Innovative NDT technique based on ferrofluids for detection of surface crack

1 Innovative NDT technique based on ferrofluids for detection of surface cracks J.I. Rojasa,1, B. Cabreraa, G. Musternia, J. Nicolasa, J. Tristanchoa,2, and D. Crespoa,3 a Universitat Politècnica de Catalunya, Escola d’Enginyeria de Telecomunicació i Aeroespacial de Castelldefels, C/ Esteve Terradas 7, 08860, Castelldefels, Spain 1 corresponding author: email: josep.ignasi.ro[email protected]; tel.: +34 93 413 4130; fax: +34 93 413 7007 2 email: [email protected] 3 email: [email protected] Abstract An innovative NDT technique is proposed for surface inspection of materials not necessarily magnetic or conductive, based on local magnetic field variations due to ferrofluid deposited in the cracks. The feasibility of the technique is assessed preliminarily, based on signal detectability without applied external magnetic field, and under applied DC fields. The signals (local magnetic flux density variations) are quantified analytically, experimentally and numerically. The model agrees well with the tests, showing that the signal increases with the applied field strength, up to the saturation magnetization of the ferrofluid, and decreases with the distance to the crack longitudinal axis, and thus it can provide useful estimations of the signal. The proposed technique, requiring application of external fields to magnetize the ferrofluid to enhance the signal, seems promising: the model suggests that signals associated to cracks significantly smaller than surface cracks in a target application like aircraft skin panel inspection NASA STD-5009 are easily detectable with commercial magnetometers. Keywords: surface flaw; magnetic particle; ferrofluid; aluminium alloys; composite materials 1. INTRODUCTION Early crack detection and monitoring is critical for, inter alia, aviation safety and, for this purpose, Non-Destructive Testing (NDT) is an indispensable tool in both production and maintenance. That is why the aerospace sector is one of the largest customers for the NDT industry: in 2008 and 2010, the global expenditure on NDT equipment was slightly over $1 billion [1,2], and was forecasted to grow up to $1.3 billion by 2013 [2], and $1.4 billion by 2017 [1]. Thus, research on NDT solutions for aerospace components that enhance safety and reduce costs is of paramount importance for the NDT and aerospace industries. 2 In this work, an innovative NDT technique is proposed for surface inspection, based on detection of local magnetic field variations due to accumulation of a ferrofluid in surface cracks. Ferrofluids are colloidal suspensions of small surfacted magnetic particles in a liquid carrier [3]; typically, iron oxide nanoparticles in a Newtonian fluid that can be polar (water) or non-polar (organic solvents). Ferrofluids can be magnetized by applying an external magnetic field, as it forces the magnetic dipole moments of the particles in suspension to align with the direction of the applied field [3]. The objective of this work is to make a preliminary assessment of the feasibility of the proposed NDT technique, based on signal detectability without applied magnetic fields, and under applied direct current (DC) magnetic fields. For this purpose, investigations are conducted to quantify analytically, experimentally and numerically the local magnetic field variations due to presence of a ferrofluid in surface cracks machined in plates of aluminium alloy (AA) 2024-T3. This alloy was chosen as it is widely used in applications for which fatigue resistance is critical, like in skin panels of military aircraft [4] and commercial civil aviation aircraft [5]. The ultimate goal of this research is to implement the proposed technique, meeting the accuracy, reliability and safety requirements of NDT applications in the aerospace industry, while trying to reduce the inspection costs. The latter can be achieved through a combination of reductions in equipment cost, inspection time, operator training, etc., while guaranteeing suitability to a wide range of aerospace NDT applications. Namely, the proposed technique would be applicable for surface inspection of materials not necessarily magnetic or conductive, e.g., aluminium alloys and Carbon or Glass Fibre Reinforced Polymers. 