Transcript TRENSFORMED MODEL FITTING

SANS examination of precipitate
microstructure in creep-exposed singlecrystal Ni-base superalloy SC16
P. Strunz1,2, G. Schumacher1, W. Chen3, D.
Mukherji4, R. Gilles5 and A. Wiedenmann1
1Hahn-Meitner-Institut,
2Nuclear
3Bundesanstalt
Physics Institute, 25068 Řež near Prague, Czech Republic
für Materialforschung und -prüfung, Unter den Eichen 87, 12205F
Berlin, Germany
4Technische
5Technische
Glienickerstr. 100, 14109 Berlin, Germany
Universität Braunschweig, 38106 Braunschweig, Germany
Universität Darmstadt, Petersenstr. 23, 64287 Darmstadt, Germany
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nickel base superalloys - rafting
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High-temperature + slow-strain-rate exposure:
an important regime of operation of turbine
blades made of Ni-base superalloys (precipitation
hardened alloys: g’ precipitates in g matrix).
In this regime:
rafting (the g’ morphological
change which significantly influences the lifetime
of the blades)
Rafting:
the initial cuboidal g’ precipitates
coarsen to a plate like or needle like morphology
(the rafts)
Very complex phenomenon depending on the g/g’
lattice misfit, rate and temperature of
deformation, initial microstructure, orientation ...
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objectives
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Rafting: simultaneous particle agglomeration and
particle growth but the mechanisms of raft
formation not fully understood at present
Small-angle neutron scattering (SANS)
measurement of initial stages of the morphological
changes in the bulk material:
help to resolve
some of the questions in the rafting phenomenon
The aim: to study the initial stages of
morphological changes during the formation of
rafted g’-precipitate structure in the SC16 single
crystal Ni-superalloy after high temperature creep
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experimental
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SC16 single crystal
bars: deformed at
950°C to different
strains (tensile stress
of 150 MPa along [001]
crystal direction, strain
rates <10-6 s-1)
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SEM, strain 0.1%
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SEM, strain 0.5%
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experimental
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V4 facility of BENSC in HMI Berlin
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sample-to-detector distance 16 m
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l = 19.4 Å (“low-Q range”) and l = 6.0 Å (“large-Q
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range”).
“low-Q range”: low flux of source => measured
without the beam-stop normally protecting 2D PSD
against overloading
samples of thickness 1.5-2 mm for SANS were cut
out of these bars after unloading and cooling to the
room temperature
The normal direction to the samples was parallel to
[010]
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measured data (SC16, creep, low-Q)
-0.006 -0.003 0.000 0.003 0.006
-0.006 -0.003 0.000 0.003 0.006
0.006 def.
0%
[100]
[001]
11
def.
0.1%
[100]
[001]
47
0.003
2E2
47
-1
Measured (gray
scale) and fitted
(solid
lines)
differential
cross-sections
dS/dW (in cm-1sr-1,
logarithmic scale)
Qy (Å )

