Elements of non-destructive damage monitoring by electrostatic potential method

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Elements of non-destructive damage monitoring by electrostatic Elements of non-destructive damage monitoring by electrostatic potential method potential method XV Portuguese Conference on Fracture, PCF 2016, 10-12 February 2016, Paço de Arcos, Portugal a

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Kiiko V.M. , Khvostunkov a b Thermo-mechanical modeling of a K.A. highb,, Odzhaev pressureR.K. turbine blade of an Kiiko V.M. , Khvostunkov K.A. Odzhaev R.K. Institute of Solid State Physics of RAS,, Chernogolovka Moscow distr., 142432 Russia airplane gas turbine engine Institute of Solid State Physics RAS,, Chernogolovka Moscow distr., 142432 Russia Lomonosov MoscowofState University, Moscow, 119992 Russia a a

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Lomonosov Moscow State University, Moscow, 119992 Russia

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P. Brandãoa, V. Infanteb, A.M. Deusc*

Abstract AbstractaDepartment of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal We establish a correlation between the magnitude of a propagating crack in current-carrying flat samples and the change in the b IDMEC, Department Mechanical Engineering, Superior Técnico, Universidade de Lisboa, Av.samples Rovisco Pais, 1, We establish a correlation between the magnitude of a propagating crack in current current-carrying flat andexperimental the1049-001 change Lisboa, indata the electric potential field of over the surface of the Instituto sample when an electric passes through it. The Portugal electric potential field over the surface of the sample when an electric current passes through it. The experimental data correspond to an analytic solution obtained using a conformal map in the two-dimensional formulation. This work can be related c CeFEMA, Department of Mechanical Engineering, Instituto Superior Técnico, Universidade de Lisboa, Av. Rovisco Pais, 1, 1049-001 Lisboa, correspond to an analytic solution obtained usinginto a conformal in the two-dimensional This work canmechanical be related to the area of converting mechanical quantities electricalmap quantities, which simplifiesformulation. the process of recording Portugal to the areaand of provides converting mechanicalform quantities into electrical quantities, which simplifies the process recording mechanical processes a convenient for controlling and managing them. This work is aimed at theof automatic control of the processes provides a convenient form for controlling and managing them. This work is aimed at the automatic control of the process ofand the destruction of conductive materials. process of the destruction of conductive materials. Abstract © 2018 The Authors. Published by Elsevier B.V. © 2018 The Authors. Published by Elsevier B.V. © During 2018 The under Authors. Published by B.V. Peer-review responsibility of Elsevier the ECF22 organizers. modern aircraft engine components are subjected to increasingly demanding operating conditions, Peer-reviewtheir underoperation, responsibility of the ECF22 organizers. Peer-review responsibility of the(HPT) ECF22 organizers. especially under the high pressure turbine blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one ofsample, whichelectric is creep. A model using theline, finite element (FEM) Keywords: conductive potential, equipotential crack length,method conformal map was developed, in order to be able to predict Keywords: conductive sample, electricblades. potential, equipotential line, crack length, mapaircraft, provided by a commercial aviation the creep behaviour of HPT Flight data records (FDR) forconformal a specific company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were 1. needed Introduction The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D 1. obtained. Introduction rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The We study the dependence on theofcrack length of the electrical potential atdistribution over of thethesurface of a thin, such flat a overall expected behaviour in terms displacement was observed, in particular the trailing edge blade. Therefore We study the dependence on the crack length of the electrical potential distribution over the surface of a thin, flat current-conducting specimen along which an electric current passes. The geometry of the potential φ field model can be useful in the goal of predicting turbine blade life, given a set of FDR data.

current-conducting specimen along which of an the electric The geometry of the potential φ field distribution is independent of the magnitude currentcurrent throughpasses. the specimen, of the specimen conductivity, and distribution is independent of the magnitude of the current through the specimen, of the specimen conductivity, 2016 The Authors. Published Elsevierthese B.V. quantities do not appear in the Laplace equation Δφ=0 describing and of©the temperature. Hence, for by example, the of the temperature. Hence, for example, these Committee quantities do appear in the Laplace equation Δφ=0 the Peer-review underthe responsibility of the boundary Scientific of PCF 2016. distribution with corresponding conditions. Ifnotthe sample contains a crack, then the describing picture of the distribution with the corresponding boundary conditions. If the sample contains a crack, then the picture of the distribution of equipotential lines connected with that crack changes as the crack length changes. Registering the Keywords: High Pressure Turbine lines Blade;connected Creep; Finite with Element Method; 3Dchanges Model; Simulation. distribution of establishing equipotential that crack as the length changes. Registering the change allows a correspondence between the crack length and the crack position of the equipotential lines. We change allows establishing a correspondence between the crack length and the position of the equipotential lines. We determine the potential distribution by calculations based on using a conformal map and compare the calculation determine potential distribution calculations basedofonestablishing using a conformal map and compare thebetween calculation results withtheexperimental data. Thisby yields a possibility a one-to-one correspondence the results with experimental data. This yields a possibility of establishing a one-to-one correspondence between the geometry of the developing crack and the geometry of the electric potential distribution and hence automatic control geometry of the developing crack and the geometry of the electric potential distribution and hence automatic control of experiments on crack propagation in specimen materials and also of real construction in the future. of experiments on crack propagation in specimen materials and also of real construction in the future. 2452-3216 © 2018 The Authors. Published by Elsevier B.V. 2452-3216 © 2018 Authors. Published Elsevier B.V. Peer-review underThe responsibility of theby ECF22 organizers. * Corresponding Tel.: +351of218419991. Peer-review underauthor. responsibility the ECF22 organizers. E-mail address: [email protected] 2452-3216 © 2016 The Authors. Published by Elsevier B.V.

