Hall Coefficient Measurement for Residual Stress Assessment in Precipitation Hardened IN718 Nickel-base Superalloy
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1 Hall Coefficient Measurement for Residual Stress Assessment in Precipitation Hardened IN78 Nickel-base Superalloy Dheeraj Velicheti, Peter B. Nagy, and Waled T. Hassan 2 Department of Aerospace Engineering, University of Cincinnati, Cincinnati, Ohio Rolls-Royce Corporation, Indianapolis, Indiana 4624 This work was supported by the Federal Aviation Administration under Grant No. 5-G rd Review of Progress in Quantitative NDE Atlanta, Georgia July 9, 26
![Residual Stress [MPa] Cold Work (Plastic Strain)](/docs-images/84/89728991/images/2-0.jpg "[%] Surface-Enhancement Techniques Shot Peening")
2 Residual Stress [MPa] Cold Work (Plastic Strain) [%] Surface-Enhancement Techniques Shot Peening (SP) Laser Shock Peening (LSP) Low-Plasticity Burnishing (LPB) Ti-6Al-4V SP Almen 4A SP Almen 2A LSP LPB Depth [mm] Ti-6Al-4V SP Almen 4A SP Almen 2A LSP LPB Depth [mm]
3 Conductivity Change [%] Conductivity Change [%] Normalized Electro-elastic Coefficient Conductivity Change [%] Why Did We Thought Eddy Current Conductivity Spectroscopy Would Work in IN78? Yu and Nagy, J. Nondestr. Eval. 25, 7 (26).4.2 parallel normal Elastic Strain [%] Plastic Strain [%] Plastic Strain [%] A Nortec 8A Nortec 4A Nortec 2A Agilent 8A Agilent 4A Agilent 2A UniWest 8A UniWest 4A UniWest 2A Stanford 8A Stanford 4A Stanford Nortec 2S Agilent 4294A UniWest US-45 Stanford Research SR Frequency [MHz]
4 ΔAECC [%] AECC Spectra of Shot-Peened IN78 Specimens of Various Hardness Abu-Nabah et al., J. Nondestr. Eval. 29, 43 (2) HRC HRC HRC A 3-6A 5-6A 2-6A 4 4-6A 4 6-6A -4A 3 3-4A 3 5-4A 2-4A 4-4A 6-4A ΔAECC [%]. ΔAECC [%]. ΔAECC [%] Frequency [MHz]. ΔAECC [%]. -. Frequency [MHz] -. Frequency [MHz] HRC HRC HRC A 9-6A -6A 8-6A 4-6A 4 2-6A 7-4A 3 9-4A 3-4A 8-4A -4A 2-4A 2 2. ΔAECC [%].. -. Frequency [MHz] -. Frequency [MHz] -. Frequency [MHz]
5 Conductivity Change [%] Why Did Eddy Current Conductivity Spectroscopy Fail in Fully Hardened IN78? 2 annealed (3-4 HRC) partially hardened (27-28 HRC) fully hardened (43-45 HRC) Plastic Strain [%] surface treatment mechanism: compressive elastic stress/strain cold work/plastic strain surface roughness effect on conductivity: increase increase / negligible / decrease negligible
6 Hall Effect Detector B 3 F Q( E v B) I F e F m a t I F2 e( E2 v B3 ) V E H 2 v B3 a I enatv x 3 x 2 x I V av B B ent H 3 3 V H V R I t H H B3 en RH en σ conductivity e charge of proton n carrier density µ carrier mobility R H Hall coefficient
7 Strain-Dependence of the Hall Coefficient in Al Nagy, Rev. Progr. QNDE 32, 482 (23) t =. mm, a = mm, D = 9 mm, B =.58 T τ Y = 43.4 MPa, E = 6.94 GPa, τ = τ Y /2, ε =.3% before during after - -2 Hall Coefficient [ m 3 /As] Repetition annealed IN78 from Kosaka et al., Rev. Progr. QNDE 35, 923 (26)
8 Measurement Configuration for Dog Bone Specimens COMSOL Multiphysics simulations cylindrical permanent magnet injected current spring-loaded sensing electrodes specimen B >> electric potential distribution B = B << current sensing electrodes
9 Permanent Magnet Hall Coefficient Measurement System SIM 9 main frame, 4 ma current pump, 4, ten-fold parallel preamplifier Velmex motion controller N42 neodymium magnet, IN78 dog bone specimen, sample holder with sensing probe SR83 digital lock-in amplifier, GPIB computer interface Newport breadboard Thorlab pneumatic isolation table
10 Electromagnet Hall Coefficient Measurement System SIM 9 main frame, 4 ma current pump, 2, forty-fold parallel preamplifier 347 C-Frame bipole water cooled electromagnet, IN78 dog bone specimen clip-on injection and spring-loaded sensing electrodes hydraulic load frame with load cell SR865 digital lock-in amplifier, GPIB computer interface Newport breadboard Thorlab pneumatic isolation table
