PLASTICITY AND VISCOPLASTICITY UNDER CYCLIC LOADINGS

Transcription

1 ATHENS Course MP06 Nonlinear Computational Mechanics March 16 to 20, 2009 PLASTICITY AND VISCOPLASTICITY UNDER CYCLIC LOADINGS Jean-Louis Chaboche ONERA, 29 av. de la Division Leclerc Châtillon, France ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

2 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

3 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

4 Non-Linear Kinematic Hardening! "! = # $ % = = = ν + ν & % ( ( ) ' ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

5 Non-Linear Kinematic Hardening )#!#% = * = ν + ν & ( ( ) ' # +% = + ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

6 Non-Linear Kinematic Hardening ψ = α % α = ψ α = α α = α #!,+ % ψ = ( α α ) % # "! "! ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

7 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings -

8 Cyclic hardening and cyclic softening!# %!#!# $ ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings.

9 Monotonic curve and cyclic curve $ +"!# +" /0 )#!# # $ ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

10 Combined hardening models 7# % ( ) 1 / $ = 5 6 = 4 %!# +" ' )#8 # =!# '!# $ 1 = ( 2 1 ) 1 = ) ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings /

11 Different kinetics for isotropic and kinematic hardening 4 % 1 = )2 ) 1 #9"#+ % //////!# ):(/ $ +"!# +" )#!# 6 % = "#+ %!# γ ://;(/// ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

12 Refractory alloy : TZM - Recristalised $ 7& =# 1 #9 cyclic test ± < ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

13 TZM - Recristalised $ #9 ):// // / / ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

14 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

15 Needs for kinematic hardening in cyclic creep Primary creep is : # $ "# >$ "#!?6 ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

16 Viscoplasticity equations Normality rule potential : Ω = Ω ( 1) hardening variables 1? Ω :Ω Ω :/ " normality : = Ω Ω ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

17 Viscoplasticity with Non-Linear Kinematic hardening potential : Ω = ( ) yield stress ) -( normality : multiplier : = = = Non-Linear Kinematic hardening : " 5( ) ( ) 1 Ω 5 = = = 6 drag stress = % Isotropic hardening superposition : on the yield stress : 1 on the hardening modulus : :(1 on the «drag stress» : 6:61 dynamic recovery factor hardening modulus ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings -

18 Modelling of creep tests 40//+##! ///A < < := := :.. :.. : :- :- :- #9+# # " 0B 6 " ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings.

19 Modelling of relaxation tests = 40//+##! ///A 9 "$ +# # "$ ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

20 Modelling of cyclic tests = =!# =!# #&!# #& < 40// +##! ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings /

21 Viscoplasticity with Non-Linear Kinematic hardening!# +" % = 40//+##! ///A :/ :/C :./C :/ ://C < ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

22 Creep plasticity interaction BE # E # // A "??1 D < # D $! # + ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

23 Static or thermal recovery 6 %! "! % $ = = "! = $ "! 4 % 1 = ) ( 2 1) 1 *##! " % $+ $C C #! * ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

24 Static recovery of isotropic hardening # BE # E # //A +!# )#8!# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

25 Modelling of cyclic relaxation = & BE # E # //A = ±/C< # # "! $$ % ++!# 9 # ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

26 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

27 Ratchetting effects +"# +#!F 8+)CCC Structural loading : primary and secondary "# $ + + &% # $#+ + E ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings -

28 Ratchetting effects E! = ± E # # # /! # D G G+ ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings.

29 Ratchetting effects and mean-stress relaxation # % #% & δ δ & #& ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

30 Ratchetting effects and mean-stress relaxation # % #% & δ δ both phenomena are : % H I# $$ ) )! +# & #& ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings /

31 No ratchetting with Linear Kinematic Hardening =& # # & # $ # $ )# = # $!# $ &# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

32 Ratchetting modelling in tension-compression with Non-Linear Kinematic Hardening & & $ +" ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

33 Ratchetting modelling in tension-compression with Non-Linear Kinematic Hardening & & $ +" = ν + ν & ( ( ) ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

34 Ratchetting modelling in tension-compression with Non-Linear Kinematic Hardening & δ & ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

35 Ratchetting modelling in tension-compression with Non-Linear Kinematic Hardening & δ & δ = B ( + ) ( ) & ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

36 Ratchetting in tension-torsion 0B 6 J % B 6 " J # # & # $ # $ )# #9! " # $ $ &# #9! ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

37 Model deficiencies for ratchetting prediction B 6 J " 0B 6 J ) $ B 0B 6 J # "% #9! +K " +! #! "# 0B 6 J 9 *# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings -

38 Non-Linear Kinematic Hardening with Thresholds γ # :# : # ) #C # # = # Subsequent modifications : H # $! "! I L M N 5 ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings.

