STRESS INTENSITY FACTORS AND FATIGUE CRACK GROWTH OF IRREGULAR PLANAR CRACKS SUBJECTED TO ARBITRARY MODE I STRESS FIELDS

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1 STRESS INTENSITY FCTORS ND FTIGUE CRCK GROWTH OF IRREGULR PLNR CRCKS SUBJECTED TO RBITRRY MODE I STRESS FIELDS Grzegorz GLINK University of Wterloo Deprtment of Mechnicl nd Mechtronics Engineering Wterloo. Ontrio, Cnd FGROW Workshop Slt Lke City, Uth September -, 3

2 FTIGUE!!!!! N i =? N p =? N T =? Ftigued kitten. Metl Ftigue is process which cuses premture irreversible dmge or filure of component subjected to repeted loding. 8 Grzegorz Glink. ll rights reserved.

3 Crck Growth Rte, m/cycle The Similitude Concept in the d/dn ΔK Method ) Structure -6 H -7 Q F -8 b) Weld detil 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 - ΔK.

4 Crck tip stress dependence on the stress intensity fctor K S y S yy K 3 yy K K < K < K 3 Stress components, ij, t the crck tip depend on the stress intensity fctors K I which is influenced by: u y r yy - the lod, S -crck dimensions, -geometry, Y K S Y y S S

5 The Weight Function WF=m() is equl to the SIF K(,) induced by unit point lod P ( D) or unit line lod (3 D) pplied to the crck surfce t position. y z P y P P m () = K (,) m () = K (,) t t

6 The Weight Functions, m (m B ), nd corresponding Stress Intensity Fctors, K (K B ), for pir of splitting forces pplied to the surfces of through crck in n infinite plte Through crck in n infinite plte: B y P= m (, ) - m ( B, ) Stress intensity fctors for crck crck tips nd B respectively: K (,, ) m P P K (,, ) B mb P P F. Erdogn, G.Sih 96 Green s Functions

7 The Weight Function, m, nd corresponding Stress Intensity Fctor, K, for pir of splitting forces pplied to the surfces of n edge crck in semi-infinite plte y Edge crck in semi-infinite plte: P= m (, ) P Stress intensity fctor for the crck tip H.Td, P K m(,, P) Green s Function 5

8 y Geometricl Prmeters nd Nottion for the Universl Weight Function y P P w w K M3 P m,, P M M 3

9 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

10 y S The use of Weight Functions for clculting Stress Intensity Fctors P M M M P K m,, P K 3 P P m,, P M M M3 3 3 () K P P,, P m, P m, P P t K m, d S

11 The Superposition Principle for Crcks nd Stress Intensity Fctors y S y S y () () t t t S S ) b) c) K = K c The Stress Intensity Fctor for ny loding cse is equl to the stress intensity fctor obtined by pplying to the crck fces the stress ditribution tht used to be there when there ws no crck.

12 Stepwise Procedure for Clculting Stress Intensity Fctors by the Weight Function Method. Clculte stress distribution () in the prospective crck plne in the bsence of the crck (un-crcked body, liner elstic nlysis). f. pply the stress distribution () to the crck surfce s trctions., 3. Choose pproprite weight function, i.e. prmeters M, M nd M 3. / 3/ m (, ) M M M3 4. Integrte the product of the stress distribution () nd the weight function m(,). K (, ) m d

13 n Edge Crck in Finite Thickness Plte under Bending Lod - Emple σ Step Step Step 3 Step 4 6M Step ; ;.; B thickness t B t t m, t K m, d t 3 d WF : K.5 ; Hndbook ( Murkmi) : K. 35 ; Difference %

14 ) T 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; t Prospective crck plne (y) S b) y crck o K I m y, y dy t t (y) y

15 Through the plte thickness stress distributions in T-butt weldment obtined for r/t = /5, = 45 o (in the weld toe cross section) FEM (y) / n y / T

