The Fracture Mechanics Method (da/dn- K)

Transcription

1 The Frcture Mechnics Method (d/dn-k) June 2 nd 6 th, 214, Alto University, Espoo, Finlnd Prof. Grzegorz Glink University of Wterloo, Cnd 21 Grzegorz Glink. All rights reserved. 1

2 Informtion pth for ftigue life estimtion bsed on the d/dn-k method F LOADING t GEOMETRY, K t PSO MATERIAL E Stress-Strin Anlysis MATERIAL Dmge Anlysis d dn n DK th DK Ftigue Life 28 Grzegorz Glink. All rights reserved. 2

3 Steps in Ftigue Life Prediction Procedure Bsed on the d/dn-k Approch (cont d) i) f) Stress intensity fctor, K (indirect method) f (x, y) Weight function, m(x,y) K A K Y n,, x y m x y dxdy Crck depth, i Ftigue Life Stress intensity fctor, K (direct method) Number of cycles, N g) K 2x I yfe FE or K du E d EG K Y n h) Integrtion of Pris eqution f i1 m C K N i i i N N N i i 28 Grzegorz Glink. All rights reserved. 3

4 The Similitude Concept in the d/dn K Method ) Structure 1-6 b) Weld detil Q H F Crck Growth Rte, m/cycle c) Specimen K K, MP m P P The Similitude Concept sttes tht if the stress intensity K for crck in the ctul component nd in the test specimen re the sme, then the ftigue crck growth response in the component nd in the specimen will lso be the sme nd cn be described by the mteril ftigue crck growth curve d/dn - K. 28 Grzegorz Glink. All rights reserved. 4

5 Crck tip stress dependence on the stress intensity fctor K S y S yy K 3 2 x yy K 2 2 x K 1 < K 2 < K 3 Stress components, ij, t the crck tip depend on the stress intensity fctors K I which is influenced by: u y r xx yy xy x - the lod, S -crck dimensions, -geometry, Y The stress field, ij, round the crck tip cn be described by one universl function vlid for ll crcks of Mode I, i.e. for = S S yy K 2 x 21 Grzegorz Glink. All rights reserved. 5

6 G. Irwin s fundmentl Frcture Mechnics principles: 1. The ner crck tip stress field expressions bove re universl, i.e. the stress distributions in the vicinity of the crck tip hve the sme generl mthemticl form regrdless of the crck geometry, loding nd geometricl shpe of the body. 2. The strin energy relese rte G I is relted to the stress intensity fctor K I nd therefore it is justified (nd esier) to clculte the strin energy relese rte (nd the criticl stress) from the purely elstic locl (ner the crck tip) stress distribution (i.e. from the Stress Intensity Fctor). G G I I S Y 2 K I E E 2 plne stress 2 S Y 2 2 K I E E plne strin 21 Grzegorz Glink. All rights reserved. 6

7 A crck becomes unstble (frcture) when the stress intensity fctor, K I, exceeds the criticl, for given mteril, stress intensity fctor K Ic! K I > K Ic Force [MN] Stress [MP] Stress Intensity Fctor [MPm] Strength prmeters trditionlly used for the sttrength nlysis of engineering components nd structures: P P P Y cr Y uts K K K I c Ic Frcture Mechnics prmeters used for the strength nlysis of engineering components nd structures: Leonrdo d Vinci 17th-century Euler, Cuchy 19th -century Irwin 2th-century 21 Grzegorz Glink. All rights reserved. 7

