Cast Stainless Steel

Modelling of Ultrasonic Propagation in Cast Stainless Steels with Coarse Grained Structures F. Jenson, L. Ganjehi and C. Poidevin, CEA, LIST, France

G. Cattiaux and T. Sollier, Institut de Radioprotection et de Sûreté Nucléaire, France

ASBSTRACT

Cast stainless steel (CSS) material has been used extensively in the primary loop of French pressurized

water reactors (PWR). Due to their particular metallurgical structure, the ultrasonic inspection of CSS

components is very challenging. As it propagates thru the structure, the transmitted field is strongly

affected by the anisotropic behaviour of the macrograins constituting the metallurgical structure. This

can lead to beam distortions and disruptions, and consequently to severe limitations of inspection

performances. In this study, an approach is proposed in order to compute wave propagation in

heterogeneous materials such as CSS. In a first step, the geometrical properties of the large scale

structure are mimicked using Voronoi diagrams. Secondly, the elastic properties of the macrograins

are estimated using a Voigt homogenization procedure applied to the colonies. Finally, the wave is

propagated thru the structure using the pencil method. For validation purpose, measurements were

performed on a pipe segment that is believed to be representative of centrifugally cast stainless steel

materials used in PWR. The back wall and corner-trap echoes were measured by scanning the probe

over large areas. It is shown that important experimental phenomena such as amplitude and time of

flight fluctuations can be reproduced thanks to the approach proposed in this paper.

CONTEXT

CSS components are made of a complex metallurgical structure. This structure exhibits very large

equiaxed or columnar grains (the so-called macrostructure). Due to their anisotropic elastic properties,

the beam transmitted thru the macrograins undergoes amplitude distortions and phase aberration. The

disruption of the transmitted field coherence properties will lead to weak inspection performances. For

instance, large notches (larger than the unperturbed beam size) will be missed in some sections of the

inspected component. The heterogeneous properties of the material will also lead to scattering of a

fraction of the incident energy in every direction of space. When measured by the receiver, the

scattered field is the source of a strong background noise also called structural noise (the modeling of

grain noise will not be addressed in this paper). Thus, the presence of a macrostructure is a limiting

factor of ultrasonic inspection capabilities and it must be accounted for when designing new NDE

methods. To assess the impact of large grain structures on ultrasonic beam propagation, CSS material

that represents those installed in primary piping circuits of French nuclear power plants was ordered.

An unflawed pipe section was available for the study. The geometrical properties of the specimen are

given in Figure 1.

40

0 m

m

937 mm

40

0 m

m

937 mm

40

0 m

m

937 mm

40

0 m

m

937 mm

75 mm

Figure 1 - CSS tube section used in the study.

Columnar

grains

Fine

equiaxed grains

Stratified

region

Mixed banded structure

Columnar

grains

Fine

equiaxed grains

Stratified

region

Mixed banded structure

Figure 2 - Macrographic pictures taken on various parts of the CSS tube section.

Areas in the circumferential-radial plane at one end of the piping segment were polished and

chemically etched to obtain photographs of the material structure. Figure 2 shows pictures resulting

from this process. The specimen contains a wide range of grain sizes and shapes. Overall, the structure

shows significant layering. This type of metallurgical configuration is a very challenging

macrostructure for ultrasonic examination because of the variability, size and layering of grains.

MODELS

Description of the macrostructure using Voronoi diagrams

As stated previously, the macrostructure is responsible of the beam distortions that are observed in

CSS materials. Since one of the objectives of this work is to model such structure induced

perturbations, the first step consists of describing the morphological properties of the various

macrostructures encountered in cast stainless steels. One simple way to achieve this is to use a

mathematical tool called Voronoi diagrams. Voronoi diagrams are decompositions of space in convex

cells. They give good qualitative representations of polycrystalline structures.

