1. 1
Grain deformation in a cast Ni superalloy: comparing
experimental and modelling results
Luqmaan Fazala
, Wei Lib
, João Quinta Da Fonsecaa
a
The University of Manchester, Manchester Materials Science Centre, Manchester
M13 9PL, UK
b
Rolls-Royce plc., PO Box 31, Moor Lane, Derby DE24 8BJ, UK
1. Introduction
The RS5 nickel-based superalloy is used in the manufacture of an investment cast
structural component used in an aero engine. The cast component has a non-
uniform grain size distribution, where grain sizes vary from 0.5-3mm. When this
material is tested in fatigue, the small number of grains per sample causes scatter
in the measured fatigue life, undermining the accuracy when predicting fatigue
life.
It is known [1] that the interactions between mechanically anisotropic grains
generate non-uniform local plastic strain even though the test sample is subjected
to uniform macroscopic loading conditions. In a test sample consisting of a few
(100) coarse grains, the different arrangement of grains in different test samples
results in different plastic strain distributions, which is likely to be responsible for
the scatter in fatigue life that is observed.
Our work aimed to investigate if this scatter can be simulated using a crystal
plasticity finite element model (CPFEM), where only grain anisotropy is
incorporated and other microstructural complexities such as dendrites and grain
boundary precipitates are ignored. Detailed below is the first step of this
investigation which looked at how well the model simulates monotonic
deformation in a flat sample at room temperature.
2. Digital Image Correlation (DIC)
A tensile specimen was loaded using an electromechanical load frame at a strain
rate of 0.0001 s-1
. The surface was imaged using a LaVision Imager ProX 4M
camera (Figure 1 (a)), for subsequent local strain measurements using DIC. The
dimensions of the flat dog bone specimen are given in Figure 1 (b). The etched
surface of the sample shown in Figure 1(c) provides surface ‘speckles’ that allow
the displacement to be measured via DIC(Figure 1 (d)). The region observed by

2. 2
the camera is a 8mm x 3mm window. The strain is calculated at 476 evenly
distributed points at a spatial resolution of 0.384mm.
3. Crystal Plasticity Finite Element Modelling (CPFEM)
Details of the CPFE implementation summarised below can be found here [2]. In
the CPFE model the microstructure is represented using a 3d mesh of 3616
elements where each grain is represented by one or more element. Electron
backscattered diffraction (EBSD) maps are taken from the front and back faces
(assumed to be the only sub surface grains) within the region shown in Figure 2
(a). Each element is assigned an orientation using the Euler angles obtained from
the EBSD data (figure 2 (b)). The resulting mesh seen in Figure 2 (c) has 3616
elements. As Figure 2 (d) shows the grains are assumed to be columnar across the
sample cross section which is a simplification of the actual 3d microstructure.
Deformation within the element can be split into elastic and plastic deformation.
Elastic deformation is determined using a 4th
order compliance tensor where the
elastic anisotropy is defined using three independent compliance moduli C1, C2
and C4.
Plastic anisotropy originates from the crystallographic nature of slip, which in this
case the only mode of plastic deformation. The active slip systems in a single
FCC at room temperature are the 12 octahedral {111}110 slip systems. During
deformation only a subset of these slips systems is active at each integration point.
Hence the stress and strain in each integration point is defined by which subset of
slip systems are active and the magnitude of slip on each of them. All the slip
systems were assigned a critical resolved shear stress of 400MPa. The
crystallographic orientation at each element defines the Schmid factor and hence
the subset of active slip systems is different within elements (and hence within
grains) with different orientations. The plastic deformation in this implementation
of CPFEM is assumed to be strain rate sensitive according to the viscoplastic
relationship:
!γ
!γ0
=
τ
τ0
!
#
$
%
1
m
where 𝛾 is the slip rate, 𝛾! is the nominal slip rate, 𝜏 is the resolved shear stress
and 𝜏! is the instantaneous slip resistance that is determined by the hardening
parameters used and 𝑚 is the strain rate sensitivity. 𝑚 effectively defines how

3. 3
many active slip systems are active at each strain step. The lower the value of 𝑚,
the lower the number of activated slip systems.
In order to realise uniaxial loading of the mesh, Strain increments of 0.0001 were
applied to the x-face (red arrow in figure 3 (a)) to simulate strain controlled
uniaxial loading up to a total strain of 2%. The y and z faces were allowed to
deform freely (blue arrows in figure 3 (a)).
4. Strain heterogeneity across the samples
At an applied average strain of εyy = 0.8%, both measurements and simulations
show heterogeneity across the sample and the grains, as seen in Figure 4. The
histograms in Figure 5 show the distribution of strain observed both
experimentally and in the model. The strain distribution observed experimentally
shows the characteristic tail of a power law distribution. This is important as the
tail of this distribution indicates high local strain that is attributed to crack
initiation during low cycle fatigue [3]. As 𝑚 is reduced, the modelled strain
distribution also resembles a power law distribution.
5. The effect of including sub surface grains in the mesh
While reducing 𝑚 increases the quantitative agreement in strain distribution, there
is still some disagreement on where the strain localises (Figure 6 (a)). Removing
the sub-surface grains from the mesh (Figure 6 (b)) shows an increase in local
strain in certain regions and a decrease in others. This shows the importance of
incorporating subsurface grains when modelling the behaviour in coarse grain
nickel based superalloys.
6. Concluding Remarks
Digital image correlation is limited to surface strain measurements and hence
cannot be used to validate the deformation of the sub surface grains predicted in
the model. The simplistic representation of the grain microstructure in the model
clearly affects the predicted surface strain measurements. This limits the models
accuracy in predicting the behaviour in cylindrical fatigue samples that have more
complex 3d geometries.

