Quantitative Evaluation of Stress Corrosion Cracking Based on Features of Eddy Current Testing Signals

Transcription

1 E-Joural of Advaced Maiteace Vol.9-2 (2017) Japa Society of Maiteology Quatitative Evaluatio of Stress Corrosio Crackig Based o Features of Eddy Curret Testig Sigals Li WANG 1,* ad Zhemao CHEN 2 1 College of Sciece, Xi'a Uiversity of Posts ad Telecommuicatios, Xi'a, , Chia 2 State Key Laboratory for Stregth ad Vibratio of Mechaical Structures, Xi'a Jiaotog Uiversity, Xi'a, , Chia ABSTRACT Stress corrosio crackig (SCC) occurs i several key structural compoets of uclear power plats over time. A sufficietly precise quatitative techique is ecessary to guaratee the safety ad efficiet operatio of the key structural compoets whe SCC occurs. Quatitative evaluatio of SCC profiles usig eddy curret testig (ECT) sigals ofte uderestimates the crack depth due to the local coductive property ad the ill-posedess of the iverse problem. I this paper, a quatitative evaluatio method based o features of ECT sigals is proposed to improve the sizig accuracy of SCC profiles. The proposed strategy icludes a umerical SCC model based o the local coductivity distributio, a hybrid iverse strategy combied with the cojugate gradiet method ad the particle swarm optimizatio algorithm, ad a quatitative evaluatio method usig features of ECT sigals. Recostructio is coducted with simulated ECT sigals from coductive cracks, ad the results show that the proposed strategy is effective i improvig the sizig precisio of SCC profiles. KEYWORDS eddy curret testig, stress corrosio crackig, recostructio, umerical model, optimizatio algorithm ARTICLE INFORMATION Article history: Received 7 Novemver 2016 Accepted 27 April Itroductio Stress corrosio crackig (SCC) is a failure pheomeo of materials used i uclear power plats, such as austeitic stailess steel ad high-ickel alloys. SCC may cause sudde catastrophes without obvious sigs. Therefore, a sufficietly precise quatitative odestructive testig techique is ecessary to ehace the safety ad availability of uclear power plats. Give its superior detectio ability for shallow surface cracks as well as serious effect of the aisotropy of the columar crystal i the weld o ultrasoic sigals, eddy curret testig (ECT) is a viable complemet to ultrasoic testig i the recostructio of cracks, especially with regard to recogizig crack legth ad evaluatig cross-sectioal profiles [1-5]. However, the SCC depth is ofte uderestimated usig ECT sigals due to the local coductive property of cracks ad ill-posedess of the iverse problem [6]. I this paper, a quatitative evaluatio method is proposed based o feature aalysis of ECT sigals to improve the sizig accuracy of SCC profiles. Recostructio results from simulated ECT sigals reveal that the proposed strategy is effective i improvig the sizig precisio of SCC profiles. 2. A umerical SCC model based o feature aalysis of ECT sigals The ECT iverse problem of crack recostructio is usually defied as a miimum problem of the mea square residual [7, 8]: mea 2 mi ( c, ) Z ( c, ) - Z (1) * Correspodig author, wl_3691@163.com ISSN / JSM ad the authors. All rights reserved. 78

2 where Z(, c ) ad Z mea are the simulated ad measured ECT sigals, respectively, at the th scaig poit; c ad is the crack shape ad coductivity parameters, respectively. A model-based umerical method is usually applied to obtai the optimal solutio by a series of iterative computatios [9, 10]. I order to establish a umerical SCC model, we first ivestigate the relatio betwee crack shape parameters ad features of ECT sigal. I this sectio, a stadard pacake coil (ier diameter 1.2 mm, outer diameter 3.2 mm ad thickess 0.8 mm) ad a plus-poit coil (ier side legth 4.5 mm, outer side 5.5 mm ad height 2.0 mm) are applied as the ispectio probe. Cracks i a SUS304 plate that is 10 mm i thickess, 200 mm i legth, 100 mm i width ad 1.4 MS/m i coductivity are take as the detectio object. The excitatio frequecy is 10 khz for the pacake probe ad 30 khz for the plus-poit probe. The liftoff is 0.5 mm ad 1.0 mm, respectively Crack legth ad ECT sigal features The crack legth maily iflueces the start ad ed positios of ECT sigals ad has little effect o the amplitude ad phase for parallel scaig ECT sigals above the crack plae as show i Fig. 1. Fig. 1. ECT sigal from a coductive crack model with differet legths usig the pacake probe (left) ad plus poit probe (right) (Crack parameters: width 0.2 mm, depth 3 mm, relative coductivity 5%) 2.2. Ifluece of crack depth ad local coductivity o ECT sigals Figure 2 describes the ECT sigals from a crack model with differet local coductivity ad shows that the variatio i crack coductivity has obvious effect o amplitude ad slight effect o phase. Figure 3 shows that the chage of crack depth iflueces both the amplitude ad phase. I geeral, the crack coductivity value ad distributio i the depth directio affect the ECT sigals i a maer that is similar to the effect of the crack depth. Therefore, i model-based recostructio of SCC profiles, the local coductivity of the crack zoe should be cosidered to obtai accurate crack depth iformatio. Fig. 2. ECT sigal from a crack model with differet crack coductivity usig the pacake probe (left) ad plus poit probe (right) (Crack parameters: legth 16 mm, depth 3 mm, width 0.2 mm) 79