Figure 3 - Illustrations of Voronoi decompositions obtained using the Voronoi decomposition

algorithm proposed in the CIVA software

This approach has been conjointly proposed by EDF (Electricité de France) and CEA (the French

Atomic Energy Commission) in a previous paper [1] in order to model ultrasonic propagation in

coarse grained structures such has those found in cast stainless steels. The Voronoi decomposition

algorithm used in this study allows one to perform a 3D tessellation of cylindrical and planar shaped

specimens. The synthetic structure can be either constituted of equiaxed or columnar shaped grains. It

is also possible to define mixed-banded structures such as those shown in figure 2. Such structures are

very common in stainless steel components which are centrifugally cast. Illustrations of Voronoi

decompositions are shown in figure 3.

Description of the elastic properties of a macrograin

As stated previously, the anisotropic elastic properties of the macrograins disrupt the ultrasonic

propagation. Thus, it is important to accurately estimate the material properties of a single macrograin

constituting the macrostructure. Macrograins are made of an aggregate of bicrystals (colonies). These

colonies are, in turn, formed of an interconnected network of austenite and ferrite (see Figure 4). This

complex substructure appears during the cooling process by solid-phase transformation from the

ferritic to the austenitic phase. The colonies correspond to areas of about 1 mm where the austenitic

phase keeps the same crystallographic orientation. The crystallographic orientations of both phases are

related by the Kurdjumov-Sachs relationships. This gives 24 possible “variants” for each austenitic

grain orientation [2]. Starting from the elastic stiffness constants matrices of austenite and ferrite, it is

possible to express the elastic properties of the 24 variants in the lab coordinates. Then, assuming

equal probability for each variant within a macrograin, one can compute the ensemble average of the

elastic properties. This ensemble average simply consists of a Voigt average of the 24 elastic stiffness

matrices [3]. The results of this homogenization approach are given in Table 1.

Ferrite

Austenite

Ferrite

Austenite Figure 4 - Micrographic picture showing the interconnected laths of austenite and ferrite

122125198CγCristallite d’austénite

(cubique)

116134231CδCristallite de ferrite

(cubique)

441211Composante

122125198CγCristallite d’austénite

(cubique)

116134231CδCristallite de ferrite

(cubique)

441211Composante

96102254CM

Macrograin moyen

(cubique)96102254C

M

Macrograin moyen

(cubique)

Component

Ferrite (cubic)

Austenite (cubic)

Macrograin

(cubic)

122125198CγCristallite d’austénite

(cubique)

116134231CδCristallite de ferrite

(cubique)

441211Composante

122125198CγCristallite d’austénite

(cubique)

116134231CδCristallite de ferrite

(cubique)

441211Composante

96102254CM

Macrograin moyen

(cubique)96102254C

M

Macrograin moyen

(cubique)

Component

Ferrite (cubic)

Austenite (cubic)

Macrograin

(cubic)

Table 1 - Elastic stiffness matrices of the austenite, ferrite and homogenized macrograin

The corresponding anisotropic constants, defined as A=2C44/(C11-C12), are Aaustenite=3.34, Aferrite=2.39

and Amacrograin=1.26. Thus, anisotropy is much weaker in the macrograin due to the averaging process

than in the individual crystallites. Yet, fluctuations of quasi-longitudinal velocity must be taken into

account in our approach. This is done by randomly generating longitudinal wave velocities from a

uniform statistical distribution. The parameters of the distribution are the average L-wave velocity VL,

and the distribution width ∆VL. ∆VL controls the fluctuations of velocities from one macrograin to the

other. The larger the distribution width is, the larger the dispersion of velocity will be. The distribution

width can be estimated from the elastic properties of the homogenized macrograin. This is done by

solving the Christoffel equation for random orientations of the macrograin. This leads to a histogram

of possible qL-wave velocities from which the width of the uniform distribution is estimated.

Following this method, a value of ∆VL=2 % of the average velocity was obtained.