16 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

17 Edge nd Semi-Ellipticl Surfce crck in plte with post shotpeening residul stressesm (Northroop Grummn) r r B B r r

18 Stress (ksi) Shot Peen Residul Stress Distribution (-D) Crck Depth (in)

19 SIF geometric correction fctors t the deepest point : Y WF nd B - Boundry Element comprison Crck depth (in) /c =.8

20 () () Crcks t Notches d b b b () b () b () b In order to determine the SIF the notch nd the crck re modelled s one crck but the stress distribution comes from the uncrcked notched body - resulting in the nlysis of prtilly loded crck. t t

21 Geometric Fctor Y σ ref Comprison with Newmn/Hndbook FEM dt Centrl Circulr Hole: r=8 nd W=8.4 d Y Ye + d Coordinte (notch + crck)

22 Riveted Stiffeners Effect S S pplied remote stress ctul stress in the bsence of the crck S S

23 Corner Crck Under In-Plne Stress Distribution y y y m y, c M M M 3 y c c c / 3/ / 3/, y B B y m y c M M M 3 y c y c c c

24 Corner Crck Under Out-of-Plne Stress Distribution σ y B b b W R t

25 Stress Intensity Fctor for n edge crck in the lug by the WF method F W σ() σ() r r d +r

26 Reltive stress, S/F Stress Distribution in Un-crcked Lug Ligment Reltive distnce from the ceneter of the lug, /W

27 Stress Intenisty Fctor K [MPVm] Stress Intenisty fctors for Corner nd Edge crck in the Koren ttchment lug Lug-Corner/Edge Crck - SIF Fctors 5 Koren dt WF_Edge-Hole WF_Corner Crck Crck depth, [mm]

28 Lod/Force [kn] The Lug Loding Histories, P m = kn 8 6 % Clipping 9% Clipping 8% Clipping No. of Reversls

29 FCG rte, d/dn [mm/cyc]. C FCG dt: l 75 T7.E-4.E-5.E-6 y =.46E-9.8E+.E-7.E-8.E-9.E- y = 8.4E-.65E+ y =.4E- 4.5E+ R=.5 Shrp R= Shrp R=.3 Lee R=, Lee R=-., Lee R=.8 Sd R=.5 R=-.3.E-.E+.E+.E+ Totl driving force, k tot [MP m]

30 Crck length [mm] Ftigue life for 8% nd % Clipped Loding History+Lod Shedding: l75 T7 5 8% Clipped Eperimentl 8% Corner+EdgeRestrined+Shedding_SP=45B3q65 % Clipped Eperimentl % Corner+EdgeRestrined+Shedding_SP=43B8q Number of blocks

31 Crck length [mm] Ftigue life: 9% Clipped Lod+Shedding: l75 T7 5 9% Clipped Eperimentl Corner+EdgeRestrined+Shedding_SP=45B3q Number of blocks

32 Depth, b [mm] Depth, b, [mm] Crck Shpe Evolution; qurter circulr initil crck Predicted vs. Mesured Crck Shpe Evolution in the Lug, % Clipping Predicted vs. Mesured Crck Shpe Evolution in the Lug, 8% Clipping; Surfce, [mm] Surfce,, [mm]

33 y D = MP S t r () S t p i b t r b e b D St pi t

34 r b r K e d d b Residul stress, r, contribution, to the stress intensity fctor, r K r () y.4 r b b K e

35 Stress, r, St (MP) Residul & hoop stress distribution 5 r 5 S t Distnce from the crck center,, ( mm)

36 Stress intens. fctor, KSt, Kr, K Stress intensity fctors 5 K K K S t r 4 K c 3 Kst Kr K Hlf crck length, (mm)

37 Summry of the WF method Very efficient computtionlly (SIF cn be clculted mny million times. fter ech ftigue crck increment), Cn produce SIF for wide vriety of loding conditions (new non-eistent solutions cn be produced in smll frction of CPU time required by other methods), Cn ccount for the residul stress effect, Cn ccount for vrible thickness effects, Cn ccount for the lod shedding effect, No necessity for stress nlysis of crcked bodies (i.e. nlyticl or FEM stress dt from un-crcked bodies re only needed!), The sme FEM model cn be used for the stress nd lod shedding nlyses (no need for specil mesh no need for dditionl FE mesh modeling for the lod shedding nlysis! )