1.1 Dimensions of the studied cracks The minimum detectable crack depends on the inspection method [6]. In aircraft structural design, the initial crack depends on the component and the type of flaw evaluated [7]. Namely, for fail-safe involving surface flaws, an initial damage of 1.27 mm (3.18 mm for slow-flaw growth) is assumed for pre-service inspections with high standard NDT, while 6.35 mm is assumed for in-service inspections. In structural applications of aluminium alloy panels in aircraft, the most common NDT method for crack monitoring is General Visual Inspection (GVI) [8]. For GVI, the length of the detectable crack ranges from 5.08 to 12.70 mm. For other NDT techniques comparable to the subject of this work, the minimum detectable surface crack is: 1) for dye penetrant testing (PT), 6.36 mm long, 0.64 mm deep, or 3.82 mm long, 1.91 mm deep; 2) for eddy current testing (ET), 5.08 mm long, 0.51 mm deep, or 2.54 mm long, 1.27 mm deep; and 3) for magnetic particle testing (MT), 9.56 mm long, 0.97 mm deep, 3 or 6.36 mm long, 1.91 mm deep [6]. Our purpose is to determine if the proposed NDT concept would allow detection of surface cracks with these dimensions or smaller, given that one of the target applications is aircraft skin panel inspection. However, for the preliminary study for the proof of concept, cracks of larger dimensions were used. Once the experimental measurements validated the model results for the local magnetic field variations, further computations were made for cracks with the aforementioned dimensions. 2. MATERIALS & METHODS 2.1 Tested specimens The tested specimens are rectangular plates 100 mm long, 20 mm wide and 2 mm thick, machine cut from sheet of as-received commercial AA 2024-T3. The thickness matches typical values for aircraft skin panels, e.g., 1–1.6 mm for plain panels without holes and 2–3 mm for heavy loaded panels like those in the wing [9]. Using a metal saw, simulated cracks were machined in the surface of the samples along the longitudinal symmetry axis. Simulated cracks can be used in research instead of real cracks grown by fatigue during operation or dynamic testing [10]. The reference crack was 60 mm in length , 1.50 mm in width , and 0.70 mm in depth . In subsequent series of tests, cracks with  in the range 34.86–66.40 mm,  in the range 1.97–2.85 mm, and  in the range 0.52–0.65 mm were used. Finally, for the transversal tests, a crack 12.75 mm long, 0.95 mm wide and 0.60 mm deep, machined in a plate 20 mm long, 20 mm wide, was used. 2.2 Ferrofluids The magnetic particles in ferrofluids are generally spherical and with diameters ranging from 5 to 15 nm [3,11,12]. Also, each particle is generally a single magnetic domain, i.e., it is an entity with a single magnetic moment, and thus behaves as a single magnetic dipole. The volume fraction of ferrofluids, i.e., the volume percentage of magnetic solid material with respect to the total volume, is usually 5 to 15%. Four ferrofluids have been considered: three generic suspensions of ferromagnetic nanoparticles and the commercial ferrofluid N-503 from Sigma Hi-Chemical Inc. (the properties of the latter are shown in Table 1, as provided by the manufacturer). The generic suspensions are made of iron (α-Fe), magnetite (Fe3O4) and maghemite (γ-Fe2O3) nanoparticles, respectively (their properties are shown in Table 2). For simplicity, the idea of synthesizing a custom-made ferrofluid was disregarded and it was decided to use only the commercial ferrofluid for the experiments, and consequently also for 4 the numerical simulations. Nevertheless, for comparison purposes, the theoretical development and calculations in Section 3 were applied to all four ferrofluids. Table 1 Properties of commercial ferrofluid N-503 supplied by Sigma Hi-Chemical Inc. Concept Value Liquid carrier Iso-paraffin Type of magnetic particles Magnetite (Fe3O4) particles Average diameter 10 nm Volume fraction 8.9% Saturation magnetization   43.8 kA/m Dynamic viscosity  20.6 mPa·s, at 293 K Table 2 Properties of iron (α-Fe), magnetite (Fe3O4) and maghemite (γ-Fe2O3) particles at room temperature (RT). Type Concept Value Reference Observations α-Fe Critical diametera 7 nm [13] Mass/specific saturation magnetization 91.3 A·m2/kg [14] 8.4 nm diameter particles Density 7870 kg/m3 Fe3O4 Critical diametera 128 nm Mass/specific saturation magnetization 46 A·m2/kg [15] 19 nm diameter particles Density 5000 kg/m3 γ-Fe2O3 Critical diametera 166 nm Mass/specific saturation magnetization 36.6 A·m2/kg [16] 9 nm diameter particles Density 4600 kg/m3 a The critical diameter is a threshold below which a magnetic particle is a single magnetic domain. Above this critical diameter, the particle consists of multiple magnetic domains. 2.3 Experimental setup & methodology The magnetic flux density   was measured before and during application of a DC magnetic field, with and without ferrofluid in the reference crack. Fig. 1 shows the experimental set. The custom-made bracket (see Appendix A and Online Resource 1) consists of two concentric Cu wire coils covered by a protective shell, and the specimen support, located such that the crack in the sample is aligned with the revolution axes of the coils. A dispenser was used for depositing the ferrofluid in the cracks. A power source supplied DC power to the coils for generating DC magnetic fields. The intensity and voltage of the current were measured with a multimeter, while   was measured with the AlphaLab magnetometer (with resolution 0.001 mT and accuracy ± 2%). The reference position of the Hall probe was 3.5 mm below the crack centre, oriented to measure the component of   in the direction of the revolution axes of the coils. Measurements were taken sequentially in a series of cases summarized in Table 3. 5 For the cases where power is supplied to the coils, the tested voltages ranged from 1 to 17 V, with the coils generating applied external fields with strengths  ranging from around 1 to 16 kA/m. Higher applied fields were not used because the gain in ferrofluid magnetization is counterbalanced by a much poorer magnetometer resolution for the signals above 20 mT. For another sample, tests were realized with the Hall probe located at increasing distance from the crack, with  of 8 kA/m. Also, tests with surface cracks of different dimensions were conducted, with the Hall probe located back in the reference position, with  of 8 and 16 kA/m. Finally, tests were made with a crack oriented perpendicular to the revolution axes of the coils, and thus to the applied field, to explore the response if the defect does not lay parallel to this field. In this case, the crack and plate were smaller to allow introducing the plate inside the support transversally. The tests were performed in a laboratory with low electromagnetic noise. Prior to testing, the background field was zeroed by applying an appropriate offset in the magnetometer. Each of the test results shown in Section 4 is the average of three individual measurements (the error bars in the figures represent one standard deviation). Fig. 1 Experimental set: ferrofluid (1), test specimen (2), magnetometer and Hall probe (3), custom-made bracket (4), multimeter (5), power source (6) and connection cables (7) Table 3 Summary of experimental conditions applied sequentially during the tests. DC test cases Sample on support Ferrofluid in the crack DC power supplied to coils DC.1 No No No DC.2 Yes No No DC.3 Yes No Yes DC.4 Yes Yesa No (before magnetizing) DC.5 Yes Yesa Yes (ferrofluid magnetized) a Namely, the volume of commercial ferrofluid in the reference crack is approximately 50 mm3. 