Electromagnetic Property Evaluation on HAZ and Base Metal of Modified 9Cr-1Mo steel by Eddy Current Method
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1. Introduction
High chromium ferritic steel (Modified 9Cr-1 Mo steel) is a high strength structural steel widely used in power plant. In recent years, some studies for this steel have pointed out that Type IV damage, which is happened in the softened heataffected zone (HAZ) of weldment and caused by different creep strength between weld metal, HAZ and base metal, is one of mid-life failure [1][2][3][4]. In order to investigate material changes in HAZ and base metal in high temperature service environment to prevent Type IV cracking, evaluation of the electromagnetic properties such as conductivity and permeability by non-destructive testing method is considered as one of prospecting approaches to monitor the microstructure change.Eddy-current method is one of rapid, portable and feasible non-destructive testing to estimate conductivity and permeability, and can carry out a direct measurement of electromagnetic properties without calibration standards. In this paper, a pancake-coil impedance model is proposed, which is derived from partial differential equation. Comparing with well established theory by Dodd and Deeds [5], the present model is simplified, but can solve thePOC: Haiyan TIAN, Katahira 2-1-1, Aoba-ku, Sendai, 9808577, Institute of Fluid Science, Tohoku University, Tel: 022-217-5298, e-mail:tian@wert.ifs.tohoku.ac.jp““overflow““ problem that sometimes occurs in the numerical calculation using Dodd's formula. The ““overflow““ problem occurs in the case of ferritic materials because they have higher relative permeability than linear material so that the value of some variables in Dodd's formula exceeds the maximum floating-point number of a given precision (single or double). Consequently, a series of base and HAZ specimens in different heat treatment conditions are measured by impedance analyzer. Then, their conductivity and permeability are determined by searching for an impedance match with theoretical values. The evaluated conductivity and permeability of HAZ and base metal specimen shows it is possible to use eddy-current method to evaluate electromagnetic properties of Modified 9Cr-1Mo steel.2. Pancake-Coil Impedance ModelFor a pancake coil paralleling to a metal plate, as shown inImpedance coil?1Metal plateFig.1 Pancake impedance coil model.- 216 -Fig.1, a closed-form solution in Eqs. (1) and (2) can be derived from Maxwell equations considering both ferromagnetic and non-ferromagnetic conductors by solving the magnetic vector potential A in an electromagnetic field.jorulnap 2011, -1)?(r, ?r,)? ba11 (12,7).[2(12 ?)+a+'(2e-all-1))?2+(e-2ad2 +e-2ad; ? 2e-alyti). a?Budaa+s““-1Table 1. Parameters of pancake coilwell equations con conductors byFig.1, a closed-form solution in Eqs. (1) and (2) can be derived from Maxwell equations considering both ferromagnetic and non-ferromagnetic conductors by solving the magnetic vector potential A in an electromagnetic field.0.5 mm 1.0 mm0.1 mm2.1 mmInner radius Outer radius Lift-off Height of coil Number of turns Exciting frequency air-reactance DC resistanceZ=_jonun?(1, -1) (0, -,)2 551°(12,71).[2(12 ? 1)30089.661 kHzta '(2-a(1-6))?2+(e-2d2 +e-2002 ? 2e-allz+1)).a-Buda33.186 12 15.02.12-1R.0-2jonu,n? Lair = (1, - 1.)2(?. ? rj2 aslo(92,) [2(12 ? h)+a-' (2e**(1-6) ? 2)]da3. Impedance coil and experiment correctidZ pode = (1, -1) (0 - 1)2＝= jonu,n?-1°(r2,r)[2(1, -) +a+'(2e-allz-4)) - 2+(e-2al2 +e-2a1 ? 2e-all2-1))(6,2 - a?)+(Q? ? B,?)ezad -(B, - a)? + (a + B,)?e20;dHere,B. = a, /,, a, = (a? + joHoH0)““'2,and1(r2,r.) = a ? * roJ, (arola I(r2,r, ) = a ? sro J, (ar, )dr , .Me and y, are permeability of free space and relativepermeability of metal plate respectively. o is conductivity of metal plate, n is the number of turns in the pancake coil, J(x) is the first-order Bessel function of the first kind. Eq.(2) is the air-impedance without measuring a metal plate. The impedance formula in Eq.(3) was derived by Dodd and Deeds. Since experimental measurement indicated the nonlinear and hysteresis effects are fairly small for low currents, this formula can be used for ferrite material [5][6]. However, due to u, >>1 for ferritic material, the term of e2a;d in some cases is too large so as to exceed the maximum floating-point number to cause ““overflow““ error. If the first term in both numerator and denominator is neglected, Eq.