Computation of the transmitted beam using a pencil method

The next step was to simulate the ultrasonic field propagation in the Vornoi polycrystal. First, the field

radiated in the coupling medium by an arbitrary transducer is computed using the Rayleigh integral

model. The beam transmitted at any position in the macrostructure is then computed using the pencil

method [4] which is an extension of a ray theory [5]. Here, the macrostructure is modeled as an

aggregation of homogeneous volumes.

VL,i-1

VL,i

VL,i+1

Ti-1→i

Ti→i+1

Transmission

coefficients

Refraction + divergence

VL,i-1

VL,i

VL,i+1

Ti-1→i

Ti→i+1

Transmission

coefficients

Refraction + divergence

Figure 5 - Computation of the transmitted beam using the pencil method.

Therefore, the propagation from the transducer to a specific position in the specimen involves

transmission and reflection at several interfaces (see Figure 5). The propagation of the central ray of a

pencil is governed by the geometrical optics laws. As the pencil is propagated through a succession of

interfaces, the wavefront deformation is also taken into account. Thus, this method can be computed

using an iterative algorithm and is well adapted to model wave propagation in heterogeneous media.

EXPERIMENTAL STUDIES

Experimental setup for the measurement of the back wall and of the end-of-block corner echoes

Two large aperture 1 MHz focused probes were used during the acquisition process. The first one was

dedicated to the back wall echo measurements and the second one to corner echo measurements. The

probes were positioned from the outside-diameter surface, such as to produce 0° and 45° refracted

beams focused near the inner surface of the specimen. The objective was to target the back wall and

the inside-diameter corner at the end of the segment. The transmitted beams for both cases were

simulated in a homogeneous stainless steel specimen. Results are shown in Figure 6 along with

illustrations of the experimental setups. The simulation ensures that the probes are capable of

producing a correct insonification in the areas of interest, thus at a depth of about 75 mm and with a

45° refracted angle for corner echo measurements. A 2D scan was acquired over a 60 mm long axial

displacement and a 320° circumferential rotation around the end-of-block corner. The back wall echo

was acquired over a 330 mm long axial displacement and a 355° circumferential rotation.

33

0 m

m

Z

θ: 0°→ 355°

75 m

m

60 mm

Rotation

Displacement

320°

Figure 6 - Experimental setup for the back wall echo (upper figure) and for the end-of-block corner

echo (lower figure) measurements

Estimation of quantitative parameters

Several quantitative parameters were defined and estimated from the experimental results. These

parameters are useful to perform quantitative comparisons between experimental and simulation

results. The first of these parameters consists of the averaged amplitude of the back wall response

determined with several probe positions. This amplitude is then compared to that of an echo measured

on a standard reflector located in a reference specimen (here, a side drilled hole positioned at a depth

of 75 mm in a homogeneous and non-attenuating specimen). Another parameter was defined and used

to characterize the back wall signal fluctuations. It is computed from the standard deviation of the set

of values that is formed from the measurement of the back wall signal amplitude for each probe

position. This value is then compared to the mean amplitude value that was previously defined and

computed. Table 2 shows results for the two parameters estimated on three distinct angular sections of

the experimental C-scan. These results show strong variations from one region to the other.

-8,2

22

-8,0

31

[40 80]

-4,8

13

Average amplitude [dB]

Amplitude fluctuations [%]

Angular section [100 135] [165 220]

Table 2 - Experimental values of the quantitative parameters characterizing the back wall response

C-scanEcho-dynamic

Blow-up

C-scanEcho-dynamic

Figure 7 - Left figures: Assessment of the baseline ultrasonic noise level. The corner response from

the pipe segment is shown on the left; grain noise with no geometrical reflectors is shown in the

middle; echo-dynamic showing the maximum amplitude of the noise for each incremental position is

shown on the right. Right figures: Determination of the detection percentage calculated from the total

specimen length scanned. The detection threshold corresponds to maximum amplitude of the grain

noise (blue line)