6 2.4 Simulations with COMSOL Multi-physics The local magnetic field variations due to the presence of ferrofluid in the reference crack were computed numerically with the AC/DC Module of COMSOL Multi-physics, a commercial finite element analysis software package for coupled physics phenomena and engineering applications, developed by COMSOL, Inc., Palo Alto, CA, USA. The mesh was a user-controlled unstructured 3D mesh of tetrahedral elements. The properties of the ferrofluid, the air and the test plates used in the simulations are summarized in Table 4. The electrical conductivity, permittivity and permeability of the commercial ferrofluid were not supplied by the manufacturer. The conductivity, measured with a Hach HQ440d Multi-Parameter Meter, was 5×10-5 S/m. The relative permittivity used in the simulations was that of the iso-paraffin. The relative permeability ( = 83.6) resulted from a calibration based on fitting the simulation results to the measured field in the probe position under an applied DC field of 16 kA/m. The solver selected for the simulations was the iterative FGMRES. Table 4 Properties of the ferrofluid, air and AA 2024-T3 at 293 K, as used in COMSOL simulations. Material Electrical conductivity (S/m) Relative permittivity (-) Relative permeability (-) Magnetite Iso-paraffin Ferrofluid 9.61×108 [17] Insulator 0 (measured)a 15 [18], 33.7–81 [19] 1.9 [20] 2 1.4–2.0 [18] – 1.5–6 [21], 3–96 [22] Air 0 (COMSOL database)a 1 (COMSOL database) 1 (COMSOL database) AA 2024-T3 1.60×107 – 1.89×107 [23] 1.44 [24], 8.0 [25] 1.00002 [26] a The electrical conductivity measured for the commercial ferrofluid was 0 S/m, and the conductivity for air in COMSOL’s materials database is 0 S/m. This is reported to cause problems in the solver. Instead, it is recommended to use a very small conductivity value, and so 10 S/m was used. 3. THEORY & CALCULATIONS The ferrofluid in the crack is modelled as a magnetic dipole with semi-length  and radius , such that it has the length of the crack and a volume equal to the volume of ferrofluid placed in the crack. The origin of the reference system used in this work is the dipole centre. The z axis is the revolution axis of the dipole, parallel to the crack and revolution axes of the coils. The y axis is perpendicular to the z axis, pointing opposite to gravity (see Online Resource 1). 3.1 Equilibrium (DC) magnetization of the ferrofluid Ferrofluids can be magnetized by external DC magnetic fields [3]. This phenomenon increases with , up to reaching  [27]. The following hypotheses are assumed: 1. The ferrofluid is mono-disperse, i.e., the particles are all identical in properties, composition, dimensions and shape (assumed spherical, with diameter 10 nm). 7 2. For being conservative, the generic ferrofluids are considered dilute colloidal suspensions with volume fraction of 7%, and  is the smallest in the literature for the corresponding type of particles (see Table 2). 3. Each magnetic particle is a single magnetic domain. This is coherent with the critical diameters found for the studied ferrofluids (see Table 2). 4. The magnetization  is homogeneous within the ferrofluid. 5. The magnetic particles in suspension are isotropic and non-interacting. If a ferrofluid is a collection of individual, non-interacting and mono-disperse magnetic dipoles, a theory by Langevin [3] states that, under a field applied in the z axis, the ferrofluid non-dimensional magnetization along that axis is  =  ⁄=coth()−1 ⁄, with the Langevin parameter =  ⁄, where  is the magnetic moment of the particles (15.5×10−19 A·m2, for magnetite [28]),  is the free space permeability constant,  is the Boltzmann constant, and  is the temperature. Fig. 2 shows the magnetization curve computed for the commercial ferrofluid at 293 K. If the applied field is suppressed,  relaxes to a new equilibrium state following an exponential decay being  = exp(−  ⁄), where  is the relaxation time [3]. Fig. 2 Magnetization of the ferrofluid  vs. applied field strength , at 293 K, by Langevin’s theory [3] 3. 2 Magnetic field of the ferrofluid For applied DC fields or absence of applied field, crack detection would be based on the local variations of   due to the ferrofluid in the crack. A magnetic field can be calculated with Maxwell’s equations [29]:  ()= ()+ ()= ()−∇∗(), where  is the position vector of the point where the field is evaluated,   is the magnetization, and ∗ is a 8 scalar potential. Inside the dipole,   depends on the ferrofluid magnetization. Outside the dipole,   is associated to the electromagnetic noise. In this work, this term is null in the z axis due to the offset applied to the magnetometer prior to testing. Thus, the magnetic flux density associated to