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Alloy yield strength modeling with MatCalc (rel )

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Presentation on theme: "Alloy yield strength modeling with MatCalc (rel )"— Presentation transcript:

1 Alloy yield strength modeling with MatCalc (rel. 5.61.0057)
P. Warczok

2 Model overview Contributions to yield strength, YS
Intrinsic strength, i Work hardening, disl Grain/subgrain boundary strengthening, gb , sgb Solid solution strengthening, ss Precipitation strenghtening, prec

3 Model overview Contributions to yield strength, YS
Intrinsic strength, i Work hardening, disl Grain/subgrain boundary strengthening, gb , sgb Solid solution strengthening, ss Precipitation strenghtening, prec

4 Intrinsic strength, i

5 Model overview Contributions to yield strength, YS
Intrinsic strength, i Work hardening, disl Grain/subgrain boundary strengthening, gb , sgb Solid solution strengthening, ss Precipitation strenghtening, prec

6 Work hardening, disl Taylor equation Taylor factor Shear stress
Burger’s vector Dislocation density

7 Work hardening, disl Taylor equation Taylor factor Shear stress
Burger’s vector Dislocation density

8 Work hardening, disl Taylor equation Taylor factor Shear stress
Burger’s vector Dislocation density

9 Work hardening, disl Taylor equation Two parameter model

10 Work hardening, disl Taylor equation Two parameter model

11 Model overview Contributions to yield strength, YS
Intrinsic strength, i Work hardening, disl Grain/subgrain boundary strengthening, gb , sgb Solid solution strengthening, ss Precipitation strenghtening, prec

12 Grain/subgrain boundary strengthening, gb , sgb
Hall-Petch equation Grain diameter Subgrain diameter Constant

13 Grain/subgrain boundary strengthening, gb , sgb
Hall-Petch equation Grain diameter Subgrain diameter Constant

14 Grain/subgrain boundary strengthening, gb , sgb
Hall-Petch equation Grain diameter Subgrain diameter Constant

15 Grain/subgrain boundary strengthening, gb , sgb
Hall-Petch equation Grain diameter Subgrain diameter Constant

16 Model overview Contributions to yield strength, YS
Intrinsic strength, i Work hardening, disl Grain/subgrain boundary strengthening, gb , sgb Solid solution strengthening, ss Precipitation strenghtening, prec

17 Solid solution strengthening, ss
Coefficient for element i Element i content in the prec. Domain (mole fraction) Exponent for element i Exponent for substitutional elements Exponent for interstitial elements Global exponent

18 Solid solution strengthening, ss
Coefficient for element i Element i content in the prec. domain Exponent for element i Exponent for substitutional elements Exponent for interstitial elements Global exponent

19 Solid solution strengthening, ss

20 Solid solution strengthening, ss

21 Model overview Contributions to yield strength, YS
Intrinsic strength, i Work hardening, disl Grain/subgrain boundary strengthening, gb , sgb Solid solution strengthening, ss Precipitation strenghtening, prec

22 Precipitation strengthening, prec
Some general parameters/settings Angle between dislocation line and Burger’s vector  (edge:screw ratio,  = 0 for pure screw,  = /2 for pure edge)

23 Precipitation strengthening, prec
Some general parameters/settings Equivalent radius, req (describes precipitate-dislocation interference area) Precipitate mean radius

24 Precipitation strengthening, prec
Some general parameters/settings Mean distance between the precipitate surfaces, LS Precipitate number density within the class Precipitate mean radius within the class

25 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

26 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

27 Non-shearable particles

28 Non-shearable particles
If req < 2ri , then

29 Non-shearable particles

30 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

31 Shearable particles Some general parameters/settings
Dislocation bending angle,  - weak and strong particles 0° ≤  ≤ 120°  “strong” particles 120° ≤  ≤ 180°  “weak” particles

32 Shearable particles Some general parameters/settings
Mean distance between the precipitate surfaces, L Strong particles

33 Shearable particles Some general parameters/settings
Mean distance between the precipitate surfaces, L Weak particles

34 Shearable particles Some general parameters/settings
Mean distance between the precipitate surfaces, L Weak particles

35 Shearable particles Some general parameters/settings
Dislocation line tension, T Simple model Advanced model

36 Shearable particles Some general parameters/settings
Dislocation line tension, T Simple model Advanced model

37 Shearable particles Some general parameters/settings
Dislocation line tension, T Simple Advanced

38 Shearable particles Some general parameters/settings
Inner cut-off radius, ri (multiplication of Burger’s vector)

39 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

40 Coherency effect Strain field due to precipitation/matrix misfit
Strong particles Weak particles Linear misfit Volumetric misfit

41 Coherency effect Shearable particles – Coherency effect
Strain field due to precipitation/matrix misfit Strong particles Weak particles Linear misfit Volumetric misfit

42 Coherency effect Strain field due to precipitation/matrix misfit
Strong particles Weak particles Linear misfit Volumetric misfit

43 Coherency effect Strain field due to precipitation/matrix misfit
Strong particles Weak particles

44 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

45 Modulus effect Elastic properties of precipitate and matrix differ  dislocation energy inside and outside the precipitate differ 2 models Nembach Siems

46 Modulus effect Elastic properties of precipitate and matrix differ  dislocation energy inside and outside the precipitate differ 2 models Nembach Siems

47 Modulus effect Nembach model Strong particles Weak particles
Particle shear modulus

48 Modulus effect Siems model Particle Poisson ratio Strong Weak

49 Modulus effect Nembach model Strong particles Weak particles
Particle shear modulus Particle Poisson ratio Particle shear modulus

