Report

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 NDCM | MAY 22ND, 2013 | PAGE 9 DYNAMIC RAY TRACING MODEL: THEORY Reformulation of the paraxial scheme (+1) (+1) () () Evaluation of matrices AMN, BMN, CMN and DMN at each time-step M Re-evaluation of the propagation matrix at each time-step S (2) (2) (1) (1) (0) (0) −1 0 1 2 3 Update of propagation matrices written as Divergence factor Divergence factor dependant of the matrix 2 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 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 DRT LIST / DISC LSMA