M. Ghosh

Material models

Work-hardening

M. Ghosh

Different Models

Kocks mechanical-threshold-strength (MTS)

Nes-Marthinsen-Holmedal Microstructural Metal Plasticity (MMP)

3 internal variable model (3IVM)Nes model

M. Ghosh

MTS Model

• 1 microstructural parameter– total dislocation density => (The way they are arranged is not considered)

TTT wf ,,*0

bTGw .

m

TCZUd

d,00

Dynamic stress Work hardening

Storage of dislocations Dynamic recovery

M. Ghosh

“Alflow” - Erik Nes - NTNUwork-hardening and dynamic recovery

Principle and inputs

M. Ghosh

Alflow: model principle

• From Erik Nes - NTNU– [E. Nes, ‘Modelling of work-hardening and stress saturation in FCC

metals', Progress in Materials Science, Vol. 41 (1998) pp.129-193]

• Only for pure metals

• For work hardening and dynamic recovery: any strain rate and temperature

• Describes the 4 stages of work-hardening

M. Ghosh

NTNU model (ALFLOW)

• 3 microstructural parameters– cell size => – dislocation density within the cell => i

– small strain: • cell wall thickness => h

• wall dislocation density => b

– large strain: sub-boundary misorientation =>

i

M. Ghosh

Alflow: model description

• 3 microstructural parameters

cell size

dislocation density within the cell

i

cell wall thickness h

sub-boundary misorientation

small strain large strain

wall dislocation density

b

M. Ghosh

WORK-HARDENING

d

d

II III IV (V)

IIIsIV s

IVIVIV C

IV

II

III*III

III0

M. Ghosh

i

1

II III IV (V)high T°

Def becomes inhomogeneous (locolised slip => shear

banding)

III

Recovery becomes significant

iii

0i

0

i

Cells more or less equiaxed

Pancake like structure saturates

IIIIV

IV

q1

.1

0

III1

saturation

II to III

III*

III

IV

0

c

i

q

s1

s

M. Ghosh

b

II III IV (V)high T°

IV

h

fh

f hqf

bfb

hcb

ihcb

qqqbqqbq

222

bK 0

bi ff 1

hqh

ibb q

bIII

.

II to III

III

M. Ghosh

II III IV (V)high T°

II to IIIS

Ss

c

b

KSS S 0

SIV

M. Ghosh

NTNU model (ALFLOW)

• 3 microstructural parameters– cell size => – dislocation density within the cell => i

– small strain: • cell wall thickness => h

• wall dislocation density => b

– large strain: sub-boundary misorientation =>

DbTGbTGTT ip

11,, 21

*

Dispersoids bypass

: particle spacingDynamic stress

bdclptat ˆ

M. Ghosh

Alflow: model description

• Flow stress

1, 21

* bTGbTGT i

Dynamic stress

Neglected

iii

iii

work -hardening dynamic recovery

M. Ghosh

General principle of work-hardening

• Athermal storage of dislocations:– In cell interiors– In old boundaries– Forming new boundaries

b

fCS

d

dinb

12

C

L p

C2

1

nbob pfS 14

Dislocation slip length: Storage probability of a moving dislocation

Dislocation in new boundaries:

Storage probability of a moving dislocation in a new boundary

Fraction of dislocation loops trapped in old boundaries

M. Ghosh

Alflow: input

• Material constant (x5)• From literature

– Burgers vector: 2.86 A– Shear Modulus: GPa– Self diffusion activation energy: 120 kJ/mol– Debye frequency:

• Model Parameters (x13)• To be determined

– Stress - microstructure constants: 1, 2

– Geometric constant: – Scaling constants: qb, qc, qh, qIV,

– Storage parameters: C, SIV

– Dynamic recovery parameters: B, , B,

).10.4.5exp(.9.29 4 TTG

M. Ghosh

Alflow: input

• Microstructure variable (x2)• Depend on process history

– Initial microstructure: 0, 0, i0, h0, b0,

– Saturation stress: s

• Process parameters• From FEM

– Temperature– Strain rate

Total: 19 input parameters

M. Ghosh

Alflow: next steps

• Precipitate and solute effects on work-hardening

1, 21 bTGbTGT ip

Dispersoids bypass

: particle spacing

grain size + particles

2

1

2

2

G

eff

LC

CL

effbLd

d 2

• Precipitate effect on the flow stress

M. Ghosh

Alflow: next steps

DbTGbTGTT ip

11,, 21

*

Grain size( / ) exp( / )

( )arcsinh[ ]2

D tt

t t m t

U kTkT

V bl B

ln( / )

1.24 2p

AGb b

x

31223

2 min ,12

rP

c

f b rM G

r r

M. Ghosh

0.00 0.04 0.08 0.12 0.160

50

100

150

200

250

300

350

400 RT-Experiment RT-Simulation 250C-Experiment 250C-Simulation

Tru

e S

tres

s (M

Pa)

True Strain

0.00 0.04 0.08 0.12 0.160

50

100

150

200

250

300

350

400

RT-Experiment RT-Simulation 250C-Experiment 250C-Simulation

Tru

e St

ress

(M

Pa)

True Strain

M. Ghosh

0 30 60 90 120 1500

500

1000

1500

2000

2500

3000

y (MPa)

250°C-Experiment RT-Experiment 250°C-Simulation RT-Simulation

(M

Pa)

0 50 100 1500

500

1000

1500

2000

2500

3000

y (MPa)

250°C-Experiment RT-Experiment 250°C-Simulation RT-Simulation

(M

Pa)

M. Ghosh

Conclusion

• More consistent theoretical approach

• More realistic microstructure prediction

• Code available

• Possibility to integrate into FEM

• Validated for a larger temperature range and composition

Alflow

3IVM

• Combined effect of Mg, Mn, Si

• Shearable particles

Future improvements