FASTRAN AN ADVANCED NON-LINEAR CRACK-CLOSURE BASED LIFE-PREDICTION CODE

Transcription

1 FASTRAN AN ADVANCED NON-LINEAR CRACK-CLOSURE BASED LIFE-PREDICTION CODE J. C. Newman, Jr. Department of Aerospace Engineering Mississippi State University AFGROW WORKSHOP Layton, Utah September 15, 2015 ffa

2 OUTLINE OF PRESENTATION Brief History on Fatigue-Crack Growth Plasticity-Induced Crack-Closure Model Crack Initiation and Small-Crack Behavior Fatigue-Crack Growth and Fracture Concluding Remarks fastran # 2

3 Stress Concentration Factor for an Elliptical Hole in an Infinite Plate Inglis (1913) c s e = S K T 2c c fastran # 3

4 Notch Strength Analysis Fracture Mechanics c c Paul Kuhn Notch Strength Analysis (Neuber ) George Irwin Fracture Mechanics (Griffith) fastran # 4

5 Father of Modern Fracture Mechanics Irwin, 1957 George Rankin Irwin ( ) + T fastran # 5 25

6 Notch-Strength Analyses: McEvily and Illg (LaRC), NACA TN-4394, T6 K N S net against da/dn fastran # 6

7 Fracture Mechanics: Paris, Gomez, and Anderson, Trends in Engineering, Seattle, WA, 1961 LEFM: K against d(2a)/dn Paris (1970): K N S net ~ K max fastran # 7

8 Plasticity-Induced Fatigue-Crack Closure: Elber, 1968 fastran # 8

9 DOMINANT MECHANISMS OF FATIGUE-CRACK CLOSURE Plastic wake O Elber, 1968 Beevers, 1979 Paris et al., 1972 Newman, 1976 Suresh & Ritchie, 1982 Suresh & Ritchie, 1981 (a) (FASTRAN) Plasticity-induced (b) Roughness-induced (c) Oxide fastran # 9 closure closure induc

10 OUTLINE OF PRESENTATION Brief History on Fatigue-Crack Growth Plasticity-Induced Crack-Closure Model Crack Initiation and Small-Crack Behavior Fatigue-Crack Growth and Fracture Concluding Remarks fastran # 10

11 FASTRAN Crack-Closure Based Life-Prediction Code -bs o fastran # 11

12 MODIFIED DUGDALE MODELS IN FASTRAN Elastic continuum Bar elements NTYP = 1 NTYP = -4 fastran # 12

13 BASIC CRACK SOLUTIONS REQUIRED FOR CLOSURE MODEL Crack solutions: K s = f s (S,d,r,w) V s = g s (S,d,r,w,x) K s = f s (s,d,r,w,b i,x) V s = g s (s,d,r,w,b i,x) fastran # 13

14 FASTRAN Version 5.4+ Plastic-zone region refined (20 elements in plastic zone instead of 10 elements, like STRIPY model in NASGRO) Crack-growth increments (Dc*) reduced to 5% of cyclic-plasticzone size instead of 20% (only used for NMAX > 100) New crack-opening-stress function developed to fit the refined model (slight increase in crack-opening stresses) for steadystate constant-amplitude loading.nmax input (normally set to 300 to 1000), but enables cycle-bycycle calculations with NMAX = 1 (recommended).k-analogy activated for all 2D and 3D crack configurations Residual strength (S n /s u ) output as function of crack length Spectrum loading (NFOPT = 8, 9 and 10) output in cycles and blocks or flights for NREP (repetitions of flight schedule) fastran # 14

15 CRACK SOLUTION INPUT REQUIRED FOR FASTRAN NTYP = 1 NTYP = 0; LTYP = 1 Pre-cracking option fastran # 15

16 MECHANICS OF THE ANALYTICAL CYCLE IN FASTRAN FASTRAN Version 5.4+ (recommend cycle-by-cycle, NMAX=1) S maxh Analytical cycle Dc* = 0.05 w or N = NMAX Applied Stress S o S' o (S o ) new S minb S mina Dc* Time fastran # 16

