Institut für Eisenhüttenkunde
Department of Ferrous Metallurgy
A Micromechanical Damage Simulation
of Dualphase Steels using XFEM
N. Vajragupta, V. Uthaisangsuk, B.Schmaling,
S. Münstermann, A. Hartmeier, W. Bleck
Overview
2
Institut für Eisenhüttenkunde
Department of Ferrous Metallurgy
This Project is a collaboration between Inter Disciplinary
Centre for Advanced Materials Simulation (ICAMS) and
Department of Ferrous Metallurgy, RWTH Aachen (IEHK)
Prof. Dr. rer.nat Alexander Hartmaier
Dipl.-Ing. Benjamin Schmaling
Prof. Dr.-Ing. Wolfgang Bleck
Dr.-Ing. Sebastian Münstermann
M.Sc. Napat Vajragupta
3
Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
4
Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
5
Motivation
• Dualphase steel consists of:
– Ferrite
– Martensite
• Advantages:
– remarkable energy absorption
– combination of high strength and good ductility
• Applications:
– Automotive body panels
– Wheels
– Bumpers
To understand or predict
fracture in multiphase steels,
failure behaviour of each
phase must be considered.Source: Bleck, International conference on
TRIP-aided high strength ferrous alloy
Source: Bleck, International conference on
TRIP-aided high strength ferrous alloy
Motivation (cont.)
Failure Mechanisms Damage Model
Ductile Failure
Damage Curve, GTN, Ductile
Failure Locus, etc.
Brittle Failure
Cohesive Zone Model, Beremin
Model, XFEM etc.
Interface Debonding
Cohesive Zone Model, etc.
Source: Anderson, Fracture mechanics: fundamentals and applications 2nd edition
7
Objective
• To study the fracture behaviour of dual phase steel under
different loading conditions.
• To investigate the competition between failure modes by
selected modeling technique.
- Ductile failure in ferrite (Damage curve)
- Brittle fracture in Martensite (XFEM)
Source: www.xfem.rwth-aachen.de
0,0
0,2
0,4
0,6
0,8
1,0
1,2
1,4
0,0 0,5 1,0 1,5 2,0 2,5 3,0
eq
uiv
ale
nt
pla
stic
str
ain
�p
l ,
stress triaxiality,
experimental damage curve
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ihc
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8
Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
Microscopic Model
9
Methodology of investigation
Derivation of failure criteria for each phases:
- Damage curve
- XFEM
RVE Generation
Approximation of individual phase
flow curve
Simulation under multiaxial loading
conditions
Identification of Failure Mechanisms
10
Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
11
Construction of RVE model
2-D RVE generation from
optical microstructure
• To make a good description of inhomogeneous phase
distribution, RVE is generated from LOM.
• For this study, 2-D RVE is implemented to improve
convergence during calculation.
• The size of RVE is 100*100 μm2.
12
Construction of RVE model (cont.)
Flow curve prediction
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N5000Mo%11Cr%60
Ni%45Cu%80Si%60P%750Mn%8077
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•Ferritic and Martensitic phase (Rodriguez, Mater. Sci. Forum 2003):
Application of model flow curves to describe the
strain hardening individually for each identified phase
Construction of RVE model (cont.)
0
500
1000
1500
2000
2500
3000
0,0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1,0
True strain,-
Tru
e s
tress,M
Pa
ferrite (true stress MPa)
martensite (true stress MPa)
• It can be noticed that saturation of martensite flow curve occured.
14
Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
Derivation of damage curve using GTN
• GTN can be used to predict limit strain in 1
single phase material e.g. ferrite.
• However, GTN might not be applicable in
the RVE scale because critical void size
can be bigger than 1 element.
• Hence, Damage curve is implemented to
investigate ductile failure in ferrite.
• For derivation, unit cells and GTN model
are used.
• P1 and P2 is varied to achieve wide range
of stress triaxiality
• Equivalent plastic strain (PEEQ) is
extracted at the increment of damage
initiation.
GTN;
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3coshfq2
2
3
y
m21
2
y
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Derivation of damage curve using GTN
0,00
0,03
0,06
0,09
0,12
0,15
0,18
0,21
0,24
0,27
0,30
0,0 0,3 0,6 0,9 1,2 1,5 1,8 2,1 2,4 2,7 3,0 3,3Triax
PE
EQ
h P1 P2
0.50 1.00 0.14
1.00 1.00 0.40
2.00 1.00 0.63
2.50 1.00 0.68
3.00 1.00 0.73
f0 εN fN SN κ fC q1 q2 q3
0.0003 0.2 0.125 0.2 3.76 0.0086 1.5 1.0 2.25
Source: Uthaisangsuk, Dissertation 2009
17
XFEM
• XFEM allows crack to be located in the
element interior.
• Phantom nodes are introduced to
represent the discontinuity of the cracked
element.
• Traction-separation law with maximum
priniple stress (MAXPS) as a criterion for
damage initiation is implemented.
Source: ABAQUS 6.9 User´s Manual
Source: ABAQUS 6.9 User´s Manual
XFEM (cont.)
• According to Steinbrunner (1988), critical strain for fracture of martensite is
approximately 0.05.
• Hence, true stress (~2300 MPa) from this reference point in the flow curve is appled as
criteria for damage initiation.
• Martensite is assumed to behave brittlely by assigning linear behaviour with δ1=0.01.
0
500
1000
1500
2000
2500
3000
0,00 0,10 0,20 0,30 0,40 0,50 0,60 0,70 0,80 0,90 1,00true strain,-
tru
e s
tre
ss
,MP
a
Critical point for
damage initiation in
martensite
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Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
Boundary conditions
• To vary the loading conditions,
4 configurations of U1 and U2
are utilized as boundary
conditions.
• Afterward, competition of failure
modes and fracture surface are
observed.
U1
U2
Condition U1, mm U2, mm
1 0.05 0.04
2 0.05 0.07
3 0.04 0.05
4 0.07 0.05
Condition1
• First, Micro-crack starts in martensite.
• These micro-crack influence ductile
fracture in ferrite in the nearby region.
• However, it does not influence
formation macro crack in the micro
structure.
Condition2
• By varying loading condition, different
crack propagation direction can be
achieved.
Condition3
Condition4
Trial with different morphology
• With higher martensite volume fraction, micro-crack in martensite influences
macro crack formation in the microstructure.
26
Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
27
Conclusions
• As it is obviously to be noticed that microstructure morphology influences
crack initiation of the component, efforts to take into consideration of the
real microstructure should be done.
• Different loading conditions leads to different crack formation and
propagation.
• For lower volume fraction of martensite, microcrack in martensite tends
not to govern macro crack formation.
• However, it still induces formation of ductile fracture in ferrite.
• For higher volume fraction of martensite, microcrack in martensite
influences macro crack formation.
• In order to examine competition between failure mode, appropriate failure
criteria should be well implemented.
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Table of contents
• Motivation and objectives
• Methodology of investigation
• Construction of RVE model
• Implementation of damage models
– Derivation of damage curve using GTN
– Extended finite element method (XFEM)
• Results and Discussion
• Conclusion
• Future works
Future works
• Coupling with real component model to investigate macro crack
formation or predict failure of component.
• Taking a consideration of inhomogeneous phase distribution by
Voronoi Tessellation technique.
• Individual phase flow curve determination by using nano-indentation
technique.
• Taking strain-based phase transformation into account.
• Improvement of damage model.
Thank you for your attention