Simulation of ultrasonic phased array technique for imaging defects.pdf

International Journal of Pressure Vessels a

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conducted to validate modeling results for pulseecho simulations of the phased array transducer on a mild-steel (MS) pipe sample with

circumferential internal surface notches of three different sizes. Experiments were carried out on the MS pipe specimen using a

important requirement and also calls for a reliable andfast non-destructive evaluation technique, especially under

infrared energy (active/passive) emitted from the compo-nent and is displayed as the temperature distribution withinthe body. Defects in the components become clearly visible

attached on the components under study to pick up stresssignals in the form of elastic waves when a crack develops

angle dictated by the laws of reection. The reected signalis picked up and the amplitude of the reected signal givesan indication of the size of the defect. Advanced ultrasonic

ARTICLE IN PRESSmethods like the time of ight diffraction (TOFD)technique [7], synthetic aperture focusing technique(SAFT) [8] and phased array techniques [9,10] have been

0308-0161/$ - see front matter r 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijpvp.2007.08.002

Corresponding author. Tel.: +91 44 2257 4662; fax: +91 44 2257 0545.E-mail address: [email protected] (K. Balasubramaniam).eld conditions [3]. Eddy current-based techniques [4] arewidely used for the detection and characterization ofsurface and near-surface cracks in conductive materials. Itis based on the principle of electromagnetic induction andessentially involves the measurement of the impedance atevery point on the scan surface. A change in the impedanceis observed if a crack is present, which is taken as anindication for the detection and sizing of the defect.Infrared thermography is based on the measurement of

or propagates, which is often associated with the release ofenergy. A number of appropriately placed sensors are usedto accurately detect and position the defects. Thistechnique has been used to study fatigue crack propagationin various power plant components. Traditional ultrasonicsis a very common and reliable technique that is used for thedetection of defects in components. It is based on theprinciple that when ultrasonic energy is incident on adefect, the surface of the defect reects the energy at ansized using the relative arrival time technique (RATT). The experimental B-scans obtained using the conventional ultrasonic techniques

were compared with the experimental B-scans obtained using the phased array instrument. Simulation studies were also carried out by

steering the beam to the requisite angles by the phased array transducer to study the effect of various angles of incidence on the defect

denition, i.e., with respect to imaging and sizing, using the RATT.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Crack sizing; Ultrasonic phased array; Circumferential surface cracks; FDTD; RATT

1. Introduction

Ascertaining the structural integrity of critical engineer-ing components such as pressure vessels [1,2] is an

as the temperature gradient between a defective and a non-defective region is distinctly high [5]. The acoustic emissiontechnique [6] has been extensively used for the conditionmonitoring of engineering components. Transducers areconventional ultrasonic technique with a 5MHz transducer at 451 refracted angle within the specimen and the defects were imaged andSimulation of ultrasonic phasand sizing of defects u

L. Satyanarayan, C. Sridhar, C.V. Krish

Center for Non-Destructive Evaluation and Department of Mechanical E

Received 3 October 2006; received in revise

Abstract

Phased array ultrasonics can be used as a rapid tool for imagin

phased array ultrasonic wave interaction with the defects using thnd Piping 84 (2007) 716729

array technique for imagingng longitudinal waves

amurthy, Krishnan Balasubramaniam

neering, Indian Institute of Technology Madras, Chennai 600 036, India

rm 26 June 2007; accepted 1 August 2007

nd sizing crack-like defects. This paper reports the simulation of

nite-difference time domain (FDTD) method. Experiments were

www.elsevier.com/locate/ijpvp

crack on its image obtained using the RATT.

ARTICLE IN PRESSof Palso been extensively used to accurately detect and sizecracks in critical engineering components.Phased array ultrasound has emerged as a rapid non-

destructive evaluation technique for the detection andimaging of crack-like defects in structural components dueto the exibility it offers in varying the angle of inspectionand/or focusing of the beam to a point of interest [1114].The principle of phased array ultrasonic beam generation isbased on the use of individual transducer elements that caneach be independently driven with controlled phase delaysof excitation. Using this phase delay, the parameters of theultrasonic beam, such as the depth of focus and/or thebeam angle can be varied while the testing is being carriedout. This results in an improved capability to image defectslocated in regions even with limited accessibility. Using thelinear scanning capability of the phased array, the manual/automated motion of the ultrasonic probe during awdetection is replaced by the near-real-time electronicscanning. Fig. 1(a) shows how a beam can be steered atan angle in a specimen with a crack-like defect that iscomputed using the nite-difference time domain (FDTD)method [15].Conducting the experiments over a wide range of defects

