Si, Yuqian
(2023)
On the use of swept frequency alternating current potential difference method and skin effect to detect feature geometry in flawed conductors.
PhD thesis, University of Nottingham.
Abstract
In many engineering situations, the unavoidable occurrence of cracks compromises the integrity of the structural components and poses a threat to safety. Reliable identification of cracks is the prerequisite of structural integrity assessment and enables the accurate prediction of the service lifetime of components. Among the various technologies developed for non-destructive testing, potential difference (PD) methods have gained wide acceptance due to the easy implementation and the ability to provide accurate and continuous detection of cracks. PD methods rely on the principle that the resistance of a conductor containing a feature increases as the crack propagates. Depending on the type of operating current, PD methods are recognised as direct current potential difference (DCPD) and alternating current potential difference (ACPD). Compared with direct current distributed on the whole cross-section of the conductor in DCPD, alternating current (AC) in ACPD is confined to a narrower layer beneath the conductor surface, i.e. skin effect. Therefore, ACPD requires a lower excitation current yet is able to achieve higher sensitivity in detecting cracks especially near conductor surfaces.
Given constant material properties and measurement distances, DC resistance of a cracked conductor is solely determined by the cross-sectional area of the crack, i.e. DCPD is only able to identify the cross-sectional area, without offering other information such as the geometry and depth of crack. In contrast, ACPD results are determined by multiple factors including the frequency and crack geometry due to the fact that AC delineates the crack edge (or part of the edge) by taking advantage of the skin effect. The potential of ACPD methods in identifying cracks by utilising the skin effect, especially different cracks with the same cross-sectional area (beyond the capability of DCPD), has been investigated. In this work, swept frequency AC was supplied in experiments to obtain abundant ACPD results in a wide frequency range. The overall behaviour of ACPD results with swept frequencies were used to identify cracks. The primary aim was to validate and comprehend the capability of the swept ACPD method in detecting and distinguishing, firstly the shapes of the conductors with the same cross-sectional area (no crack-like feature), and secondly cracks/features with different opening geometries (i.e. widths) on the external surfaces and depths inside the conductors.
The first part of the investigation were focused on four samples made of nonmagnetic material with the same gauge dimension and of different cross-sectional shapes. In the second part, five different features were manufactured at uniform locations of five samples made of ferromagnetic material and with the same dimension to simulate cracks. AC and PD signals were input and measured from uniform positions on all the samples. Measured signals in the time interval were then converted to results in the frequency domain by the use of a MATLAB script. The detection capability of the ACPD method was investigated upon the performance of two types of processed results in the frequency range: PD measured from the uniform positions and internal impedance further calculated from processed results of AC and PD. Experimental methodology, particularly the reliability of the data processing, were validated by conducting several preliminary experiments.
Furthermore, the electromagnetic models of the ACPD samples have been approximated by a theoretical methodology involving several established theories and the numerical methodology of finite element analysis (FEA) via ANSYS. Several theoretical frameworks based on distinct principles were used to calculate internal impedance of the non-magnetic samples of various cross-sectional shapes. Finite element (FE) models were created to simulate the current distributions on the four cross-sectional shapes and around the five features. Internal impedance of the four non-magnetic samples approximated by FE models were compared with theoretical solutions to assess the reliability of the theories and evaluate the precision of FEA. Subsequently, FEA was used to approximate PDs from the uniform measurement path to compare with experimental results, and hence analyse the detection capability of the ACPD method. Moreover, FEA was applied to measure PDs from paths in the vicinity of the measurement path to provide error bars covering possibly measurement uncertainties in experiments. Eventually, the approximated current distributions (and electric fields) were employed to comprehend and elucidate the conclusions obtained from the experiments and FEA.
The swept ACPD method has been demonstrated by FEA to have the capability to distinguish between different cross-sectional shapes of non-magnetic conductors with the same cross-sectional area. The capability is attributed to the current crowding which refers to the current localisation around edges of conductors with polygonal cross-sections. The current crowding is apparent on the surfaces of non-magnetic conductors and shows an increasing intensity as the cross-sectional shape varying from circular to triangular. For the non-magnetic (SS316) samples with the same gauge size of 55 mm × 100 mm^2, PDs measured from the uniform positions on FE models of circular and triangular cross-sectional shapes reach 0.22 mV and 0.39 mV at 300 kHz (i.e. difference of 77%), respectively. However, this finding is only supported by FEA but has not been observed in experiments due to measurement uncertainties. This motivates the use of ferromagnetic conductors in feature detection experiments to reduce the effect of current crowding on surface measurements, i.e. the impact of measurement uncertainties on experimental results. Experimental results measured from the featured ferromagnetic samples show distinct differences between different features, which agrees well with FEA results. For example, PDs measured from the uniform positions on ferromagnetic (EN1A) samples across three features, which have the same cross-sectional area of 9 mm^2 and various opening widths of 0.11, 0.21, and 0.42 to the sample size, reach 0.47, 0.72, and 1.08 mV at 50 kHz, respectively. This is due to the varying disturbances of different opening widths of features on the current distribution (or skin effect) around the features. Narrow openings lead to shallow current distributions, while wide openings result in deep penetration of current.
The present work has demonstrated the potential of the ACPD method in identifying surface features within ferromagnetic materials, which relies on the impact of the feature opening widths on the resulting current distributions. Future work may look to quantify the capability/limitation of the detection capability, for example, by constructing a current attenuation equation relating the current density along the feature depths to parameters of feature openings including dimensions, shapes, and positions. This may be used to determine the maximum detection depth of the ACPD method in identifying cracks/features with certain openings. Any situations within the detection region, e.g. unexpected propagating profiles and shorter depths (shorter than the maximum detection depths), may be detected by contrasting measured PDs with results predicted by the current attenuation equitation.
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