1. Mathematical Models and Novelty in Steels www.msm.cam.ac.uk/phase-trans Tata Steel Jamshedpur

2. teraT1 000 000 000 000 gigaG1 000 000 000 megaM1 000 000 kilok1 000 hectoh1 00 decada1 0 1 decid0.1 centic0.01 millim0.001 micro  0.000 001 nanon0.000 000 001 picop0.000 000 000 001

3. Problem: to design a bulk nanocrystalline steel which is very strong, tough, cheap ….

4. Brenner, 1956

5. Scifer, 5.5 GPa and ductile Kobe Steel

7. 1 Denier: weight in grams, of 9 km of fibre 50-10 Denier Scifer is 9 Denier

8. Morinobu Endo, 2004

9. Claimed strength of carbon nanotube is 130 GPa Edwards, Acta Astronautica, 2000 Claimed modulus is 1.2 TPa Terrones et al., Phil. Trans. Roy. Soc., 2004

10. Equilibrium number of defects (10 20 ) Strength of a nanotube rope 2 mm long is less than 2000 MPa

12. Strength produced by deformation limits shape: wires, sheets... Strength in small particles relies on perfection. Doomed as size increases. Summary

13. Smallest size possible in polycrystalline substance?

15. Yokota & Bhadeshia, 2004

16. Thermomechanical processing limited by recalescence Summary Need to store the heat Reduce rate Transform at low temperature

17. Swallow and Bhadeshia, 1996

19. cementite forced to inherit the substitutional solutes in parent Lord, Bhadeshia, Svensson, 2003

20. Kozeschnik & Bhadeshia, 2005

22. Temperature / °C Lengthening rate / m s -1 Bhadeshia, 1985

23. Quasichemical approximation, atoms are not distributed at random. Pairs of atoms are treated as independent entities Solution models

26. Distant and near-neighbours

27. Reference state Chen, Hansip & Bhadeshia, 2004

28. 2.17 eV -0.17 eV Chen, Hansip & Bhadeshia, 2004

29. Bhadeshia, 1981

31. 0 200 400 600 800 00.20.40.60.811.21.4 Carbon / wt% Temperature / K Fe-2Si-3Mn-C wt% B S M S

32. 1.E+00 1.E+04 1.E+08 00.511.5 Carbon / wt% Time / s Fe-2Si-3Mn-C wt% 1 month 1 year

33. Chatterjee & Bhadeshia, 2004 Fe-1.75C-Si-Mn wt%

34. wt% Low transformation temperature Bainitic hardenability Reasonable transformation time Elimination of cementite Austenite grain size control Avoidance of temper embrittlement

35. Temperature Time 1200 o C 2 days 1000 o C 15 min Isothermal transformation 125 o C-325 o C hours-months slow cooling Air cooling Quench AustenitisationHomogenisation

36. 0 100 200 300 400 500 600 700 1.E+001.E+021.E+041.E+061.E+08 Time / s Temperature/ o C B S ~ 350 o C M S = 120 o C

38. 200 Å      Mateo, 2002

39. Low temperature transformation: 0.25 T/T m Fine microstructure: 20-40 nm thick plates Harder than most martensites (710 HV) Carbide-free Designed using theory alone

40. 200 Å      Very strong Huge uniform ductility No deformation No rapid cooling No residual stresses Cheap Uniform in very large sections

41. Hammond and Cross, 2004 Velocity km s -1 Stress / GPa

42. “more serious battlefield threats”

43. ballistic mass efficiency consider unit area of armour

44. Charpy fatigue corrosion tensile critical stress intensity

45. non-linear functions

50. Brun, Robson, Narayan, MacKay & Bhadeshia, 1998

51. Kimura et al., 2001

52. precipitates solid solution iron + microstructure 550 °C 600 °C Murugananth & Bhadeshia, 2001 Components of Creep Strength, 2.25Cr1Mo

59. Howard Stone