the ferrofluid   is [29]: Eq. 1  ()=−∇∗()=−∇ ∫ (′)·󰆒 |󰆒|d′  where  is the volume of magnetized material (i.e., the volume of ferrofluid) and ′ is the position vector of a differential magnetic dipole. If the ferrofluid in the crack is modelled as a cylindrical dipole with semi-length  and radius , when the applied field is aligned with the dipole longitudinal axis, i.e., the z axis, Eq. 1 becomes: Eq. 2  ()=− [(  (()) − (()) )+(  (()) −  (2+2+(−)2)32 )+( + (2+2+(+)2)32 −− (2+2+(−)2)32 ) ] To explore the response if the applied field is perpendicular to the crack/dipole longitudinal axis, the dipole is rotated 90º to align it with the x axis. Then, Eq. 1 becomes: Eq. 3  ()=− [(  (()) ()− (()) ()+ () (()) ()−() (()) ())+( () (()) ()− () (()) ()−() (()) ()+() (()) ())+ ( (()) ()+() (()) ()+() (()) ()−  (()) ()−() (()) ()−() (()) ()) ] 3.3 Magnetic field of the ferrofluid in the xy plane After preliminary computations with Eq. 2, the field associated to the ferrofluid was observed to be very significant in the z axis close to the dipole tip (see Online Resource 2), but it is not possible to take measurements there. Also, the field vanishes dramatically with the distance to the z axis, and the direction of the field lines changes significantly in short distances. Thus, it 9 is very complex to establish the most appropriate position and orientation of the probe if it is to be placed in the vicinity of the tip of the crack/dipole but separated from the z axis (the magnetometer is only able to measure the field in one direction). Conversely, in the xy plane the field is expected to have component only in the z axis, , which facilitates taking measurements. For these reasons, the study was focused on the xy plane, where the signal when the applied field is aligned with the dipole longitudinal axis, as obtained from Eq. 2, is: Eq. 4 | ()| = =−   ()   For the reference crack, modelled by a dipole with a of 30 mm and  of 0.51 mm (see Online Resource 1), Fig. 3 shows  as obtained from Eq. 4 for the generic ferrofluids and the commercial ferrofluid, all at their . On the other side, if the applied field is perpendicular to the dipole longitudinal axis, from Eq. 3, the signal in the xy plane is: Eq. 5 | ()| = =−   (()) − (())   Fig. 3 For the reference crack (modelled by a dipole with  of 30 mm and  of 0.51 mm), analytical  vs. x and y coordinates, in the xy plane, for ferrofluids made of a) iron (α-Fe) nanoparticles, b) magnetite (Fe3O4) nanoparticles, c) maghemite (γ-Fe2O3) nanoparticles, and d) for the commercial ferrofluid, all at their  16 Table 8 For version Tech-DC.II at 293 K for the reference crack, variations of  obtained from the model and from the simulations with COMSOL for applied field strength  of 16 kA/m (test 1) and 716 kA/m (test 2) at 1.0 mm from the dipole axis. Sample Crack dimensions Dipole Numerical   variation Analytical   variation #1  = 60.00 mm  = 30.00 mm test 1: -3.1 μT test 1: -6.9 μT  = 1.50 mm  = 0.510 mm test 2: -7.9 μT test 2: -7.9 μT  = 0.70 mm 5. CONCLUSIONS An innovative NDT technique is proposed for surface inspection of materials not necessarily magnetic or conductive, based on detection of local magnetic field variations due to ferrofluid deposited in the crack. A preliminary feasibility assessment is made, based on signal detectability without applied magnetic field, and under applied DC fields. For this purpose, the signals (local magnetic flux density variations) are quantified analytically, experimentally and numerically for cracks in plates of AA 2024. The main conclusions are:  For the reference crack, filled with approximately 50 mm3 of ferrofluid, the magnetic field of the ferrofluid in absence of an applied field is below the sensor resolution. Detectable signals are obtained if the ferrofluid is being magnetized by an external field. The signals increase with the applied field strength , e.g., reaching -7 μT at a distance of around 3.5 mm from the longitudinal axis of the reference crack, for  of 16 kA/m.  