38 THE FUTURE rbitrry Plnr Crcks under rbitrry Stress Field

39 Weight Function for rbitrry Plnr Crcks i K m (, y; P) i P P j i i c c b bi P ji i i n P j (,y) n i P j (,y) ci Γ c - inverted contour of the crck front; Γ b - inverted contour of the eternl boundry; ρ P - distnce between the point lod P nd point on the crck front Grzegorz Glink. ll rights reserved. 39

40 Point lod Weight Function for rbitrry plnr crcks under rbitrry stress distribution i i bi P ji n i G. Glink nd W. Reinhrd, Clcultion of Stress Intensity Fctors for Crcks of Comple Geometry nd Subjected to rbitrry Non-liner Stress Fields, 3st Ntionl Symposium on Ftigue nd Frcture Mechnics, Clevelnd, OH, June -4, 999. Best pper wrd. STM STP.. n ci P j (,y) Wu, Z., Glink G., Jkubczk, H., nd Nilsson, L., Clcultion of Stress Intensity Fctors for Crcks in Structurl nd Mechnicl Components Subjected to Comple Stress Fields Ftigue Testing nd nlysis Under Vrible mplitude Loding Conditions, STM STP 439, P. C. McKeighn nd N. Rngnthn, Eds., STM interntionl, West Conshohocken, P, K m (, y; P) i i P P j i c c b

41 ) P( j,y j ) ( j,y j P j j c,j (,y) b, jn j, yj j K (, y) m (, y ; P)ddy j c, j j P c, j b,

42 c t /c=. /t=.8 /c=.6 c/t=.8 c t

43 Uniform tensile stress comprison with J.Newmn FEM dt.6 SIF correction fctor, Y=K/ () / Prmetric ngle, F/ YWF,/c=. Y[9],/c=. Ywf,/c=.5 Y[9],/c=.5

44 Squre crck under uniform tension y l l

45 Squre crck under uniform tension comprison with FEM dt (Murkmi s Hndbook of SIFs).9 Stress intensity fctor, Y=K/ ) / Reltive distnce long the crck contour, s/ Y[8] Ywf

46 Semi-ellipticl surfce crcks in cylindricl brs /c=.6, /R=.6 /c=., /R=. R R F F m b c

47 Residul Stress Field in Cylinder Residul stress field in cylindricl br [7]

48 Y=K/ O ( b) / SIF Comprison for Semi-ellipticl Crck in Cylinder with Residul Stresses Ywf Y[7] Prmetric ngle, F/F m Comprison of SIF for semi-ellipticl surfce crck in cylindricl br subjected to -D residul stress field, c=.6, /R=.6

49 y[mm] Semi-ellipticl crcks in finite thickness plte n= n=6 n= σ 5 y [mm]

50 Semi- ellipticl/tunnel crck under uniform stress distribution STGE 4 8 STGE 3 6 STGE 4 STGE

51 Reltive dimensions of the inclusion (d=-3 μm) nd the finl crck size ( f = 7 μm)

52 Loction of mimum sher stress D=8.5 mm, d=4 mm Fig.. Geometry nd dimensions of the spring

53 Distribution of stresses in the criticl cross section C.55 ref B. ref B C D. ref.4 ref.85 ref D ref D 6F 6T 8FD 8F torque 4.65 d d d d 3 3 3

54 ) b) σ ref σ ref,m = 58.5 MP d =. -.3 mm σ ref,min = 9.5 MP t - time Loctions of initil crcks (flws) in the cross section; ssumed penny shpe crck of size i =. mm nd ellipticl crck./.3 mm, b) Cyclic history of the reference stress σ ref

55 Edge of the cross section N f = 5,96,9 cycles Boundry Strt Ftigue crck growth; d=.3. mm, depth.5 mm, σ C, m = 3 MP, σ C, min = 39 MP