Numerical Analysis of Magnetic Pulse Welding Process
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Thermal investigation of Crack detection by Eddy Current Thermography Method

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Non-destructive testing techniques are commonly used in a various industrial and research fields, in order to evaluate the properties of a wide variety of materials without causing damages. Some of the frequently used methods, are the Electromagnetic-field techniques. They are utilized for the non-contact inspection of conductive materials to detect and characterize surface and sub-surface defects, through Eddy current non-destructive testing. Since it is recognized as being fast, simple, non-expensive and reliable, this technology is now widely used in the aerospace, automotive, petrochemical and power generation industries.

The principle of eddy current technique is based on the interaction between a magnetic field source and the test material. An Alternating magnetic current is created over the tested specimen when placing above it one or more coils carrying an AC current. The existence of flaws (cracks, corrosion, ...) and material variations in the specimen affects the strength and the flows of the eddy currents.
Currently, one of the most investigated NDT techniques, the Infrared Thermography (IR) method where the material inhomogeneities or defects are detected through a distortion in the temperature field. Two categories of heating techniques are applicable to NDT defect detection: Passive thermography in which heat is deposed as an external source on the material surface and then rely on the heat to propagate through it to detect subsurface cracks. And active thermography in which the material is excited itself by inducing a heating energy inside it through subsurface eddy currents.

Eddy current pulsed thermography ECPT

Active Infrared thermography method, based on induction heating phenomenon, is immensely developing for NDT due to its reliability and accuracy in material defect inspection. Electromagnetic-thermal non-destructive inspection has been proposed as an alternative to classical eddy current NDT techniques, by combining electromagnetic excitation, induction heating and inspection by transient infrared thermography technology. This thermo-inductive method uses induced eddy currents to heat the sample being tested and detect defects through the disturbance of the thermal distribution captured by an infrared IR camera. Analyzing the camera images can give information about the flaws in the tested material. This technique is characterized by wide scope application, high detection speed, contactless inspection, etc.
There is no interference from applied heating or excitation equipment since the change in temperature of the coil itself is very small and there is little chance of damage to the material under inspection, as heating is limited to a few °C.

In this study, the effectiveness of ECPT technique has been investigated numerically using FEM method. The analyzed model consists of spiral coil enrolled around a U-shaped ferrite core. Both are inspecting a defected structural steel workpiece. A schematic illustration of the ECPT technique with the studied 3D design are shown in figure 1.

a) Schematic illustration of the ECPT [1] b) 3D design of the studied model
Figure 1 - a) Schematic illustration of the ECPT [1] b) 3D design of the studied model

Problem description

The AC magnetic module of EMS is used in this analysis, coupled to the transient thermal solver, to compute and visualize the eddy current and temperature distribution around the specimen crack. The use of the ferromagnetic core is explained to its utility as a flux concentrator around the defect, to obtain both uniform induction heating and an open-view IR imaging for cracks quantitative evaluation.

The semi-elliptical crack shape is illustrated in the figure below. The detailed dimensions of each component are exposed in table 1.

Geometry of the tested plate containing a semi-elliptical surface-breaking crack
Figure 2 - Geometry of the tested plate containing a semi-elliptical surface-breaking crack [1]
Table 1 - Components dimensions
Part Dimensions
Coil Turns:  3 Main diameter: 25 mm Wire diameter: 6.35 mm
Outer dimensions of the ferrite yoke Length:58.5 mm Width:43 mm Height:27.5 mm
Inner dimensions of the ferrite yoke Length:56.1 mm Width:31 mm Height:27.5 mm
Specimen Length: 130 mm Width: 65 mm Height: 7.5 mm
Semi-elliptical crack Length: 12 mm Width: 0.6 mm Depth: 2.4 mm
Gap between yoke and specimen 1mm
Table 2 - material properties.
Part  Material Density
(kg/m au cube)
Magnetic permeability Electrical conductivity   
Thermal conductivity
Specific heat capacity
Coil Copper (Cu) 8900 0.99 6 E+07 385 390
Specimen Structural steel 7800 200 4.032 E+6 44.5 475
Yoke Ferrite 4900 2300 0.15  Not Required

Boundary conditions 

1-Electromagnetic input 

The copper inductor is defined as solid coil, supporting a current input range of 55 A rms and a frequency of 155 kHz.

2-Thermal input

Thermal convection is applied on the air body surrounding the model at ambient temperature of 20°C with a heat transfer coefficient set to 5 W/m²C.


Since eddy current are localized across the skin depth of the tested plate, a fine mesh was applied to the top surface of the specimen and to the crack using the mesh control feature of EMS.

The meshed model
Figure 3 - The meshed model.


After 500 ms of induction heating, the simulation revealed the results shown below. The current density distribution around the crack on the specimen surface shows a clear perturbation of eddy currents. It attains its maximum around the end points of the detected defect. The flow directions of currents are changed by the crack, leading to the surface being unevenly heated.

Vector plot of current density distribution
Figure 4 - Vector plot of current density distribution

The induced temperature is shown in the figure 5. The temperature of the central region of the U-shaped core on the specimen is almost evenly distributed. The maximum value is dedicated to the crack contours, reaching 23.13 °C, which is in a good coincidence with Reference [1] results.

Temperature distribution
Figure 5 - Temperature distribution

The figure 6 shows the heated air part delimited by the crack. The temperature at the end points of the defect is much higher than that at the other parts, and it sharply decreases in the depth direction. These characteristic features are used to predict the length of the crack from the two peak temperature points of the edges, and to determine the temperature difference between the crack and the other parts.

Temperature distribution across the crack
Figure 6 - Temperature distribution across the crack.


In this Multiphysics analysis, a ferrite-yoke based pulsed induction thermography is proposed to produce relative uniform induction heating in ferromagnetic material and have an open-view IR imaging for cracks detection. The uniform induced heating is generated through uniform magnetic flux and eddy current at the area between two poles of the ferrite-yoke.
The general behavior and physical mechanism of the proposed ECPT method are analyzed and verified by numerical simulation using EMS tool. The multi- physical interactions of the electromagnetic-thermal effect on the existing crack are investigated. The revealed results confirmed the effectiveness of ECPT for the inspection of material surface inhomogeneities and flaws. This technique proved its reliability as a fast and simple NDT tool.


[1]- He, Min, Laibin Zhang, Wenpei Zheng, and Yijing Feng. "Investigation on a new inducer of pulsed eddy current thermography." AIP Advances 6, no. 9 (2016): 095221.