Mathematical Models and Novelty in Steels www msm

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

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

tera giga mega kilo hecto deca T G M k h da deci centi

tera giga mega kilo hecto deca T G M k h da deci centi milli micro nano pico d c m m n p 1 000 000 1 000 10 1 0. 01 0. 000 001 0. 000 000 001

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

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

Brenner, 1956

Brenner, 1956

Scifer, 5. 5 GPa and ductile Kobe Steel

Scifer, 5. 5 GPa and ductile Kobe Steel

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

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

Morinobu Endo, 2004

Morinobu Endo, 2004

Claimed strength of carbon nanotube is 130 GPa Edwards, Acta Astronautica, 2000 Claimed modulus

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 (1020) Strength of a nanotube rope 2 mm long is

Equilibrium number of defects (1020) Strength of a nanotube rope 2 mm long is less than 2000 MPa

Summary • Strength produced by deformation limits shape: wires, sheets. . . • Strength

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

Smallest size possible in polycrystalline substance?

Smallest size possible in polycrystalline substance?

Yokota & Bhadeshia, 2004

Yokota & Bhadeshia, 2004

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

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

Swallow and Bhadeshia, 1996

Swallow and Bhadeshia, 1996

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

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

Kozeschnik & Bhadeshia, 2005

Kozeschnik & Bhadeshia, 2005

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

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

Solution models Quasichemical approximation, atoms are not distributed at random. Pairs of atoms are

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

Distant and near-neighbours

Distant and near-neighbours

Reference state Chen, Hansip & Bhadeshia, 2004

Reference state Chen, Hansip & Bhadeshia, 2004

-0. 17 e. V 2. 17 e. V Chen, Hansip & Bhadeshia, 2004

-0. 17 e. V 2. 17 e. V Chen, Hansip & Bhadeshia, 2004

Bhadeshia, 1981

Bhadeshia, 1981

Fe-2 Si-3 Mn-C wt% Temperature / K 800 BS 600 400 MS 200 0

Fe-2 Si-3 Mn-C wt% Temperature / K 800 BS 600 400 MS 200 0 0 0. 2 0. 4 0. 6 0. 8 1 Carbon / wt% 1. 2 1. 4

Fe-2 Si-3 Mn-C wt% 1. E+08 1 year Time / s 1 month 1.

Fe-2 Si-3 Mn-C wt% 1. E+08 1 year Time / s 1 month 1. E+04 1. E+00 0 0. 5 Carbon / wt% 1 1. 5

Fe-1. 75 C-Si-Mn wt% Chatterjee & Bhadeshia, 2004

Fe-1. 75 C-Si-Mn wt% Chatterjee & Bhadeshia, 2004

Low transformation temperature Bainitic hardenability Reasonable transformation time Elimination of cementite Austenite grain size

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

Homogenisation Austenitisation Temperature 1200 o. C 2 days Isothermal transformation 1000 o. C 15

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

700 Temperature/ o. C 600 500 400 BS ~ 350 o. C 300 200

700 Temperature/ o. C 600 500 400 BS ~ 350 o. C 300 200 MS = 120 o. C 100 0 1. E+02 1. E+04 Time / s 1. E+06 1. E+08

g g a a a Mateo, 2002 200 Å

g g a a a Mateo, 2002 200 Å

Low temperature transformation: 0. 25 T/Tm Fine microstructure: 20 -40 nm thick plates Harder

Low temperature transformation: 0. 25 T/Tm Fine microstructure: 20 -40 nm thick plates Harder than most martensites (710 HV) Carbide-free Designed using theory alone

Very strong Huge uniform ductility g g a No deformation No rapid cooling a

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

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

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

“more serious battlefield threats”

“more serious battlefield threats”

ballistic mass efficiency consider unit area of armour

ballistic mass efficiency consider unit area of armour

Charpy fatigue tensile critical stress intensity corrosion

Charpy fatigue tensile critical stress intensity corrosion

non-linear functions

non-linear functions

Brun, Robson, Narayan, Mac. Kay & Bhadeshia, 1998

Brun, Robson, Narayan, Mac. Kay & Bhadeshia, 1998

Kimura et al. , 2001

Kimura et al. , 2001

Components of Creep Strength, 2. 25 Cr 1 Mo 550 °C iron + microstructure

Components of Creep Strength, 2. 25 Cr 1 Mo 550 °C iron + microstructure solid solution 600 °C precipitates Murugananth & Bhadeshia, 2001

Howard Stone

Howard Stone