8 Generl Stress Intensity Fctor Expressions for Crcks in Mode I The stress intensity fctor is defined s: K I S in which S is the stress (usully the nominl) wy from the crck. The geometry fctor, Y, ccounts for the effect of geometry of the crck nd the body, the boundry conditions nd the type of loding. Determining stress intensity fctor mens in essence the derivtion of the function describing the geometricl fctor Y. One of the confusing issues while determining stress intensity fctors is tht the remotely pplied stress S nd the geometry fctor Y re inter-relted. The vlue of prmeter Y depends on the definition of the remote (termed often s nominl) stress S. In cses where the nominl or hot spot stress is well defined there is no problem in the definition of the remote stress S. However, if the stress distribution is non-uniform it my not be cler which stress should be used in the expression for the stress intensity fctor. Theoreticlly, ny reference stress S cn be chosen for the determintion of the geometricl fctor Y, s fr s the stress vries proportionlly with the pplied lod. However, the user of given expression for K hs to use the sme definition of the reference stress while crrying out ftigue nd frcture nlyses. Nominl or the mximum stress in the cse of non-uniform stress distributions is most often used in stress intensity fctor expressions. Therefore, it is good professionl prctice to define the reference stress S when quoting the geometry fctor Y. 21 Grzegorz Glink. All rights reserved. 8 Y

9 Center Crck Plte under Uniform Tension 2 W t (1) 2 KI FI( ),, FI W Y ( ) F I ( ) sec 2 Reference: C.F. Federsen (1), H. Td (2) Method: Empiricl formul bsed on Isid s results Accurcy: +.3% for 2/W.7 nd 1.% for 2/W=.8 or (2) KI 2 4 F( ) Accurcy: Better thn.2% for ny vlue of (Y. Murkmi et. l) 21 Grzegorz Glink. All rights reserved. 9

10 The SIF geometry correction fctor Y; K I = SY; (centrl crck) Geometry correction fctor, F I () = Y 2/W Grzegorz Glink. All rights reserved. 1

11 Exmple A thick center-crcked plte of high strength luminum lloy is 2 mm wide nd contins crck of length 8 mm. If it fils t n pplied stresses of 1 MP, wht is the frcture toughness of the lloy? Wht vlue of pplied stress would produce frcture for the sme length of crck in: ) n infinite plte b) 12 mm wide plte? 2 2W 21 Grzegorz Glink. All rights reserved. 11

12 ) Finite width plte 2W 2 mm, 2 8 mm, 1MP K Y; Y f ; W See nottion in the Hndbook : 2 2 W 2W W hndbook exmple exmple W W 1 hndbook exmple 2 Y W K Y MP m K K MP m c c) Plte 12mm wide W W 6 hndbook exmple 2 Y W K c K; MP b) Ininitely wide plte K Y; nd Y 1 K c K; MP.4 21 Grzegorz Glink. All rights reserved. 12

13 Geometry Effects on the Stress Intensity Fctor Stress Intensity fctors for crcks in butt weldment nd flt plte of the sme thickness Y S S K I S () t (x)=s t /t.5 Y S y S K I S (b) t (x) t x () /t.5 S 21 Grzegorz Glink. All rights reserved. 13

14 The Weight Function method for clculting Stress Intensity Fctors y S 2P x x x 1,, 1 M M M 2 x1 P1 K m x P K A P 2P 2 2 x2 x2 x2 A m x2,, P2 1 M1 1 M2 1 M x2 x 2 x 1 A (x) x K P A 1 P 2,, P mx, P m x 1 1 2, 2 P 1 P 2 t K A x xm x, dx S 21 Grzegorz Glink. All rights reserved. 14

15 Geometricl prmeters nd nottion for weight functions y y x P A x P x x A x W 2 2W K 2 x x x M3 1 2 x P1 A m x,, P M M 21 Grzegorz Glink. All rights reserved

16 Centrl through crck in finite width plte subjected to symmetric loding M M M w w w w w w w w w w w w w w w w w w w w Edge crck in finite width plte M M M w w w w w w w w w w w w w w w w w w w w w w w w w w w w 8 21 Grzegorz Glink. All rights reserved. 16

17 The Weight Function method for clculting Stress Intensity Fctors y S y S y (x) (x) x x x t t t S S ) b) c) K = K b The Stress Intensity Fctor for ny loding cse is equl to the stress intensity fctor obtined by pplying to the crck fces the stresses tht used to be there when there ws no crck. 21 Grzegorz Glink. All rights reserved. 17

