PHYSICAL MODEL OF ELECTROMAGNETIC EMISSION IN SOLIDS

Transcription

1 DGZfP-Poceedings BB 9-CD Poste 24 EWGAE 24 PHYSICAL MODEL OF ELECTROMAGNETIC EMISSION IN SOLIDS P. KOKTAVY, Bno Univesity of Technology, Bno, Czech Republic J. SIKULA, Bno Univesity of Technology, Bno, Czech Republic Abstact Cacks ceation in solids can be accompanied by electomagnetic emission (EME). On the faces of new ceated cack electic chages constitute electic dipole system and due to cack walls vibation an EME signal is detected with fequency fom 1 to 1 MHz coesponding to cack length.1 to 1 mm. The second souce of EME signal is late activated due to whole sample mechanical vibations with a fequency given by sample bounday conditions, which ae in the ange 5 to 5 khz. KEYWORDS: non-destuctive testing, electomagnetic emission, acoustic emission, cacks ceation 1. INTRODUCTION Electomagnetic signals can be obseved when solids, especially non-metallic mateials, ae mechanically stessed. Mico- and maco-cacking pocesses ae often accompanied by electomagnetic emission (EME). This phenomenon is apat fom NDT also studied in geophysics as a eathquake pecuso [1] [3]. The oigin of EME fom factued mateials is still not well undestood. Seveal mechanisms wee suggested [4] - [9], based on sepaation of electic chages at cack fomation, dislocation movement o piezoelectic effect. It was obseved [1], that chages moved simultaneously with the cack tip motion and then EME was excited by a dipole, consisting of the chages in the two cack tips and of the length equal to entie length of the cack. Acceleation of the cack tips duing popagation inceased the length of the dipole am and consequently gave ise to EME. Laboatoy expeiments, caied out on ock stuctues have poved that the failue pocess is moe complicated. Two type of EME signals wee obseved: (i) coesponding bittle failue, (ii) shea failue o compessional displacement. Fom ou pevious expeiments follows that electomagnetic emission signal pecedes AE signal. EME signal has highe damping coefficient and lowe elaxation constant than AE one. Signal of EME senso depends on cack dimension and fo the time inteval less than 2 µs fequency of EME signal is given by bounday condition of cack eigen functions. AE signal is coelated with EME signal, but only with component, fo which wave velocity is pependicula to cack face aea. Sample electical conductivity and mechanical damping of cack wall vibations detemine EME signal damping constant in the fist peiod afte cack ceation. Electical conductivity is esponsible fo electic chage equilibation and this time when cack faces ae chaged is given by the low fequency EME signal. When cack faces ae dischaged, EME signal disappea, wheeas AE signal is still measuable. EME signal depends on cack face 899

2 DGZfP-Poceedings BB 9-CD Poste 24 EWGAE 24 oientation with espect to EME senso. When the cack face is paallel to EME senso, the signal has maximum value. 2. EXPERIMENTAL A standad expeiment set-up was used which allowed loading the samples up to 1 kn, to ecod the total defomation and the time evolution of the load. Samples of ganite of size cm 3 wee povided with conducting sheets placed symmetically, thus making up a plate capacito whose dielectic is the mateial unde test. The measuing set-up diagam was descibed in [3]. To eliminate intefeence aising fom the ambience, the sample and the peamplifie wee shielded electically and magnetically. Two types of EME signals can be obseved as ae shown in Fig.1 and τ = 9.6 µs f = 1 MHz u / V t / µ s Fig.1. Time dependence of electomagnetic emission signal fo bittle sample U / mv t / µs Fig. 2. EME signal time dependence with constant aveage value 9

3 DGZfP-Poceedings BB 9-CD Poste 24 EWGAE MODEL OF AN EME SIGNAL CREATION The electic chages +q and -q appea at the faces of the cack when the cack is poduced. Thei motion with the velocity v in the electic field E changes the voltage u on the paallel plate capacito and the electic cuent i flows ove the load esisto R (see Fig. 3). Ou model is based on the enegy consevation law N E qkvk k = 1 2 dt = Ri dt + Cudu N whee E qkvk dt is the electical enegy ceated by chaged cack walls motion, k = 1 Ri 2 dt is the electical enegy dissipated on the load esistance, Cudu is the electostatic enegy of the capacito senso and N is a numbe of electic chages between the plates of the capacito C. x (1) n -q +q l /2 α l /2 y p d E y R u(t) Fig. 3. A model fo a cack Then the diffeential equation fo the voltage u(t) is in the fom N du u 1 + = E q v 1 k k (2) dt τ C k = 1 E 1 whee E1 = = fo the paallel plate capacito and τ = RC is the time elaxation u d constant. The cack walls vibate and the cack width is a function of time. The time dependent displacement of the cack faces esults in an AC electomagnetic signal component whose fequency coesponds to that of mechanical vibations of the specimen. The chages +q and -q ae at the equilibium distance l and thei displacement y(t) is given by y = y e -δt sin ωt (3) whee δ and ω ae damped hamonic motion constants. The electical conductivity is dischaging the elementay capacito epesenting cack walls. We will suppose the electic chage exhibits exponential time dependence in the fom 91