(3) is equivalent to Eq.(1). This means the solution in Eq.(1) that is derived from partial differential equations is accordant with Dodd and Deeds theory.3. Impedance coil and experiment correctionAn air-cored probe is fabricated by winding a coil. Parameters of the coil are listed in Table 1. Ten tested specimens of Modified 9Cr-1Mo steel in different heat treatment conditions are listed in Table 2. Because of the nonideal coil behavior, two corrections have to be considered when processing the experiment data. First, in Eq. (1), the DC resistance of a coil (when w = 0) is zero. However, any practical coil has DC resistance R, shown in Table 1. Therefore the experimental resistance Rexp should be corrected to match the theoretical value R?a calculated by Eq.(1). The corrected resistance ReXP shown in Eq.(4) is thatmeasured resistance Rmed minus DC resistance R.Secondly, since the coil was wound in layers, it is not an absolute ideal pancake inductance coil. The self-reactance between the measured and theoretically calculated value by Eq.(2) are different. The error between them is 1.32%. This error can be solved after normalizing the reactance by dividing the self-reactance in both calculated and measureddata. In Eq.(5), wl, mea is measured air-reactance, xexp isnornormalized experimental reactance. In Eq.(6), z cal iscalculated air-reactance by Eq.(2), o?cal is imaginary part calculated by Eq.(1). X cal is normalized calculatedormreactance. At last, by seeking an approximate equal between theoretical and experimental impedance in Eqs.(7) and (8) with assumed conductivity and permeability, the evaluated217Table 2. Specimen list of Modified 9Cr-1 Mo steelHeat treatmentconditionBase materialSize (mm)HAZ Size (mm)N.A. (no heat treatment)33 X 15 X 5t25 X 15 X 5t500 °CX 600 hr A.C.33 X 15 X 6t25 X 15 X 50550 °C X 600 hr A.C.33 X 15X5t25 X 14 X 5t600 °C X 600 hr A.C.34X 15 X 5t25 X 13 X 4t650 °C X 600 hr A.C.33 X 15 X 6.5t15 X 14 X 5t600 °C X 600 hr A.C.34X15X5t25X 13 X 4tU BaseE HAZ650 °C X 600 hr A.C.33 X 15X6.5t 15X 14 X 5tconductivity and permeability is determined.Reactance (Ohm)Rexp = Rmea ? R.N.A.500 C550 C600 C650 Cx normes = jo?ma / jol, menFig.3 Measured reactance in different heat treatment conditions.Xpormal = jo[cal I ZaincalnormRcal = Rexp5. Evaluated results and discussion The evaluated conductivity and permeability are shown in Figs.4 and 5 respectively. In order to validate the evaluated results, a four-terminal conductivity measurement device andX norm.cal = X normexpnorm4. Experiment dataThe measurement device is Hewlett Packard 4294A impedance analyzer. A low exciting current 10 mA with frequency 89.661 kHz was given to the pancake impedance coil. The induced maximum magnetic field in specimens is about 70 Gauss. The measured resistance is shown as in Fig.2. The data needs to be processed by Eq.(4) to obtain corrected experimental resistance for comparing with theoretical values. The measured reactance is shown in Fig.3. The data also needs to be normalized by air-reactance using Eq. (5). Both of corrected resistance and normalized reactance are compared with theoretically calculated value using Eq. (1). When the best match between corrected experiment value and theoretically calculated value is found with an assumed conductivity and permeability, the evaluated conductivity and permeability are accepted.Basea HAZResistance (Ohm)N.A500 C5 50 C600 C650 CFig.2 Measured resistance in different heat treatment conditions.Fig.3 Measured reactance in different heat treatment conditions.5. Evaluated results and discussionThe evaluated conductivity and permeability are shown in Figs.4 and 5 respectively. In order to validate the evaluated results, a four-terminal conductivity measurement device and magnetic measurement device SQUID were applied to measure the same specimens. The evaluated conductivities agree with the four-terminal conductivity measurement device in the same quantity level. But this device did not provide enough accuracy digital to distinguish the difference among each specimen. SQUID results also show there exist the permeability difference between these specimens. All of information to some extent supports the evaluation by the presented impedance coil model.6. SummaryAn impedance coil model is presented to evaluate the conductivity and