ADVANCED SIMULATION OF ULTRASONIC INSPECTION

OF WELDS USING DYNAMIC RAY TRACING

Audrey GARDAHAUT (1) , Karim JEZZINE (1), Didier CASSEREAU (2), Nicolas LEYMARIE (1) , Ekaterina

IAKOVLEVA (1)

NDCM - May 22nd, 2013

(1) CEA – LIST, France(2) CNRS, UMR 7623, LIP, France

OUTLINE

NDCM | MAY 22ND, 2013 | PAGE 2

Context: Ultrasonic simulation of wave propagation in welds

Dynamic Ray Tracing Model for a smooth description of the weldDescription of the paraxial ray modelApplication to a simplified weld descriptionApplication to a realistic bimetallic weld

Conclusions and perspectives

NDT of defects located inside or in the vicinity of weldsBimetallic welds → ferritic and stainless steelDifficulties of control → anisotropic and inhomogeneous structuresExperimental observation of ultrasonic beam splitting or skewing due to the grain structure orientation of the weld

Simulations tools to understand the inspection results

NDCM | MAY 22ND, 2013 | PAGE 3

CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS

Ferritic Steel

Stainless Steel

Cladding

Buttering

Weld

Macrograph of a bimetallic weld (primary circuit of a PWR)

Time

Scanning position

Observation of longitudinal and transverse wave-fronts

Observation of longitudinal and transverse waves in the backwall

Scanning position

Increment position

LLT

NDCM | MAY 22ND, 2013 | PAGE 4

CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS

Input data required for simulation codeGeometry of the weldPhysical properties of the materials (elastic constants, attenuation …)Knowledge of the crystallographic orientation of the grain at any point of the weld

Description of the weld obtained from a macrographImage processing technique applied on the macrograph of the weld

Macrograph of the weld

ZX

Grain orientation

Model associated to description

Smooth description→ Weld described with a continuously variable orientation

Dynamic Ray Tracing ModelPropagation of the rays at each point of the weld as a function of the

variations of the local properties (implementation in progress in CIVA platform)Limits of validity

High frequency approximationCharacteristic length >> λ

NDCM | MAY 22ND, 2013 | PAGE 5

CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS

Crystallographic orientation

DYNAMIC RAY TRACING MODEL

CEA | 20 SEPTEMBRE 2012

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DYNAMIC RAY TRACING MODEL: PARAXIAL RAY THEORY

NDCM | MAY 22ND, 2013 | PAGE 7

Evaluation of ray-paths and travel time→ Eikonal equation in smoothly inhomogeneous media :

Differential equation of the ray trajectory

Computation of ray amplitude→ Transport equation in inhomogeneous anisotropic media :

Cartography of crystallographic orientation

: Position of the ray: Slowness of the ray

Axial Ray

Paraxial Ray

γ can be a take-off angle

V. Cerveny, Seismic Ray Theory, Cambridge University Press, 2001.

Ray parameter

Existence of three eigenvalues associated to three eigenvectors of the matrix representing the three plane waves that propagate in the medium

Eigenvalues of matrix

Polarization vector

Energy velocity vector

Paraxial Ray expressed in function of the paraxial quantities

Axial and paraxial ray systems solved simultaneously by using numerical technique such as Euler method

Axial Ray System

Paraxial Ray System

DYNAMIC RAY TRACING MODEL: PARAXIAL RAY THEORY

NDCM | MAY 22ND, 2013 | PAGE 8

Spatial deviation of the paraxial ray from the axial ray

Slowness deviation of the paraxial ray from the axial ray

DYNAMIC RAY TRACING MODEL: THEORY

Paraxial scheme used to evaluate the amplitude of the ray at each stepExpressions of AMN, BMN, CMN and DMN Matrices