Quantitative parameters characterizing the corner echo signal and the inherent structural noise were

also assessed. The C-scan data was evaluated for signal and noise information as well as the presence

or absence of the corner-reflected signal. First, an assessment of the baseline ultrasonic noise level in

the specimen was made by processing the signal acquired for probe positions far enough from the end

of block so that no corner-trap response could contribute. This step is illustrated in Figure 7. The

corner-trap is detected with a maximum signal-to-noise ration of 5 dB. Yet, a loss of the corner-trap

response is observable for several angular positions of the probe. An analysis of the C-scan data was

conducted to quantify the detection percentage of the total specimen length scanned. The noise level

previously assessed was used to fix a detection threshold. The analysis performed on the results in

Figure 7 gave a detection percentage of 64 %. This result illustrates the strong impact of the

metallurgical structure on the detection performances. Note that the corner-trap represents a 100 %

through-wall flaw. Thus, it can be seen as a perfect ultrasonic inspection reflector.

COMPARISONS WITH SIMULATION RESULTS

Simulation of the transmitted beam

The radiated beam was computed for both L0 and L45 configurations. The input parameters of the

simulation were ∆VL=2 % and a mean grain size of 14 mm. The radiated beam was also computed for

a homogeneous and non attenuating specimen. As it is shown in Figure 8, the presence of a Voronoi

diagram strongly disrupts the transmitted beam.

L0

Homogeneous

Voronoi

Mean grain diameter:

14 mm

L45

Figure 8 - Simulation of a beam radiated thru a homogeneous (left) and a coarse grained (right)

specimen.

Simulation of the back wall response

The back wall echo was computed for several probe positions allowing to display B-scans in a similar

way to those measured experimentally. The results are shown in Figure 9. The input parameters of the

simulation were ∆VL=2 % and a mean grain size of 12 mm. Both the amplitude and time-of-flight

fluctuations are well reproduced. The morphological properties of the macrostructure were unknown

when the study was performed. Thus, a sensitivity study on the mean cell size of the Voronoi diagram

was performed. For each input value, the simulation was carried out and the quantitative parameters

were estimated. The results of the study are plotted in Figure 10.

Displacement

Tim

e

Displacement

Tim

e

Displacement

Displacement

Am

pli

tud

eA

mp

litu

de

Displacement

Tim

e

Displacement

Tim

e

Displacement

Displacement

Am

pli

tud

eA

mp

litu

de

Sim

ula

tio

nE

xp

eri

men

tal

Figure 9 - Simulation and experimental results of the back wall response.

-10

-5

0

5

10

15

20

0,0 1,0 2,0 3,0 4,0 5,0

Mean grain size [cm]

Me

an

am

pli

tud

e [

dB

]

Mean amplitude Amplitude fluctuations

0

5

10

15

20

25

30

35

0,0 1,0 2,0 3,0 4,0 5,0

Mean grain size [cm]

Am

plitu

de f

luctu

ati

on

[%

]

Experimental results

Experimental results

Simulation results

Simulation results

Figure 10 - Mean echo amplitude and amplitude fluctuations as a function of the mean grain size:

Simulation (▲marks) and experimental (lined band) results

The results show that the mean amplitude tends to increase with the grain size. As described in a

previous paper [1], this relationship can be predicted by theoretical models for frequencies

corresponding to the geometrical domain, i.e. when the wavelength is larger than the typical grain size

of the metallurgical structure [6,7]. Yet, simulation seems to overestimate the mean amplitude since

the experimental values are lower then the simulation even for a mean grain diameter of 0.5 cm. This

result shows that additional sources of attenuation may be needed to complement the approach. For

instance, the losses due to the interaction of the beam with the substructure could be evaluated by

computing the attenuation coefficient due to the substructure only. Another interesting result concerns

the particular bell shape of the relationship between the back wall signal fluctuations and the mean

grain size. The fluctuations are weak for either small or large grains, going thru a maximum value

obtained for a particular grain size. This result is quite intuitive since the structure can be considered to

be homogeneous for the wave propagation when the grains are either very small or very large when

compared to the wavelength. The results also show that experimental values of the amplitude

fluctuations can be reproduced for particular values of the input parameter.