39 Non-Linear Kinematic Hardening with Thresholds BE # E # /A = #+# # # 9 + # = //./ = = / = B6?0B6?0B6* = / = #+# / =!# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

40 Mean-stress relaxation in tests controlled with 1 :/ =& +" =&!# #& #9 # +% # #& # O# / # +%!# #! #& )#8 ## +% #& )#8 = / ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings /

41 Incomplete mean-stress relaxation 1 :/ & +##! 0. ((/A 9 # 0B 6 J 9 *# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

42 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

43 Strain-range memorization effect BE # E # /A ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

44 Strain-range memorization effect, )Q- =! +$% = ζ, ζ, = η J ζ = η J % P P = +# % ( 2, 1) 1 = ) η = η < " "#!# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

45 Strain-range memorization effect BE # E # /A 9 #"# Q #C- #+# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

46 TZM refractory alloy : 3 preparations =# 7& N O E1 1 Cyclic test with increasing levels ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

47 TZM refractory alloy : As Worked 7& =# N Cyclic test with increasing levels 0B6 B64EL # ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings -

48 TZM refractory alloy : Recristalised 7& + $!# =# 1 Cyclic test with increasing levels +# 9 ) " ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings. 0B6 B64EL

49 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings

50 Multi-mechanisms and multi-criteria models (αmβc) = : # %Ω $ % $ = Ω Ω = = $ $ +# &C0B6 % α = α = α &% +# #! ## +. # % =+# M E# = % $ ( ) ' + = R.- ## +E ( ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (/

51 Multi-mechanisms and multi-criteria models (αmβc) =+# M =+# = % =+# M E# = % $ = = 5 $ = = 5 $ ( ) ' + = 5 5 ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

52 Multi-criteria : coupled plasticity and creep = = + " " $ =/ ## + M. = λ $ " $ " $ " = 6 $ = λ " 1 " &C0B6 % α = α 1 +# % = α + α + " " = " "" α α " " ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

53 Cyclic plasticity modelling MODELLING OF REVERSED AND CYCLIC BEHAVIOUR CYCLIC HARDENING AND SOFTENING CYCLIC VISCOPLASTICITY AND STATIC RECOVERY RATCHETTING EFFECTS AND MEAN-STRESS RELAXATION STRAIN RANGE MEMORIZATION AND OTHER COMPLEX EFFECTS MULTIPLE MECHANISMS AND CRITERIA EXAMPLE OF SINGLE CRISTAL VISCOPLASTICITY ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

54 Multi-mechanisms and Multi-criteria : Example of cristal plasticity (single cristal) E % # ## = ( ) # + # # # ## + #.- "#! % $ = τ & " = γ $ 6 = " Eτ & #" % τ = # = $ = τ & = γ J & ) 9! γ ( & ) ) = 2 " ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

55 Traction on a FCC single cristal in various directions # :(/S ://S ://S ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings ((

56 Thermomechanical fatigue tests (MPa) m <001> # # +##! = 1100 T C (%) 1 Tests : AM1 (ENSMP tests) Models : macroscopic cristal viscoplasticity 1600 (MPa) <111> 1600 (MPa) <101> (%) (%) 0.6 ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

57 Traction shear on a FCC single cristal <> *+)+# <> <> +)!! T//U T/U ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (-

58 Traction shear on a FCC single cristal < > *+)+# +)!! // / ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (.

59 Multiaxial thermomechanical fatigue of AM1 QCD// '* + * +)+# ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings (

60 Multiaxial thermomechanical fatigue of AM1 validation of cristal viscoplasticity model of Ecole des Mines!!"! γ!" # )#8!#% "##" ATHENS Course MP March 2009 Plasticity and viscoplasticity under cyclic loadings /