# Edge Effect Analysis and Edge Defect Detection of Titanium Alloy Based on Eddy Current Testing
## 1 Introduction  
In the aerospace industry, the demand for titanium has expanded dramatically due to its intrinsic features of light weight, excellent corrosion resistance, and high strength, etc. Titanium alloy is widely used for airframe and engine parts of aircrafts [1]. To ensure the safety operation of those key structures of aircrafts, the detection of titanium alloy structures becomes increasingly important in aircraft maintenance programs. Nondestructive Testing (NDT) is a variety of methods involving the identification and characterization of damages or defect of materials without altering the original attributes or damaging the test object. NDT techniques possess wide applications in aerospace, military and defense, composite defects characterization, and pipe and tube inspection [2]. Commonly used NDT techniques include ultrasonic testing (UT), thermography, radiographic testing (RT), and eddy current testing (ECT). Among all NDT techniques, eddy current testing has the benefit of cost effective and detection efficient, and is especially sensitive to surface and near-surface defects. Other advantages of ECT include easy-operation and environmental-friendly. The principle of eddy current detection is based on electromagnetic induction [3, 4]. More specifically, a coil carrying an alternating current will producean electromagnetic field (EMF) according to [PERSON]'s law. With a conductive material being placed in the proximity of this changing magnetic field, eddy currents will be then induced in the material. The induced eddy currents generate a secondary magnetic field which can be detected by the receiving coil. If flaws exist on the surface or near the surface of the material, the presence of the flaw will disturb eddy current distribution, which in turn will cause impedance variation of the coil. The applied current passing through the coil is generally sinusoidal with a frequency ranging from hundred Hz to a few MHz [5]. To obtain the best response, the excitation frequency should be determined based on the test material and the depth of the defect. Many works have been devoted to studying ECT [6; 7; 8], including electromagnetic (EM) computation, sensor design, optimization, and instrument development. The classic EM computation solution is proposed by [PERSON]. By assuming the conductor is semi-infinite and axial symmetry (typically a coil placed above a plate or a coil encircling a tube), [PERSON] proposed analytical solutions for eddy current phenomenon [9]. To our knowledge, only a few studies are devoted to investigating edge effect and edge defect detection. The edge effect in eddy current detection has been systematically investigated in [10]. An analytic 3D eddy current model was proposed and its edge effect was investigated in [11]. A truncated region eigen function expansion (TREE) model was built in [12; 13; 14] to investigate the edge defects. Many ways to detect edge defects were proposed in [15; 16; 17; 18; 19], such as dual-frequency eddy current and eddy current pulsed thermography. However, edge defect detection is very important to industrial safety. Defects commonly develop from the edge of the material because of stress concentrations [20]. Compared with non-edge defects, since the stress at edge defects is more concentrated, edge defects are easier to expand and bring higher security risks, and even cause accidents. However, it is challenging to identify and characterize edge defects due to edge effect, since both the defect and the edge of the material will distort eddy currents, leading to an overlapped response [21; 22]. Therefore, it is urgent to quantitatively investigate edge effect and edge defect detection. In this work, a method aiming to optimize coil parameters to improve the capability of edge defect detection is proposed. More specifically, this work investigates the influences of sensor parameters on edge effect and defect detection capability separately.