permeability of HAZ and base metal of Modified 9Cr-1 Mo steel in different heat treatment conditions. The evaluated results with the verification by conductivity and magnetic measurement devices indicate there is possibility to eddy-current method as a non218destructive testing approach to estimate the electromagnetic properties of high chromium ferric steel for predicting the microstructure change in Type IV damage investigation.AcknowledgementThis work was performed under the sponsorship of Ministry of Education, Culture, Sports, Science and Technology.2.25BaseHAZ2.2....2.15Conductivity (>106S/m)2.12.051.95N.A.500 C550 C600 C650 CFig.4 Evaluated conductivities of Modified 9Cr-1 Mo specimens in different heat treatment conditions.BaseHAZRelative permeabilityN.A.500C550 C600C650 CFig.5 Evaluated permeability of Modified 9Cr-1Mo specimens in different heat treatment conditions.References[1] Yukio, T., “Study on type-IV damage prevention in hightemperature welded structures of next-generation reactor plants, part II fatigue and creep-fatigue behavior of welded joints of modified 9Cr-1 Mo steel”, Proceeding ofPVP2006-ICPVT-11, July, 2006. [2] Takahashi, Y., Tabuchi M., “Study on Type-IV damageprevention in high temperature welded structures of next-generation reactor plants, part I fatigue and creepfatigue behavior of welded joints of modified 9Cr-1 Mo steel”, Proceeding of ASAEM pressure vessels and pipingdivision conference, 2006. [3] S.K.Albert, M.Matsui, T. Watanabe, H.Hongo, K.Kubo,and M.Tabuchi “Variation in the Type IV cracking behaviour of a high Cr steel weld with post weld heat treatment”, International Journal of Pressure Vessels andPiping 80, 2003, pp.405-413. [4] Lundin C.D., Liv P. and Cui Y., “A Literature review onCharacteristics of High Temperature Ferritic Cr-Mo Steelsand weldments”, WRC Bulletin, No.454, 2000, pp.1-36. [5] Dodd C.V. and Deed W.E., “Integral Solutions to someEddy Current Probleens”, International Journal ofNondestructive Testing, Vol.1, 1969, pp. 29-90. [6] Jack Blitz, Electrical and magnetic methods ofnondestructive testing, IOP Press, 1991, pp.89-116.219“ “ Electromagnetic Property Evaluation on HAZ and Base Metal of Modified 9Cr-1Mo steel by Eddy Current Method“ “Haiyan TIAN,Tetsuya UCHIMOTO,Toshiyuki TAKAGI,Yukio TAKAHASHI
High chromium ferritic steel (Modified 9Cr-1 Mo steel) is a high strength structural steel widely used in power plant. In recent years, some studies for this steel have pointed out that Type IV damage, which is happened in the softened heataffected zone (HAZ) of weldment and caused by different creep strength between weld metal, HAZ and base metal, is one of mid-life failure [1][2][3][4]. In order to investigate material changes in HAZ and base metal in high temperature service environment to prevent Type IV cracking, evaluation of the electromagnetic properties such as conductivity and permeability by non-destructive testing method is considered as one of prospecting approaches to monitor the microstructure change.Eddy-current method is one of rapid, portable and feasible non-destructive testing to estimate conductivity and permeability, and can carry out a direct measurement of electromagnetic properties without calibration standards. In this paper, a pancake-coil impedance model is proposed, which is derived from partial differential equation. Comparing with well established theory by Dodd and Deeds [5], the present model is simplified, but can solve thePOC: Haiyan TIAN, Katahira 2-1-1, Aoba-ku, Sendai, 9808577, Institute of Fluid Science, Tohoku University, Tel: 022-217-5298, e-mail:tian@wert.ifs.tohoku.ac.jp““overflow““ problem that sometimes occurs in the numerical calculation using Dodd's formula. The ““overflow““ problem occurs in the case of ferritic materials because they have higher relative permeability than linear material so that the value of some variables in Dodd's formula exceeds the maximum floating-point number of a given precision (single or double). Consequently, a series of base and HAZ specimens in different heat treatment conditions are measured by impedance analyzer. Then, their conductivity and permeability are determined by searching for an impedance match with theoretical values. The evaluated conductivity and permeability of HAZ and base metal specimen shows it is possible to use eddy-current method to evaluate electromagnetic properties of Modified 9Cr-1Mo steel.2. Pancake-Coil Impedance ModelFor a pancake coil paralleling to a metal plate, as shown inImpedance coil?1Metal plateFig.1 Pancake impedance coil model.