17 CALCULATED CRACK-OPENING STRESSES AT A LOW APPLIED STRESS LEVEL (MIDDLE-CRACK TENSION; NTYP = 1) S o /S max T3 B = 0.09 in. W = 3 in. 0.8 S max = 10 ksi Pre-cracking R = 0.05 R = -1 DS eff / S max c n c i Crack length, c, in. fastran # 17

18 CRACK-OPENING STRESSES UNDER CONSTANT-AMPLITUDE LOADING S o /S max = f(r, S max /s o, a, Dc/c) R = S min /S max s o = (s ys + s ult )/2 a = 1 for plane-stress conditions a = 3 for plane-strain conditions fastran # 18

19 CRACK-OPENING STRESSES AS A FUNCTION OF CRACK-OPENING STRESSES AS FUNCTION OF STRESS RATIO FOR A HIGH CONSTRAINT FACTOR STRESS RATIO FOR A HIGH CONSTRAINT FACTOR FASTRAN S max /s o 1.0 S o /S max a = 2 Dc = Equation S min /S max R fastran # 19

20 CRACK-OPENING STRESSES AS A FUNCTION OF CRACK-OPENING STRESSES AS FUNCTION OF APPLIED STRESS FOR VARIOUS CONSTRAINT FACTORS APPLIED STRESS FOR VARIOUS CONSTRAINT FACTORS Plane stress a = a = 2 S o /S max a = 3 Plane strain 0.1 R = 0 Dc = S max /s o fastran # 20

21 FATIGUE-CRACK-GROWTH RATES USING LEFM ANALYSES FATIGUE-CRACK-GROWTH RATES USING LEFM ANALYSES T3 Middle crack tension B = 2.3 mm Hudson, Phillips & Dubensky 10-6 dc/dn m/cycle R DK, MPa-m 1/2 fastran # 21

22 FATIGUE-CRACK-GROWTH RATES CORRELATION USING CRACK-CLOSURE ANALYSES Hudson, Phillips & Dubensky 2024-T3 Middle crack tension B = 2.3 mm Fracture a = 1 regime dc/dn m/cycle Flat-to-slant crack growth a = 2 Threshold regime R DK eff, MPa-m 1/2 fastran # 22

23 FLAT-TO-SLANT FATIGUE-CRACK GROWTH Schijve (1966): Observed transition occurs at constant rate Newman and Hudson, 1966 Dk T ksi- in Constraint loss appears to occur on M(T) specimens, but not on deep-cracks in C(T) or bending specimens Stress ratio, R fastran # 23

24 FLAT-TO-SLANT FATIGUE-CRACK GROWTH TRANSITION Newman, 1992 M(T) specimens: fastran # 24

25 CONSTRAINT EFFECTS IN THREE-DIMENSIONAL CRACKED BODIES Newman, Bigelow & Shivakumar, 1993 fastran # 25

26 ELASTIC-PLASTIC STRESS-INTENSITY FACTORS Newman, c / r = K i / K J Crack Parameters: K i = S (pd) 1/2 F(d/r) where d = c + g g = 0 elastic g = ¼ elastic-plastic c / r = 0.05 K p / K J K e / K J J = K p 2 /E / c fastran # 26

27 CRACK-CLOSURE ANALYSES OF 2024-T3 ALUMINUM ALLOY dc/dn m/cycle Hudson, Phillips & Dubensky 2024-T3 Middle crack tension B = 2.3 mm Fracture regime a = 1 Flat-to-slant crack growth Small crack regime a = 2 Threshold regime (DK eff ) T DK eff R DK eff, MPa-m 1/2 fastran # 27

28 COMPARISON OF MEASURED AND PREDICTED CRACK GROWTH USING LEFM AND FASTRAN 2024-T3 B = 0.09 in. W = 3 in. S max = 7.5 to 30 ksi fastran # 28

29 VARIABLE-AMPLITUDE LOADING OPTION (NFOPT = 1) fastran # 29

30 SPECTRUM LOADING OPTIONS IN FASTRAN TWIST or MINI-TWIST - Transport Spectra (NFOPT = 2 or 3) FALSTAFF - Fighter Spectra (NFOPT = 4) SPACE SHUTTLE Load Spectra (NFOPT = 5) Gaussian (R ~ -1) Load Sequence (NFOPT = 6) Felix & Helix Helicopter Flight-Load Sequence (NFOPT = 7) Spectrum Read from List of Stress Points (NFOPT = 8) Spectrum Read from Flight-by-Flight Loading (NFOPT = 9) Spectrum Read from Flight Schedule (NFOPT = 10) fastran # 30

