Architectured Microstructures in Steel

Architectured Microstructure in Steel

G.Anand*, P.Dey, P.Kok, D.Chakraborty, P.P. Chattopadhyay*

*Bengal Engineering and Science University, Shibpur, India

Acknowledgements:

Ministry of Steel, Government of India and Indian Institute of Metals

Architecture and Microstructure

Integration is the key

Order of Architecture=LRVE/L architecture

μmnm mm cm m

Ord

er o

f arc

hite

ctur

e

Core-shell structures

Microstructures

Functional Systems

Super-structure

Length scale of architecture

Reference: D. Das and P. P. Chattopadhyay, J. Mat. Sci., 44 (2009) 2957

Architecturing martensite morphology in DP steel

50 m

IQ

50 m

WQ

50 m

SQ

M

F

Architecturing martensite morphology in DP steel

5 m

IAM

F

Reference: D. Das and P. P. Chattopadhyay, J. Mat. Sci., 44 (2009) 2957

20 m

M

F

SQ

5 m

IQ F

M

Parameter for Architectured Microstructures

2Ferrite Contiguity Parameter (FCP)

2

2Martensite Contiguity Parameter (MCP)

2

FF

FF FM

MM

MM FM

N

N N

N

N N

NFF; Number of ferrite-ferrite interface intersectionsNFM; Number of ferrite-martensite intersectionsNMM; Number of martensite-martensite intersections

Microstructure generation

Voronoi tessellation

Micro-mechanical

AnalysisOptimization

Elasto-plastic Finite Element

Method

Genetic Algorithm

Objective

Architecturing DP microstructure by Micro-mechanical modeling

Voronoi Tessellation

First level: fine tessellation

Second level: coarse

tessellation

Multi level Voronoi principles of the new algorithm

0.05 0.10 0.15 0.20 0.250

5

10

15

20

25

30

35

40

Pe

rce

nta

ge

of

no

de

s

Strain

FCP=0.32 and MCP=0.27 Von Mises stress (VMS) distribution

Equivalent plastic strain (EPS) distribution

VMS distribution

EPS distribution

0.05 0.10 0.15 0.20 0.250

5

10

15

20

25

30

35

40

Pe

rce

nta

ge

of

no

de

s

Strain

FCP=0.46 and MCP=0.29

VMS distribution

EPS distribution

0.05 0.10 0.15 0.20 0.250

5

10

15

20

25

30

35

40

Per

cen

tag

e o

f n

od

es

Strain


EPS distribution

VMS distribution

0.04 0.08 0.12 0.16 0.20 0.240

5

10

15

20

25

30

35

40

Pe

rce

nta

ge

of

no

de

s

Strain

FCP= 0.52 and MCP=0.14

VMS distribution

EPS distribution

0.05 0.10 0.15 0.20 0.250

5

10

15

20

25

30

35

40

Pe

rce

nta

ge

of

no

de

s

Strain


VMS distribution

EPS distribution

0.05 0.10 0.15 0.20 0.250

5

10

15

20

25

30

35

40

Per

cen

tag

e o

f n

od

es

Strain


Contiguity correlation

0.12 0.16 0.20 0.24 0.28

0.12

0.16

0.20

0.24

0.28

Pre

dic

ted

are

a (

%)

Actual area (%)

R2=0.978

0.27240.1563 0.01766

0.2637

FCPStrain

MCP

0.6 0.9 1.2 1.5 1.8

0.6

0.9

1.2

1.5

1.8

Pre

dic

ted

are

a (%

)

Actual area (%)

R2=0.992

0.44574.1935 0.1566

0.5936

MCPStress

FCP

Elasto-plastic Finite Element Formulation

Assumptions:1.Bilinear Material behavior.2.Plane strain condition.3.Stress and strain calculation at centroid of linear strain triangle.

F

Elasto-plastic Finite Element Formulation : Elastic regime

Load increment{F+ΔF}=[K]{u}

Calculation of strain; {ε}

Calculation of stress; {σ}{Δ σ}=[D]{Δ ε}

Von Mises yielding criteriaF(σ,YS)

Plastic regime

F≤0

F>0

Elasto-plastic Finite Element Formulation : Plastic regime

Proportional reduction

Calculation of corrected stress and strain

σC= σB+R. Δ σεP=(1-R). Δ ε

Stress by Euler forward sub-division

{Δ σ}=[D]{εP/ n}

Correction of yield surface drift

σ2

σ1

F=0

VMS distribution

EPS distribution

FormulationANSYS

Conclusion

• Voronoi construction has been employed for construction of microstructure.

• Von Mises stress and equivalent plastic strain have been estimated by micro-mechanical analysis.

• Suitable finite element code has been developed for its use as the objective function in optimization of microstructure.