NDCM | MAY 22ND, 2013 | PAGE 9

(x): general cartesian coordinates(y): wavefront orthonormal coordinates

Matrix formulation of the paraxial scheme

Reformulation of the paraxial schemeMatrix formulation

New position Last positionPropagation Matrix

Transformation matrix from general cartesian to wavefront orthonormal coordinates

Expression of the Hamiltonian

DYNAMIC RAY TRACING MODEL: THEORY

Re-evaluation of the propagation matrix at each time-step

NDCM | MAY 22ND, 2013 | PAGE 10

Update of propagation matrices written as

Update of interface matrices expressed as

Evaluation for the longitudinal wave

Reformulation of the paraxial scheme

Evaluation of matrices AMN, BMN, CMN and DMN at each time-step

S

M

(𝑄(0 )

𝑃(0))(𝑄(1)

𝑃(1))(𝑄(2)

𝑃(2))

(𝑄(𝑟+1)

𝑃(𝑟+1))(𝑄(𝑟 )

𝑃(𝑟 ))

𝐿0𝐿1𝐿2𝐿3𝐿𝑟− 1

𝐿𝑟

Divergence factor dependant of the matrix of the propagation matrix

Divergence factor

⇒ Amplitude of the ray tube evaluated thanks to the divergence factor

DYNAMIC RAY TRACING MODEL: ANALYTICAL LAW - APPLICATION

Ray-based method applied on smooth description of weldAnalytical description of the crystallographic orientation of the weld

J.A. Ogilvy, Computerized ultrasonic ray tracing in austenitic steel, NDT International, vol. 18(2), 1985.

Comparison of the ray trajectories G.D. Connolly, Modelling of the propagation of ultraound through austenitic stainlees steel welds, PhD Thesis, Imperial College of London, 2009.

NDCM | MAY 22ND, 2013 | PAGE 11

Weld parametersT = 1,0 D = 2,0 mm η = 1,0 α = 21,80°

- Dynamic ray tracing modeloo Connolly (PhD thesis 2009)

Observation point

Emitter

Comparison and validation with FE methodWave field representation (particle velocity in 2D) at 2MHz

⇒ Excellent agreement between the Dynamic Ray Tracing Model and the Hybrid Finite Element Code

DYNAMIC RAY TRACING MODEL: ANALYTICAL LAW - VALIDATION

NDCM | MAY 22ND, 2013 | PAGE 12

Dynamic Ray Tracing (CIVA)Hybrid Code (CIVA/ATHENA)

-- Hybrid Code-- Dynamic Ray Tracing

Ray-based method applied on smooth descriptionTransducer: Ø 12,7mmComputation of the longitudinal waveWave field representation (particle velocity in 2D) at 2MHz

⇒ Good agreement between the Hybrid Code and the Dynamic Ray Tracing Model

DYNAMIC RAY TRACING MODEL: NUMERICAL VALIDATION

NDCM | MAY 22ND, 2013 | PAGE 13

Hybrid Code (CIVA/ATHENA) Dynamic Ray Tracing (CIVA)

-- Hybrid Code-- Dynamic Ray Tracing

Contribution of the transverse wave

Transverse wave

Cartography of crystallographic orientation

CONCLUSIONS AND PERSPECTIVES

CEA | 20 SEPTEMBRE 2012

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DYNAMIC RAY TRACING: CONCLUSIONS AND PERSPECTIVES

ConclusionsAccurate computation of the paraxial quantities in 3DApplication on a simplified description of a weld

Validation of the ray trajectories with the literatureValidation of the wave field with FE model

Application on a realistic weld descriptionGood agreement for the comparison of the wave field with FE

PerspectivesComputation of transverse wave to validate the complete model Experimental validations (in progress)Increase of the order of the method used to solve the paraxial scheme (Common fourth-order Runge-Kutta method) to improve computing efficiency

| PAGE 15NDCM | MAY 22ND, 2013

DRT

LIST / DISC

LSMA

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CEA | 20 SEPTEMBRE 2012

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