31 CRACK CONFIGURATION OPTIONS IN FASTRAN Two-dimensional crack configurations (15) - Middle-crack tension - Compact and bend type specimens - Crack(s) from an open hole - Crack in a pressurized cylinder - Periodic array of cracks at holes - User defined crack configuration Three-dimensional crack configurations (11) - Surface crack (tension or bending loads) - Surface or corner crack(s) at an open hole - AGARD small-crack specimen - Periodic array of surface or corner cracks at pin-loaded holes fastran # 31

32 LABORATORY SPECIMENS 99 Example of user defined crack configuration (NTYP = -99 Crack(s) from hole) fastran # 32

33 RIVETED AIRCRAFT JOINT CRACK CONFIGURATION fastran # 33

34 AGARD SMALL-CRACK SPECIMEN fastran # 34

35 CRACK-CLOSURE CORRECTION FOR FREE SURFACE DK f=0 = b R DK B DK f=90 = DK A fastran # 35

36 FATIGUE-CRACK GROWTH RATE OPTIONS C Equation: dc/dn = C 1 DK 2 eff f(dkth ) / g(k c ) - f(dk th ) = 1 (DK o /DK eff ) p DK o = C 3 (1 + C 4 R) or DK o = C 3 (1 R) C 4 - g(k c ) = 1 (K max /C 5 ) q Table Look-up: dc/dn = f(dk eff ) (Max 35 points) C - f(dk eff ) = C 1i DK 2i eff (i = 1 to 34) C - f(dk eff ) = C 1i DK 2i eff f(dk th ) / g(k c ) Crack growth (da/dn = dc/dn or da/dn # dc/dn) fastran # 36

37 FRACTURE CRITERIA Two-Parameter Fracture Criterion K F and m - m = 0 LEFM (K c = K F for S n < s ys ) - m = 1 Plastic-collapse criteria (K F large) Cyclic fracture toughness exceeded (K max > C 5 ) Plastic-zone size exceeds net-section region fastran # 37

38 Elastic-Plastic Stress- and Strain-Concentration Factors using Neuber s Equation Neuber (1961): 2c Hutchinson, Rice (1968) showed that the stress-strain field for a crack in a non-linear elastic material verified Neuber s equation Crews (1974) experimentally validated Neuber s equation for elliptical hole in finite plate under remote uniform stress fastran # 38

39 Original Two-Parameter Fracture Criterion Inglis stress-concentration equation for elliptical hole, K T = (c/ ) Neuber s equation: K s K e = K 2 T K F = K Ie / F F = 1 m (S n / s u ) for S n < s ys F (s ys / S n ) [1 m (S n / s u )] for S n s ys Constraint effects on net-section NOT considered! fastran # 39

40 Two-Parameter Fracture Criterion Analysis on 2219-T87 Aluminum Alloy M(T) Specimens S K Ie K F = 1- m(sn / S u ) w = 610 mm w = 76 mm 2c i 2c i 2w 2w S (a) fastran # 40

41 Crack-Opening Displacements for Stably Tearing Crack using Critical CTOA and Finite-Element Analyses C.T. Sun Purdue University Mild steel x / c f fastran # 41

42 Crack-Opening Displacements for Stationary and Stably Tearing Crack using Critical CTOA-FEA Analyses x / c f fastran # 42

43 Elastic Stress-Intensity Factor at Failure for Wide Range of Middle-Crack Tension Specimens S 2c i 2c i 2w 2w S (a) fastran # 43

44 OUTLINE OF PRESENTATION Brief History on Fatigue-Crack Growth Plasticity-Induced Crack-Closure Model Crack Initiation and Small-Crack Behavior Fatigue-Crack Growth and Fracture Concluding Remarks fastran # 44

45 CRACK INITIATION AND SMALL-CRACK BEHAVIOR AGARD Structures and Materials Panel ( ) and NASA/CAE ( ) Small-Crack Test and Analysis Programs Small- and Large-Crack Growth Rates DARPA SIPS Program ( ) fastran # 45

