ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS

Size: px

Start display at page:

Download "ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS"

Carmella Caldwell
5 years ago
Views:

1 ADVANCEMENT OF THE CLOSELY COUPLED PROBES POTENTIAL DROP TECHNIQUE FOR NDE OF SURFACE CRACKS F. Tkeo 1 nd M. Sk 1 Hchinohe Ntionl College of Technology, Hchinohe, Jpn; Tohoku University, Sendi, Jpn Abstrct: DCPD technique is powerful tool for quntittive NDE of crcks. The technique using four probes which re in close proximity to ech other hs been proposed for NDE of surfce crcks; tht is the closely coupled probes potentil drop (CCPPD) technique. It hs been shown tht the sensitivity of the CCPPD technique is enhnced significntly in comprison with the usul method. The objective of this study ws to dvnce the CCPPD technique. An pproprite probes distnce to enhnce reproducibility ws found by experiment. The d-c potentil fields were nlyzed for mny cses of crck length, crck depth b nd mteril thickness t by using FEM. By using the numericl results, the clibrtion eqution which relte the potentil drop to, b, nd t ws obtined. Then the procedure to evlute crck depth more ccurtely in two steps ws proposed. Experiments vlidted the use of the technique for NDE of surfce crcks. Introduction: D-c potentil drop technique is suitble for quntittive NDE of crcks. It hs been pplied not only to single crck but lso multiple crcks [1]. The technique using four probes, which re in close proximity to ech other, hs been proposed [][3]; tht is the closely coupled probes potentil drop (CCPPD) technique. It hs been shown tht the sensitivity of the CCPPD technique is enhnced significntly in comprison with the usul method using uniform current flow in the region fr from the crck. In ddition, the CCPPD technique is suitble for fields which require smller equipment nd sensor being esy to del with. There re some cses where the reproducibility of potentil drop mesurement is required to be enhnced. An error in probes positioning is sometimes encountered in those cses. The potentil bruptly increses s closing the current input-output probes becuse current density tkes higher vlue in the vicinity of these points. So lrger error my be introduced in the mesured potentil drop due to smll error in probe positioning. The purpose of this study is to enhnce the reproducibility of evlution of the crck depth on the surfce by the CCPPD technique. At first, pproprite distnce between probes to enhnce reproducibility of mesurement is found by experiment. Next, the potentil drops for mny cses of crck length, crck depth b nd mteril thickness t re nlyzed by using the pproprite probe distnce by finite element method (FEM). By using the nlyzed results, the clibrtion eqution tht pproximtely reltes the potentil drop with, b nd t is obtined. Then the method to evlute crck depth with two steps is dopted. Through these two steps, more ccurte b cn be evluted. The reproducibility of crck depth evlution is scertined by experiment. I s 1 s V s s 1 I Crck I V I = 1A 5 Specimen 114 Dimensions in mm φ.4 s s 1 = 6mm s 5 mm 4 mm 3 mm () Specimen (b) Sensor Fig.1 Schemtic of experimentl pprtus