18 Stepwise Procedure for the Stress Intensity Clcultion using the Weight Function Method 1. Clculte stress distribution (x) in the prospective crck plne in the bsence of the crck (un-crcked body, liner elstic nlysis). x f x, 2. Apply the stress distribution (x) to the crck surfce s trctions. 3. Choose pproprite weight function, i.e. prmeters M 1, M 2 nd M 3. 1/2 1 3/2 2 x x x m( x, ) 1 M11 M2 1 M3 1 2 x 4. Integrte the product of the stress distribution (x) nd the weight function m(x,). K x m ( x, ) dx 21 Grzegorz Glink. All rights reserved. 18

19 ) T 2 The superposition principle for clcultion of stress intensity fctors using the weight function pproch; r ) stress distribution in the prospective crck plne in the un-crcked body; b) the un-crcked stress field pplied to the crck surfces of identicl body with crck; x t Prospective crck plne (y) S b) T 2 y crck o K I m y, y dy t x t (y) 21 Grzegorz Glink. All rights reserved. 19 y

20 Through the plte thickness stress distributions in T-butt weldment obtined for r/t = 1/25, = 45 o (in the weld toe cross section) FEM (y) / n 21 Grzegorz Glink. All rights reserved. 2 y / T

21 Geometricl Stress Intensity Correction Fctor Y for n Edge Crck Emnting from the Weld Toe (Comprison of WF nd FEM dt) T-butt welded joint; Tension loding T-butt welded joint; Bending lod 21 Grzegorz Glink. All rights reserved. 21

22 (x) (x) Clcultion of SIF for crcks t notches using the weight functions for edge nd through crcks d b b b (x) (x) (x) b b 2 b t 2t 21 Grzegorz Glink. All rights reserved. 22

23 Frcture Mechnics Approch to Ftigue Crck Growth Anlysis Ftigue crck growth equtions Integrtion of ftigue crck growth expressions The effect of the initil crck size The effect of the weld geometry Residul stress effect Exmple 21 Grzegorz Glink. All rights reserved. 23

24 Ftigue Crck Growth Micro-Mechnism A shrp crck in tension stress field cuses high stress concentrtion t the its tip resulting in slip nd plstic deformtion in the crck tip vicinity. The mteril bove nd below the crck tip my slip long fvorble slip plne in the direction of mximum sher stress. b c Stress () (b) Time (c) (d) (e) d e (C. Lird, ASTM, STP 415, 1967) 21 Grzegorz Glink. All rights reserved. 24 (R.Pelloux, ASTM, STP 415, 1967)

25 Experimentl dt for the determintion of the ftigue crck growth curve Crck length, S 1 > S 2 > S 3 S 1 S 2 f, N f S 3 N Applied nominl stress history d/dn= / N S Number of pplied cycles, N - Experimentl test dt Stress, S S Time, t Crck length, S i, N i d/dn The vs. N dt is obtined in prctice by periodic mesurement of the crck length,, together with the number of cycles, N. The rw dt is usully given in the form of series of points s shown in the figure. Number of pplied cycles, N 21 Grzegorz Glink. All rights reserved. 25

26 The Frcture Mechnics pproch to ftigue or the d/dn - K method is technique bsed on the nlysis of ftigue crck growth. The combintion of lod/stress nd geometry prmeters, necessry for the quntifiction of dmge due to crck growth, is represented by the stress intensity fctor, K, in the cse of monotonic lod nd by the rnge of the stress intensity fctor, K, in the cse of cyclic loding. The ftigue mteril properties re chrcterized by the threshold stress intensity rnge, K th, the ftigue crck growth rte reltionship, d/dn vs. K, nd the criticl stress intensity fctor, K c, to be often the sme s the frcture toughness, K Ic. The crck growth rte is then described by n expression being function of the stress intensity rnge: d f K dn, The stress intensity rnge ssocited with stress cycle is clculted s: K K K S Y S Y mx min mx min where is the crck size, S mx nd S min is the mximum nd minimum nominl (or reference) stress respectively, chrcterizing stress cycle, nd Y is the geometry correction fctor. The im of the finl nlysis of the d/dn-k dt is to determine necessry constnts nd prmeters ppering in expression f(k). It should be noted tht the d/dn - K curve in frcture mechnics represents the mteril ftigue resistnce similrly to the S-N curve in the nominl stress pproch or the - N reltionship in the locl strin-life methodology. As soon s the crck growth curve for the mteril of interest is known the ftigue life of the structurl component cn be determined s shown in the figure below. 21 Grzegorz Glink. All rights reserved. 26