Simulation of the corner-trap response

The corner echo was also computed for several probe positions. Here, the displacement was made in

the rotational direction. The results are shown in Figure 11. The input parameters of the simulation

were ∆VL=2 % and a mean grain size of 12 mm.

rotation (°)

time (µs)

180 185 190 195 200 205 210

88

88.5

89

89.5

90

90.5

91

91.5

92

180 185 190 195 200 205 210-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

rotation (°)

Amplitude (dB)

rotation

Tim

eA

mp

litu

de

Tim

eA

mp

litu

de

rotation

Figure 11 - Experimental (left) and simulation (right) results of the corner response.

The strong amplitude and time-of-flight fluctuations are predicted by the model. Yet, quantitative

comparisons such as those performed on the back wall echo must be realized to complement the

validation work. For instance, C-scans such as those shown in the Figure 7 must be computed in order

to obtain an accurate estimation of the detection percentage. Since structural noise is not modeled in

this approach, the detection threshold must be fixed from the experimental noise level. These studies

are currently under way.

CONCLUSIONS

A method was proposed in this paper in order to model fluctuations of the transmitted beam induced

by the metallurgical structure of cast stainless steel. This method is based on a description of the

morphological properties of the macrostructure using Voronoi diagrams. The elastic properties of the

macrograin are obtained from a homogenisation of the substructure which is made of colonies of

austenite. An isotropic assumption is made for computational efficiency purpose and the transmitted

beam is obtained using a pencil model. This algorithm allowed us to reproduce the fluctuations in

amplitude and time of flight of the back wall and end-of-block corner-trap responses. Additional

sources of attenuation are required to accurately predict the losses incurred by the propagating field.

ACKNOWLEDGMENTS

This work has been funded as part of a collaborative project between the US NRC and the IRSN. The

objectives of this project are:

• To improve and/or develop and validate simulation to get a better understanding of the effect

of grain structures on ultrasonic propagation.

• To assess a large number of CSS materials, maximising de variability of macrostructures.

• To develop new efficient phased array techniques for application on CSS, taking into account

the simulation studies.

REFERENCES

1) Jenson F., Fortuna T. and Doudet L., 2009, “Modeling of Ultrasonic Propagation in a

Coarse Grain Structure”, Review of Progress in QNDE, Volume 28B, D. O. Thompson

and D. E. Chimenti, eds., AIP Conference Proceedings, pp. 1201-1208.

2) Besson J., Devillers-Guerville L. and Pineau A., 2000, “Modeling of scatter and size

effect in ductile fracture: application to thermal embrittlement of duplex stainless steels”,

Engineering Fracture Mechanics, 67, pp. 169-190.

3) Han Y.K. and Thompson R.B., 1997, “Ultrasonic backscattering in duplex

microstructures: theory and application to titanium alloys”, Metallurgical and Material

Transactions A, 28A, pp. 91-104.

4) N. Gengembre and A. Lhemery, “Pencil method in elastodynamics: application to

ultrasonic field computation”, Ultrasonics, 38, pp. 495-499 (2000).

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polycrystalline materials”, J. Acoust. Soc. Am., 91(1), January 1992, pp. 151-165.

6) F.E. Stanke and G.S. Kino, “A uniform theory for elastic wave propagation in

polycrystalline materials”, J. Acoust. Soc. Am., 75(3), March 1984, pp. 665-681.

7) F.C. Karal and J.B. Keller, “Elastic, electromagnetic, and other waves in a random

medium”, J. Math. Phys., 5, pp. 537-547 (1964).