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)
(1)
CEA – LIST, France
(2) CNRS, UMR 7623, LIP, France
NDCM - May 22nd, 2013
OUTLINE
Context: Ultrasonic simulation of wave propagation in welds
Dynamic Ray Tracing Model for a smooth description of the weld
Description of the paraxial ray model
Application to a simplified weld description
Application to a realistic bimetallic weld
Conclusions and perspectives
NDCM | MAY 22ND, 2013 | PAGE 2
CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS
NDT of defects located inside or in the vicinity of welds
Bimetallic welds → ferritic and stainless steel
Difficulties of control → anisotropic and inhomogeneous structures
Experimental observation of ultrasonic beam splitting or skewing due to the grain
structure orientation of the weld
Buttering
Ferritic Steel
Weld
Cladding
Scanning position
T
L
L
Observation of longitudinal and
transverse waves in the backwall
Time
Macrograph of a bimetallic weld
(primary circuit of a PWR)
Increment position
Stainless
Steel
Scanning position
Observation of longitudinal and
transverse wave-fronts
Simulations tools to understand the inspection results
NDCM | MAY 22ND, 2013 | PAGE 3
CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS
Input data required for simulation code
Geometry of the weld
Physical 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 macrograph
Image processing technique applied on the macrograph of the weld
X
Z
Macrograph of the weld
Grain orientation
NDCM | MAY 22ND, 2013 | PAGE 4
CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS
Model associated to description
Smooth description
→ Weld described with a continuously variable orientation
Crystallographic orientation
Dynamic Ray Tracing Model
Propagation 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 approximation
Characteristic length >> λ
NDCM | MAY 22ND, 2013 | PAGE 5
DYNAMIC RAY TRACING MODEL
CEA | 20 SEPTEMBRE 2012
| PAGE 6
DYNAMIC RAY TRACING MODEL: PARAXIAL RAY THEORY
Evaluation of ray-paths and travel time
→ Eikonal equation in smoothly inhomogeneous media :
Cartography of
crystallographic orientation
Differential equation of the ray trajectory
Energy velocity vector
: Position of the ray
: Slowness of the ray
Polarization vector
Computation of ray amplitude
→ Transport equation in inhomogeneous anisotropic media :
γ can be a take-off angle
Ray parameter
Paraxial Ray
Eigenvalues of
V. Cerveny, Seismic Ray Theory, Cambridge University Press, 2001.
matrix
Existence of three eigenvalues
associated to three
eigenvectors
of the
matrix representing the
three plane waves that propagate in the medium
NDCM | MAY 22ND, 2013 | PAGE 7
DYNAMIC RAY TRACING MODEL: PARAXIAL RAY THEORY
Paraxial Ray expressed in function of the paraxial quantities
Spatial deviation of the paraxial ray from the axial ray
Slowness deviation of the paraxial ray from the axial ray
Axial and paraxial ray systems solved simultaneously by using numerical technique such
as Euler method
Axial Ray System
Paraxial Ray System
NDCM | MAY 22ND, 2013 | PAGE 8
DYNAMIC RAY TRACING MODEL: THEORY
Paraxial scheme used to evaluate the amplitude of the ray at each step
Expressions of AMN, BMN, CMN and DMN Matrices
Expression of the Hamiltonian
Matrix formulation of the paraxial scheme
(x): general cartesian coordinates
(y): wavefront orthonormal coordinates
Transformation matrix from general cartesian to wavefront orthonormal coordinates
Matrix formulation
Reformulation of the paraxial scheme
New position
Last position
Propagation Matrix
𝑳𝒓
NDCM | MAY 22ND, 2013 | PAGE 9
DYNAMIC RAY TRACING MODEL: THEORY
Reformulation of the paraxial scheme
𝑄(𝑟+1)
𝑃 (𝑟+1)
𝑄(𝑟)
𝑃 (𝑟)
Evaluation of matrices AMN, BMN, CMN
and DMN at each time-step
M
Re-evaluation of the propagation
matrix at each time-step
S
𝑄(2)
𝑃 (2)
𝑄(1)
𝑃 (1)
𝑄(0)
𝑃 (0)
𝐿𝑟
𝐿𝑟−1
𝐿0
𝐿1
𝐿2
𝐿3
 Update of propagation matrices written as
Divergence factor
Divergence factor dependant of the matrix
𝑄2𝑡𝑜𝑡 of the propagation matrix
⇒ Amplitude of the ray tube evaluated
thanks to the divergence factor
 Update of interface matrices expressed as
 Evaluation for the longitudinal wave
NDCM | MAY 22ND, 2013 | PAGE 10
DYNAMIC RAY TRACING MODEL: ANALYTICAL LAW - APPLICATION
Ray-based method applied on smooth description of weld
Analytical 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.
Emitter
Weld parameters
T = 1,0
D = 2,0 mm
η = 1,0
α = 21,80°
- Dynamic ray tracing model
oo Connolly (PhD thesis 2009)
Observation point
NDCM | MAY 22ND, 2013 | PAGE 11
DYNAMIC RAY TRACING MODEL: ANALYTICAL LAW - VALIDATION
Comparison and validation with FE method
Wave field representation (particle velocity in 2D) at 2MHz
Hybrid Code (CIVA/ATHENA)
Dynamic Ray Tracing (CIVA)
-- Hybrid Code
-- Dynamic Ray Tracing
⇒ Excellent agreement between the Dynamic Ray Tracing Model and the Hybrid Finite Element Code
NDCM | MAY 22ND, 2013 | PAGE 12
DYNAMIC RAY TRACING MODEL: NUMERICAL VALIDATION
Ray-based method applied on smooth description
Cartography of
crystallographic orientation
Transducer: Ø 12,7mm
Computation of the longitudinal wave
Wave field representation (particle velocity in 2D) at 2MHz
Hybrid Code (CIVA/ATHENA)
Transverse wave
-- Hybrid Code
-- Dynamic Ray Tracing
Dynamic Ray Tracing (CIVA)
Contribution of the
transverse wave
⇒ Good agreement between the Hybrid Code and the Dynamic Ray Tracing Model
NDCM | MAY 22ND, 2013 | PAGE 13
CONCLUSIONS AND PERSPECTIVES
CEA | 20 SEPTEMBRE 2012
| PAGE 14
DYNAMIC RAY TRACING: CONCLUSIONS AND PERSPECTIVES
Conclusions
Accurate computation of the paraxial quantities in 3D
Application on a simplified description of a weld
Validation of the ray trajectories with the literature
Validation of the wave field with FE model
Application on a realistic weld description
Good agreement for the comparison of the wave field with FE
Perspectives
Computation 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
NDCM | MAY 22ND, 2013 | PAGE 15
THANK YOU FOR YOUR ATTENTION !
| PAGE 16
CEA | 20 SEPTEMBRE 2012
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