27 The nottion for the cyclic stress history prmeters nd the steps necessry for the determintion of the d/dn - K reltionship re explined lter in the following sections of the notes. The ftigue life in terms of the number of cycles necessry to propgte the crck from its initil size,, to the finl or criticl crck size, f, is determined by integrting the crck growth eqution. N f f d d f K f S Y The determintion of the integrl bove needs numericl tretment becuse the geometry correction fctor, Y, becomes frequently complex function of the crck size,. Subsequent stges of the ftigue life prediction method bsed on the crck growth nlysis re shown grphiclly in the Figure. 21 Grzegorz Glink. All rights reserved. 27

28 Constnt Amplitude Cyclic Lod - Nottion S mx Stress, S S m S min 1 cycle S S Time, t S min - minimum stress S mx - mximum stress S = S mx -S min - stress rnge S = S /2 = (S mx -S min )/2 - men stress R = S min / S mx - stress rtio 21 Grzegorz Glink. All rights reserved. 28

29 Ftigue Crck Growth Rte vs. Stress Intensity Fctor S K S Y nd K S Y 21 Grzegorz Glink. All rights reserved. 29

30 Sctter of ftigue crck growth dt; Low lloy steel 18G2VA 4 mm thick plte 4 mm thick welded plte 21 Grzegorz Glink. All rights reserved. 3

31 The Ftigue Crck Growth Expression The Pris eqution The first mthemticl reltionship relting ftigue crck growth rte nd the stress intensity rnge ws proposed by Pris nd Erdogn. This reltionship is up to dte the most populr mthemticl expression used if vrious ftigue/frcture mechnics nlyses. It ws obtined by fitting power lw curve into the experimentl dt. Where: Where: d C K dn m d/dn - ftigue crck growth rte [in/cycle or m/cycle] C - Pris eqution prmeter (vlid for given R) m - K - - crck length/depth Pris eqution exponent stress intensity rnge S mx - mximum stress in stress cycle S min - minimum stress in stress cycle K mx - mximum stress intensity fctor K min - minimum stress intensity fctor Y K K K for K mx min min K K for K mx mx min mx min min K S Y K S Y - geometry correction fctor in the stress intensity fctor expression 21 Grzegorz Glink. All rights reserved. 31

32 Complete Ftigue Crck Growth Rte Curve, d/dn - K Soon fter the Pris eqution gined wide cceptnce s tool for ftigue crck growth nlysis, it ws found tht the simple expression proposed by Pris nd Erdogn hd some limittions. As the Figure below illustrtes the complete log-log plot of d/dn vs. K is sigmoidl rther then liner nd limited by the threshold stress intensity rnge, K th, nd the criticl stress intensity fctor K c. At low growth rtes, the d/dn vs. K curve becomes steep nd ppers to pproch verticl symptote denoted K th, which is clled the ftigue threshold stress intensity rnge or ftigue crck growth threshold. This quntity is interpreted s lower limiting vlue of the stress intensity fctor rnge K below which ftigue crck growth does not ordinrily occur. The ftigue crck growth threshold is nlogous to the ftigue limit in the S-N pproch. At high growth rtes, the d/dn vs. K curve my gin become steep. This is due to rpid unstble crck growth just prior to finl frcture when K mx K c. The increse of the ftigue crck rte ner the criticl stress intensity fctor K c is due to mixture of sttic (monotonic -frcture) nd ftigue mechnisms driving the crck growth. Also, the ftigue crck growth rte exhibits dependence on the stress rtio R. The stress rtio R ffects the ftigue crck growth rte in mnner nlogous to the effects observed in the S-N nd -N methods, i.e. for given K, incresing R-rtio increses the ftigue crck growth rte, nd vice-vers. The effect of the R -rtio (or men stress) on Ftigue Crck Growth is most often explined using the phenomenon discovered by Elber. By mesuring the complince of specimens with ftigue crcks he noticed tht the crck tip got closed during the descending prt of the stress cycle in spite of the fct tht the pplied stress/lod remined tensile (see Figure). Elber postulted tht crck closure decreses the ftigue crck growth rte by reducing the effective stress intensity rnge. 21 Grzegorz Glink. All rights reserved. 32

