1. Effects of modelling parameters on the accuracy of
modelling deformation in a coarse grain nickel based super
alloy
11th International Conference on Advances in Experimental Mechanics
University of Exeter, 05th September 2016
Luqmaan Fazal, João Quinta da Fonseca
University of Manchester
Wei Li
Rolls-Royce plc. (Derby)
2. Ø Some nickel-based superalloys are employed in the manufacture of large
investment cast aerospace structural components.
Ø Casting results in large grain sizes ranging from 0.5 - 3 mm
Image Courtesy of Helmink et al.
Industrial significance of material
Image Courtesy of Helmink et al.
3. Ø Scatter makes it difficult to determine the exact fatigue life of the component
Image Courtesy of Helmink et al.
Industrial significance of material
Image Courtesy of Helmink et al.
Functionofstrain
Fatigue life
Graph courtesy of Rolls-Royce plc.
4. Ø When specimens have a few coarse grains, the mechanical anisotropy of the
individual grains affect the overall mechanical properties of the test specimen
which will vary based on the arrangement of the grains.
Ø This causes scatter for the different specimens that are tested
Research Hypothesis
5. Research Question
Ø Can we use crystal plasticity finite element modelling (CPFEM) to predict the
scatter by taking into account grain anisotropy alone?
6. Research PlanUniaxialloading
1. Validate CPFE model
using a representative
experimental technique
2.Run CPFE model with
various grain configurations
in order to see the type of
scatter that is predicted
Cyclicloading
1. Validate CPFE model for
first cycle using a
representative experimental
technique
2. Validate CPFE model for
multiple (~5) cycles using
representative experimental
technique.
3. Run CPFE model with
various grain configurations in
order to see the type of scatter
that is predicted
Presentation Today
7. Material – RS5 nickel based superalloy
Ni Mn Si P S Cr Co Mo C
~58 0.01 0.01 0.0005 0.0009 15.92 10.03 4.92 0.064
W Nb Ti Ta Al B Fe Zr
2.01 4.83 2.68 1.32 0.98 0.0038 0.02 0.0116
Ø low Al/Ti ratio (1/2.7) allows good weldability
Ø Nb (4.8 wt.%) that has low diffusivity thereby slowing down the kinetics of γ'
precipitation
8. Material – RS5 nickel based superalloy
500 µm
200 µm
Grain boundary precipitates
Coarse grain structure(0.5-2mm) with both primary and
secondary dendrites
9. Experimental Technique – Digital Image Correlation
(DIC)
Ø Digital image correlation requires a series of images taken by a CCD camera to be
taken while the sample is being deformed to measure strain across the sample.
Ø Allows the history of sample deformation to be mapped
Image Courtesy of Devin Harris
11. Crystal Plasticity Finite Element Modelling
(CPFEM)
Ø Finite element modelling is a discretisation technique involves breaking a
problem into discrete components of simple geometry called finite
elements.
Concepts for Integrating Plastic Anisotropy into Metal Forming Simulations D. Raabe et al
12. Crystal Plasticity Finite Element Modelling
(CPFEM)
Elas%c
deforma%on
-‐
Elas%c
Anisotropy
Ø Compliance
tensors
are
used
by
the
model
to
define
the
elas%c
anisotropy
of
the
material
being
modelled.
Ni
z
x
y
Python script courtesy of Dr. João Quinta da Fonseca
13. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
plas%city
–
Slip
systems
Ø The
type
of
slip
systems
that
are
ac%ve
depends
on
the
crystal
structure
of
the
materials
and
the
temperature
at
which
the
deforma%on
takes
place.
The
slip
systems
are
defined
in
terms
of
their
slip
plane
normals
and
slip
direc%ons.
14. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Plas%c
slip
Ø The
amount
of
slip
in
each
slip
system
is
propor%onal
to
the
applied
shear
stress
and
inversely
propor%onal
to
the
instantaneous
slip
resistance.
Ø The
smaller
the
value
of
the
strain
rate
sensi%vity
the
greater
the
amount
of
slip
for
a
given
resolved
shear
stress
value.
slip rate
m
1
00
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
τ
τ
γ
γ
!
!
15. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Plas%c
slip
Ø The
amount
of
slip
in
each
slip
system
is
propor%onal
to
the
applied
shear
stress
and
inversely
propor%onal
to
the
instantaneous
slip
resistance.
