ONERA Fatigue Model. December 11, 2017

Transcription

1 December 11, 2017

2 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

3 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

4 ONERA 4 / 66 Fatigue Model F1 : Uniaxial fatigue curves Woehler (N f, σ a = σ ) curve from symmetric fatigue tests (R = 1) 2 F2 : Loading ratio / mean-stress dependence Woehler curves with loading ratios R > 1, Haigh diagram F3 : Non-linear cumulation dependence of the loading path history on the damage results F4 : Temperature Effect F5 : Multiaxiality F6 : Creep damage F7 : Creep-Fatigue interaction

5 ONERA 5 / 66 model (Chaboche) σ cycle period T σ max σ = σmax+σmin 2 σ a = σ 2 N f = 1 (β + 1) [1 α(σ a, σ)]» σa β M( σ) σ min with α = 1 a σa σ l ( σ) σ u σ max time N f = σ u σ max a (β + 1) σ a σ l ( σ)» σa β M( σ) Mean stress dependence: σ l ( σ) = σ l b 1 σ, M( σ) = M b 2 σ Coefficients : σ u, σ l0, β, M 0, b 1, b 2

6 F1: 6 / 66Calibration of symmetric fatigue results (1/2) σ a = σ 2 σ u N f = [ σu σmax σa a (β+1) σa σl 0 M0 ] β increasing β decreasing M 0 σ l e+06 1e+08 1e+10 Nf Active coefficients on symmetric fatigue tests (R σ = 1) UTS : σ u fatigue limit : σ l0 slope : β position along N f axis : M 0

7 F1: 7 / 66Calibration of symmetric fatigue results (2/2) demo reset open terminal

8 F2: 8 / 66Mean stress dependence (1/2) Haigh diagram σa = σ Woehler curve σa = σ 2 R = 1 Nf = 10 6 R = mean stress σ e+06 1e+08 1e+10 Nf b 1 : decrease of σ l depending on mean stress σ σ l0 σ l ( σ) = 1 + b 1 σ b 2 : translation to smaller N f values M 0 M( σ) = 1 + b 2 σ demo reset open terminal

9 F2: 9 / 66Mean stress dependence (2/2) demo reset open terminal

10 F3: 10 / 66 Non-linear cumulation (1/4) For complex loading paths σ load sequence Linear cumulation (Miner s rule) is not conservative sequence effect: mildly damaging cycles have a greater effect if they occur after strongly damaging one cycles with amplitude below the fatigue limit do have an effect if prior fatigue damage occurred Needs a multi-axial rainflow procedure (see tools) time

11 F3: 11 / 66 Non-linear cumulation (2/4) Fatigue damage evolution equation: δd = h 1 (1 D) β+1i» α(σ β a, σ) σ a δn M( σ) (1 D) with α = 1 a σa σ l ( σ) σ u σ max integration of D between 0 and 1 N f = 1 (β + 1) [1 α(σ a, σ)]» σa β M( σ)

12 F3: 12 / 66 Non-linear cumulation (3/4) σ D i 1 cycle i D i σ σ load sequence time integration between D i 1 and D i above the fatigue limit: σ a > σ l ( σ), α < 1 [ 1 (1 Di ) β+1] 1 α [ 1 (1 Di 1 ) β+1] 1 α = 1 N f ( σ, σ, σ max ) below: σ a σ l ( σ), α = 1 [ 1 (1 Di ) β+1 ] ln 1 (1 D i 1 ) β+1 ( ) σ a β = (β + 1) M( σ)

13 F3: 13 / 66 Non-linear cumulation (4/4) demo reset open terminal

14 F4: 14 / 66 Temperature Effect N f = 1 S max a (β + 1) S 2 σ l( S) " # S β 2 where S(T ) = σ(t ) M( S) σ u Normalized coefficients : σ l0, M, b 1, b 2 demo reset open terminal

