highlight of my thesis presentation

2. SECTION TWO
Post-necking identification-HBT
SECTION THREE
Post-necking identification-DIC
SECTION FOUR
Flow stress curve validation-FEA
SECTION FIVE
Finale
SECTION ONE
Post-necking identification-EM
INTRODUCTION
Motivations & Methods

3. Motivations
Methods
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crashes involving cars,
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The
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*Forbes
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
3/21

4. The sheet has different dimensions and
deforms under totally different boundary
conditions
Forming simulation needs material’s behaviour
in much larger strain levels than necking
Inhomogeneous plastic deformation within the
gage length
Flow stress curve cannot be drawn from force
vs elongation data (i.e. uniaxial tensile test
results has no use!)
In tensile test
up to diffuse
necking
In tensile test
beyond diffuse
necking
In sheet
forming
processes
Motivations
Methods
Homogeneous plastic deformation within the
gage length
Flow stress curve can be drawn directly from
force vs elongation data (i.e. uniaxial tensile test
results are enough to draw flow stress curve)
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
4/21

5. Motivations
Methods
‘Complete solution’ of the general
problem, employing uniaxial
tensile test in combination
with DIC technique
Extrapolating the pre-
necking response
(Extrapolation Method)
combining the uniaxial
tensile test and hydraulic
bulge test results
Validating the equivalent
stress-equivalent plastic
strain curve by FEA of the
UTT
The present study on post-necking behaviour of metallic materials can be grouped into four main parts,
5/30
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
S E C T I O N F I V E
Finale
I N T R O D U C T I O N
Motivations & Methods
5/21

6. Relying solely on the EM at large plastic strains cannot be a reliable
approach in post-necking flow curve identification studies.
xtrapolation of the pre-necking data deep into the diffuse necking regime strongly depends on
the employed hardening law, while the material behaviour above diffuse necking is completely
ignored.
E
PRE-NECKING
POST-NECKING
Post-neckingbehaviouridentificationusingextrapolationmethod
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N O N E
Post-necking identification-EM
6/21

7. Neither the Uniaxial Tensile test nor Bulge test is able to describe
accurately the whole material’s plastic behaviour!
The idea!
A complete description can be achieved through combining the data
coming from the two tests.
Post-necking identification-ISO 16808
From yield point to fracture by combining tensile test data with bulge test data
16808
2014
1. How to determine ‘Equibiaxial stress ratio’
2. How to Scale bulge test results
3. How to Extend the uniaxial stress-strain curve beyond uniform elongation
Uniaxial Tensile Test: for deformation around the yield point
Bulge Test: for deformation beyond uniform elongation
One Approach!
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N T W O
Post-necking identification-HBT
7/21
The problem!
Based on ‘The plastic work principle’

8. Post-necking identification-ISO 16808
From yield point to fracture by combining tensile test data with bulge test data
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N T W O
Post-necking identification-HBT
8/21

9. Post-necking identification-ISO 16808
From yield point to fracture by combining tensile test data with bulge test data
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N T W O
Post-necking identification-HBT
9/21

10. Aim
To construct the equivalent stress-equivalent plastic strain curve which is able to
reproduce and extend the flow curve coming from tensile test machine.
Proposed method
Equivalent stress-equivalent plastic strain will be obtained using: 𝜎𝑒𝑞 = 𝑔(𝜀𝑒𝑞
𝑝𝑙
, 𝑝)
Yield Criterion
Strain field from DIC technique
Strain Hardening Law
𝑓 𝜎1, 𝜎2, 𝜎3, 𝑌 = 0
Post-necking identification-DIC
Neckingmechanism-DIC
𝝈𝒕𝒓𝒖𝒆 − 𝜺𝒑𝒍
Flow stress curve from
tensile test machine
where elongation is
measured via DIC
technique
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N T H R E E
Post-necking identification-DIC
10/21

11. Averagestrainvaluesatneck 𝜺𝒂𝒗𝒈,𝒙 & 𝜺𝒂𝒗𝒈,𝒚
8.56%
7.73%
0
1
2
3
4
5
6
0 0.1 0.2 0.3 0.4 0.5 0.6
distance
along
the
width
[mm]
local strain (εx) []
Identifying necked section
7.73%
8.56%
0
0.1
0.2
0.3
0.4
0.5
0.6
12 17 22
local
strain
(
𝜀
x
)
[]
distance along the GL [mm]
specimen engineering strain
4.27%
6.20%
7.23%
7.73%
8.56%
9.19%
9.63%
9.93%
10.38%
10.71%
8.56%
7.73%
0
1
2
3
4
5
6
-0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0
local strain (εy) []
10.55%
10.19%
9.76%
9.47%
9.19%
8.89%
8.56%
8.31%
8.03%
7.73%
7.47%
7.23%
6.91%
6.45%
6.20%
5.93%
5.68%
5.45%
5.21%
4.95%
4.71%
4.50%
4.27%
3.13%
Observing 2D strain fields at necked section
Finding average values both for (𝜀𝑥) and (𝜀𝑦)
As it can be seen, the
distributions are nearly uniform,
up to 7.73% total engineering
strain.
parallel to loading direction (𝜀𝑥)
transversal direction (𝜀𝑦)

