τxz τyz z s = Sn = T T n s = n Sn τ= s n T ( ) ( ) T T τ = τ τ= s n s n = s s

3 Henri Mtisse ( ): L Vgue (195) Musée Mtisse, Nice Out-of-phse plne-stress cycles ( t) = + sin ωt, x xm x ( t) = m+ sin ( t ), ( t) = m+ ( t ) ω α y y y y τ τ τ sin ω α, xy xy xy xy τ = τ = = 0. xz yz z 3

4 Norml nd sher stresses on φ plne ( ) φ = φ+ φ+ τ φ φ x cos y sin xy sin cos, ( ) = ( y x) + xy( ) τ φ sinφ cosφ τ cos φ sin φ. Stright-line High digrm t ftigue limit ccording to FKM Guideline nd Hempel- Morrow 4

5 High digrm ccording to FKM Guideline = M τ m τ = τ M τ τ m = = f f R τ m ( ) ( τ τa) τa M = = R [MP] b M A A m = = f M τ τ Empiricl mteril prmeters ccording to FKM Guideline 5

6 Sines criterion t ftigue limit for proportionl cycling = + M I r, Mises 1m = + + 3τ I, Mises x y x y xy = + 1m xm ym Criticl-plne criteri t ftigue limit for non-proportionl cycling Norml stress Findley { ( ) M ( )} { τ ( φ) ( φ) } { ( )} MI = mx φ + φ r m 0 φ π f = mx + k f 0 φ π mx crit Tresc-Sines = mx τ φ + r 1m 0 φ π 1 ( ) ( t ) φ mx ( ) = mx ( ; ) 0 t T { } { ( t )} t T { t φ } τ φ = mx τ ; φ min τ ; φ 0 t T 0 6

7 Findley s criterion in terms of conventionl ftigue limits f crit + + = τ 1+ k τ A 1+ 4k ( )( k 1 k ) ( A )( k+ 1+ 4k ) r τ φ ( ) + k ( φ) = mx 0 φ π 1 mx ( k+ 1+ k ) τ = τ sinωt xy ( ) ( ) Mohr's circle: Findley s f crit in terms of τ τ = τ cosφ = τ cos φ xy = τ sin φ = τ sin φ mx xymx Findley. prmeter: f φ = τ + k = τ cos φ + kτ sin φ mx Criticl plne ssocited with mx is given by f φ = τ sin φ + kτ cosφ = 0 tn φ = k cosφ = k, sin φ = 1 1+ k f = mxf = τ 1+ k + kτ k 1+ k = f f mx crit φ crit = τ 1+ k f 7

8 Ftigue prmeters for Findley model Ftigue prmeters for wrought steel 8

9 ASME BPV-III-1 SSC (simultneous stress components) criterion mx { ( tt, ˆ; )} 0 φ π, 0 tˆ T, tˆ t T 1 ( tt, ˆ; ) = ( t; ) ( tˆ ; ) = τ φ r τ φ τ φ τ φ SSC formultion of the Findley criterion mx { τ (, ˆ; φ) (, ˆ; φ) } 0 φ π, 0 tˆ T, tˆ t T 1 ( tt, ˆ; ) = ( t; ) ( tˆ ; ) ( tt, ˆ; ) = mx { ( t; ), ( tˆ ; )} f = tt + k tt f τ φ τ φ τ φ φ φ φ mx ( ) nd ( φ) τ φ mx mx crit now refer to the sme instnts in time, mking their (physicl) interction more likely. 9

10 ftigue criteri stted in engineering design codes nd stndrds Criterion Code Norml stress API RP 17G (ISO) Findley - Mises BPVC-VIII- Mises-Sines - Tresc BPVC-III-1 Tresc-Sines BPVC-VIII-3 * * Men stress correction bsed on men norml stress on criticl plne insted of I 1m Ftigue limits from n = 0 tension-torsion test series compiled from nine different sources 10

11 Ftigue limit predictions for symmetric tension-torsion cycles x ( τxy ) ( x ) ( τxy ) ( x ) ( τxy ) Norml stress + = 1 Mises + 3 = 1 Tresc + 4 = 1 Ftigue limit test dt nd predictions for tension-torsion cycles 11

12 Ftigue limit predictions for symmetric tension-torsion cycles p= m s p = r n i= 1 n p n, p i= 1 i p i ( p m ) ( n ) = 1, Exmple: p = 0.8 unsfely predicts tht r hs only reched 80% of the vlue required for ftigue filure, lthough test dt indicte tht the tension-torsion cycle is lredy t the ftigue limit. Normlised predictions of r t the ftigue limit from different multixil ftigue criteri for 0 tension-torsion cycles 1

13 Reference Ø. A. Bruun, Ftigue ssessment of components subjected to non-proportionl stress histories. MSc Thesis, NTNU, 013. (Received the Prize of the Swedish Ftigue Network for the best Finl Yer Project in 008.) Ø. A. Bruun, G. Härkegård, A comprtive study of design code criteri for prediction of the ftigue limit under inphse nd out-of-phse tension-torsion cycles. Submitted to the Interntionl Journl of Ftigue. 13