Alloy yield strength modeling with MatCalc ( rel. 5.61.0057)

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