12. Equivalentstress-equivalentplasticstraincurve 𝝈𝒆𝒒 − 𝜺𝒆𝒒
𝒑𝒍
Equivalent Stress
Assumptions
…
… .
Equivalent Plastic Strain is influenced mostly by
train hardening law
lastic instability
S
P
𝝈 = 𝒌 𝜺𝒑
𝒏
Considère criterion 𝜺𝒑 = 𝒏
… .
lastic equivalent strain
P
r Normal anisotropy coefficient
𝛃 strain ratio
𝛂 stress ratio
two other assumptions,
quivalent stress
E
Simplified Hill’s 48 yield function:
plane stress condition
material exhibiting only normal anisotropy: (𝒓𝟎 = 𝒓𝟗𝟎 = 𝒓) & 𝝈𝟎 = 𝝈𝟗𝟎
Ramberg-Osgood (RO)

13. Flow stress curves are found in a strain range almost twice as wide as the uniform elongation.
Post-necking identification-DIC (results)
Neckingmechanism-DIC
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N T H R E E
Post-necking identification-DIC
13/21

14. Parallel shape ‘|||’
4stages
In the elastic and
homogenous plastic
deformation range, there
is no change in the local
strain distribution
Hourglass shape ‘)(’
local strain distribution
starts to curve, and
concentrate in the middle of
the specimen forming two
crossing localization bands
X shape ‘X’
hourglass shape
narrows progressively
and turns into an ‘X’
shape
Slash shape ‘/’
Then the deformation
concentration starts to localised in
one of the bands called the
dominant band. The other band
disappears gradually giving a slash
shape ‘/’ and finally the specimen
breaks along the dominant band.
In this study, the transition between the symmetric
hourglass and the asymmetric ‘X’ is interpreted as
the onset of localised necking.
Post-neckingidentification-DIC
Necking mechanism-DIC
in the development of Necking subsize specimen
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N T H R E E
Post-necking identification-DIC
14/21

15. Strain fields at necked region
Isotropic hardening
Aim
To validate the
How
‘equivalent stress-equivalent plastic strain curve’
using FEA.
Hill’s 48 yield criterion
Force-displacement Curves Comparison
Strain gradient comparison along the gage length
Finite element modelling and analysis
Equivalent flow curve
C H A P T E R S I X
Flow stress curve validation-FEA
Numerical Simulation of the
original Tensile Test
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
S E C T I O N F O U R
Flow stress curve validation-FEA
15/21

16. Acceptable …
Beyond necking,
Small difference …
not enough data points …
initial yield point …
Force-displacementCurvesComparison

17. longitudinal strain distribution
At
6%
of
overall
longitudinal
strain
in
GL
(diffuse
necking)
longitudinal strain distribution
At
10%
of
overall
longitudinal
strain
in
GL
(diffuse
necking)
Straingradientcomparisonalongthegagelength
11%
10.5%
6.29%
5.87%
….
…
…
…
…
At
10%
of
overall
longitudinal
strain
in
GL
(diffuse
necking)

18. C H A P T E R S E V E N
Conclusion and possible future
works
General approaches …
EM leaded …
The most comprehensive approach can be based on:
(……..+ …..)
…
…
A linear combination of …
Based on ‘a complete solution …
….
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
18/21

19. Good reproduction ….
The position of the neck …
More similar necking …
The calculation of …
An alternative …
Future study should be initiated with …
According to the literatures, ‘complete solutions’ …
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
19/21

20. Another interesting observation …
Acquiring the micromechanical …
The variation of …
Concerning the transition …
The effectiveness ….
S E C T I O N T W O
Post-necking identification-HBT
S E C T I O N F O U R
Flow stress curve validation-FEA
S E C T I O N O N E
Post-necking identification-EM
S E C T I O N T H R E E
Post-necking identification-DIC
I N T R O D U C T I O N
Motivations & Methods
S E C T I O N F I V E
Finale
20/21

21. GoodNews
was killedglobally in crashes
involving cars, buses,
motorcycles, bicycles, trucks, or
pedestrians”
one
WHO reported in 20xx
No
The
very
PROMISINGFUTURE