Peer-review under responsibility of the Scientific Committee of PCF 2016. 2452-3216  2018 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the ECF22 organizers. 10.1016/j.prostr.2018.12.297

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2. Experimental setup We set up the problem for determining the equipotential line geometry in a sample without a crack and a sample with a lateral crack. The specimen is simulated with electrically conductive paper. We apply an electric voltage to the flat sample along the ends, and an electric current passes through it (Fig. 1). We establish a picture of the equipotential line distribution as follows. Two wires with probes are connected to a voltmeter. One probe is fixed at the desired point (e.g., at the edge of the sample), and the other probe is moved along the surface of the sample, starting from the stationary probe such that the voltage between the probes is zero. The trajectory of the moving probe gives an equipotential line (Fig.1). A crack is modeled by a cut in the paper. We show the results of two variants of a crack-cut in Figs. 1b and 1c.

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Fig. 1. Equipotential lines in a specimen when passing an electric current through the specimen vertically: (a) without a crack, (b) with a side crack, and (c) with a central crack.

We consider a flat electrically conductive sample containing a side crack (Fig. 2a). In the vicinity of the crack, we select a point M where the fixed probe is placed. Moving the other probe along the edge of the sample, we find a contact point N where the voltage between the points M and N is zero as indicated by the voltmeter attached to the probes. The points M and N are then on one equipotential line.

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Fig. 2. (a) Schematic of converting the growth Δl=l2- l1 of the crack length l in a shift Δx of the movable contact and (b) a technical realization. V is a voltmeter, I is an electric current, A and B are electrical contacts.



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Increasing the crack length by Δl leads to a change in the potential field geometry and a shift in the equipotential lines. Consequently, a different equipotential line passes through the point M, and there is a new point N´ on the edge such that the voltage between M and N´ is zero. We find the new position N´ by shifting the movable probe from the contact point N through a distance Δx along the edge. We thus establish a unique dependence of the contact shift Δx on the crack growth Δl. Because the picture of the potential distribution is symmetric with respect to the central longitudinal sample axis in the case of a central crack, this dependence holds for both side and central cracks. This scheme was realized in an automatic device for measuring the growth of fatigue cracks [1, 2], and we show one variant of the corresponding construction in Fig. 2b. A similar scheme was also implemented in other devices [3–6]. 3. Calculations and measurements We define the distribution of electrical current and equipotential lines in a two-dimensional problem setup. The studied field corresponds to a current field in an infinitely long strip with a cut for which the field is also uniform across the strip at a sufficiently large distance from the cut. We use the method of conformal maps to calculate the field, d is a width of specimen, l is a length of crack [7]. The function 𝑊𝑊 =

𝜋𝜋𝜋𝜋 𝜋𝜋𝜋𝜋 𝜋𝜋𝜋𝜋 2𝑉𝑉0 𝑎𝑎𝑎𝑎𝑎𝑎ℎ {cos √𝑡𝑡ℎ2 + 𝑡𝑡𝑡𝑡2 } 𝜋𝜋 2𝑑𝑑 2𝑑𝑑 2𝑑𝑑

maps the domain occupied by the strip with a cut in the plane of the complex variable z = x +iy (Fig. 2b) to a strip without a cut in the plane of W= U+iV (Fig. 3).

Fig. 3. Range of the conformal map.

The correspondence of points on the boundaries of these regions is noted in Fig. 3. The lines U = const in the plane of W are lines of equal potential, and the lines V = const are lines of current. Consequently, the analytic function W is the complex potential field of an infinite strip with a cut. In this formula, the quantity V0 is equal to the value V2 of the current function on the upper boundary of the strip at y = d; the lower boundary of the strip in the plane of z corresponds to the axis of the abscissa in the plane of W, i.e., V = 0. To draw the lines of the current and of equal potential, we find an expression for z:

𝑧𝑧 =

2𝑑𝑑 artanh 𝜋𝜋

2

√(th 𝜋𝜋𝜋𝜋 ) −(sin 𝜋𝜋𝜋𝜋 ) 2𝑉𝑉0

𝜋𝜋𝜋𝜋 2𝑑𝑑

cos

2𝑑𝑑

2

(1)

For a sample of width d = 100 mm with a cut length l = 50 mm, a plot of the current lines has the form shown in Fig. 4a and the position of equipotential lines shown in Fig. 4b. As the crack length grows, the picture of the equipotential line distribution changes (Fig. 5). From Eq. (1), we obtain the solution

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y

y

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100

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80

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60

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20

0

a

20

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x

50

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Fig. 4. Forms of (a) the current lines and (b) the distribution of equipotential lines.