3 Fig. 3. ECT sigal from a coductive crack model with differet depths usig the pacake probe (left) ad plus poit probe (right) (Crack parameters: legth 16 mm, width 0.2 mm, relative coductivity 5%) 2.3. Crack width ad ECT sigal features Whe crack legth, depth, ad local coductivity are fixed, the amplitude of the ECT sigal above the crack plae chages obviously ad the phase chages oly slightly with chages i crack width; this tred is similar to the effect of crack coductivity chages. Figure 4 depicts the comparisos of ECT sigals whe the crack width raged from 0.2 to 0.4 mm (legth depth: 16 mm 3 mm), i which the relative icrease of amplitude is far greater tha that of phase. Accordigly, variatios i crack width ca be cosidered to be just as ifluetial as chage i the crack coductivity [11, 12]. Therefore, if depth ad legth are kept costat ad the error i the amplitude ad phase is maitaied at low values, ECT sigals of differet crack widths ca be approximated usig a certai width crack with its equivalet coductivity. For example, for crack legth (16 mm) ad depth (3 mm), the ECT sigals of width (0.3 mm) ad relative crack coductivity (5.0%) ca be approximated usig the sigals of width (0.2 mm) ad relative crack coductivity (1.76%) or width (0.4 mm) ad relative crack coductivity (6.70%) without chagig the crack legth ad depth. Based o the results of umerical aalysis ad the measuremet of the coductivity distributio for a artificial SCC i the crack zoe [13-15], a 2D umerical SCC model that cosiders the crack coductivity distributio with multiple coductivity parameters i the crack depth directio is proposed, i which the width is fixed to a certai value ad crack shape parameters comprise oly the crack legth ad depth. Fig. 4. ECT sigal from a coductive crack model with differet widths usig the pacake probe (left) ad plus poit probe (right) (Crack parameters: legth 16 mm; depth 3 mm; relative coductivity 5%) 3. A hybrid iverse strategy with the particle swarm optimizatio algorithm Quatitative evaluatio of SCC profiles is a multi-dimesio optimizatio problem because the 80