3.7E3
1.6E4
6.7E4
0.000
6.7E4
3.7E3
1.6E4
8.6E2
2E2 8.6E2
-0.003
2.6
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low-Q region: the
effect dominated
by the scattering
from g' phase
w-scan: fitted at
once (3 meas.)
0.006 def.
0.5%
def.
1.4%
[100]
[001]
[100]
[001]
47
0.003
2E2
8.6E2
1.6E4
-1
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strains 0, 0.1, 0.5
and 1.4%
Qy (Å )
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0.000
3.7E3
6.7E4
1.6E4
6.7E4
47
3.7E3
8.6E2
2E2
-0.003
-0.006 -0.003 0.000 0.003 0.006
-0.006 -0.003 0.000 0.003 0.006
-1
-1
Qx (Å )
Qx (Å )
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measured data (SC16, creep, large-Q)
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SANS pattern measured in large-Q range for the most deformed
sample (1.4% strain)
0.02
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scattering from
TCP is
comparable with
the scattering
from g' in this
Q-range
85.2 -- 279
26.1 -- 85.2
7.98 -- 26.1
2.44 -- 7.98
0.747 -- 2.44
0.228 -- 0.747
< 0.747
0.01
-1
streaks in <320>
directions
=>
presence of
topologically
close packed
(TCP) phase
Qy (Å )
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g'
[001]
0.00
[302]
-0.01
-0.02
-0.02
TCP
<320>
-0.01
0.00
-1
Qx (Å )
0.01
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0.02
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microstructural model and evaluation
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Anisotropic SANS evaluation: direct 3D "binary map" modeling followed by
Transformed Model Fitting
The used model: partially ordered cubiodal and/or plate-like particles
Realistic approximation of a partial ordering:
simulation of positions and sizes of particles
A long-range size distribution included into one 3D "binary map"
The model of the individual cuboidal particle: according to the model
introduced by Schneider et al. (J. Appl. Cryst. 33, 465-468 (2000))
In 3D space, the point belongs to the particle when the following is fulfilled:
 x - x 
0


 Rx 
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a Monte Carlo based
1
2



y
y
0

  
 Ry 


b
1
2

 z - z 
0
  



 Rz 

b
1
2

 1

b
x0, y0, z0 ... coordinates of the center; Rx, Ry, Rz ... "radii”
b defines shape: sphere or ellipsoid for b=1; it becomes more cuboidal, rod-like or
plate-like when b decreases towards zero (exact cube or block with rectangular edges
for b -> 0)
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models resulting from the fit
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y (m)
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two models used to fit the SANS data: the cuboidal one
(Rx=Ry=Rz)
and
the plate-like one (Rx=Ry>Rz) - rafts
3
Real-space models
0.0 %
0.1 %
resulting from the
2
SANS-data evaluation
(corresponding to the
1
presented fits)
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For 0.5% strain, both
models were necessary
to apply simultaneously
The gray scale: a slice of the
3D model having the thickness
approximately equal to twice
mean
distance
between
precipitates was projected to
2D
assuming
a
certain
transparency of the modeled
precipitates
0
3
y (m)
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0.5 %
1.4 %
2
1
0
0
1
x (m)
2
3 0
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x (m)
2
3
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results and discussion
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For the deformations 0.0% and 0.1%, cuboidal precipitates were
sufficient to describe the observed SANS patterns
A combination of both cuboidal and plate-like precipitates was
necessary to apply for the deformation 0.5%
The data from 1.4% deformation could be successfully described
by plate-like rafts alone
----------------------------------------------------------------------Nearly no indication of rafting after deformation to 0.1%.
However, the change of the shape of precipitates during this
initial deformation period occurred:
originally rather cubic
precipitates transform to cuboids at 0.1% strain
Indications that diffusion flow during initial stages of creep can
cause such rounding were published earlier
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results and discussion
The evolution of the refined shape parameter b for cuboids
1.0
b (dimensionless)
1.0
0.8
0.6
0.4
0.8
shape
of the cuboidal
precipitates
Volume fraction:
cuboidal precipitates
rafted precipitates
0.6
0.4
0.2
0.2
0.0
Relative volume fraction of cuboidal
and rafted precipitates (dimensionless)
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0.0
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
strain (%)
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The evolution of the proportion "individual cuboids - rafts"
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conclusions
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Presented SANS: bulk information on g'-phase morphology
changes during creep deformation of SC16
Evolution of precipitate microstructure:
three stages
First stage: no rafting occurs but the precipitates become
significantly more rounded
Second stage: the rafts develop as more and more cuboidal
precipitates agglomerate with each other
Transition between 1st and 2nd stage: between 0.1 and 0.5%
Above 1.4% strain, practically all precipitates in the bulk of
the sample are rafted
ACKNOWLEDGEMENT
Two of the authors (R. Gilles and D. Mukherji) thank BENSC for support
enabling to carry out the SANS experiment.
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