www.msm.cam.ac.uk/phase-trans neural networks in design and manufacture
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www.msm.cam.ac.uk/phase-trans
Neural Networks in Design and Manufacture
Variables include
C, Mn, Si, Cr, Mo, Ni, Nb, WP, S, O, N
Welding processWelding parameters
Prolonged high temperaturetempering heat treatment (1000 K, 4h)
0.5 µm
NF616600 °C
1e-03 1e+00 1e+03
0.00000
0.00500
0.01000
0.01500
0.02000
0.02500
M2X
M3C
Laves
Time / h
M23C6
Empirical Equations
y = a + b (%C) +c (%Mn)
+ d (%Ni) ....
y = a + b (%C) +c (%Mn)
+ d (%Ni) ....
1223
y = a + b (%C) +c (%Mn)
y = a + b (%C) +c (%Mn)
+ d(%C x %Mn)
y = a + b (%C) +c (%Mn)
y = a + b (%C) +c (%Mn)
+ d(%C x %Mn)
y = a + b (%C) +c (%Mn)
y = a + b (%C) +c (%Mn)
+ d(%C x %Mn)
y = sin (%C) + tanh (%Mn)
y = a + b (%C) +c (%Mn)
y = a + b (%C) +c (%Mn)
+ d(%C x %Mn)
y = sin (%C) + tanh (%Mn)
Hyperbolic Tangents
y
f{x }j
1
2(a) (b)
765432100
1
2
3
4
5
6
7
x
86420-100
0
100
200
300
400
x
86420-100
0
100
200
300
400
x
86420-100
0
100
200
300
400
x
Complexity of model
test error
training error
(a) (b)
(c)(d)
y
x
A
B
Predict what the next two numbers are likely to be:
2, 4, 6, 8, …….
0.0 0.2 0.4 0.6 0.8 1.00
50
100
150
200
250
300
Nickel / wt.%
10CrMoW
104 h, 550 °C
0.00 0.02 0.04 0.06 0.080
50
100
150
200
250
300
Aluminium / wt.%
10CrMoW
104 h, 600 °C
Brun, Robson, Narayan, MacKay & Bhadeshia, 1998
precipitates
solid solution
iron + microstructure550 °C
600 °C
Murugananth & Bhadeshia, 2001
Components of Creep Strength, 2.25Cr1MoComponents of Creep Strength, 2.25Cr1Mo
0 5000 100000
100
200
300
400
Life / hours
GTA weld at 923 K (data from Nippon Steel)
Cole & Bhadeshia, 1999
20000 30000 400000
100
200
300
400
500
600
Life / hours
GTA weld at 823 K (data from Nippon Steel)
Cole & Bhadeshia, 1999
0 5000 10000 15000 200000
100
200
300
400
500
600
Life / hours
GTA weld at 873 K (data from Nippon Steel)
Cole & Bhadeshia, 1999
Cool, 1996
Cool, 1996
As-welded 600 °C
650 °C700 °C
Cool, 1996
Siemens
Mitsui Babcock
Nippon Steel
ABB
Nickel base alloy FT750dc
wt%
0
200
400
600
800
1000
0 200 400 600 800 1000 1200
Temperature / °C
Yie
ld s
tres
s /
MP
aTancret & Bhadeshia,
2002
