Modeling the Survival of Hard-Alpha Inclusions in Titanium

1. Modeling the Survival of Hard-Alpha Inclusions in Titanium Ernesto Gutierrez-Miravete, Rensselaer at Hartford Tony Giamei, Belcan Indresh Padmonkar, Rensselaer Hartford Srikanth Bandlamudi, Rensselaer Hartford Mas Hongoh, Pratt & Whitney Brice Cassenti, UTRC and Pratt&Whitney

2. Outline • Introduction • Model Description • Description of Code • Preliminary Results • Summary

3. Introduction • Undetected N- and/or O-containing particles in Ti alloys (hard-alpha) can result in catastrophic failure of aircraft engine components. • The process metallurgy of Ti alloys provides many potential sources of N and/or O. • Better understanding of the dissolution behavior of N- and/or O containing Ti inclusions in Ti alloys during thermal processing is required.

4. Model Description • When N and/or O come in contact with Ti several different phases can form depending on composition and temperature. • The Ti-N phase diagram (Fig 1a). • The Ti-O phase diagram (Fig 1b). • If an isolated N-rich or O-rich seed particle is embedded in a Ti matrix, the various phases appear as concentric layers on the original particle.

5. Fig 1a

6. Fig 1b

7. Model Description (contd.) • The concentration of impurity decreases with distance from the center of the seed particle. • Dissolution of the resulting layers involves mass transport of N and/or O away from the seed particle. • See Figure 2.

8. C Flux of N (or O)    L x Fig 2 Concentration profile around a dissolving inclusion.

9. Model Description (contd.) • Assumptions and Limitations • Binary Systems (Ti-N or Ti-O) • Chemical Equilibrium at all Interfaces • All Phases form Ideal Solutions • Temperatures restricted to within beta transus of pure Ti and first peritectic • 882 - 2020 C for Ti-N • 882- 1720 C for Ti-O • Necessary Diffusivity Data Available • Porosity Neglected

10. Model Description (contd.) • Governing Equation dc/dt = div ( D grad a) dc/dt = div ( grad a*) where c = concentration of N (or O) D = diffusivity of N (or O) a = activity of N (or O) (Fig 3) da* = D da (Fig. 4)

11. a    L C Fig 3

12. a*    L a Fig 4

13. Model Description (contd.) • Solution Methodology: • Finite Difference, Fixed Domain Method • Fixed Mesh • Explicit Scheme • Physico-Chemical Data: • Phase Diagrams • Diffusivities

14. Description of the Code • Derived from earlier code MICRO developed at UTRC. • FORTRAN program embedded in a UNIX wrapper. • Code can be used from a computer anywhere anytime via the internet. • Inputs: • Inclusion size and geometry • Inclusion and matrix concentration • Thermal history • Mesh

15. The GROW Code (contd.) • Outputs • Concentration profiles around inclusion at selected times during specified temperature history • Extent of the various layers as functions of time. • Extent of the diffusion zone surrounding the inclusion as function of time.

16. Preliminary Results (Ti-N) • 250 micron inclusion with 32 a/o N • Isothermal Hold at 1200 C (Figs. 5a and 5b) • Isothermal Hold at 1600 C (Figs. 6a and 6b) • Isothermal Hold at 2020 C (Figs. 7a and 7b) • Sample Thermal History (Figs. 8a and 8b) t (min) 0 1 5 10 12 13 15 T(C) 2000 1670 1000 1000 1300 1500 1000

17. Fig 5a

18. Fig 5b

19. Fig 6a

20. Fig 6b

21. Fig 7a

22. Fig 7b

23. Fig 8a

24. Fig 8b

25. Preliminary Results (Ti-N) (contd.) • Two-dimensional system (250 by 1000 micron inclusion). Figs. 9a and 9b. • Three-dimensional system (250 by 500 by 1000 micron inclusion). Figs. 10a and 10b.

26. Fig 9a

27. Fig 9b

28. Fig 10a

29. Fig 10b

30. Preliminary Results (Ti-O) • 250 micron inclusion with 50 a/o O • Isothermal Hold at 1200 C (Figs. 11a and 11b) • Isothermal Hold at 1600 C (Figs. 12a and 12b) • Isothermal Hold at 1720 C (Figs. 13a and 13b) • Sample Thermal History (Figs. 14a and 14b) t (min) 0 1 5 10 12 13 15 T(C) 2000 1670 1000 1000 1300 1500 1000

31. Fig 11a

32. Fig 11b

33. Fig 12a

34. Fig 12b

35. Fig 13a

36. Fig 13b

37. Fig 14a

38. Fig 14b

39. Example Runs (Ti-N) (contd.) • Two alternative calculation methods of phase thickness under thermal history (Figs. 15 and 16) • Two alternative calculation methods of phase thickness under isothermal hold at 2020 C (Fig. 17).

40. Fig 15

41. Fig 16

42. Fig 17

43. Web Enabled Simulation • The code is now being made available for execution within a web browser. • Users can execute the program using their own inputs from anywhere anytime while a single version of the code is maintained in our local server. • See Figs. 18 and 19.

44. Screen Navigation Process Home Page Select and Execute Program Results Page Select Files for Display Fig. 18

45. Fig. 19a

46. Fig. 19b

47. Fig. 19c

48. Fig. 19d

49. Parametric and Sensitivity Studies • Effect of Initial Seed Particle Size on Extent of Diffusion Zone under Specified Thermal History (Triple Melt VAR). • Effect of Initial Seed Particle Concentration on Extent of Diffusion Zone under Specified Thermal History (Triple Melt VAR).

50. Summary (contd.) • A mathematical model and associated computer code are now available to investigate the spread of diffusion zones around N- or O-rich inclusion particles in Ti as a function of thermal history, inclusion geometry and composition.