Diapositive 1

1
Modeling of Ultrasonic Propagation in a Coarse
Grain Structure
F. Jenson(1), T. Fortuna(1) and L. Doudet(2)

• Commissariat à lEnergie Atomique, CEA, LIST,
  CEA-Saclay, 91191, Gif-sur-Yvette, France
• Electricité de France, EDF RD, MMC, 77818,
  Moret-sur-Loing, France

2
Modeling of Ultrasonic Propagation in a Coarse
Grain Structure

• Motivation Detection and characterization of
  defects in centrifugally cast stainless steal
  components (CCSS).
• Background Inspection difficulties due to the
  particular metallurgical structure of these
  materials
• large grains (up to 20 mm)
• heterogeneous equiaxed/columnar structure
• stratified structure

Large grains
Columnar grains
Equiaxed grains
3
Modeling of Ultrasonic Propagation in a Coarse
Grain Structure

• Example Inspection of a CCSS specimen
  containing artificial defects with a TRL probe

Side drilled holes ?2 mm
Notches 10 and 15 mm high
Cscan measured over the specimen
CCSS specimen
Strong variability of the echoes depending on the
transducer position

• Aim of the study To model distortions and
  disruptions incurred by ultrasonic fields
  propagating in the coarse metallurgical structure
  of CCSS

4
Model assumptions Description of the coarse
grained structure using Voronoi diagrams

• Definition Decomposition of 3D space using
  convex cells computed from a cloud of points
• Various applications Voronoi diagrams can
  describe growth phenomena and distance
  relationships between objects
• In materials science, polycrystalline
  microstructures in metallic alloys are commonly
  represented using Voronoi tessellations

• Method To connect Voronoi diagrams with
  existing CIVA tools to compute the wave
  propagation in coarse grained structures

5
Exemples of 3D Voronoi diagrams computed using
the CIVA software
Columnar structure in a cylindrical specimen
Equiaxed structure in a planar specimen
6
Model assumptions Description of elastic
properties

• Isotropic elastic material properties
  (computation efficiency, inspection using
  compressional waves)

• Values of VL for each cells are fixed randomly
  by using a uniform distribution

Equiaxed structure
VL randomly fixed for each macrograin
Model inputs (elastic properties) VL,mean
5900 m/s ?VL X
7
Model assumptions Transmitted field and echo
computation

• Once the material properties are defined
  (Voronoi diagram and elastic properties), the
  simulation is performed using the existing CIVA
  tools
• The ultrasonic field computation is based on the
  pencil method (ray theory) applied to an
  heterogeneous medium
• The beam-defect interaction can be computed
  using various models (Kirchoff, GTD, Born)

Refraction divergence
VL,i-1
Ti-1?i
VL,i
Transmission coefficients
Ti?i1
VL,i1
8
Mapping of the transmitted field at the back-wall
Ultrasonic field mapping system
Transmitted field computations
cells 1000 Mean cell size 11 mm
Voronoi diagram
L45 1 MHz Hwater 80 mm Pfocuslt 70 mm
Inspection setup
y
y
Front-wall
400
x
x
?VL3
?VL0
Scanning size 55100 mm2
68.5
Transmitted field measurements
100
Back-wall
y
y
Scanned zone
The receiver consist in a small piezoelectric
transducer bounded to a plexiglas cone
x
x
9
Measurement of the back-wall echo for various
positions of the transmitter
Back-wall echo measurement setup
Back-wall echo computation
cells 1500 Mean cell size 12 mm
Voronoi diagram
Position
L0 1 MHz Hwater150 mm Pfocus70mm
Inspection setup
Time
68.5
?VL3
?VL0
Displacement 0-250 mm
Back-wall echo measurement
400
100
External radius 417 mm
Transmitter displacement along the cylinder axis
10
Measurement of the back-wall echo for various
positions of the transmitter
Assessment of the mean echo amplitude
Computation for various grain sizes and ?VL values
Bscan
Mean value
Echo-dynamic
Reference back-wall echo on a ferritic specimen
with similar geometrical properties
Experimental results
11
Measurement of the back-wall echo for various
positions of the transmitter
Assessment of the echo fluctuations
Computation for various grain sizes and ?VL values
Bscan
Fluctuations
Echo-dynamic
Expressed in of the averaged amplitude
Experimental results
12
Measurement of the back-wall echo for various
positions of the transmitter
Mean amplitude loss dB/mm for various grain
sizes and ?VL values
Theoretical results for the attenuation
coefficient
log-log plot
log-log plot
Stanke and Kino Karal and Keler
Scattering mechanism 3 frequency regions
Rayleigh domain   ad3 Stochastic domain  
ad Geometric domain   a1/d
Amplitude loss 1/d
13
Simulation of an inspection in a coarse grain
structure using Voronoï diagrams
A general approach
Simulation of an inspection Example Back-wall
echo

• Material properties
• Cij,austenite
• Cij,ferrite
• Structure at various scales

Parametric study
Algorithm
Experimental data
Grain size
?VL
Simulation of various inspection setups
14
Compressional wave fluctuations (?VL) Reminders
on the structure of a macrograin
Structure of a duplex austenitic-ferritic steel
(A type)
Micromechanical modeling of the behavior of
duplex stainless steels Bugat, Besson et Pineau
Macrograins prior ferritic grains randomly
orientated.
Colonies one of possible variants for austenite
resp. ferrite orientation
Crystallites (same orientations) two percolated
networks of austenite and ferrite
15
Evaluation of the compressional wave fluctuations
(?VL) based on the elastic properties of a
macrograin CM
Ultrasonic Backscattering in Duplex
Microstructures Theory and Application to
Titanium Alloys Han and Thompson

• Variants fixed by the symmetry group of the
  primary phase (cubic)
• crystallographic Orientation Relationships (OR)
• Example of OR Kurdjumov-Sachs (K-S)
• 111austenite//110ferrite and one
  lt110gtaustenite//lt100gtferrite in those planes

24 variants for each austenitic grain / primary
ferritic orientation

• To be expressed in terms of Euler angles with
  respect to cubic axes of the prior ferritic grain

• Elastic stiffnesses Cmacro Voigt average over
  the 24 variants orientations (over the colonies)
• Cmacro

?VqL
Random orientation of the macrograins
16
Evaluation of the compressional wave fluctuations
(?VL) based on the elastic properties of a
macrograin CM

• Estimation of the VqL distribution
• Set of (?,?,f) randomly fixed and computation of
  VqL(?,?,f) by solving the Christoffel equation
  using CM
• Velocity histogram

Reminder The fluctuations of VL were modeled
using a uniform distribution
2?VL
Frequency
VL,max
VL,min
17
Conclusions

• Description of the macrostructure based on the
  Voronoï diagrams
• existing modeling CIVA tools (field and echo
  computation)

Good qualitative description of field distortions

• Sensitivity study (mean grain size, ?VL)
  comparison to a reference model (Stanke and Kino)

Good trend of  quantitative  parameters (mean
amplitude, fluctuations) estimated on the
back-wall echo

• Estimation of the input parameter ?VL based on
  the elastic properties of a macrograin

18
Perspectives

• Modeling of elastic properties in a textured
  columnar structure (does the isotropic
  approximation holds?)
• Description of stratified equiaxed/columnar
  structures using Voronoi diagrams
• Modeling of the structural noise (macro and
  sub-grains contributions, multiples scattering
  contributions?)