- 216 -Fig.1, a closed-form solution in Eqs. (1) and (2) can be derived from Maxwell equations considering both ferromagnetic and non-ferromagnetic conductors by solving the magnetic vector potential A in an electromagnetic field.jorulnap 2011, -1)?(r, ?r,)? ba11 (12,7).[2(12 ?)+a+'(2e-all-1))?2+(e-2ad2 +e-2ad; ? 2e-alyti). a?Budaa+s““-1Table 1. Parameters of pancake coilwell equations con conductors byFig.1, a closed-form solution in Eqs. (1) and (2) can be derived from Maxwell equations considering both ferromagnetic and non-ferromagnetic conductors by solving the magnetic vector potential A in an electromagnetic field.0.5 mm 1.0 mm0.1 mm2.1 mmInner radius Outer radius Lift-off Height of coil Number of turns Exciting frequency air-reactance DC resistanceZ=_jonun?(1, -1) (0, -,)2 551°(12,71).[2(12 ? 1)30089.661 kHzta '(2-a(1-6))?2+(e-2d2 +e-2002 ? 2e-allz+1)).a-Buda33.186 12 15.02.12-1R.0-2jonu,n? Lair = (1, - 1.)2(?. ? rj2 aslo(92,) [2(12 ? h)+a-' (2e**(1-6) ? 2)]da3. Impedance coil and experiment correctidZ pode = (1, -1) (0 - 1)2＝= jonu,n?-1°(r2,r)[2(1, -) +a+'(2e-allz-4)) - 2+(e-2al2 +e-2a1 ? 2e-all2-1))(6,2 - a?)+(Q? ? B,?)ezad -(B, - a)? + (a + B,)?e20;dHere,B. = a, /,, a, = (a? + joHoH0)““'2,and1(r2,r.) = a ? * roJ, (arola I(r2,r, ) = a ? sro J, (ar, )dr , .Me and y, are permeability of free space and relativepermeability of metal plate respectively. o is conductivity of metal plate, n is the number of turns in the pancake coil, J(x) is the first-order Bessel function of the first kind. Eq.(2) is the air-impedance without measuring a metal plate. The impedance formula in Eq.(3) was derived by Dodd and Deeds. Since experimental measurement indicated the nonlinear and hysteresis effects are fairly small for low currents, this formula can be used for ferrite material [5][6]. However, due to u, >>1 for ferritic material, the term of e2a;d in some cases is too large so as to exceed the maximum floating-point number to cause ““overflow““ error. If the first term in both numerator and denominator is neglected, Eq.(3) is equivalent to Eq.(1). This means the solution in Eq.(1) that is derived from partial differential equations is accordant with Dodd and Deeds theory.3. Impedance coil and experiment correctionAn air-cored probe is fabricated by winding a coil. Parameters of the coil are listed in Table 1. Ten tested specimens of Modified 9Cr-1Mo steel in different heat treatment conditions are listed in Table 2. Because of the nonideal coil behavior, two corrections have to be considered when processing the experiment data. First, in Eq. (1), the DC resistance of a coil (when w = 0) is zero. However, any practical coil has DC resistance R, shown in Table 1. Therefore the experimental resistance Rexp should be corrected to match the theoretical value R?a calculated by Eq.(1). The corrected resistance ReXP shown in Eq.(4) is thatmeasured resistance Rmed minus DC resistance R.Secondly, since the coil was wound in layers, it is not an absolute ideal pancake inductance coil. The self-reactance between the measured and theoretically calculated value by Eq.(2) are different. The error between them is 1.32%. This error can be solved after normalizing the reactance by dividing the self-reactance in both calculated and measureddata. In Eq.(5), wl, mea is measured air-reactance, xexp isnornormalized experimental reactance. In Eq.(6), z cal iscalculated air-reactance by Eq.(2), o?cal is imaginary part calculated by Eq.(1). X cal is normalized calculatedormreactance. At last, by seeking an approximate equal between theoretical and experimental impedance in Eqs.(7) and (8) with assumed conductivity and permeability, the evaluated217Table 2. Specimen list of Modified 9Cr-1 Mo steelHeat treatmentconditionBase materialSize (mm)HAZ Size (mm)N.A. (no heat treatment)33 X 15 X 5t25 X 15 X 5t500 °CX 600 hr A.C.33 X 15 X 6t25 X 15 X 50550 °C X 600 hr A.C.33 X 15X5t25 X 14 X 5t600 °C X 600 hr A.C.34X 15 X 5t25 X 13 X 4t650 °C X 600 hr A.C.33 X 15 X 6.5t15 X 14 X 5t600 °C X 600 hr A.C.34X15X5t25X 13 X 4tU BaseE HAZ650 °C X 600 hr A.C.33 X 15X6.5t 15X 14 X 5tconductivity and permeability is determined.Reactance (Ohm)Rexp = Rmea ? R.N.A.500 C550 C600 C650 Cx normes = jo?ma / jol, menFig.3 Measured reactance in different heat treatment conditions.Xpormal = jo[cal I ZaincalnormRcal = Rexp5. Evaluated results and discussion The evaluated conductivity and permeability are shown in Figs.4 and 5 respectively. In order to validate the evaluated results, a four-terminal conductivity measurement device andX norm.cal = X normexpnorm4. Experiment dataThe measurement device is Hewlett Packard 4294A impedance analyzer. A low exciting current 10 mA with frequency 89.661 kHz was given to the pancake impedance coil. The induced maximum magnetic field in specimens is about 70 Gauss. The measured resistance is shown as in Fig.2. The data needs to be processed by Eq.