Load Sequence Interaction Effects in Structural Durability

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1 Load Sequence Interaction Effects in Structural Durability M. Vormwald 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik

2 Introduction S, S [ log] S constant amplitude S variable amplitude load , [ log] cycles 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 2

3 Fatigue damage evolution d n n 2 n 3 d σ a Physical measure of damage d f d 0 σ a σ a2 σ a3 n d f various affine const. damage amplitude growth curves levels d 0 n n σ a3 n 3 σ a2 n 2 n 3 3 n 2 2 ni i σ a σ a2 σ a3 CA life curve ni D = = i 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 3

4 Integration of a crack growth law da d = C K n m crack length a σ π a Y ( a,g) a a Y j ( a,g) K = at failure a e σ a j ( ) high medium ( π ) m j j j da m = C σ n m low 2 3 σ j = σ 2 σ 3 a j a j start a 0 n j 0 cycles n j, j 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 4

5 crack growth curves from Paris-type laws are affine crack length a at failure a f a a 0 a f a ( a Y ( a,g) ) 0 ( ) m j j j da m = C σ π n ( a Y ( a,g) ) m ( ) m j j j da m = C σ π m = n j j linear damage accumulation hypothesis n j j = a j a j start a 0 normalised cycles Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 5 n j j for all σ j Such Miner-type life prediction results do not depend on the load sequence

6 Origins of load interaction effects Plasticity Geometrical alterations May be subject to revision with increasing scientific insight 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 6

7 Fatigue strength expressed in terms of life curves and stress lines life curves for R = const. stress lines for = const. σ a σ a Haigh-Diagram R < R = 2 R > 2 3 R < R = R > σ 3 m + R = R σ a 0 σ m 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 7

8 Type sequence effects due to mean stress rearrangement S S σ t ε ε a strain life curves σ m > 0 σ m = 0 σ m < 0 Solve the propblem by using an appropriate version of the local strain approach 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 8

9 Mean stress effects in the crack growth regime 0-3 Crack growth rates for S460 various R-rates (R = σ min /σ max ) R = 0.4 R = 0 R = -0.4 R = - da/dn [mm/cycle] 0-4 R = K = K max - K min [MPa m] 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 9

10 Crack closure, experimental observation load fatigue crack closure near tip crack flank displacement 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 0

11 Closure-free crack growth rates for S460 da/dn [mm/cycle] R = 0.7 R = 0.4 R = 0 R = -0.4 R = K = K max - K op = K eff [MPa m] 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik

12 Origin of crack closure Plasticity Oxides Roughness Penetrating media Martensite transformation 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 2

13 Empirical equations da dn da dn 0 Keff p m K th da f K = C K dn R K max K eff K f A m = C U K ; U= R K eff 2 3 ( ) ( 0 ) A + A R+ A R + A R for R> 0 = A + A R for R 0 π σ = cos 2 σ max F ( ) m = C U K ; U= R+ 0.2R ( ) c q σ A= σ max A = 2 A + A A = A A A F Elber Schijve Forman-Mettu 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 3

14 Extended Dugdale-Barenblatt Model acc. to Seeger, Führing, ewman S max S min y elastic domain y plastic strips crack x x a ω a ω σ ασ 0 σ ασ 0 x x σ 0 stress distributions σ 0 contact stresses 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 4

15 Simulation for initial overload followed by constant amplitude cycling 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 5

16 Explanation of sequence effects load sequence max min = 0 crack opening (max) (min) flattening by contact crack tip X 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 6

17 Type 2a sequence effects; long cracks S da/dn a b c d e a S S da/dn f g h i a 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 7 2a S

18 Short cracks ε tin y g a g e 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 8

19 Crack opening strains rather than stress 00MPa a=mm σ a=0.5mm σ a=mm a=0.5mm 0.% ε tinygage ε tinygage ε op ε op ε a= 0.5% life = 7700 Ssp. ε a= 0.2% = Ssp. 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 9