33 Crck Growth Rte, d/dn [mm/cycle] K, Stress Intensity Rnge, [ksiin] A533B-1 steel, u =627 MP K th () (b) d C K dn R=.1 m (c) d/dn. Crck Growth Rte, d/dn [inches/cycle] Ftigue crck growth rtes for ductile pressure vessel steel (the Pris eqution) d C K dn m The d/dn-k curve is the ftigue mteril curve independent of the geometry, i.e. the sme curve for ll geometricl crck-body configurtions! K, Stress Intensity Rnge, MPm 21 Grzegorz Glink. All rights reserved. 33 Source: N. Dowling, ref(2)

34 21 Grzegorz Glink. All rights reserved. 34 For simplicity resons the complete ftigue crck growth rte is usully pproximted by three liner pieces with the two of them being verticl limiting symptotes.

35 Pris eqution constnts for steel mterils t R = Crck Growth Rte, m/cycle ys K, MPm Ferritic-Perlitic Steel: d dn Mrtensitic Steel: d dn d dn Austenitic Stinless Steel: K 3. K 2.25 K 3.25 for: d/dn in [m/cycle] nd K in [MPm] J. Brsom, Ftigue Crck Propgtion in Steels of Vrious Yield Strengths Journl of Engineering for Industry, Trns. ASME, Series B, Vol. 93, No. 4, 1971, Grzegorz Glink. All rights reserved. 35

36 Estimtion of the Ftigue Crck Propgtion Life Bsic Steps: 1. Estimte the initil crck size nd shpe, o ; - non-destructive testing - o - proof lod - o 2. Estimte the criticl crck size c bsed on the frcture toughness K IC, i.e. the crck size tht the component will tolerte when the pplied stress reches its mximum S mx. 1 K IC KICSmx cyc c Smx Yc 3. Using the sme expression for the stress intensity fctor clculte the stress intensity rnge K. 2 K S Y for R K S Y for R ( if!!) mx r 21 Grzegorz Glink. All rights reserved. 36

37 4. Substitute K into ftigue crck growth eqution (Pris or Formn) d C ( K ) C ( S ) Y dn m m m 5. Integrte the eqution bove from = o to = c nd determine the number of cycles, N, necessry to grow the crck from the initil crck size of o to the criticl size of c. This is the estimted ftigue crck propgtion life of given component! N c o dn d C( K) c d d m C( K) C( S Y) o m Note! In most prcticl cses the integrtion requires numericl solution due to the complexity of the geometric fctor Y. 21 Grzegorz Glink. All rights reserved. 37

38 Integrted Pris Eqution for Constnt Geometric Fctor, Y = const. d dn m C K C( S Y ) m N for m ( m 2) C( SY) m m/2 ( m2)/2 ( m2)/2 o c ; form 2 N CS 1 Y 2 2 c ln ; o 21 Grzegorz Glink. All rights reserved. 38

39 Numericl Integrtion of the Pris Eqution If the Y fctor is not constnt numericl technique hs to be pplied. The most often used is the cycle by cycle technique bsed on the clcultion of crck increments i corresponding to ech lod cycle. In this cse, the infinitesiml increments d nd dn re replced by finite differences nd N= 1. i C( K ) C( S Y ) ; ; C( S Y) N N i m m 1 1 N m i i i i i o i i i i1 i i i1 N ; N 1; N 1; C S Y ; ; N 1; N 1; C S Y ; ; N 1; N 1; C S Y ; ; N 1; N 1; C S Y ; ; m N 1; N 1; C S Y ; ; i i i i i 1 i 1 i i 1 i until i c m m m m Clcultions hve to be crried out for ech cycle!! 21 Grzegorz Glink. All rights reserved. 39