46 SMALL-CRACK MEASUREMENTS IN ALUMINUM ALLOYS (a) 7075-T6 (b) Lc9CS (7075-T6 clad)

47 SMALL- AND LARGE-CRACK GROWTH RATES IN 7075-T6 1e-3 1e T6 [23] K T = 3.15 R = -1 DK eff da/dn or dc/dn mm/cycle 1e-5 1e-6 FASTRAN (a = 1.8) a i = c i = 6 m Phillips Large cracks (DK; dc/dn) 1e-7 Small surface cracks at notch (DK) S max = 80 MPa 1e DK or DK eff, MPa m fastran # 47

48 TYPICAL INITIATION SITES IN SIPS 7075-T651 2a i c i 2a i Average flaw size: a i = 4.3 m (along bore) c i c i = 9.9 m (depth from hole) Semi-circular: 6.2 m (equal area) Not an EIFS, but RIFS Real Initial Flaw Size fastran # 48

49 SIPS LABORATORY WING SPECTRUM 1.0 NGC-Lab Wing Spectrum N max = 2,519 cycles Applied stress Maximum stress Cycles fastran # 49

50 CALCULATED CRACK-OPENING STRESSES UNDER SIPS LABORATORY WING SPECTRUM LOADING FASTRAN Ver Cycle-by-cycle calculations - Rainflow-on-the-fly logic (33 seconds) fastran # 50

51 METHOD USED TO ANALYZE TWO-HOLE COUPONS S S Countersunk or straightshank holes 2r 2r 2r Countersunk hole c c W S Two-hole coupon c 2w S Modeled B 2r Surface crack Initial flaw assumed to be a surface crack along hole bore and neglecting countersunk fastran # 51

52 MEASURED AND PREDICTED CRACK GROWTH UNDER SPECTRUM LOADING fastran # 52

53 INITIATION SITE IN NAVAIR THREE-HOLE COUPON S L 2r L 2w S 10 m ASSUMED FLAW SIZE (8 x 24 m) fastran # 53

54 MEASURED CRACK GROWTH UNDER SPECTRUM LOADING ON NAVAIR TESTS S S S C L 2r 2r 2r L 2r 2w L 2w W 2w S S S fastran # 54

55 MEASURED AND PREDICTED CRACK GROWTH UNDER SPECTRUM LOADING ON NAVAIR TESTS S S S C L 2r 2r 2r L 2r 2w L 2w W 2w S S S fastran # 55

56 OUTLINE OF PRESENTATION Brief History on Fatigue-Crack Growth Plasticity-Induced Crack-Closure Model Crack Initiation and Small-Crack Behavior Fatigue-Crack Growth and Fracture Concluding Remarks fastran # 56

57 FATIGUE CRACK GROWTH Thresholds for large cracks Cold-worked hole effects Spectrum loading effects fastran # 57

58 ASTM LOAD-REDUCTION PROCEDURES S max (S max ) i % (0.5 mm) Middle-crack tension specimen w = oo c n = 10 mm c i = 20 mm R = constant Dc = c - c i e -0.08(Dc) 5% (0.5 mm) 0.2 e -0.2(Dc) Crack length, c, mm fastran # 58

59 TYPICAL BEHAVIOR FOR LOAD-REDUCTION AND COMPRESSION PRE-CRACKING THRESHOLD TESTING R = constant DK eff dc dn Compression pre-cracking DK < DK < DK DK 3 DK 2 Steady state DK 1 DK 2 DK 1 Load reduction DK < DK 1 2 DK fastran # 59

60 COMPRESSION - COMPRESION PRECRACKING AND CONSTANT- AMPLITUDE (CPCA) LOAD TESTING Tension Load Compression Time fastran # 60

61 COMPRESSION - COMPRESION PRECRACKING AND LOAD-REDUCTION (CPLR) THRESHOLD TESTING Tension Load reduction Load Compression Time fastran # 61