Nomenclature

c longitudinal wave velocityCijkl elastic stiffness tensorE Youngs modulusf frequencyG shear modulusu velocity along x-directiont timev velocity along y-directionx, y Cartesian directionsZ acoustic impedance

L. Satyanarayan et al. / International Journaland specimen geometries is both time consuming andcostly. The high cost of a phased array transducer is also afactor that motivates the use of models for simulation ofthe experimental procedures. In such cases, numericalmethods such as the FDTD method can be suitably used tosolve for the displacement and stress values in the domainof interest. The simulation results may be utilized in thedesign of experiments, optimal selection of experimentalparameters such as the transducer frequency, depth offocus, angle of inspection, determination of focal laws andthe interpretation of defect images. Fig. 1(b) shows theinteraction of a phase steered wave at different instances ofits propagation with a bottom surface crack simulated bythe FDTD method. The corner trap and the tip diffractedechoes are clearly seen.In this paper, simulation of the phased array ultrasound

wave propagation in a 10-mm thick mild-steel (MS) pipespecimen with circumferential internal surface notches has2. Finite-difference time domain formulation of the problem

The FDTD model for the simulation and visualization ofthe elastic wave propagation is based on a rst-ordervelocitystress nite-difference method for homogeneousisotropic material [16]. The equation of motion, thestressstrain relation together with constitutive equations,completely describes the elastic wave propagation in ahomogenous material.In the elastic media, the relationship between stressesbeen demonstrated using the FDTD method. The simula-tions of B-scans were compared with the correspondingexperimentally obtained B-scans using the phased arrayinstrument.The effect of varying angles of incidence on the

denition, ease and accuracy of sizing of the defects usingthe relative arrival time technique (RATT) was alsoexplored by changing the refracted angles within thespecimen by the phased array transducer. The study alsoinvestigates the effect of the inclination of a bottom surface

tn required time delay to the nth elementN total number of active elementsn element number (0,1,2,y,N1)d center-to-center spacing between the elementsF depth of focusa attenuation factorl, m Lames constantstxx, tzz normal stresstxz shear stressn Poisons ratioy angle of incidence or steerr density

ressure Vessels and Piping 84 (2007) 716729 717and strains can be written as

tij cijkluk;l , (1)where the summation convention has been implied.The cijkl term is a matrix of the order 6 6 and contains

36 elastic moduli. For an isotropic case, the number ofelastic moduli reduces to only 2, and can be written interms of Lames constants, l and m.The derivative of Eq. (1) with respect to the time variable

can be written as

tij cijklvk;l , (2)

where v is the velocity and based on Newtons law

rvi tij;j . (3)The above equation leads to a set of rst-order partial

differential equations that are coupled. The elastic wave

ARTICLE IN PRESSf PL. Satyanarayan et al. / International Journal o718equation in two dimensions are given by

rqvxqt

qtxxqx

qtxzqx

,

rqvzqt

qtxzqx

qtzzqz

,

qtxxqt

l 2m qvxqx

l qvzqz

, (4)

qtzzqt

l 2m qvzqz

l qvxqx

, (5)

qtxzqt

l qvxqz

qvzqx

. (6)

The differential equations are discretized by the nite-difference scheme, which are obtained by truncating Taylor

Fig. 1. (a) Beam streeing and focusing in a phased array transducer. (bressure Vessels and Piping 84 (2007) 716729series expansion. This may lead to numerical errors thatcannot be avoided. The choice of programming schemeand the parameters must be so chosen that numerical errorand instability do not diversify at any point in the wavepropagation. The nite-difference discretization of the setof equations leads to a staggered nite-difference grid asshown in Fig. 2. Here the normal stresses, namely txx andtzz, are represented at a single node and the remaining eld(velocity) variables, vz and vx, and the shear component txzare represented in the grid at half-spatial steps to eachother.The velocity and the stress components in the grid are

not known at the same position in time and space and areoffset by Dt/2 and Dx/2, Dy/2 as shown in the Fig. 2. Thisleads to a leap frog scheme in which the velocitycomponents are updated at the (Dt/2) rst half-time stepand then in the next half-time step, stress components are

) Interaction of a phase steered wave with the crack tip and corner.