4 crack shape ad multiple coductivity parameters both eed to be recostructed. Whe the crack coductivity ad shape parameters are recostructed simultaeously, the error o the crack shape parameters ofte icreases ad the result may be ot coverget because differet kids of crack parameters have differet modified scales. Therefore, we use a hybrid iverse strategy combied with the cojugate gradiet method ad the particle swarm optimizatio algorithm to recostruct respectively the crack shape ad coductivity parameters i order to solve the problem of multi-dimesio ad differet modified scales. Specifically, for a set of give coductivity parameters, the cojugate gradiet method was used to optimize crack shape parameters ad to obtai a miimal evaluatio fuctio correspodig to the give coductivity parameters. The the particle swarm optimizatio algorithm was utilized to guide the crack coductivity parameters to optimal solutios accordig to the correspodig miimal evaluatio fuctio [16, 17]. Though the hybrid iverse strategy eeds more computatioal time tha a sigle method, it is more stable ad gives better results for the iverse problem of SCC profiles recostructio. 4. A evaluatio strategy of SCC based o features of ECT sigals Crack legth is easily idetified usig the start ad ed positios of parallel scaig ECT sigals above the crack plae i the detectio process ad it is rarely affected by other crack parameters. Accordigly, this sectio maily cosiders the crack depth ad coductivity parameters to simplify the problem of the quatitative evaluatio of SCC profiles. Numerical experimets show overall similarities with certai differeces i the effect of the ECT sigal features with the chage of crack depth ad local coductivity as show i Fig. 2 ad Fig. 3. I geeral, the real ad imagiary parts of ECT sigals vary differetly with chages i the crack depth ad local coductivity. I recostructig crack profiles, if the coductivity parameters are set as smaller tha the real values, the recostructed crack depth is ofte smaller tha the actual values i accordace with the miimum priciple of the mea square error. This differece usually causes the absolute value of the real part of the ECT sigals to be larger while the absolute value of the imagiary part to be smaller tha the true values. I cotrast, if a larger crack coductivity value is set, the the recostructed depth will ofte be larger, the absolute value of the real part of the ECT sigals will usually be smaller tha the true values. Cosequetly, the recostructio precisio of crack profiles is expected to be improved by settig a proper crack coductivity value whe usig the miimal mea square residual of the real ad imagiary parts of the ECT sigals. Therefore, we proposed a strategy to recostruct SCC profiles usig features of ECT sigals to reduce the ill-posedess of SCC profiles recostructio. 5. Numerical results To validate the strategy, a example of SCC recostructio is performed by takig umerical simulatio ECT sigals as target sigals. The simulatio sigals are from a coductive elliptical crack model of 14 mm legth, 3 mm depth ad 0.4 mm width. The excitatio frequecy is 30 khz ad lift-off is 1.0 mm. The ispectio probe is take as the above-metioed plus-poit coil. For the fast forward solver [18], databases of uflawed potetials were established for a search regio of 18 mm i legth, 5.5 mm i depth ad 0.4 mm i width. The search regio was subdivided ito 198 ( ) cells. The crack relative coductivity is expressed as 3 parameters, that is, 2%, 5% ad 8% from the surface to the bottom layers of the ispectio specime. Each coductivity parameter correspods to 1 mm thickess of the ispectio specime. Take the crack coductivity, depth ad legth as recostructed parameters. 7 times recostructio was performed with differet iitial values usig the proposed strategy. O coditio that the relative 7 error of mea square of ECT sigals is less tha , the recostructed crack depth is from 2.96 mm to 3.12 mm, ad the average depth is 3.04 mm. The recostructed crack legth is from mm to mm. By comparig with the true crack profiles, all of 7 times recostructio results coverge to the true values with high accuracy. The results correspodig to the recostructed maximum depth (3.12 mm) ad the miimum depth (2.96 mm) from the repeat processes are show i Fig. 5(a). Compariso of ECT sigals is show i Fig. 5(b). Sice the recostructio results of crack 81

5 coductivity distributio are equivalet values, there may be some errors betwee the recostructed values ad the true oes as show i Tab. 1. Nevertheless, as SCC complicated coductive property is described usig multiple coductivity parameters ad the effect betwee the crack depth ad coductivity is distiguished usig features of ECT sigals, recostructio precisio of crack depth is improved. (a) Compariso of crack profiles (b) Compariso of ECT sigals Fig. 5. Compariso of recostructio results from a coductive elliptical crack model Table 1 Recostructed crack coductivity distributio usig 3 coductivity parameters Figure 6 depicts a recostructio result from simulated ECT sigals with 5% white oise. 6 times recostructio process are implemeted usig the proposed strategy with differet iitial values. O 5 coditio that the relative error of mea square of ECT sigals is less tha , the recostructed average depth of crack is 3.09 mm ad the average legth is mm. Good predictios o the crack profiles are obtaied eve for the sigals with 5% white oise. Recostructios of several other crack models are also coducted. All the results reveal that the scheme is efficiet for recostructio of SCC profiles. (a) Compariso of crack profiles (b) Compariso of ECT sigals Fig. 6. Recostructio results from ECT sigals with 5% white oise from a coductive crack model 82