62 METHODS TO GENERATE STEADY-STATE DATA Current DK eff or High R dc dn DK fastran # 62

63 CPCA AND LOAD-REDUCTION TESTING AT MEDIUM STRESS RATIO ON TITANIUM b-stoa ALLOY dc/dn m/cycle Ti-6Al-4V (b-stoa) C(T) B = 9.5 mm W = 76.2 mm R = 0.4 CPCA CPLR CPCA LR LR Maximum rate allowed in ASTM E ASTM Load Reduction Compression Precracking Load Reduction DK, MPa-m 1/2 fastran # 63

64 CPCA AND LOAD-REDUCTION THRESHOLD TESTING ON 7075-T7351 AT R = 0.1 CONDITIONS fastran # 64

65 CPCA AND LOAD-REDUCTION THRESHOLD TESTING ON 7075-T7351 AT R = 0.1 CONDITIONS fastran # 65

66 CPCA AND LOAD-REDUCTION THRESHOLD TESTING ON 7075-T7351 AT R = 0.4 CONDITIONS fastran # 66

67 COLD-WORKED HOLE TEST SPECIMEN S S or Test procedure: 2a 2w 2h 2r 2w a Sikorsky: (1) Holes drilled (2) Cold-worked (4.5%) (3) Reamed (4) EDM Notched Tested at MSU: (5) Constant-amplitude loading S S or fastran # 67

68 SIMULATION OF COLD-WORKING AND NOTCHING Cold-worked plastic zone Overload plastic zone r + p r + (a) Cold-worked hole (b) Simulated cold-worked hole r +. r m Cold-worked plastic zone r + r m Overload plastic zone a i a i (c) Cold-worked hole after reaming and cutting notch (d) Simulated cold-worked hole after reaming and cutting notch fastran # 68

69 RESIDUAL STRESSES AFTER COLD-WORKING Normalized residual stress s rs / s ys T6 s ys = 517 MPa FEA Cold-worked hole (4.5%) FASTRAN (S OL = 350 MPa) FASTRAN (S OL = 420 MPa) Normalized distance from hole center, x / r fastran # 69

70 RESIDUAL STRESSES AFTER COLD-WORKING, REAMING AND NOTCHING Normalized residual stress s rs / s ys T6 s ys = 517 MPa FEA (Reaming and notching) FASTRAN (S OL = 350 MPa) FASTRAN (S OL = 420 MPa) Normalized distance from hole center, x / r fastran # 70

71 MEASURED AND PREDICTED CRACKING BEHAVIOR ON COLD-WORKING HOLE SPECIMENS fastran # 71

72 CALCULATED CRACK-OPENING STRESSES FOR CRACK GROWTH WITH OR WITHOUT COLD-WORKED HOLE Simulated cold-worked hole S o / S max Residual-stress-free hole Crack length, a, mm fastran # 72

73 MEASURED AND PREDICTED CRACK-GROWTH UNDER TWIST SPECTRUM LOADING T3 Alclad B = 3.1 mm TWIST (Level III) S 40 mf = 70 MPa a = 1 Crack length, c, mm a = 2 Tests (Wanhill) Flights x 10 3 FASTRAN a = 2 to 1 a = 1 or 2 fastran # 73

74 Measured and Calculated Crack-Length-Against- Cycles for Modified FSFT Spectrum Loading fastran # 74

75 Typical Crack-Opening Stress Calculations for P-3C Modified FSFT Spectrum Loading (NMAX = 1) fastran # 75

76 CONCLUDING REMARKS FASTRAN is an advanced life-prediction code, which accounts for the effects of plasticity on fatigue-crack growth behavior in metallic materials for a variety of crack configurations and loading conditions. Fatigue is crack propagation from micro-structural features for many engineering materials and fatigue lives can be predicted with small-crack theory. Fatigue-crack growth can be predicted reasonably well under aircraft spectrum loading with the plasticityinduced crack-closure concept. Constraint effects and non-linear fracture mechanics parameters are keys to improving life-prediction models. Fatigue-crack growth-rate data in the near threshold regime should be obtained with no load-history effects. fastran # 76

77 Future FASTRAN Modifications Incorporate T-stress in the evolution of plastic deformation around crack fronts (bending crack configurations have +T stresses, while tension-loaded configurations have T stresses) Include roughness- and debris-induced crack-closure behavior in the model Development of plasticity, creep, and relaxation behavior in time-dependent crack growth during load-time-temperature cyclic histories (creep brittle and creep ductile materials) fastran # 77