20 Type 2b sequence effects; short cracks 00MPa a=mm σ a=0.5mm 0.5% ε 26cyc 0.% ε tinygage 0.% - 0.3% - 0.5% t ε op life in Experiment = cyc life calculated with Miner's rule = 27/(/ /200000) = cyc 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 20

21 Simple model σ ε ε op ε op ε t 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 2 t

22 Crack opening stresses σ σ op F R = ewman AlMg4.5Mn S460 A36 0 Cr Mo 9 0 AISI σ max 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 22 σ F

23 Model performance dealing with a random sequence 0.6 ε [%] a) frequency distribution of reversal point strains b) crack opening strains upper reversal points AlMg4.5Mn crack length 2a = 0.25 mm predicted by the proposed algorithm crack length 2a = 0.50 mm scatter band of experimental data (dimension of strain gage: 0.25 mm x 0.2 mm) lower reversal points frequency per sequence occurrence of the largest cycle 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 23 cycles within the 7th repetition of the sequence

24 Comparison experiment-prediction, Gaussian distributions, I = 0.99, R = -, AlMg4.5Mn max. nominal stress amplitude S a [MPa] , Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 24 4 H 0 = 0, R = H 0 = 5 0, R = constant amplitude, R = 5 notch strain simulation K t = 2.5 AlMg4.5Mn P J S

25 Cyclic J-integral for short cracks as crack driving force semi circular surface crack For σ σ ε = + E K n there is 2 σ.02 J =.24 + σ ε p a E n ( ) 2 σmax σ cl.02 σmax σ cl J eff =.24 + ( σmax σ cl ) ( ε max ε cl ) a E n E Integration of da m = C ( Jeff ) dn is equivalant to a Miner-type damage accumulation in terms of a P J - curve 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 25 P J

26 Fatigue crack growth, approaching monotonic strength, threshold and endurance limit da dn [ log] region 3 region 2 Paris-law m da C K dn = R = const. m Type K3 th sequence = E effects a due Y to a, G interference of monotonic failure modes: Kth non-power σe = crack growth laws yield non-affine crack πagrowth Y( a, curves G) failure condition fracture leads to endurance stress-dependent limit final crack lengths σ E σ π ( ) Usually, [log] this sequence effect plays a minor role. 2 region threshold K th K [log] K c 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 26 Y( a, G= ) const. crack length a [log]

27 Relation between crack length, endurance limit and damage sum 8 a / a f 0 8 a / a f 0 crack length a/a o ( a 0 / a) ( a / a ) 0 f m / 2 m / damage sum ΣD = n/ = Type 4 sequence effect due to decreasing fatigue limit. Cycles with amplitudes smaller than the constant amplitude fatigue limit cause damage (FCG) if applied after some pre-damage due to large amplitude cycles. Usually, this sequence effect plays a major role. D 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 27 crack length a/a o damage sum D = Σn/ σ / σ = a / a E E, 0 0 ( σe / σe, 0 ) m = 2 3 = 4 ( a / a ) 0 endurance limit σ E / σ E,0 e m 2 m / 2 = D

28 Considering decreasing endurance limit in a damage accumulation rule σ j= 2 3 j= j E CA life curve je h j 0 D σ E σ j= j ( j + ) ( j ) x = D = D x ( D( j + ) D( σ j )) E = E E j j= j E endurance limit σe h j E j σ n= x H0 with H0= h j j= j f n n n = H 0 = H D D ( σ j + ) D( σ j ) E j E j= h ( σ j + 2) D( σ j + ) 2 0 j + = H D E E j= h ( σ j + 3) D( σ j + 2) 3 0 j + 2 E E j= h j j j j j j D E E frequency h and cycles to failure [log] j j f E = H D ( σ j + i) D( σ j + i ) 0 je+ i i= E j= h j j E 0 D D2 D3 D 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 28