ARTICLE IN PRESSof Pupdated. In the next Dt/2, with the stress components at theend of the rst time step, Dt, the velocity components at(Dt+Dt/2) are calculated.The velocity components u and v are determined from

Eq. (1):

ruk1i;j uk1i;j

Dt txx

ki1;j txxki1;j

Dx

" #

txzki;j1 txzki;j1

Dz

" #,

uk1i;j uk1i;j txxki1;j txxki1;j

rDx=Dt

" #

txzki;j1 txzki;j1rDz=Dt

" #, 7

rvk1i;j vk1i;j

Dt txz

ki1;j txzki1;j

Dx

" #

tyyki;j1 tyyki;j1

Dz

" #,

vk1i;j vk1i;j txzki1;j txzki1;j

rDx=Dt

" #

Fig. 2. Finite difference grid of the domain showing the positions of each

eld variable.

L. Satyanarayan et al. / International Journal tyyki;j1 tyyki;j1rDz=Dt

" #. 8

The stress components (two normal components and oneshear component) are determined by

txxk1i;j txxk1i;jDt

l 2mui1;j ui1;jDx

mvi;j1 vi;j1Dz

,

txxk1i;j txxk1i;j l 2mui1;j ui1;j

Dx=Dt

mvi;j1 vi;j1Dz=Dt

, 9tzzk1i;j tzzk1i;jDt

l 2mvi1;j vi1;jDx

lui;j1 ui;j1Dz

,

tzzk1i;j tzzk1i;j l 2mvi1;j vi1;j

Dx=Dt

lui;j1 ui;j1Dz=Dt

, 10

txzk1i;j txzk1i;jDt

lvi1;j vi1;jDx

lui;j1 ui;j1Dz

,

txzk1i;j txzk1i;j lvi1;j vi1;j

Dx=Dt

lui;j1 ui;j1

Dz=Dt

.

11Courant number is the ratio of the distance the elastic

wave travels in one time step to the length of a step of themesh. In order to ensure stability and obtain numericalconvergence in the FDTD method, it is essential that theCourant number is less than or equal to one. Hence, in thesimulations, stability criteria of Courant number (cDt/Dx)lesser than one are always considered.Appropriate boundary conditions need to be applied while

implementing the FDTD technique to dene the defect and thespecimen boundaries. A variety of techniques are available toapply a free boundary condition for staggered grid FDTDschemes. In this study, the velocities along the back wall andthe defect boundaries were set to zero [17], i.e., u 0; v 0.During modeling, in order to reduce the computational

resource requirements a sub-domain region of the specimenis used. This domain process creates articial freeboundaries that lead to undesirable reections and modeconversions that do not occur in the experiments. In orderto eliminate these artifact reected waves, the absorbingboundary conditions were applied on the appropriatedomain boundaries. The absorbing boundary conditionscan be implemented by incorporating the perfectly match-ing layer (PML) boundary conditions [18]. Perfectlymatching layers are an extra set of layers that areincorporated outside the domain of the model whoseimpedance and phase velocity match with that of thedomain and also have an attenuation function that rapidlydecays the wave that proceeds though the layers. Sincethere is no impedance mismatch between the perfectlymatching layer and the domain, very little reection occursat the domainperfectly matching layer boundary.However, in discrete space, the lossy layer will not be

perfectly matched to the solution space domain and slightreections occur at the interface. In order to minimize thesereections, a tapered loss prole function was chosenwithin the lossy layers

ressure Vessels and Piping 84 (2007) 716729 719ai amaxi ipml=Npml2, (12)

mental setup and generates A-scans and B-scans that

transducer of 5MHz center frequency. A three-cycle

taken as (wavelength) l/15.

tn F=cf1 N 1=2d=F 2

2N 1=2d sin y=F 1=2

1 n N 1=2 1nd=F 2

2n N 1=2d sin y=F 1=2g. 13If the beam is unfocused, the above expression for the

time delay to the nth element reduces to

tntransmit nd sin y=c during transmission; (14)

tnreceive N nd sin y=c during reception: (15)During transmission, the nodes that represent the active

transducer elements were provided displacements at time

ARTICLE IN PRESS

Fig. 3. Finite difference model for phased array transmission and

reception.