Ø The
smaller
the
value
of
the
strain
rate
sensi%vity
the
greater
the
amount
of
slip
for
a
given
resolved
shear
stress
value.
slip rate
nominal
reference slip
rate
m
1
00
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
τ
τ
γ
γ
!
!
16. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Plas%c
slip
Ø The
amount
of
slip
in
each
slip
system
is
propor%onal
to
the
applied
shear
stress
and
inversely
propor%onal
to
the
instantaneous
slip
resistance.
Ø The
smaller
the
value
of
the
strain
rate
sensi%vity
the
greater
the
amount
of
slip
for
a
given
resolved
shear
stress
value.
slip rate
nominal
reference slip
rate
m
1
00
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
τ
τ
γ
γ
!
!
resolved shear stress.
(Depends on the Schmid
factor and hence the
orientation of the grain)
17. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Plas%c
slip
Ø The
amount
of
slip
in
each
slip
system
is
propor%onal
to
the
applied
shear
stress
and
inversely
propor%onal
to
the
instantaneous
slip
resistance.
Ø The
smaller
the
value
of
the
strain
rate
sensi%vity
the
greater
the
amount
of
slip
for
a
given
resolved
shear
stress
value.
slip rate
nominal
reference slip
rate
m
1
00
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
τ
τ
γ
γ
!
!
resolved shear stress.
(Depends on the Schmid
factor and hence the
orientation of the grain)
strain rate
sensitivity
18. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Plas%c
slip
Ø The
amount
of
slip
in
each
slip
system
is
propor%onal
to
the
applied
shear
stress
and
inversely
propor%onal
to
the
instantaneous
slip
resistance.
Ø The
smaller
the
value
of
the
strain
rate
sensi%vity
the
greater
the
amount
of
slip
for
a
given
resolved
shear
stress
value.
slip rate
nominal
reference slip
rate
m
1
00
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
τ
τ
γ
γ
!
!
instantaneous slip
resistance for a given slip
system. Depends on the
hardening rate.
resolved shear stress.
(Depends on the Schmid
factor and hence the
orientation of the grain)
strain rate
sensitivity
19. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Hardening
Ø The
instantaneous
slip
resistance
evolves
at
the
end
of
each
%me
step
according
to
an
empirical
Voce
law
hardening
equa%on.
Ø The
satura%on
slip
resistance
is
assumed
to
be
dependent
on
the
net
local
plas%c
strain
rate
calculated
from
the
net
sum
of
the
local
plas%c
strain
rates.
Θ = ΘIV +Θ0 1−
τ
τs
α
sgn 1−
τ
τs
#
$
%
&
'
(
)
*
+
+
,
-
.
.
Final
hardening
rate
Initial
hardening rate
Saturation slip
resistance
Slip
resistance
20. Crystal Plasticity Finite Element Modelling
(CPFEM)
Crystal
Plas%city
–
Hardening
Ø The
instantaneous
slip
resistance
evolves
at
the
end
of
each
%me
step
according
to
an
empirical
Voce
law
hardening
equa%on.
Ø The
satura%on
slip
resistance
is
assumed
to
be
dependent
on
the
net
local
plas%c
strain
rate
calculated
from
the
net
sum
of
the
local
plas%c
strain
rates.
WorkHardeningRate(MPa)
0
10000
20000
30000
40000
50000
60000
175 3500 525 700
Shear Stress (MPa)
τs
=
580
MPa
ΘIV=
50000
MPa
Θ0=
500
MPa
α
21. Crystal Plasticity Finite Element Modelling
(CPFEM)
Hardening
values
calibra%on
Ø Hardening
values
are
selected
by
ploRng
simulated
polycrystalline
curves
against
room
temperature
polycrystalline
curves
with
more
than
100
grains
in
the
sample.
TrueStress(MPa)
True Strain
22. Strain Calculation
Vector calculated
Gauss points within elements
Movement of nodes tracked
εyy calculated
Speckles in individual grids
Displacement of speckles tracked
Vector calculated
εyy calculated
Digital image correlation (DIC) Crystal plasticity finite element
model (CPFEM)
24. DIC: Observed Region
8mm
3 mm
Region of gauge
observed by CCD
camera
Loading Direction
28mm
3 mm
Ø DIC measures strain on a fraction of the
front surface
Surface etched
using Kalling’s
Waterless
Reagent
25. 8mm
3 mm
Region of gauge
observed by CCD
camera
CPFEM: Obtaining Orientations
EBSDRegion
5mm
TD
RD
ND
Back FaceFront Face
111
101100
The orientation of
each grain is defined
in terms of 3 euler
angles φ1, Φ & φ2
EBSD Maps (IPFX)
Ø Electron backscattered diffraction (EBSD)
used to obtain the grain orientations from
both the back and front faces.
