Mathematical Models and Novelty in Steels Tata Steel Jamshedpur

teraT gigaG megaM kilok1 000 hectoh1 00 decada1 0 1 decid0.1 centic0.01 millim0.001 micro  nanon picop

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

Brenner, 1956

Scifer, 5.5 GPa and ductile Kobe Steel

1 Denier: weight in grams, of 9 km of fibre Denier Scifer is 9 Denier

Morinobu Endo, 2004

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

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

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

Smallest size possible in polycrystalline substance?

Yokota & Bhadeshia, 2004

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

Swallow and Bhadeshia, 1996

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

Kozeschnik & Bhadeshia, 2005

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

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

Distant and near-neighbours

Reference state Chen, Hansip & Bhadeshia, 2004

2.17 eV eV Chen, Hansip & Bhadeshia, 2004

Bhadeshia, 1981

Carbon / wt% Temperature / K Fe-2Si-3Mn-C wt% B S M S

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

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

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

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

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

200 Å      Mateo, 2002

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

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

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

“more serious battlefield threats”

ballistic mass efficiency consider unit area of armour

Charpy fatigue corrosion tensile critical stress intensity

non-linear functions

Brun, Robson, Narayan, MacKay & Bhadeshia, 1998

Kimura et al., 2001

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

Howard Stone