Table 1

Settings used in the simulation study

Transducer specications

Central frequency 5MHz

Transducer length 46mm

Transducer width 15mm

Type of wave used Longitudinal

Inspection angle 451

Discretization parameters

Time step size 9.43e9 sElement size 8.4e002mm (l/15)

Material properties (mild steel)

L-wave velocity 5900m/s

S-wave velocity 3200m/s

Density 7900 kg/m3

f PHanning window pulse was chosen as input to thetransducer elements for the simulations. The elements ofthe transducer (assumed to be point sources) generatesspherical wave fronts which interfere constructively ascan be compared with the corresponding experimentalA-scans and B-scans. The time delay/focal laws [19] givenin Eq. (14) have been used to simulate phased arraytransmission and reception of unfocused phase steeredbeams. Fig. 3 shows the nite-difference model of thespecimen along with the transmission and receptiondelay scheme applied to simulate the phased arraytransducer. In order to replicate the experimental condi-tions, the number of elements in the simulation thathave been kept active was 16 for all scans and the beamwas steered at 451 to the normal with respect to thecenter of the probe from an ultrasonic phased arraywhere Npml is the thickness of the perfectly matching layersin terms of the number of cells and i ipml is the position inthe perfectly matching layers.

3. Phased array ultrasonic system

The experimental setup used in this study consists of acommercial ultrasonic phased array system with thearray probe using the electronic scanning feature on theMS pipe specimen. The data presented in this paper wereacquired using 5MHz center frequency and a 64-element(46mm 15mm area) array probe. The defects wereimaged by phasing the elements of the probe to generatea longitudinal wave steered at the requisite angle ofinspection in the linear scan mode.

4. Simulation of A-scan signals and B-scan images usingnite-difference time domain technique

A two-dimensional (2D) model was developed using theFDTD technique to simulate the phased array wavepropagation in rectangular block and pipe-like structures.The density of the MS pipe was taken as 7900 kg/m3

and the longitudinal wave velocity was assumed to be5900m/s while the shear wave velocity was assumed to be3200m/s. The defects simulated in the pipe sample weresurface notches from the inner diameter (ID) of threedifferent sizes.The 2D model was developed in MATLABs to simulate

the propagation of the ultrasonic wave in the specimen ofan arbitrary geometry. The 2D plane of the pipe was in therz direction and hence can be approximated as a plateusing the plane wave assumption. The simulated crackswere modeled to be oriented in the ry plane. The codetakes input parameters that dene a phased array experi-

L. Satyanarayan et al. / International Journal o720dictated by the phase delay laws and get steered at therequired angle of inspection. The grid size in the model wasressure Vessels and Piping 84 (2007) 716729delay values given by the well-known transmit delay lawprovided in Eq. (14). Using these time delays, the wave was

steered at the requisite angle within the specimen. Thereceived signals are then time-advanced using the receptiondelay law and then summed together to generate theA-scan at that inspection point. The defects in the specimenare modeled as free surfaces which reect/diffract the entireacoustic energy incident on them. Once a wave meets aninterface, new reected waves are created based on theangle of incidence taking into account mode conversion.This model does not account for attenuation the wave

of the defect. In case of a 451 LW inspection, the size of thedefect is equal to the displacement of the probe between themaximum positions of the tip diffracted and the cornertrap echo peaks. Since, in the electronic scanning feature ofthe phased array, the resolution of the alternate techniqueis limited by the inter-element spacing, the RATT methodhas been employed to size the defect.Fig. 5(c) shows a B-scan image of a 5-mm deep bottom

surface notch in a 10-mm deep MS pipe specimen. The 451phase steered beam rst interacts with the top tip of thedefect and is diffracted, which is seen as the rst echo inthe image. The compressional/longitudinal wave then hitsthe defect corner and gets mode converted into acompressional/longitudinal component (PP wave) and ashear component (PS wave). Since the velocity of theP-wave is higher, it arrives earlier when compared with theS-wave in the B-scan image.Fig. 6(a)(c) shows a comparison of experimental and

simulated B-scans for a pipe with notches of three differentsizes present on the inner diameter. The notches were sizedusing the RATT [2023]. The estimated sizes of the defects

ARTICLE IN PRESSL. Satyanarayan et al. / International Journal of Pressure Vessels and Piping 84 (2007) 716729 721undergoes as it travels in the specimen. The internalreection within the transducer, which accounts for thenoise near the front wall region, has also not been modeled.The settings that have been used for the simulation studyare given in Table 1.