The model agrees well with the tests: the average error excluding the results for a crack oriented perpendicular to the applied field is -5.3 %, and both follow similar trends. For instance, the signal increases with  up to the saturation magnetization of the ferrofluid and, in a plane perpendicular to the crack longitudinal axis in the crack centre, decreases with the distance to the axis. Thus, it is concluded that the model can provide useful estimations of the signal.  The signals measured for a crack oriented in the direction of the applied external field and perpendicular to it are virtually identical. This suggests that not knowing the direction of the defect when applying the external field may not be relevant to the performance of the proposed NDT method.  The proposed NDT technique, requiring application of DC external fields to magnetize the ferrofluid to enhance the signal, seems promising: the model suggests that signals associated to cracks significantly smaller than surface cracks in a target application like aircraft skin panel inspection NASA STD-5009 are easily detectable with commercial magnetometers. 17  Compared to PT, an advantage of the proposed NDT method is that it is quantitative and, therefore, can be used to estimate the size of the cracks.  The use of non-commercial ferrofluids may provide some advantages like higher , leading to more intense signals (this can be achieved using α-Fe particles), or lower coercivity/hysteresis effects, or the possibility of developing ferrofluids with tailored properties, like reduced viscosity and surface tension, making easier for the ferrofluid to sip into the surface cracks, etc. The ideas being considered for future work are: 1) to refine the research using, for instance, a 3-components Hall probe with higher sensitivity; 2) to correlate patterns in the local magnetic field variations with crack morphology; 3) to study the applicability of the technique to detect cracks in magnetic materials; 4) to study the effect of ferrofluid viscosity in crack penetration; 5) to study the feasibility of recycling classic eddy current equipment for implementing the proposed NDT technique; 6) perform PT, ET, MT (if possible, depending on the tested material) and tests with the proposed NDT method on small defects in the sub-mm range, to establish the limits of the NDT technique; and finally 7) to study the performance of the proposed technique upon application of AC fields. In AC, crack detection could be based on the phase lag between the field close to the crack and the applied field. This approach has inherent advantages: the phase lag, as opposed to  , is independent of  and the quantity of ferrofluid in the crack, and increases significantly with the frequency of the applied AC field. APPENDIX A – Technical specifications of the custom-made bracket Coil #1 and coil #2 in the custom-made bracket are radially thick, multi-layered solenoids consisting of 1000 and 2800 turns, respectively, of solid Cu wire, 1 mm in diameter. Both coils are 100 mm long. Coil #1 has 30 (40) mm inner (outer) radius, while coil #2 has 40 (68) mm inner (outer) radius. Fig. 7 shows a photograph of the bracket and its lateral, frontal and top views, created with the commercial multiphysics software SolidWorks, from Dassault Systèmes SolidWorks Corp., Waltham, MA (USA). The DC magnetic field created by the coils when supplied with DC current can be estimated using a model by Brown and Flax [30]. In Fig. 8, the results from this model are compared with measurements using the AlphaLab magnetometer, for supplied DC voltages ranging from 1 to 17 V. 18 Fig. 7 Lateral, frontal and top views created using commercial multiphysics software SolidWorks, from Dassault Systèmes SolidWorks Corp., Waltham, MA (USA) (left), and photograph of the custom-made bracket (right) Fig. 8  for the DC field created by the coils vs. supplied DC voltage ACKNOWLEDGEMENTS Work supported by the MINECO grant FIS2014-54734-P and the Generalitat de Catalunya/AGAUR grant 2014SGR00581. We want to thank also the support by Dr. O. Casas, and the helpful comments and feedback from the reviewers. REFERENCES [1] Global Industry Analysts Inc. (2011) Nondestructive Test Equipment: A Global Strategic Business Report. San Jose, CA. 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