4 DGZfP-Poceedings BB 9-CD Poste 24 EWGAE 24 q = q e β t. (4) The dipole moment p (t) is given by βt δt p = q e ( l + 2y e sinωt p (5) ) The velocity of the damped hamonic motion of chages on the cack walls is given by + δt v = v e sin( ωt + ϕ p (6) ) v δt = ve sin( ωt + ϕ)( p ) (7) whee v = yb, ω 2 2 tg ϕ =, b = ω + δ. δ Then the fom of the diffeential equation (2) is in the fom du u γt + = ge sin( ωt + ϕ) dt τ (8) 2qv cosα whee g =, γ = δ + β, ν is the velocity amplitude, d is the paallel plate Cd capacito thickness and α is the angle between the electic field intensity E and the electic chage velocity v. Its solution is in the fom t γt ge u( t) = u1( t) + u2 ( t) = U e τ sin( ωt + ϕ) (9) 2 2 ω + ω whee U is an integation constant and ω = γ 1/ τ is a cut off angula fequency. This electic voltage u(t) on the capacito C is given as a sum of two components. The fist component u 1 (t) (DC component) chaacteizes the dischaging of the capacito C ove the load esisto R. It will be dominant if cack walls ae collinea to the plates of the measued capacito C. The second component u 2 (t) (AC component) chaacteizes the damped hamonic motion of chages on the cack walls. 4. DISCUSSION Expeimentally we have obseved two diffeent type of signals like damped hamonic motion with: (i) constant aveage value and (ii) exponentially time dependent tansient value as is shown in Fig. 4. Electical signal of EME is given by supeposition of the DC tansient component and AC high fequency voltage. Time constant fo DC voltage elaxation is given by amplifie input RC cicuit: fo R = 1 MΩ and C = 2 pf we have time constant τ = 2 µs, which is in good ageement with expeiment. 92

5 DGZfP-Poceedings BB 9-CD Poste 24 EWGAE 24.2 U / mv V = V exp(- t/τ) V =.15 mv τ = 2 µs t / µs Fig. 4. Electic voltage time dependence 4.1. The EME signal model.25.2 U / mv t / µs Fig. 5. Electic voltage time dependence We will give a list of paametes coesponding to ou model in Fig. 5: V =.15 mv, R = 1 MΩ, C = 2 pf, q = C, u = m, v = 1 2 ms -1, α =, d = 1-2 m, γ = s -1, ω = s -1, ϕ = π. Then ω is much less than angula fequency ω. In this case equation (9) can be witten as V ( t) = V e ge ω γt t / τ ϕ [ cos( ωt + )] (1) EME senso will detect AC component, which is popotional to g/ω. 93

6 DGZfP-Poceedings BB 9-CD Poste 24 EWGAE CONCLUSION Fom eq. (1) follow, that AC component of EME signal is popotional to cack face electic chage q, cack wall velocity amplitude and cack aea oientation with espect to EME senso aea. EME signal will be not detected, when cack aea is pependicula to EME senso plates. AC component of EME signal is invesely popotional to the distance between EME senso plates d. Thin samples ae moe suitable fo this expeiment. The last is dependence on capacity. EME senso will have high sensitivity fo low total capacity C, it is the senso capacity including peamplifie input capacity and montage capacity (coaxial cable). Acknowledgement This eseach has been suppoted by gants GA CR 25/3/71, GA CR 12/2/D73 and also as a pat of a eseach poject VZ MSM and VZ MSM REFERENCES (1) T. Yoshino: Low-Fequency Seismogenic Electomagnetic Emission as Pecusos to Eathquakes and Volcanic Euptions in Japan, Jounal of Scientific Exploation, Vol. 5, No. 1, pp , Pegamon Pess, 1991 (2) N. G. Chatiašvili: Vozmožnye mechanizmy elektomagnitnovo izlučenija pi azušenii kistallov i gonych pood ( in Russian). Geofizičeskij žunal, 1988, t. 1, s (3) J. Šikula, B. Koktavý, P. Vašina and T. Lokajíček, Cacks and quality testing by acoustic and electomagnetic emission, Poc. of the 23d Euopean Confeence on Acoustic Emission Testing, TUV Austia, Vienna 6-8, May, 1998, p (4) J. Šikula, B. Koktavý, P. Vašina and T. Lokajíček, Detection of Cack Position by AE and EME Effects in Solids Poc. of Acoustic Emission Conf. Bulde, USA, (5) Ogawa, K. Oike and T. Miua: Electomagnetic adiation fom ocks, J. Geophys. Res., 9, , (6) I. Yamada, K. Masuda, H. Mizutani: Electomagnetic and acoustic emission associated with ock factue, Phys. Eath. Planet Int., 57, , (7) J. Šikula, B. Koktavý, P. Vašina, Z. Webe, M. Kořenská a T. Lokajíček: Electomagnetic and Acoustic Emission fom Solids, Poc. of 22nd Euopean Confeence on Acoustic Emission Testing, Abedeen, UK, (8) T. Lokajíček and J. Šikula, Acoustic emission and electomagnetic effects in ocks, Pogess in Acoustic Emission VIII, 1996, pp (9) Y. Moi, K. Sauhashi and K. Mogi, Acoustic emission fom ock specimen unde cyclic loading, Pogess in Acoustic Emission VII, 1994, pp (1) Y. Moi, K. Sato, Y. Obata and K. Mogi, Acoustic emission and electic potential changes of ock samples unde cyclic loading, Pogess in Acoustic Emission IX,