11 Engineering Stress [ksi] Hall Coefficient [ - m 3 /C] Hall Coefficient versus Hardness ε max 42% at 5 HRC (as received) ε max 28% at 3 HRC (partially hardened) ε max 22% at 44 HRC (fully hardened) measurement with permanent magnet t = mm, I =.4 A, B =.53 T f = 6 Hz, T = 25 C 25 2 fully hardened partially hardened as received measured data trendline Strain [%] Rockwell Hardness [HRC] annealed IN78 from Kosaka et al., J. Nondestr. Eval. 35, 38 (26): R H = 8.4 ±. - m 3 /C
12 Temperature-Dependence IN78, measurement with permanent magnet (t = mm, I =.4 A, B =.53 T) 4 raw data trendline - measured data trendline Hall Coefficient [ - m 3 /C] 9 8 Hall coefficient specimen temperature ambient temperature Time [hour] 3 2 Temperature [ C] Hall Coefficient [ - m 3 /C] 9 8 RH RH T Temperature [ C] Temperature Coefficient [ /⁰C] Hardness [HRC] average measurement with permanent magnet and Plexiglas electrode holder: β = -4,4 ppm/ C average measurement with electromagnet: β = -2,8 ppm/ C annealed IN78 from Kosaka et al., J. Nondestr. Eval. 35, 38 (26): β = -,9 ppm/ C
13 Current-Dependence measurement with electromagnet (t = mm, B =.3 T, f = 6 Hz, T = 25 C)...2 Normalized Magnitude measured data average Relative Phase [deg] measured data average Normalized Hall Coefficient..99 RH RH measured data trendline I Injected Current [A] Injected Current [A] Injected Current [A] average current coefficient: γ =.6 ±. A - for annealed IN78 from Kosaka et al., J. Nondestr. Eval. 35, 38 (26): γ = -.6 A -
14 Normalized Hall Coefficient Frequency-Dependence fully hardened IN78, measurement with electromagnet (t = mm, I =.4 A, B =.3 T, T = 25 C).2. measured data low-frequency asymptote.9.8 Frequency [Hz]
15 Normalized Hall Coefficient Thermal Exposure four fully hardened IN78 ( HRC) measurement with permanent magnet (t = mm, I =.4 A, B =.53 T, f = 6 Hz, T = 25 C).5 cumulative effect of subsequent 24-hour thermal exposures measured data trendline Thermal Exposure [ C]
16 Hall Coefficient [ - m 3 /C] Stress/Strain Dependence, Galvanomagnetic Gauge Factor fully hardened IN78, measurement with electromagnet (t = mm, I =.4 A, B =.3 T, f = 6 Hz, T = 25 C) 9.6 raw data linear regression 9.6 averaged data linear regression Hall Coefficient [ - m 3 /C] RH RH E 9.4 R 2 = Stress [ksi] 9.4 R 2 = Stress [ksi] τ Y = ksi, ν =.3, α = 2.8 ppm/ C R H = m 3 /C, κ = 2.95
17 Hall Coefficient and Galvanomagnetic Gauge Factor in IN78 measurement with electromagnet (t = mm, I =.4 A, B =.3 T, f = 6 Hz, T = 25 C) 5 Hall Coefficient [ - m 3 /C] measured data trendline Hardness [HRC] Galvanomagnetic Gauge Factor measured data trendline Hardness [HRC] annealed IN78 from Kosaka et al., J. Nondestr. Eval. 35, 38 (26): R H = 8.4 ±. - m 3 /C and κ = 2. ±.4
18 Hall Coefficient [ - m 3 /C] Hall Coefficient versus Plastic Strain in IN78 measurement with permanent magnet (t = mm, I =.4 A, B =.53 T, f = 6 Hz, T = 25 C) 9.5 fully hardened (42-44 HRC) partially hardened (27-28 HRC) annealed (3-4 HRC) Plastic Strain [%]
19 Conclusions Hall coefficient measurements could be a valuable addition to our NDE arsenal of electromagnetic materials characterization. The elastic strain dependence of the Hall coefficient in IN78 is high enough for applications in residual stress assessment. The plastic strain dependence of the Hall coefficient will have to be compensated for, but it will not be a showstopper. Numerous technical difficulties will have to be solved, e.g., - temperature-dependence ( bulk effect) - thermal aging ( bulk effect) - inspection frequency range (inductive crosstalk) - etc.
20 Questions?
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