1. 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

2. 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 weld Description of the paraxial ray model Application to a simplified weld description Application to a realistic bimetallic weld Conclusions and perspectives

3. 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 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 L LT

4. NDCM | MAY 22ND, 2013 | PAGE 4 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 Macrograph of the weld Z X Grain orientation

5. Model associated to description Smooth description → Weld described with a continuously variable 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 CONTEXT: UT SIMULATION OF WAVE PROPAGATION IN WELDS Crystallographic orientation

6. DYNAMIC RAY TRACING MODEL CEA | 20 SEPTEMBRE 2012 | PAGE 6

7. 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

8. 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

9. DYNAMIC RAY TRACING MODEL: THEORY Paraxial scheme used to evaluate the amplitude of the ray at each step Expressions of A MN, B MN, C MN and D MN 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 scheme Matrix formulation New position Last position Transformation matrix from general cartesian to wavefront orthonormal coordinates Expression of the Hamiltonian

10. 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 A MN, B MN, C MN and D MN at each time-step S M Divergence factor ⇒ Amplitude of the ray tube evaluated thanks to the divergence factor

11. 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. NDCM | MAY 22ND, 2013 | PAGE 11 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 Emitter

12. Comparison and validation with FE method Wave 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

13. Ray-based method applied on smooth description Transducer: Ø 12,7mm Computation of the longitudinal wave Wave 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

14. CONCLUSIONS AND PERSPECTIVES CEA | 20 SEPTEMBRE 2012 | PAGE 14

15. 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 | PAGE 15 NDCM | MAY 22ND, 2013

16. DRT LIST / DISC LSMA Commissariat à l’énergie atomique et aux énergies alternatives Institut Carnot CEA LIST Centre de Saclay | 91191 Gif-sur-Yvette Cedex T. +33 (0)1 69 08 40 26 | F. +33 (0)1 69 08 75 97 Etablissement public à caractère industriel et commercial | RCS Paris B 775 685 019 CEA | 20 SEPTEMBRE 2012 | PAGE 16 THANK YOU FOR YOUR ATTENTION !