Surface etched
using Kalling’s
Waterless
Reagent
26. 8mm
3 mm
Region of gauge
observed by CCD
camera
CPFEM: Obtaining Orientations
EBSDRegion
5mm
TD
RD
ND
Back FaceFront Face
111
101100
These 3 euler angles
are assigned to each
element in the mesh
EBSD Maps (IPFX)
CPFE Mesh
Front Face
Back Face
(subsurface
grains)
Surface etched
using Kalling’s
Waterless
Reagent
27. 8mm
3 mm
Region of gauge
observed by CCD
camera
CPFEM: Assumptions on grain shape
CPFERegion
CPFE Mesh
Front Face
Back Face
(subsurface
grains)
CPFE Mesh side view
Ø The CPFE mesh assumes that the grains are
flat and one element thick
Front Face Back Face
Surface etched
using Kalling’s
Waterless
Reagent
28. 8mm
3 mm
Region of gauge
observed by CCD
camera
CPFEM: Region of interest
DIC region in
CPFE mesh
Surface etched
using Kalling’s
Waterless
Reagent
30. DIC vs CPFEM – Strain maps
Ø Even at 0.8% strain some regions have strains going upto 2.5%
experimentally.
Average εyy=0.8%
DIC CPFEM
0.0
1.88
2.5
1.25
0.62
εyy%
31. DIC vs. CPFEM – effects of m
Average εyy=0.8%
CPFEM DIC
m= 0.5 m = 0.02 m = 0.001
0.0
1.88
2.5
1.25
0.62
εyy%
m
1
00
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
τ
τ
γ
γ
!
!
strain rate
sensitivity
32. DIC vs. CPFEM – effects of m
Average εyy=0.8%
εyy%
RelativeFrequency
0.8%
Ø Experimental data shows more similarities towards a power law distribution.
tail indicates the high
local strain
33. DIC vs. CPFEM – effects of m
Average εyy=0.8%
εyy%
RelativeFrequency
0.8%
Ø At m=0.5 the model shows a normal strain distribution which is not what is
observed experimentally.
tail indicates the high
local strain
At higher m values a greater
fraction of the slip systems
contribute to the local strain.
34. DIC vs. CPFEM – effects of m
Average εyy=0.8%
εyy%
RelativeFrequency
0.8%
Ø The modeled data begins to show increased resemblance to a power law
distribution as the strain rate sensitivity value is reduced.
tail indicates the high
local strain
At lower m values, there are
fewer slip systems that have
significant contribution to the
local strain than at relatively
higher m values
35. DIC vs. CPFEM – effects of m
Average εyy=0.8%
εyy%
RelativeFrequency
0.8%
tail indicates the high
local strain
Ø The modeled data begins to show increased resemblance to a power law
distribution as the strain rate sensitivity value is reduced.
36. DIC vs. CPFEM – effects of m
Average εyy=0.8%
εyy%
RelativeFrequency
0.8%
tail indicates the high
local strain
DICCPFEM
m=0.001
Ø The regions of localised strain are still not the same.
37. DIC vs. CPFEM – effects of subsurface grains
Average εyy=0.8%
m = 0.001 m = 0.001
CPFEMDIC
0.0
1.88
2.5
1.25
0.62
εyy%
Including sub-
surface grains
Excluding sub-
surface grains
38. Summary
Ø A simple uniaxial experiment was carried out to validate how well a simple CPFE
model predicted the local strain distribution of a coarse grain nickel based
superalloy during uniaxial loading
Ø Strain heterogeneity is observed both experimentally and in the simulations
Ø While the strain rate sensitivity has no physical meaning, reducing the strain rate
sensitivity to 0.001 results in better agreement between the model and
experimental results.
Ø Excluding the sub-surface grains from the mesh does not affect the quantitative
strain distribution significantly but does have a noticeable effect on where the
strain actually localises.
39. Further Work
Ø Extract a single grain thick sample and compare simulations with experimental
data
Ø Slip line analysis to study the active slip systems
Ø Digital image correlation at higher magnifications to observe if dendrites have any
effects on the strain localisation within the grains
Ø Run simulations with synthetic microstructures to observe how the strain rate
sensitivity affects the scatter observed for different synthetic microstructures.