5. Experimental results

5.1. Imaging and sizing of circumferential bottom surface

notches in pipes

Experiments were conducted on a 10-mm thick MS pipesample with 3-, 5- and 7-mm deep (i.e., 30%, 50% and 70%of the pipe thickness) vertical electrical discharge machinedsurface notches using phase steered 451 longitudinal waveusing 64-element phased array transducer of 5MHz centerfrequency. The MS pipe sample is shown in Fig. 4. Thedetails of electrical discharge machined notches withrespect to the vertical of a 10-mm thick MS pipe sampleare given in Table 2.Fig. 5(a) shows the schematic representation of the

ultrasound ray path between crack tip and corner trapsignal for an internal surface breaking crack. The size ofthe defect was then determined by time of ight techniqueby reading the A-Scans obtained from the B-scan data. Arectied A-scan with two distinct echo signals from thecrack is shown in Fig. 5(b). The echo of smaller amplitudeis from the crack tip and the echo of higher amplitudecorresponds to the reection from the corner trap. Thecrack height at that point can be estimated from the A-scansignal by measuring the relative time difference between thetwo echo peaks taking into consideration the angle ofincidence and the material properties. An alternate methodinvolves the analysis of the B-scan image and measuringthe relative displacement of the probe position (at themaximum height of the signals) as an indication of the sizeFig. 4. Line sketch of 10-mm thick mild-steel pipe sample with tand the associated percentage errors are given in Table 3. Itwas observed that the simulated results were in goodagreement with the experimental results.

5.2. Effect of varying angles of inspection in relative arrival

time technique on imaging of circumferential bottom surface

notches in pipes

The RATT method involves the measurement of thecorner trap and the top tip diffracted echoes by thesame angle for the estimation of the size of the crack.If the relative ultrasound path between the corner trap and

Table 2

Details of circumferential EDM notches with respect to vertical of 10-mm

thick mild-steel pipe sample

Defect

number

Type Length

(mm)

Width

(mm)

Depth

(mm)

D1 Internal surface breaking

(rectangular)

10 0.4 7


(rectangular)

10 0.4 5


(rectangular)

10 0.4 3hree inner diameter notches in the circumferential direction.

ARTICLE IN PRESSf PL. Satyanarayan et al. / International Journal o722the top tip diffracted echo is UTpath, then

H UTpath= cos y, (16)where H crack height and y angle of inspection.UTpath CD AB.

Fig. 5. (a) Ultrasound path between crack tip and corner trap signal for a sur

surface crack. (c) Experimental B-scan image of a 5-mm bottom surface notchressure Vessels and Piping 84 (2007) 716729The angle of inspection is inbuilt in the estimation of thesize of the crack, which automatically compensates forthe change in the ultrasound path due to the change in theinspection angle. But, the determination of an optimuminspection angle is desirable for a clear image of the defectsignals in the B-scan. Thus, the defects were imaged using

face crack. (b) A-scan showing crack tip and corner trap echo signal for a

.

ARTICLE IN PRESS

Fig. 6. Comparison of simulated and experimental B-scan images on a 10-mm thick mild-steel pipe sample with bottom surface notches. (a) 7-mm,

(b) 5-mm and (c) 3-mm bottom surface notchs.