6 6. Coclusio I this paper, a quatitative evaluatio method based o features of ECT sigals is proposed to improve the sizig accuracy of SCC profiles. The method icludes a 2D umerical SCC model cosiderig crack coductivity distributio, a hybrid iverse strategy combied with the cojugate gradiet method ad the particle swarm optimizatio algorithm, ad a quatitative evaluatio method usig feature aalysis of ECT sigals. Recostructio results from simulated ECT sigals due to coductive cracks reveal that the proposed strategy is effective for the sizig of SCC profiles. Ackowledgemet This work is supported i part by the Natioal Magetic Cofiemet Fusio Program of Chia (2013GB113005), Natural Sciece Foudatio of Chia ( ad ) ad the Scietific Research Scheme of Educatio Departmet of Shaaxi Provice, Chia (15JK1677). Refereces [1] K. Miya: ''Recet advacemet of electromagetic odestructive ispectio techology i Japa'', IEEE trasactios o magetics, Vol. 38, No. 2, pp (2002). [2] Z. Che, N. Yusa, K. Miya: ''Some advaces i umerical aalysis techiques for quatitative electromagetic odestructive evaluatio'', Nodestructive Testig & Evaluatio, Vol. 24, No. 1, pp (2009). [3] F. Kojima, N. Kubota, K. Kobayashi, T. Takagi: ''Shape recovery of atural crack usig evolutioary programmig related to eddy curret testig'', It J Appl Electromag Mech., Vol. 15, No. 1, pp (2001). [4] T. Takagi, H. Huag, H. Fukutomi, J. Tai: ''Numerical evaluatio of correlatio betwee crack size ad eddy curret testig usig a very fast simulator'', IEEE Tras. Mag., Vol. 34, No. 5, pp (1998). [5] N. Yusa, H. Hashizume: '' Evaluatio of stress corrosio crackig as a fuctio of its resistace to eddy currets'', Nuclear Egieerig & Desig, Vol. 239, No. 12, pp (2009). [6] N. Yusa, H. Huag, K. Miya: ''Numerical evaluatio of the ill-posedess of eddy curret problems to size real cracks'', NDT & E It., Vol. 40, No. 3, pp (2007). [7] S. Norto, J. Bowler: ''Theory of eddy curret iversio'', Joural of Applied Physics, Vol. 73, No.2, pp (1993). [8] BA Auld, JC Moulder: ''Review of Advaces i Quatitative Eddy Curret Nodestructive Evaluatio'', Joural of Nodestructive Evaluatio, Vol. 18, No. 1, pp (1999). [9] N. Yusa, Z. Che, K. Miya, T. Uchimoto, T. Takagi: ''Large-scale parallel computatio for the recostructio of atural stress corrosio cracks from eddy curret testig sigals'', NDT & E It., Vol. 36, No.7, pp (2003). [10] Y. Li, L. Udpa, S. Udpa: ''Three-dimesioal defect recostructio from eddy-curret sigal by usig a geetic local search algorithm'', IEEE Tras. Mag., Vol. 40, No. 2, pp (2004). [11] Z. Che, M. Rebica, N. Yusa, K. Miya: ''Fast simulatio of ECT sigal due to a coductive crack of arbitrary width'', IEEE Trasactios o Magetics, Vol. 42, No.4, pp (2006). [12] N. Yusa, K. Miya: ''Discussio o the equivalet coductivity ad resistace of stress corrosio cracks i eddy curret simulatios'', NDT & E It., Vol. 42, No. 1, pp (2009). [13] T. Huag, D. Zhag, Z. Che: ''A study o the distributio of coductivity of a stress corrosio crack based o ECT'', J Measuremet Tech., Vol. 24, No. 1, pp (2010). [14] H. Huag, N. Yusa, K. Miya, H. Hashizume, T. Sera, S. Hirao: ''Electromagetic modelig of Stress Corrosio Cracks i Icoel welds'', E-Joural of Advaced Maiteace, Vol. 2, pp (2010/2011). [15] Z. Che, L. Jaousek, N. Yusa, K. Miya: ''A odestructive strategy for the distictio of atural fatigue ad stress corrosio cracks based o sigals from eddy curret testig'', ASME J Pressure Vessel Techology, Vol. 219, No. 4, pp (2007). [16] L. Wag, Z. Che: ''A multi-frequecy strategy for recostructio of deep stress corrosio cracks from ECT sigals of multiple liftoffs'', It J Appl Electromag Mech., Vol. 33, No. 3, pp (2010). [17] L. Wag, Z. Che: ''Recostructio of stress corrosio cracks usig high-dimesio hybrid optimizatio algorithm from eddy curret sigals'', It J Appl Electromag Mech.,Vol.52, No. 4, pp (2016). [18] Z. Che, K. Miya: ''ECT iversio usig kowledge based forward solver'', J Nodestruct Eval., Vol. 17, No. 3, pp (1998). 83