4. 4
7. References
[1] Z. Zhao, M. Ramesh, D. Raabe, a. M. Cuitio, and R. Radovitzky,
“Investigation of three-dimensional aspects of grain-scale plastic surface
deformation of an aluminum oligocrystal,” Int. J. Plast., vol. 24, no. 12, pp.
2278–2297, 2008.
[2] P. Bate, “Modelling deformation microstructure with the crystal plasticity
finite-element method,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol.
357, no. 1756, pp. 1589–1601, Jun. 1999.
[3] M. R. Bache, F. P. E. Dunne, and C. Madrigal, “Experimental and crystal
plasticity studies of deformation and crack nucleation in a titanium alloy,” J.
Strain Anal. Eng. Des., vol. 45, no. 5, pp. 391–399, 2009.

5. 5
7. List of Figures
Figure 1 (a) DIC experimental setup for monotonic loading at room
temperature (b) Tensile sample dimensions (c) Surface etched using Kalling’s
extra waterless reagent (d) The average displacement of the pixels is calculated
across user assigned subsets or interrogation windows
LoadingDirection
Uniform Light
Source
4 MP CCD Camera
Tensile Sample
(a)
Experimental setup for
DIC at room
temperature
8mm
3 mm
DIC region
(c)
Surface etched
using Kalling’s
Waterless
Reagent
3 mm
Tensile ‘dogbone’ test
sample
28mm
LoadingDirection
(b)
DIC
region
8mm
3 mm
Displacement
calculations
(d)

6. 6
Figure 2 (a) Region of tensile gauge used in EBSD map (b) EBSD maps of
both the back and front face (c) CPFE mesh generated using the EBSD maps
with 3616 elements (d) Top view of the mesh showing that it is only 2 grains
thick with the assumption that the front and back grains are columnar across the
thickness
EBSD Region
(a)
Test Sample
5mm
TD
RD
ND
Back FaceFront Face
111
101100
EBSD Maps (IPFX)
(b)
These 3 euler angles
are assigned to each
element in the mesh
The CPFE Mesh
Front Face
Back Face
(subsurface
grains)
(c)
Front
Face
Back
Face
z
y
x
Top view of
mesh
(d)

7. 7
Figure 3 (a) Generated CPFE mesh showing the loading direction (red arrow)
and the free z and y faces (b) Comparison of the actual observed DIC region
and the meshed DIC region
z
y
x
Free Faces
DIC region
(a)
DIC region in
actual gauge
LoadingDirection
DIC region in
simulated gauge
(b)

8. 8
Figure 4 (a) Experimental and simulated strain maps obtained at average strain
of εyy = 0.8% showing strain heterogeneity across the sample. The histograms
show the strain heterogeneity in labeled grains.
DICCPFEM
0.0
1.88
2.5
1.25
0.62
εyy%
0.8
1.2
1.4
0.6
εyy%
1.0 2.00.5 1.50 2.5 3.0
NormalisedFrequency
1.0
1.6
0.4
0.2
0
0.8
1.2
1.4
0.6
εyy%
1.0 2.00.5 1.50 2.5 3.0
NormalisedFrequency
1.0
1.6
0.4
0.2
0
0.8
1.2
1.4
0.6
εyy%
1.0 2.00.5 1.50 2.5 3.0
NormalisedFrequency
1.0
1.6
0.4
0.2
0
0.8
1.2
1.4
0.6
εyy%
1.0 2.00.5 1.50 2.5 3.0
NormalisedFrequency
1.0
1.6
0.4
0.2
0
Averageεyy=0.8%

9. 9
Figure 5 (a) Experimental distribution of strain across the sample at εyy = 0.8%.
(b), (c) and (d) compare the modelled strain distribution with the experimental
distribution at different strain rate sensitivity values of m=0.5, 0.02 and 0.0001
respectively.
0.5
1.5
2.0
2.5
3.0
1.0
εyy%
1.0 2.00.5 1.5
0
0 2.5 3.0
DIC valuesNormalisedFrequency
(a)
0.5
1.5
2.0
2.5
3.0
1.0
εyy%
1.0 2.00.5 1.5
0
0 2.5 3.0
DIC values
NormalisedFrequency
m=0.5m=0.5
(b)
0.5
1.5
2.0
2.5
3.0
1.0
εyy%
1.0 2.00.5 1.5
0
0 2.5 3.0
NormalisedFrequency
m=0.02
DIC values
(c)
0.5
1.5
2.0
2.5
3.0
1.0
εyy%
1.0 2.00.5 1.5
0
0 2.5 3.0
NormalisedFrequency
m=0.001
DIC values
(d)

10. 10
Figure 6 (a) Comparison of simulated strain maps at m values of 0.5, 0.02 and
0.001 against the experimental strain map at an average strain of εyy = 0.8% (b)
difference in including and excluding the sub surface from the meshed surface
CPFEM DIC
m= 0.5 m = 0.02 m = 0.001
0.0
1.88
2.5
1.25
0.62
εyy%
(a)
m = 0.001m = 0.001
CPFEM DIC
Including sub-
surface grains
Excluding sub-
surface grains
0.0
1.88
2.5
1.25
0.62
εyy%
(b)