2 Approprite Distnce between Probes: The pproprite distnce between probes to enhnce reproducibility of mesurement ws exmined through n experiment. The specimen ws mde of ustenitic stinless steel AISI34, nd hd the width 114mm, the length mm nd the thickness 5mm s shown in Fig. 1(). The crck ws modeled by semi-ellipticl slit hving the width.1mm, which ws introduced by electric-dischrge mchining. The crck length ws 9.8mm nd the depth.7mm. Two probes for current input-output nd two probes for mesuring potentil drops were locted t ±s 1 nd ±s from the crck respectively, nd on perpendiculr bisector of the crck line s shown in Fig. 1(). Constnt d-c current in the mount of 1A ws pplied to the specimen through the current input nd output probes. The potentil drop V ws mesured between mesuring probes. All four probes were synthesized to build pen-like sensor. So the sensor is smll nd esy to del with. The contct of every probe to the specimen surfce ws mde constnt by using springs. At the top of the sensor, there re some holes to insert probes s shown in Fig. 1(b). So the probe distnces cn esily be chnged. In this experiment, the distnce between current input-output probes s 1 ws mde constnt s 6mm, nd the distnce between mesuring probes s ws chnged with 3, 4, nd 5mm. The vlues of potentil drop t uncrcked prt V nd tht t crcked prt V 1 were mesured for 5 times respectively, nd the effect of probe distnce on the reproducibility of mesurement ws exmined. Frequency V V V1V 1 Frequency VV V1V Potentil drop (µv) Fig. Frequency distribution of the mesured potentil drop (s = 5mm) Potentil drop (µv) Fig. 3 Frequency distribution of the mesured potentil drop (s = 4mm) 3 Frequency V V V1V 1 Potentil ( µv ) V 1 V s =3 s =4 s = Potentil drop (µv) Distnce from the center of the sensor (mm) Fig. 4 Frequency distribution of the mesured potentil drop (s = 3mm) Fig. 5 Distribution of the potentil

3 Figures, 3 nd 4 show the frequency distribution of mesured potentil drops. The potentil drop V nd V 1 become lrge s s. There re some vritions in ll cses. The rnge of vrition for the cse of s = 5mm is lrger thn tht for the cse of s = 3mm. As one of the reson for this, it my be possible to consider tht the probes distnces contin slight error cused by clernce between probe nd inserted hole. Figure 5 shows the distribution of potentil in the hlf region between current input-output probes. Potentil in Fig. 5 ws clculted by using FEM for the cse of resistivity of mterils ρ = Ωm. The positions of mesuring probe for the cses of s = 3, 4 nd 5mm re shown in Fig. 5. It ws found tht potentil bruptly increses s close to current inputoutput probe. When mesuring probes re locted in this region, lrger error my be introduced in the mesured potentil drop from slight error in probes positioning. For the cse of s = 3mm, mesuring probe is locted t the position where the distribution of potentil is not so steep nd rther lrge vlue of voltge cn be mesured. And lso the big chnge in potentil drop cn be obtined by crck. Then s = 3mm is decided to be suitble probe distnce to enhnce reproducibility of mesurement for s 1 = 6mm. Clibrtion Eqution: Let us consider the wy to evlute crck depth by using the probe distnce s 1 = 6mm nd s = 3mm tht obtined from the previous discussion. In this study, only n open crck on the surfce ws considered. Then crck length nd mteril thickness t cn be mesured, nd only crck depth b is unknown. The rnges of crck size nd mteril thickness treted in this study re s follows: 1.mm t mm nd t =.5mm mm nd =.5mm b mm (only the rnge b nd b < t ) At first, the reltions between potentil drop nd crck size for mny cses were clculted. The problem of d-c current flow in mteril is governed by the Lplce eqution s φ = (1) where φ is the electricl potentil nd is the three-dimensionl Lplce opertor. Eqution (1) cn esily be solved by using FEM. The potentil drops for vrious combintions of, b nd t were nlyzed by FEM. Next, the reltions between potentil drop nd, b nd t were pproximted with the following clibrtion eqution [3]: V b b = F D, + 1 C(, b, s, t) V s s 1 () where β b ln α b + 1 F = s ln + 1 ξ s γ D s b, = ex p δ s ζ b η + ϕ s (3) (4)

4 C(, b, s, t) = κ s b λ + 1 t s t s θ t χ 3 b + 1 t b (for mm) (for = ) (5) (5b) nd V is the potentil drop in n uncrcked prt. Coefficients of Eqs. (3) to (5) were obtined for the following four cses: Cse 1: mm, t = Cse : mm, t mm Cse 3: =, t = Cse 4: =, t mm Tble 1 Coefficients of the clibrtion eqution Cses Coefficients t Cse 1 Cse t = mm t mm b 1st step nd step nd step 1st step b 1.5 b 1 1.5< b < 1 b b 1 < b < 1 α β γ ξ δ ζ η ϕ λ κ Cses Coefficients t Cse 3 Cse 4 t = = t mm b 1st step nd step nd step 1st step b b 1 < b < 1 b b 1 < b < 1 α β γ ξ θ χ