50 Modulus effect Elastic properties of precipitate and matrix differ  dislocation energy inside and outside the precipitate differ 2 models Nembach Siems

51 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

52 Anti-phase boundary (APB) effect
Dislocation passing through ordered precipitate increases the energy by creating the APB Strong particles Weak particles APB energy Interaction parameter between the leading and trailing dislocation - Number of pair dislocations

53 Anti-phase boundary (APB) effect
Dislocation passing through ordered precipitate increases the energy by creating the APB Strong particles Weak particles APB energy Interaction parameter between the leading and trailing dislocation - Number of pair dislocations

54 Anti-phase boundary (APB) effect
Dislocation passing through ordered precipitate increases the energy by creating the APB Strong particles Weak particles

55 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

56 Stacking fault (SF) effect
Passing dislocation creates a stacking fault – energy difference between the SF in the precipitate and matrix Burger’s vector of particle Stacking fault energy of particle Stacking fault energy of matrix

57 Stacking fault (SF) effect
Passing dislocation creates a stacking fault – energy difference between the SF in the precipitate and matrix Strong particles Weak particles

58 Stacking fault (SF) effect
Passing dislocation creates a stacking fault – energy difference between the SF in the precipitate and matrix Burger’s vector of particle Stacking fault energy of particle Stacking fault energy of matrix

59 Stacking fault (SF) effect
Passing dislocation creates a stacking fault – energy difference between the SF in the precipitate and matrix Burger’s vector of particle Stacking fault energy of particle Stacking fault energy of matrix

60 Stacking fault (SF) effect
Passing dislocation creates a stacking fault – energy difference between the SF in the precipitate and matrix Burger’s vector of particle Stacking fault energy of particle Stacking fault energy of matrix

61 Stacking fault (SF) effect
Passing dislocation creates a stacking fault – energy difference between the SF in the precipitate and matrix Strong particles Weak particles

62 Precipitation strengthening, prec
Derived from prec Non-shearable particles (Orowan mechanism) Shearable particles (weak or strong) Coherency effect Modulus effect Anti-phase boundary effect Stacking fault effect Interfacial effect

63 Interfacial effect Passing dislocation increases the area of precipitate/matrix interface Strong particles Weak particles - Precipitate/matrix interface energy

64 Interfacial effect Passing dislocation increases the area of precipitate/matrix interface Strong particles Weak particles - Precipitate/matrix interface energy

65 Interfacial effect Passing dislocation increases the area of precipitate/matrix interface Strong particles Weak particles

66 Precipitation strengthening, prec
Evaluation Identifying the regime for each precipitate separately Summation of the calculated tregime of each precipitate Conversion of tprec to prec

67 Precipitation strengthening, prec
Evaluation Identifying the regime for each precipitate separately Summation of the calculated ti,regime of each precipitate Conversion of tprec to prec

68 Regime of each precipitate
For every precipitate phase i: Values of  evaluated for each of three regimes (Non-shearable, shearable weak, shearable strong)

69 Regime of each precipitate
For every precipitate phase i: Values of  evaluated for each of three regimes (Non-shearable, shearable weak, shearable strong)

70 Regime of each precipitate
For every precipitate phase i: Values of  evaluated for each of three regimes (Non-shearable, shearable weak, shearable strong)

71 Regime of each precipitate
i,regime with the lowest value for the precipitate phase i is taken for the further operations If coherency radius ≠ 0 and the mean radius of precipitate is greater than the coherency radius  the non-shearable regime is taken for further calculation

72 Precipitation strengthening, prec
Evaluation Identifying the regime for each precipitate separately Summation of the calculated ti,regime of each precipitate Conversion of tprec to prec

73 Summation of ti,regime Shearable particles contribution (weak and strong regime) Non-shearable particles contribution

74 Summation of ti,regime

75 Summation of ti,regime Precipitation strengthening, prec (derived from prec) Evaluation of prec

76 Precipitation strengthening, prec
Evaluation Identifying the regime for each precipitate separately Summation of the calculated ti,regime of each precipitate Conversion of tprec to prec

77 Precipitation strengthening, prec
Evaluation Identifying the regime for each precipitate separately Summation of the calculated ti,regime of each precipitate Conversion of tprec to prec Taylor factor

78 Total yield strength, YS
Summation of contributions

79 Total yield strength, YS
Summation of contributions

80 Total yield strength, YS
Summation of contributions

81 Thank you for your attention !

82

83 Precipitation hardening
Shape factor influence on LS Shape factor Sonderegger B., Kozeschnik E., Scripta Mater., 66 (2012) 52-55

84 Precipitation hardening
Shape factor influence on LS Shape factor Sonderegger B., Kozeschnik E., Scripta Mater., 66 (2012) 52-55

85 Precipitation hardening
Shape factor influence on LS Shape factor Sonderegger B., Kozeschnik E., Scripta Mater., 66 (2012) 52-55

86 Precipitation hardening
Non-shearable particles (Orowan mechanism) Equivalent radius for edge disl. Equivalent radius for screw disl. Fraction of edge disl. Fraction of screw disl.

87 Precipitation hardening
Shearable particles – (e.g. coherency effect) Equivalent radius for edge disl. Equivalent radius for screw disl.

88 Precipitation hardening
Shearable particles – Coherency effect for non-spherical particles Strong particles Weak particles ,if

89 Summing up… Total yield strength, YS Summation of contributions
Influence of strain rate,

90 Summing up… Total yield strength, YS Summation of contributions
Influence of strain rate,

91 Summing up… Total yield strength, YS Summation of contributions
Influence of strain rate,

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