40 Subsequent stges of ftigue life prediction method bsed on the crck growth nlysis Anlysis of externl forces cting on the structure nd the component in question (), Anlysis of internl lods in chosen cross section of component ( b), Selection of individul welded joints in the structure (c), Identifiction of pproprite nominl or reference stress history (d), Extrction of stress cycles (rinflow counting) or reversls from the stress history (Fig.e), Determintion of the stress intensity fctor (i.e. the fctor Y) for postulted or existing crck, - indirect method (Fig.f): nlyze un-crcked weldment nd determine the stress field, (x,y), in the prospective crck plne; normlize the clculted stress distribution with respect to the nominl or ny other reference stress, i.e. (x,y)/ n, choose pproprite weight function, clculte stress intensity fctor determine the stress or displcement field ner the crck, or the strin energy relese rte, clculte stress intensity fctor using. Determintion of crck increments for ech stress cycle (Fig. h), Determintion of the number of cycles, N, necessry to grow the crck from its initil size,, up to the finl size, f. A summry of necessry input dt nd procedures used in the, d/dn - K, pproch to ftigue life estimtion is lso presented in the Figure. 21 Grzegorz Glink. All rights reserved. 4

41 Exmple: A very wide SAE 12 cold-rolled thin plte is subjected to constnt mplitude uni-xil cyclic lods tht produce nominl stresses vrying from S mx =2MP (29ksi) to S min =-5 MP (-7.3ksi). The monotonic properties for this steel re Y =63 MP (91 ksi), uts =67 MP (97 ksi), E=27 MP (3 ksi), K c =14 MPm (95 ksiin). Wht ftigue life would be ttined if n initil through-thickness edge crck existed nd ws 1 mm (.4 in) in depth? The ftigue crck growth dt re: K th(r=) =6 MPm, nd Pris eqution prmeters C= nd m=3. S Stress S mx time S min W >> S 21 Grzegorz Glink. All rights reserved. 41

42 A. Wht is the stress intensity fctor expression? Semi-infinite plte with n edge crck. K S Y S mx mx mx 1.12 B. Is Liner Elstic Frcture Mechnics (LEFM) pplicble? Nominl stress level : S MP YES! mx Y Plstic zone size : K S Y MP m mx mx K mx ry.635m.635mm 2 Y 63 r y YES! Grzegorz Glink. All rights reserved. 42

43 C. The effective stress rnge S Smx Smin for Smin S S for S mx mx mx min S 2MP nd S 5MP thus S S 2MP D. Is the Pris eqution pplicble? min Pris eqution is vlid for K K Smllest K K occurs for.1 m. K S Y MP m K 12.6 K 6 MP m YES, Pris eqution is pplicble! th th! 21 Grzegorz Glink. All rights reserved. 43

44 E. Wht is the criticl/finl crck size? E. Integrtion of the Pris eqution K K S Y c finl mx c Anlyticl integrtion is possible becuse Y= const K c 1 14 c.68m 68mm Smx Y N N m C K C( S Y ) c c c d d 1 d C K C( S Y ) C S Y d dn m m m m 2 m 2 m for m 2nd Y const ( m 2) C ( S Y) m m/2 ( m2)/2 ( m2)/2 c m ; N /2 (32)/2 (3 2) (2 1.12).1.6 (32)/ ( 2)/2 ( 2)/ m m c Grzegorz Glink. All rights reserved. 44 cycles

45 Ftigue Crck Growth under Vrible Amplitude Loding: the retrdtion effect d dn d dn C f K m K,K mx 27 Grzegorz Glink. All rights reserved. Pge 45

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47 Evolution of the crck tip plstic zone hed of ftigue crck & crck tip closure Stress, S A Stress, S B Time, t Time, t Time, t Time, t Stress, S C Stress, S D Crck Crck Crck tip open Crck tip strts to close Extended crck tip closure Crck tip strts to open Crck tip plstic zone Envelope of plsticlly deformed mteril in the wke of growing crck 21 Grzegorz Glink. All rights reserved. 47