15 F5: 15 / 66 Multiaxiality Fig. Sines criterion in reversed loading (σ l means σ l0 = σ l (0))

16 F6: 16 / 66 Creep damage (1/2) Rabotnov-Kachanov model: D C = σeq r 1 A (1 D C ) k where: σ eq = (1 α β) J(σ ) + α σ p + β σ and: J(σ ) Mises invariant of σ σ p first principal stress σ mean trace of σ r, k, A material parameters that depend on temperature Integration between 0 and 1 yields the critical time t C for creep initiation: t C = 1 k+1 ` σeq r A

17 F6: 17 / 66 Creep damage (2/2) 800 sim 1000 exp 1000 sim 800 exp sig (MPa) tc (hours) demo reset open terminal

18 F7: 18 / 66 Creep-Fatigue interaction (1/2) For each cycle damage goes from D i to D f : damage increases from D i to D c due to creep C = 1 N c = (1 D i ) k+1 (1 D c) k+1 damage increases from D c to D f due to fatigue F = 1 N f = ˆ1 (1 D f ) β+1 1 α ˆ1 (1 Dc) β+1 1 α where: C increase of damage on one cycle due to pure creep F increase of damage on one cycle due to pure fatigue α = 1 a σa σ l ( σ) σ u σ max coefficient a controls the amount of of cumulation non-linearity: 0 a 1 a 1 : quasi-linear a 0 : strongly non-linear

19 F7: 19 / 66 Creep-Fatigue interaction (2/2) symmetric cyclic test with hold time interaction (a=0.1) pure fatigue pure creep 700 siga (MPa) e+06 1e+07 1e+08 1e+09 nr demo reset open terminal

20 Fatigue 20 / 66 models summary Inputs required by the fatigue model: From the constitutive model used in FE analysis: cyclic hardening modeling (σ a ) mean stress relaxation modeling ( σ) Dedicated post-processing tools: calculation of the amplitude of a multiaxial stress path multiaxial rainflow algorithm

21 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

22 Manson-Coffin 22 / 66 LCF model classical strain-based fatigue model doesn t account for non-zero mean stress effects ɛ 2 = A N α f ɛ 2 = ɛp 2 + ɛe 2 + B N β f = ɛp 2 + σ 2 E A, α (plastic), B, β (elastic) fatigue model coefficients, E Young s modulus A ramberg-osgood equation calibrated from cyclic hardening experimental curves can be used to obtain ɛ p from σ and transform standard S-N curves to ( ɛ,n f ) plots «σ ɛ p n = K 2 2 Note that (K, n) are linked to manson coefficients: n = β α, K = EB A n

23 Manson-Coffin 23 / 66 demo calibration of (A, α) on (N f, ɛp ) points using the plastic function item 2 and the opt_plastic otimization item calibration of (B, β) on (N f, ɛe ) points using the elastic function item 2 and the opt_elastic otimization item check the whole (N f, ɛ ) curve using the woehler_manson external 2 simulation item built with Zpost and the strain_control.z7p script the woehler_manson_ramberg simulation item recalculates the plastic strain from the stress input using the ramberg-osgood equation given in the previous slide use the multiplot item to compare manson-coffin with the onera model calibration done previously (see onera R=-1 calibration) demo reset open terminal

24 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

25 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

26 Multiaxial 26 / 66 loading path amplitude (1/2) solve the Smallest Enscribed Hypersphere problem (SEH) j n o ff i J(σ X ) min X R(X ) = max i generic geometrical problem with applications in many fields (pattern recognition, protein analysis, political science, ray-tracing...) still, efficient algorithms are fairly recent (Bend Gartner, "Fast and Robust Smallest Enclosing Balls" 1999)

27 Multiaxial 27 / 66 loading path amplitude (2/2) Iteratively solve optimization problems SEH(S) on subsets S of P At each iteration, solution of SEH(S) is found by solving a linear system with size the number of points in S Fast convergence to the solution of SEH(P)