29 German FKM-guideline rule for assessing damage of small cycles: Consequent Miner s rule ominal stress S S E,0 S = E,0 E,0 / k E S = ( D) stress-life curve S E, S E,0 S S E,0 D = k n according to Haibach i i E,0 [ log] 0 D D2 D3 D 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 29

30 Comparison of Miner s rules variants σ, σ max [MPa] th a σ -9 mm C=5 0 MPa m Ssp. K = 5MPa m σ j / σ ( ) 3 a a 0 e constant amplitude m = 3 = mm = 00 mm variable amplitude elementary modified consequently original crack growth =H 0 cumul. frequency H , 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 30

31 Comparison experiment-prediction, Gaussian distributions, I = 0.99, R = -, AlMg4.5Mn max. nominal stress amplitude S a [MPa] , Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 3 4 H 0 = 0, R = H 0 = 5 0, R = constant amplitude, R = 5 notch strain simulation K t = 2.5 AlMg4.5Mn P J S

32 Omission of small cycles discloses their contribution to fatigue damage ormalised filter level P SWT,Filter P SWT,E,0 notch strain simulation K t = 2.5 AlMg4.5Mn Gaussian Sa = 08 MPa 5 H0 = 5 0 R = ; I = 0.99 Runs through the spectrum until failure (0.5mm surface crack initiation) 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 32

33 Omission of small cycles discloses their contribution to fatigue damage 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 33

34 Damage contribution of omitted cycles Straight line distribution otch strain simulation 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 34

35 Variable amplitude life: Two-level testing of autofrettaged specimens p [bar] p max =3000bar p max =2250bar p=500bar 2.4 factor p=25bar? 800 p= 800bar 2.5 p ? 000 x 400 constant amplitude; R=0 constant amplitude; R= two-level; :000; p max =3000bar two-level; :000; p max =2250bar? two-level; :0000;p max =2250bar Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 35 factor n

36 Life estimates based on various methods; Two-level-tests nicht autofrettiert p [bar] nicht autofrettiert p [bar] experimental LA 200 LEFM M2 LA + LEFM M [-] experimental LA 200 LEFM M2 LA + LEFM M [-] 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 36

growth dc/dn crack rate 0 5 (mm/cycle) 0 6 A A B B D E C C D E Medium carbon steel (S45C)

37 Micro crack growth acc. to Tokaji and Ogawa Pearlite Ferrite grain boundary I H G C I F E D B H G E F A D C B A growth dc/dn crack rate 0 5 (mm/cycle) 0 6 A A B B D E C C D E Medium carbon steel (S45C) σ=240 MPa R = 0 7 mm/cycle surface crack length c (mm) 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 37

38 Model acc. to Tanaka σ grain boundery crack slip band idealised micro structure σ y a d c mechanics model σ F σ F2 yield stress distibution 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 38

39 Crack growth passing grain boundary da dn σ = 700 MPa n σ = 350 MPa σ F2 = 800 MPa F σ = 469 MPa da dn δ = mm 5.5 crack length [µm] crack length [µm] 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 39

40 Type 5 sequence effect due to (micro structural) inhomogeneities n high low n low high n =0.6 n 2 2 =0.6 ni i =.2 n =0.4 n2 =0.4 2 ni =0.8 i crack length [µm] crack length [µm] 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 40

41 Summary Type : Macroscopic mean stress rearrangement Type 2: Crack closure Short cracks Long cracks Type 3: monotonic failure Type 4: decreasing fatigue limit Type 5: Inhomogeneities Plasticity Geometrical alterations 25. Oktober 200 Technische Universität Darmstadt Fachgebiet Werkstoffmechanik 4

Stress Concentration. Professor Darrell F. Socie Darrell Socie, All Rights Reserved

Stress Concentration. Professor Darrell F. Socie Darrell Socie, All Rights Reserved Stress Concentration Professor Darrell F. Socie 004-014 Darrell Socie, All Rights Reserved Outline 1. Stress Concentration. Notch Rules 3. Fatigue Notch Factor 4. Stress Intensity Factors for Notches 5.