48 The stress-strin evolution nd the monotonic nd plstic zone hed of ftigue crck tip A K mx t: A r p 1 K mx ys 2 K K Stress ys B K min Crck x Time r p Monotonic plstic zone Stress, A t: B Crck Stress r c 1 K 4 ys 2 x Strin, B r c ys Cyclic plstic zone 21 Grzegorz Glink. All rights reserved. 48

49 The effect of the crck tip closure Stress intensity fctor, K K mx K th K opn K min K th,eff? K eff K th K R U U K K K K 1 1 min mx opn mx K K or eff R Time, t 21 Grzegorz Glink. All rights reserved. 49

50 Ftigue Growth of Corner Crcks in Lug Subjected to VA Loding History F 2W (x) (x) r x r x d +r Experimentl dt from: Jong-Ho Kim, Soon-Bok Lee, Seong-Gu Hong, Int. Journl of Ftigue, vol. 4, Grzegorz Glink. All rights reserved. 5

51 The VA Lod/Stress History The Lug Loding Histories, P mx =21 kn 1% Clipping 9% Clipping 8% Clipping Lod/Force [kn] No. of Reversls 21 Grzegorz Glink. All rights reserved. 51

52 Clcultions vs. Experiment Ftigue life for 8% nd 1% Clipped Loding History+Lod Shedding: Al75 T7 25 8% Clipped Experimentl 8% Corner+EdgeRestrined+Shedding_SP=A45B23q65 Crck length [mm] % Clipped Experimentl 1% Corner+EdgeRestrined+Shedding_SP=A43B182q Number of blocks Experimentl dt from: Jong-Ho Kim, Soon-Bok Lee, Seong-Gu Hong, Int. Journl of Ftigue, vol. 4, Grzegorz Glink. All rights reserved. 52

53 Crck Shpe Evolution; qurter circulr initil crck Predicted vs. Mesured Crck Shpe Evolution in the Lug, 1% Clipping Predicted vs. Mesured Crck Shpe Evolution in the Lug, 8% Clipping; Depth, b [mm] Depth, b, [mm] Surfce, [mm] Surfce,, [mm] Experimentl dt from: Jong-Ho Kim, Soon-Bok Lee, Seong-Gu Hong, Int. Journl of Ftigue, vol. 4, Grzegorz Glink. All rights reserved. 53

54 Weight Function for Arbitrry Plnr Crcks 1 i K m ( x, y; P) A i P 2 2 PA j i A i c c b bi 2 P jai A i A i n P j (x,y) n i P j (x,y) 1 ci 2 A 1 c - inverted contour of the crck front; b - inverted contour of the externl boundry; 3 A 2 PjAi - distnce between the point lod P nd point A on the crck front 3 A 3 21 Grzegorz Glink. All rights reserved. 54

55 Loction of mximum sher stress D=18.5 mm, d=4 mm Fig. 1. Geometry nd dimensions of the spring 21 Grzegorz Glink. All rights reserved. 55

56 Reltive dimensions of the inclusion (d=2-3 m) nd the finl crck size (2 f = 7 m) 21 Grzegorz Glink. All rights reserved. 56

57 2-D Stress Field in the Spring Criticl Cross Section nd the Loction of the Initil Crck (non-metllic inclusion) ref D 16F 16T 2 8FD 8F torque d d d d C 1.55 ref ref B 1. ref.4 ref B C time, t D ref ref A.85 ref A D 21 Grzegorz Glink. All rights reserved. 57

58 Edge of the cross section N f = 5,296,9 cycles Boundry Strt Ftigue crck growth; d=.3x.2 mm, depth.25 mm, C, mx = 13 MP, C, min = 39 MP 21 Grzegorz Glink. All rights reserved

59 Min steps in ftigue design flow chrt Strt Collecting dt Selecting criteri Simultion 3 Dt nlysis 4 Designing 5 Stress relive! The End! 21 Grzegorz Glink. All rights reserved. 59