28 SEH 28 / 66example Initialization: first point σ 1 in the loading path P σ 1

29 SEH 29 / 66example Farthest of σ 1 is Fst(σ 1 ) = σ 2 σ 1 Fst(σ 1 ) = σ 2

30 SEH 30 / 66example Solve SEH(σ 1, σ 2 ) : solution is H 1 with center X 1 σ 1 X 1 σ 2

31 SEH 31 / 66example Farthest of X 1 is Fst(X 1 ) = σ 3 σ 1 Fst(X 1 ) = σ 3 X 1 σ 2

32 SEH 32 / 66example Solve SEH(σ 1, σ 2, σ 3 ) : solution is H 2 with center X 2 σ 1 σ 3 X 2 σ 2

33 SEH 33 / 66example Farthest of X 2 is Fst(X 2 ) = σ 4 σ 1 σ 3 Fst(X 2 ) = σ 4 X 2 σ 2

34 SEH 34 / 66example Solve SEH(σ 1, σ 2, σ 3, σ 4 ) : solution is H 3 with center X 3 all points are in H 3, end σ 1 σ 4 X 3 σ 3 σ 2

35 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

36 Multiaxial 36 / 66 rainflow algorithm (1/4) extract sub-cycles from a complex stress path for (non-)linear damage cumulation σ generalize the 1D rainflow method to multiaxial stress states (6 independent components) use the concept of active surface used in some plasticity models (Melnikov, Semenov) time

37 Multiaxial 37 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B from O to A time

38 Multiaxial 38 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B from O to A time

39 Multiaxial 39 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B from O to A time

40 Multiaxial 40 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B at point A time

41 Multiaxial 41 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D B O time unloading from A to B

42 Multiaxial 42 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D B O time unloading from A to B

43 Multiaxial 43 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B at point B time

44 Multiaxial 44 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B from B to C time

45 Multiaxial 45 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B from B to C time

46 Multiaxial 46 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D O B at point C time

47 Multiaxial 47 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D B O time extra loading from C to D

48 Multiaxial 48 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D B O time extra loading from C to D

49 Multiaxial 49 / 66 rainflow algorithm (2/4) follow the stress path and recursively builds active surfaces included in one another a cycle is detected when the size of the current surface exceeds the previous one σ A C D B O time extra loading from C to D

50 Multiaxial 50 / 66 rainflow algorithm (3/4) An active surface s is defined by: U s its closing point created when unloading occurs X s its center Update of center: X s(s i) intersection of the mediatrix of (U s 1, S i) with (X s 1, U s 1) X s 1 X s (S i ) U s 1 i S i 1 2 (U s 1 + S i )

51 Multiaxial 51 / 66 rainflow algorithm (3/4) An active surface s is defined by: U s its closing point created when unloading occurs X s its center Update of center: X s(s i+1) intersection of the mediatrix of (U s 1, S i+1) with (X s 1, U s 1) X s 1 X s (S i+1 ) U s 1 S i S i (U s 1 + S i+1 )

52 Multiaxial 52 / 66 rainflow algorithm (4/4) Initialization: X 0 = X SEH center of the SEH calculated for the whole loading path U 0 = 0 to avoid residuals reorganize the path to begin by the maximum point σ m such that: J(σ m X SEH) = max J(σ i X i P SEH) σ σ m σ σ m time time

53 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

54 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

55 **process 55 / 66 onera (multiaxial) rainflow sub-cycles extraction (nonlinear) cumulation **output_number... **material_file mat **process onera [*cycle beg1-end1/rep1... begn-endn/repn] [*preload beg1-end1/rep1... begn-endn/repn] *mode NLC_ONERA LC *fatigue fatigue_rainflow 2 [*creep creep 2] [*reverse 3] % material file ***post_processing_data **process onera a 0.1 % (0<a<1) ***return

