architectured microstructures in steel
DESCRIPTION
TRANSCRIPT
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
FCP=0.49 and MCP=0.18
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
FCP=0.56 and MCP=0.31
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
FCP=0.62 and MCP=0.38
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.