5 The clibrtion eqution which ws obtined for the ll rnge of b,.5mm b mm, would contin the regions where the ccurcy of pproximtion is not enough. Then the evlution procedure with two steps ws dopted in this study. In the first step, n pproximte vlue of b ws evluted by using the clibrtion eqution for the ll rnge of b. In the second step, clibrtion eqution obtined for nrrow rnge of b ws selected bsed on the evluted vlue of b in the first step. At lst, the precise vlue of b ws evluted through the selected clibrtion eqution. The coefficients of the eqution obtined re shown in Tble 1. Results nd Discussions: Figure 6 shows n exmple of the reltionship between V 1 /V nd b. Plotted mrks nd lines show the numericl results of FEM nd clibrtion eqution, respectively. The clibrtion eqution shown in Fig. 6 is for the rnge of b 1mm. It cn be scertined tht the eqution pproximtes the potentil drop in tht rnge. From Fig. 6, it cn be found tht the grdient of the clibrtion eqution becomes smller s crck depth becomes lrger. This mens the sensitivity decreses with incresing crck depth. So the dequte rnge of crck depth to evlute sensitively seems to be b 5mm for the sensor with s 1 = 6mm nd s = 3mm V 1 /V =b, = b, t= t = by by FEM =b, = b, t= t = by by eq.() Eq.() =mm, = t= t = by FEM =mm, = t= t = by eq.() Eq.() b (mm) Fig.6 Exmple of the reltionship between V 1 /V nd b b Crck L W t Tble Size of the specimen Specimen No. 11-L 36 Mteril W (mm) AISI L (mm) 34 5 t (mm) (mm) b (mm).69.6 Fig.7 Shpe of the specimen

6 Evluted Actul b (mm) Evluted b (mm) 1 Actul Repetition number of evlution Repetition number of evlution Fig.8 Exmple of evluted result (No. 11-L) Fig.9 Exmple of evluted result (No. 36) The vlidity of the technique proposed in this pper ws verified by experiment. The specimens ws mde of ustenitic stinless steel AISI34, nd their width W, length L, thickness t, crck length nd crck depth b re shown in Fig. 7 nd Tble. The crck ws modeled by semi-ellipticl slit hving the width.1mm, which ws introduced by electric-dischrge mchining. Figures 8 nd 9 show the evluted depth which ws mesured continuously 1 times by hnd. Lines in Figs. 8 nd 9 show the ctul depth of crck. There ws tendency to evlute slightly deeper thn the ctul depth in both cses. The result generlly shows good reproducibility of this technique. Conclusions: In order to enhnce the reproducibility of evlution of the crck depth on the surfce by the CCPPD technique, pproprite distnce between probes ws found by experiment. The clibrtion eqution tht pproximtely reltes the potentil drop with, b nd t ws obtined bsed on FEM. The procedure to evlute crck depth with two steps ws dopted to enhnce the ccurcy of evlution. The reproducibility of crck depth evlution is scertined by experiment. References: [1] H. Liu, M. Sk, H. Abé, I. Komur nd H. Skmoto, Trns. ASME, J. Applied Mechnics, Vol. 66, 468 (1999). [] M. Sk, A. Oouchi nd H. Abé, Trns. ASME, J. Pressure Vessel Technology, Vol. 118, 198 (1996). [3] M. Sk, D. Hirot, H. Abé nd I. Komur, Trns. ASME, J. Pressure Vessel Technology, Vol. 1, 374 (1998).

Applications of Bernoulli s theorem. Lecture - 7

Applications of Bernoulli s theorem. Lecture - 7 Applictions of Bernoulli s theorem Lecture - 7 Prcticl Applictions of Bernoulli s Theorem The Bernoulli eqution cn be pplied to gret mny situtions not just the pipe flow we hve been considering up to now.