(4) to obtain corrected experimental resistance for comparing with theoretical values. The measured reactance is shown in Fig.3. The data also needs to be normalized by air-reactance using Eq. (5). Both of corrected resistance and normalized reactance are compared with theoretically calculated value using Eq. (1). When the best match between corrected experiment value and theoretically calculated value is found with an assumed conductivity and permeability, the evaluated conductivity and permeability are accepted.Basea HAZResistance (Ohm)N.A500 C5 50 C600 C650 CFig.2 Measured resistance in different heat treatment conditions.Fig.3 Measured reactance in different heat treatment conditions.5. Evaluated results and discussionThe evaluated conductivity and permeability are shown in Figs.4 and 5 respectively. In order to validate the evaluated results, a four-terminal conductivity measurement device and magnetic measurement device SQUID were applied to measure the same specimens. The evaluated conductivities agree with the four-terminal conductivity measurement device in the same quantity level. But this device did not provide enough accuracy digital to distinguish the difference among each specimen. SQUID results also show there exist the permeability difference between these specimens. All of information to some extent supports the evaluation by the presented impedance coil model.6. SummaryAn impedance coil model is presented to evaluate the conductivity and permeability of HAZ and base metal of Modified 9Cr-1 Mo steel in different heat treatment conditions. The evaluated results with the verification by conductivity and magnetic measurement devices indicate there is possibility to eddy-current method as a non218destructive testing approach to estimate the electromagnetic properties of high chromium ferric steel for predicting the microstructure change in Type IV damage investigation.AcknowledgementThis work was performed under the sponsorship of Ministry of Education, Culture, Sports, Science and Technology.2.25BaseHAZ2.2....2.15Conductivity (>106S/m)2.12.051.95N.A.500 C550 C600 C650 CFig.4 Evaluated conductivities of Modified 9Cr-1 Mo specimens in different heat treatment conditions.BaseHAZRelative permeabilityN.A.500C550 C600C650 CFig.5 Evaluated permeability of Modified 9Cr-1Mo specimens in different heat treatment conditions.References[1] Yukio, T., “Study on type-IV damage prevention in hightemperature welded structures of next-generation reactor plants, part II fatigue and creep-fatigue behavior of welded joints of modified 9Cr-1 Mo steel”, Proceeding ofPVP2006-ICPVT-11, July, 2006. [2] Takahashi, Y., Tabuchi M., “Study on Type-IV damageprevention in high temperature welded structures of next-generation reactor plants, part I fatigue and creepfatigue behavior of welded joints of modified 9Cr-1 Mo steel”, Proceeding of ASAEM pressure vessels and pipingdivision conference, 2006. [3] S.K.Albert, M.Matsui, T. Watanabe, H.Hongo, K.Kubo,and M.Tabuchi “Variation in the Type IV cracking behaviour of a high Cr steel weld with post weld heat treatment”, International Journal of Pressure Vessels andPiping 80, 2003, pp.405-413. [4] Lundin C.D., Liv P. and Cui Y., “A Literature review onCharacteristics of High Temperature Ferritic Cr-Mo Steelsand weldments”, WRC Bulletin, No.454, 2000, pp.1-36. [5] Dodd C.V. and Deed W.E., “Integral Solutions to someEddy Current Probleens”, International Journal ofNondestructive Testing, Vol.1, 1969, pp. 29-90. [6] Jack Blitz, Electrical and magnetic methods ofnondestructive testing, IOP Press, 1991, pp.89-116.219“ “ Electromagnetic Property Evaluation on HAZ and Base Metal of Modified 9Cr-1Mo steel by Eddy Current Method“ “Haiyan TIAN,Tetsuya UCHIMOTO,Toshiyuki TAKAGI,Yukio TAKAHASHI