L. Satyanarayan et al. / International Journal of Pressure Vessels and Piping 84 (2007) 716729 723

ARTICLE IN PRESS

ed

err

s

E

d

ye

7

4

3

f PTable 3

Comparison of the simulated and experimental estimated notch sizes obtain

451 angle of incidence

Defect

number

Actual depth

(mm)

Estimated depth (mm):

simulated

Percentage

simulated

D1 7 7.2 2.85D2 5 4.8 +4.0

D3 3 3.1 3.33

Table 4

Comparison of estimated defect sizes (simulated) of circumferential bottom

angles of inspection

Actual depth

(mm)

Estimated

depth (mm):

y 301 (%error)

Estimated

depth (mm):

y 351 (%error)

Estimated

depth (mm):

y 401 (%error)

7 6.8 (+2.85) 6.8 (+2.85) 7.2 (2.85)5 5.1 (2.0) 4.8 (+4.0) 5.1 (2.0)3 2.9 (+3.33) 2.8 (+6.66) 2.9 (+3.33)

L. Satyanarayan et al. / International Journal o724phased array by steering the beam for an angular range of30601 at an angular increment of 51. This variable anglesteer can be easily and elegantly achieved by varying thefocal law to steer the beam at the required angles, whichwould otherwise be a cumbersome procedure using aconventional transducer. Moreover, it is also possible tosend a focused beam at different depths of foci in case ofphased array to obtain a relatively clearer image of thedefect when compared with a conventional transducer.The simulated and experimental sizes (estimated) of threebottom surface defects in the MS pipe specimen and thepercentage errors are given in Tables 4 and 5, respectively,for three angles of inspection, and the correspondingsimulated and experimental B-scan images indicatingthe corner trap and the tip diffracted signals are shownin Figs. 79.It was observed that the separation between the corner

trap and the tip diffracted echoes increased with thedecrease in the inspection angle and a sufcient separationwas achieved at angles 301 and 401. Separation between thetip diffracted and the corner trap echoes is highly desirablewhen sizing small cracks. However, since the ultrasoundpath also increases or decreases with a corresponding

Table 5

Comparison of estimated defect sizes (experimental) of circumferential bottom

angles of inspection

Actual depth

(mm)

Estimated

depth (mm):

y 301 (%error)

Estimated

depth (mm):

y 351 (%error)

Estimated

depth (mm):

y 401 (%error)

E

d

ye

7 6.8 (+2.85) 6.7 (+3.13) 6.8 (+2.85) 6

5 4.8 (+4.0) 4.9 (+1.99) 4.8 (+4.0) 4

3 2.8 (+6.66) 2.8 (+6.66) 2.7 (+9.99) 2by relative arrival time technique on 10-mm thick mild-steel pipe sample at

or: Estimated depth (mm):

experimental

Percentage error:

experimental

7.4 5.714.7 +5.99

2.9 +3.33

urface notches in mild-steel pipe obtained using phased array for various

stimated

epth (mm):

451 (%rror)

Estimated

depth (mm):

y 501 (%error)

Estimated

depth (mm):

y 551 (%error)

Estimated

depth (mm):

y 601 (%error)

.2 (2.85) 6.7 (+3.13) 7.2 (2.85) 6.7 (+3.13)

.8 (+4.0) 5.2 (4.0) 4.7 (+5.99) 5.3 (5.99)

.1 (3.33) 2.9 (+3.33) 2.8 (+6.66) 2.8 (+6.66)

ressure Vessels and Piping 84 (2007) 716729increase or decrease in the inspection angle, the probe hasto be placed accordingly with respect to the defect position.A larger angle would mean that the probe should be placedat a larger distance away from the defect, which may beundesirable as it calls for a large scan length axis apartfrom having a low separation distance between the cornertrap and the tip diffracted echoes. It was observed that forimproved size estimation for small crack-like defects usingL-wave, the angles 35401 are recommended. Thus, it wasinferred that operating at 35401 angles of incidence wasoptimal for inspection using the RATT.The simulation was then extended to study the imaging

of inclined bottom surface cracks (7151 with respect to thevertical) of 5mm length in the 10-mm thick MS pipespecimen. The inclined crack B-scan images were comparedwith the B-scan image of the vertical bottom surface crackof similar dimensions. The simulated B-scan images ofinclined bottom surface defects obtained for the 451 angleof inspection for the three congurations is given in Fig. 10.In the B-scan images, it was observed that the tip diffractedecho of the +151 inclined crack appears to the left whilethe tip diffracted echo of the 151 inclined crack appearsto the right, when compared with the position of the tip

surface notches in mild-steel pipe obtained using phased array for various

stimated

epth (mm):

