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

pl

ihc

1

pl2ec ������

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

���� ����

���� ���� ���� ���� ���� ���� ���� ���� ���� ����

���� ���� ���� ���� ss

0

0

N5000Mo%11Cr%60

Ni%45Cu%80Si%60P%750Mn%8077

Lk

kMexp1bM

������������������������

������������������������������������������������

����

����������������������������������������������������������������

•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;

���� ���� 0fq1q2

3coshfq2

2

3

y

m21

2

y

V ����������������������������

����

��������������������������������

��������

����

��������

��

��

�

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

19

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.

28

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