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Alloy yield strength modeling with MatCalc ( rel. 5.61.0057)

Alloy yield strength modeling with MatCalc ( rel. 5.61.0057). P. Warczok. Model overview. Contributions to yield strength ,  YS Intrinsic strength ,  i Work hardening ,  disl Grain / subgrain boundary strengthening ,  gb ,  sgb Solid solution strengthening ,  ss

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Alloy yield strength modeling with MatCalc ( rel. 5.61.0057)

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

  2. Model overview • Contributionstoyieldstrength, YS • Intrinsicstrength, i • Work hardening, disl • Grain/subgrainboundarystrengthening, gb, sgb • Solid solutionstrengthening, ss • Precipitationstrenghtening, prec

  3. Model overview • Contributionstoyieldstrength, YS • Intrinsicstrength, i • Work hardening, disl • Grain/subgrainboundarystrengthening, gb, sgb • Solid solutionstrengthening, ss • Precipitationstrenghtening, prec

  4. Intrinsic strength, i

  5. Model overview • Contributionstoyieldstrength, YS • Intrinsicstrength, i • Work hardening, disl • Grain/subgrainboundarystrengthening, gb, sgb • Solid solutionstrengthening, ss • Precipitationstrenghtening, 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 • Contributionstoyieldstrength, YS • Intrinsicstrength, i • Work hardening, disl • Grain/subgrainboundarystrengthening, gb, sgb • Solid solutionstrengthening, ss • Precipitationstrenghtening, 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 • Contributionstoyieldstrength, YS • Intrinsicstrength, i • Work hardening, disl • Grain/subgrainboundarystrengthening, gb, sgb • Solid solutionstrengthening, ss • Precipitationstrenghtening, 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 • Solid solution strengthening, ss

  21. Model overview • Contributionstoyieldstrength, YS • Intrinsicstrength, i • Work hardening, disl • Grain/subgrainboundarystrengthening, gb, sgb • Solid solutionstrengthening, ss • Precipitationstrenghtening, 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 • Precipitate mean radius • Some general parameters/settings • Equivalent radius, req (describes precipitate-dislocation interference area)

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

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

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

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

  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 • Linear misfit • Volumetric misfit • Strain field due to precipitation/matrix misfit • Strong particles • Weak particles

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

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

  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 • Particle shear modulus • Nembach model • Strong particles • Weak particles

  48. Modulus effect • Particle Poisson ratio Weak Strong Siems model

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

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

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