451 (%rror)

Estimated

depth (mm):

y 501 (%error)

Estimated

depth (mm):

y 551 (%error)

Estimated

depth (mm):

y 601 (%error)

.7 (+3.13) 6.8 (+2.85) 6.8 (+2.85) 6.7 (+3.13)

.8 (+4.0) 4.7 (+5.99) 4.6 (+8.0) 4.5 (+10.0)

.8 (+6.66) 2.7 (+9.99) 2.6 (+13.33) 2.6 (+13.33)

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Fig. 7. Comparison of simulated and experimental B-scan images of 3-mm bottom surface crack obtained for the various angles of incidence. (a) 351,(b) 451 and (c) 551 angle inspections: 3-mm bottom notches.


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L. Satyanarayan et al. / International Journal of Pressure Vessels and Piping 84 (2007) 716729726

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ARTICLE IN PRESSf PL. Satyanarayan et al. / International Journal o728diffracted echo of the vertical notch. Thus, it is inferredthat the position of the tip diffracted echo relative to thecorner trap position can be used as an indication todetermine the inclination of the bottom surface crack usingthe phased array B-scan images.

Fig. 10. Simulated B-scan image of inclined 5mm bottom surface defects in the

inclined, (b) 01 and (c) 151 inclined: 5-mm bottom surface notches.ressure Vessels and Piping 84 (2007) 7167296. Summary and conclusions

The simulation of phased array ultrasonic wave propa-gation and interaction with internal surface notches in amild-steel pipe was studied. A 2D nite-difference time

mild-steel pipe specimen obtained for the 451 angle of inspection. (a) +151

domain model was successfully developed to simulate thephased array experiments on blocks and pipes and thesimulation results were then compared with the experi-

[7] Baskaran G, Balasubramaniam K, Rao CL. Ultrasonic TOFD aw

sizing and imaging in thin plates using embedded signal identication

technique (ESIT). InsightNon-Destructive Testing and Condition

Monitoring 2004;46:53742.

[8] Baby S, Balasubramanian T, Pardikar RJ, Jayakumar T, Rajkumar

KV, Raj B. Sizing of cracks embedded in sub-cladding using the

ultrasonic synthetic aperture focusing technique (SAFT). Insight

ARTICLE IN PRESSL. Satyanarayan et al. / International Journal of Pressure Vessels and Piping 84 (2007) 716729 729The 2D nite-difference time domain model developed inthis study can also be used to study interaction of theultrasonic waves with defects of various congurationsand/or wave propagation in specimens with complexgeometries. The model can thus be a useful tool inunderstanding signals that might otherwise be difcult tointerpret in an experiment.Ultrasonic testing of pipes is conventionally carried out

using a 451, 5MHz (or 4MHz) transducer. The effect ofvarying angles of inspection on the defect denition withregard to image clarity and size in the B-scan was alsostudied by steering the beam at the required angles usingthe phased array and it was inferred that when operating atlower inspection angles (35401), the tip diffracted and thecorner trap echoes were well separated and, hence, it wasmore convenient to size the defects using the relative arrivaltime technique.The imaging of inclined (7151) bottom surface notches

using the relative arrival time technique was carried outand it was inferred that the position of the tip diffractedecho can be used as an indication to determine theinclination of the notch.

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/http://www.ndt.net/article/wsho0597/wuesten2/wuesten2.htmS.comparison was made with the actual sizes of the defects. Non-Destructive Testing and Condition Monitoring 2004;46:2630.[9] Satyarnarayan L, Pukazhendhi DM, Balasubramaniam K, Krishna-mental results. The results obtained from experimentsvalidate the simulations. The simulated and the experi-mental B-scan data were used to size the defects and a

Simulation of ultrasonic phased array technique for imaging and sizing of defects using longitudinal wavesIntroductionFinite-difference time domain formulation of the problemPhased array ultrasonic systemSimulation of A-scan signals and B-scan images using finite-difference time domain techniqueExperimental resultsImaging and sizing of circumferential bottom surface notches in pipesEffect of varying angles of inspection in relative arrival time technique on imaging of circumferential bottom surface notches in pipes

Summary and conclusionsReferences

Documents

Simulation of ultrasonic phased array technique for imaging defects.pdf