Fig. 5. Equipotential lines passing through the point (1 mm, 10 mm) for different crack lengths l (shown in the plot): points denote measurement results, and solid lines denote analytic solution results.

∆𝑙𝑙 = 𝑙𝑙2 − 𝑙𝑙1 =

(sh2 𝑥𝑥2 − sh2 𝑥𝑥0 sin2 𝑦𝑦0 − ch2 𝑥𝑥0 cos 2 𝑦𝑦0 ) sh2 𝑥𝑥2 2𝑑𝑑 (arccos √ sh2 𝑥𝑥0 sin2 𝑦𝑦0 − sh2 𝑥𝑥2 𝜋𝜋 − arccos √

(sh2 𝑥𝑥1 − sh2 𝑥𝑥0 sin2 𝑦𝑦0 − ch2 𝑥𝑥0 cos 2 𝑦𝑦0 ) sh2 𝑥𝑥1 ) sh2 𝑥𝑥0 sin2 𝑦𝑦0 − sh2 𝑥𝑥1

We take a specimen of width d=100 mm and fix a contact at the point (1 mm, 10 mm) with coordinate dimensions in mm. Each position of the movable contact located on the upper edge of the sample on an equipotential line passing through the fixed point M then corresponds to a definite crack length. This dependence is shown in Fig. 6. For the given sample dimensions, coordinates of the fixed point M, and initial crack length 10 mm, we obtain the dependence of the shift x of the movable contact on the crack length l (see Fig. 6). We compared the obtained theoretical results with experimental results obtained with a model conducting specimen of width 100 mm, length 600 mm, and thickness 0.25 mm prepared from thermally expanded graphite foil. The crack was modeled by a side cute perpendicular to the edge of the sample. The electrical scheme was arranged



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similarly to that shown in Fig. 1a. The laboratory instruments used were a stabilized TEC-18 as a constant current source and a digital multimeter Shch4300 as a voltmeter. Measurements were obtained as follows. An initial cut of 10 mm was made in the sample. An electrical current (2 amperes) was passed through the sample. An immobile voltmeter contact (“fixed point”) was placed at the end of the cut, and a movable voltmeter contact was placed at a series of points (“movable points”) such that the voltage measured by the instrument was zero. As a result, the movable point represented the position of the equipotential line passing through the fixed point. The cut (crack) was then lengthened, and the new position of the equipotential line was determined. The results are shown in Fig. 5. In addition, the dependence on the cut length l of the shift x of the exit point of the equipotential line at the edge opposite to the beginning of the cut was established (shown in Fig. 6).

Fig. 6. Dependence of the shift x of the movable contact N on the crack length l (see Fig. 2a): “points” show the results of three series of measurements, and the solid kine shows the analytic calculation results.

4. Conclusions 1. The calculated and measured fields of equipotential lines on the surface of flat specimens containing a crack practically coincide. It is important that the calculations are done based on the analytic dependence obtained in this paper. 2. The calculated dependence on the crack length of the shift of the point where an equipotential line passing through a given point intersects a line defined along the edge of the sample practically coincides with the measurement results. 3. The obtained results lead to the possibility of automatically tracking the length of a developing conductive crack and controlling the destruction process. Acknowledgements This research was supported by the Russian Foundation for Basic Research (Project: 17-08-01739 a). References Markochev V. M, Bobrinsky A. P, Kiiko V. M., 1979. New method for measuring the length of conductive samples. Laboratory, vol. 45,№ 9, pp. 861-862. Markachev V. M, Bobrinsky A. P, Kiyko V. M., 1978. Method for measuring the length of developing cracks in conductive samples and device for its implementation. Patent: 561441. Sosnin F. R., Podmasteryev K. V., 2004. Non-destructive testing: Handbook in 7 volumes. Under the editorship of Klyuev V. V.. Vol.5. №. 2: electrical control M.: mechanical engineering, pp 677. Shkatov P. N., Chernenko P.I., 2013. Measurement of depth and angle of surface cracks by electro-potential method. Vestnik MGUPI - №44 Litvinov L. N., Tsypushtanov F. G., Parks V. A., Bakumov V. N., 1988. Electro-potential crack depth meter. Patent: 1408205 Osiecki D. A., Tsvelev V. V., 1996. Method of measuring crack propagation in conductive samples. Patent: 1834491 Lavrentyev M. A., Shabat B. V., 1987. Methods of the theory of functions of complex variable. - M.: Nauka. – pp. 736.