A general Kirchhoff approximation for echo simulation in ultrasonic NDT

Transcription

1 A genera rchhoff approxmaton for echo smaton n trasonc NDT V. Dorva, S. Chaton, B. L, M. Darmon, S. Mahat (CEA, LIST) CEA, LIST, F-99 Gf-sr-Yvette, France

2 Pan A genera rchhoff approxmaton for echo smaton n trasonc NDT Introdcton. Genera rchhoff mode. fned rchhoff mode Concson

3 Introdcton Defect sponse mode n the Cva smaton patform Smaton method comptaton of emtted and receved feds wthot defects (penc method) convoton wth the defect response tted fed ceved fed Interacton Severa modes are avaabe to smate the nteracton wth dfferent defects rchhoff Vods, srfaces, cracs (specar) GTD Cracs (dffracton) SOV Sde dred hoes Modfed Born Sod ncsons 3

4 Introdcton Free srface rchhoff approxmaton «trasonc scatterng from smooth fat cracs: an eastodynamc rchhoff dffracton theory», 984 Dspacement on the srface of the faw rchhoff approxmaton: nfnte pane Tota fed= Incdent wave+ refected L wave + refected T wave Incdent L wave β fected T wave δ fe Appcaton of the Green theorem Integra on the faw srface p p x j x j x, x n j x d S Dffracted fed Dspacement Green s fncton x Faw srface rface Expresson of the dffracted fed as a fncton of srface dspacement A dffracton coeffcent can be obtaned by tang the far-fed mt Expresson of the dffracton coeffcent Exampe: L L coeffcent v L T BLL, sn sn A Lt cos sn vt vl Depends on ncdence and observaton anges ated to refecton coeffcents v A Ln Avec: A A Lt Ln R R LL LL v v v v L T L T cot tan R R LT LT 4

5 Introdcton Lmtatons of the free-srface rchhoff mode Propagaton of waves aong the defect not taen nto accont Case of sde dred hoes: a wave not taen nto accont by rchhoff crces the defect SOV mode (separaton of varabes) avaabe n Cva Free srface approxmaton Appcabe ony n cases where the srface can be consdered as free (cracs, bacwa echoes ) Extenson of the mode to nterfaces between any two materas Inaccraces n crac tp dffracton rchhoff s sed for specar echoes, GTD s sed for dffracton Deveopment of a mode that combnes rchhoff and GTD 5

6 Pan A genera rchhoff approxmaton for echo smaton n trasonc NDT Introdcton. Genera rchhoff mode. fned rchhoff mode Concson 6

7 Genera rchhoff mode Formasm Ad s recprocty theorem emtter defect S F recever S F Defect echo proportona to: ba 4P S F D D D: tted fed wth defect : ceved fed wthot defect nˆ ds rchhoff approxmaton apped on the defect srface Insonfed srface ocay approxmated by an nfnte pane Fed = tangent ncdent wave pane + refected L wave defect + refected T wave Fed assmed to be zero n the defect shadow Expresson of D and σ D on the defect srface 7

8 Genera rchhoff mode Pane wave approxmaton Expresson of the stress and dspacement on the defect srface Comptaton of the refected pane waves The dspacement can be expressed drecty D nc Tref The expresson of stress s factated by the pane wave decomposton j Cj x Hooe s aw for a pane wave D j nc nc Tref Tref Expresson of the scatterng coeffcent Coeff Tref Tref Tref C j nˆ j Stress wth defect Dspacement wth defect Expresson vad for any ncdent and scattered modes 8

9 Genera rchhoff mode For each probe poston For each mode (L/T, drect/refected ) Sampng of the nsonfed sde For each sampe pont Comptaton method Comptaton of emtted fed and receved fed (recprocty) sng the penc method Approxmaton by pane waves For the emtted fed: comptaton of the drectons and amptdes of the refected waves Comptatons of rchhoff coeffcents refector Smmaton over the srface + 9

10 Genera rchhoff mode Comparson wth prevos mode and expermenta rests The free srface mode cannot be sed for srface echoes: p p x j x j x, x n j x d S Free srface rchhoff: dspacement on the srface x Terme negected by the free srface mode The genera mode taes nto accont an addtonna contrbton ba 4 P S F v D nˆ v D nˆ Genera rchhoff: dspacement and stress on the srface ds 4mm 5mm Pate (STEEL) WATER Pate (STEEL) Experment Free srface rchhoff Rgd rchhoff Genera rchhoff Stee/Water 6 db 7.5 db -. db 7. db Water/Stee 5 db -3.3 db 6. db 5.9 db Srface echoes / reference echoes The genera rchhoff mode s appcabe to both echoes The genera rchhoff mode removes the need for two modes and can be sed n other cases (sod-sod for exampe)

11 Genera rchhoff mode Adaptaton to varos materas Lst of refected waves dependant on the propagaton medm In qds, se of a smpfed expresson eqvaent to: Coeff Pref Pref Pref C j nˆ j In sotropc sods: Coeff Tref Tref Tref C j nˆ j In ansotropc sods: Coeff q q qtref qtref qtref qtref qtref qtref C j nˆ j Drectons of refected waves dependant on the propagaton medm Amptdes of refected waves dependant on the propagaton and refectng medm

12 Pan A genera rchhoff approxmaton for echo smaton n trasonc NDT Introdcton. Genera rchhoff mode. fned rchhoff mode Concson

13 Pressre fned rchhoff mode Lmtaton de to approxmatons on edge.5 Exampe of a rgd haf-pane n a fd Exact rchhoff defect.5 Exact soton rchhoff x / norma ncdent wave θ=5 ; r = λ Oscatons on defect edges not modeed by rchhoff Lead to naccraces n tp dffracton Separaton of the specar and dffracted parts: A x nc G x, x' x' x n d ' Statonary pont (specar refecton) ower ntegraton mt contrbton (dffracton x =) A ( GO) A dff x x D A, e r r D A e / 4 tan tan 3

14 fned rchhoff mode Combnaton wth GTD mode refecton Geometrca Theory of Dffracton mode yeds accrate rests for crac tp dffracton dvergence for refected and transmtted waves Inc 3.5 GTD GTD( GO) D GTD, D GTD e, / 4 e r r cos cos 8 4 transmsson 7 Exact GTD 3 θ=5 ; r = λ defect 33 Prncpe of the refned rchhoff mode: rchhoff mode for the refected and transmtted part, GTD mode for the dffracted part RA A( spec) A D GTD A dff D A e A dff r r GTD dff Correcton of the rchhoff dffracton 4

15 fned rchhoff mode RA Improvement of the rchhoff mode A D GTD D A e r r D GTD - D rchoff nc = D GTD D rchoff dvergence of the GTD coeffcent canceed by the dvergence of rchhoff for a sem-nfnte pane = Inc zoom Fd-rgd (presented here) Improvement of the dffracton rests 4 Exact A 33 fned-a 3 Exact A fned-a Sod-vod Encoragng premnary rests: Improvement more sgnfcant 7 fd-rgd case 5

16 Pan A genera rchhoff approxmaton for echo smaton n trasonc NDT Introdcton. Genera rchhoff mode. fned rchhoff mode Concson 6

17 Concson Deveopment of a genera rchhoff mode Generc formasm Appcabe to nterfaces between any types of materas (fds, sotropc sods, ansotropc sods) Extends the appcaton doman of the rchhoff mode n Cva fnement of the rchhoff mode to mprove dffracton rests Coaboraton wth Approach vadated for the fd-rgd case (edge) Wor n progress: mpementaton of the sod-vod case (edge) Ftre wors: deveopments for other materas and geometres 7