56 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

57 **process 57 / 66 fatigue_rainflow number of cycles to failure according to the ONERA fatigue model **material_file mat **process fatigue_rainflow *var sig [*mean_stress (standard variant)] [*mode with_a] [*normalized_coeff] [*reverse 3] % material file ***post_processing_data **process fatigue_rainflow sigma_u sigma_l 0.2 M 40.0 beta 2.0 [ a 0.1 ] [ b1 0.1 b2 0.1 sigma_n sigma_p 0.01 ] ***return

58 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

59 **process 59 / 66 manson_coffin number of cycles to failure according to the Manson-Coffin model **material_file mat **process manson_coffin *var sig % name of the plastic strain tensor (epi) or cyclic_hardening % to derive epi from sig using a ramberg-osgood equation *plastic epi cyclic_hardening [ *infinity_is 1.0e+08 ] [ *full_output ] % additional ee_alt, ep_alt output % material file ***post_processing_data **process manson_coffin A 0.01 alpha 0.1 B 0.01 beta 0.1 young ***return

60 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

61 Stress-controlled 61 / 66 script Input file (file stress): Command: *frequency 20.0 *temperature *material endo.mat *stress *load_factor -1.0 [*creep] [*delay] Zrun -zp stress_control.z7p -s ZLanguage.args stress Output (file stress.out): # nr dsig/2 dsig sig_max sig_min nf nc e e e e e e e... Use in SimOpt: demo terminal

62 Strain-controlled 62 / 66 script Input file (file strain): Command: *frequency 20.0 *temperature *material endo.mat *behavior comportement.mat *strain 3.e-3 1.e-2 5.e-4 *load_factor -1.0 [*creep] [*delay] Zrun -zp strain_control.z7p -s ZLanguage.args strain Output (file strain.out): e e e e e e e... Use in SimOpt: demo terminal

63 Goodman 63 / 66 diagram script Input file (file goodman): Command: *frequency 1. *target 1.e7 *temperature *material mat.mat *steady_stress [*creep] [*delay] Zrun -zp goodman.z7p -s ZLanguage.args goodman Output (file goodman.out): # ss sa nr e e e e e e Use in SimOpt: demo terminal

64 Plan 1 ONERA Model 2 Manson-Coffin Model 3 Basic Tools Multiaxial stress amplitude (SEH) Multiaxial rainflow 4 Z-post input commands process onera process fatigue_rainflow process manson_coffin Calibration scripts 5 Experimental database

65 Calibration 65 / 66 experimental database (1/2) For each temperature spanning the operating temperature range, ie. at least 4 temperature levels including T min (room temperature) and T max: E1: Creep tests with at least 3 points in the (σ, t f ) diagram E2: Pure fatigue symmetric tests (R σ = 1) High frequency tests (50 Hz) to uncouple from creep If not possible lower frequency tests (>0.5 Hz) Several frequencies if possible Characterization of the full S-N curve: 3 points in the LCF regime (N f < 10 5 ), 2 points in the HCF regime (fatigue limit) ¾ σu σl ½ ½¼ ½¼¼ ½¼¼¼ ½¼¼¼¼ ½ ½ ½ ½ ½ Æ

66 Calibration 66 / 66 experimental database (2/2) E3: Non symmetric fatigue tests to characterize the mean stress effect A least 1 non symmetric loading ratio (Rσ 1), and ideally 2 to characterize the full Haigh diagram. For each loading ratio, S-N curve as in E2 E4: Creep-fatigue interaction tests Symmetric R σ = 1 tests with hold time Typically T = 220 s with T l = 10 s and T h = 90 s (check T h with creep tests in E1) S-N curve in the low cycle regime (at least 3 points) σ T l T h T time Simplifications: E1 and E4 are not needed at low temperature E3 can be skipped for some temperatures Cyclic tests at R ɛ = 1 available from material behavior tests and performed up to failure can be used to build the S-N curves