Eddy Current Inspection Formulas

$I= \frac{V}{Z}$

$$Where:

I = Current (amp)

V = Voltage (volt)

R = Resistance (ohm)

More about ohm's Law

$\bar{Z}=R+X_{L}-X_{c}$

and

$\vert \bar{Z}\vert=\sqrt{R^{2}+(X_{L}-X_{c})^{2}}$

$$Where:

$\bar{Z}$ = Complex Impedance (ohm)

$\vert \bar{Z}\vert$ = Amplitude of the Impedence (ohm)

R = Resistance (ohm)

X_L = Inductive Reactance(ohm)

X_c = Capacitive Reactance(ohm)

Impedance Calculation Example

$\tan\phi= \frac{X}{R}$

$$Where:

ϕ = Phase Angle (radians)

X = Reactance (ohm)

R = Resistance (ohm)

Phase Angle Calculation Example

$\mu= \frac{B}{H}$

$$Where:

$\mu$ = Magnetic Permeability (Henries/meter)

B = Magnetic Flux Density (Tesla)

H = Magnetizing Force (Am/meter)

$\mu_{r}= \frac{\mu}{\mu_{0}}$

Where:

$\mu$_r = Relative Magnetic Permeability (dimensionless)

$\mu$ = Any Given Magnetic Permeability (H/m)

$\mu$_o = Magnetic Permeability in Free Space (H/m), which is 1.257 x 10-6 H/m

Permeability Calculation Example

$\sigma= \frac{1}{\rho}$

$$Where:

$\sigma$ = Electrical Conductivity Siemens/m

$\rho$ = Electrical Resistivity (ohm-m)

More on Resistance and Conductivity

When resistivity is known

$\sigma_{\text{$

Where:

$\sigma$_%IACS = Electrical Conductivity (% IACS)

$\rho$ = Electrical Resistivity (mohm-cm)

$\sigma$_mS/cm = Electrical Conductivity (mSiemens/cm)

When conductivity in S/m or mS/cm is known

$\sigma_{\text{$

or

$\sigma_{\text{$

Where:

$\sigma$_%IACS = Electrical Conductivity (% IACS)

$\sigma$_S/m = Electrical Conductivity (Siemens/meter)

$\sigma$_mS/cm = Electrical Conductivity (mSiemens/cm)

More on Electrical Conductivity Conversion

$J_{x}=J_{0}e^{\frac{-x}{\delta}}$

Where:

J_x = Current Density (amps/m2)

J_o = Current Density at Surface (amps/m2)

e = Base Natural Log = 2.71828

x = Distance Below Surface

$\delta$ = Standard Depth of Penetration

More on Eddy Current Density

When Electrical conductivity (S/m) is known

$\delta\approx \frac{1}{\sqrt{\pi f\mu\sigma}}$

Where:

$\delta$ = Standard Depth of Penetration (m)

$\pi$ = 3.14

f = Test Frequency (Hz)

$\mu$ = Magnetic Permeability (H/m) (1.257 x 10-6 H/m for nonmagnetic mat'ls)

$\sigma$ = Electrical Conductivity (Siemens/m)

More on Standard Penetration Depth

When Electrical conductivity (%IACS) is known

In mm: $\delta_{mm}\approx \frac{661}{\sqrt{f\mu_{r}\sigma}}$

In Inches: $\delta_{inch}\approx \frac{26}{\sqrt{f\mu_{r}\sigma}}$

Where:

$\delta$ = Standard Depth of Penetration (mm or in)

f = Test Frequency (Hz)

$\mu$_r = Relative Magnetic Permeability (dimensionless)

$\sigma$ = Electrical Conductivity (%IACS)

More on Standard Penetration Depth

When electrical resistivity (mohm-cm) is known

In mm: $\delta_{mm}\approx 50 \sqrt{\frac{\rho}{f\mu_{r}}}$

In inches: $\delta_{inch}\approx 1.98 \sqrt{\frac{\rho}{f\mu_{r}}}$

Where:

$\delta$ = Standard Depth of Penetration (mm or in)

$\rho$ = Electrical Resistivity (mohm-cm)

f = Test Frequency (Hz)

$\mu$_r = Relative Magnetic Permeability (dimensionless)

More on Standard Penetration Depth

In Radians $\theta=\frac{x}{\delta}$

$$ In Degrees: $\theta=\frac{x}{\delta}\times57.3$

Where:

$\theta$ = Phase Lag (Rad or Degrees)

x = Distance Below Surface (in or mm)

$\delta$ = Standard Depth of Penetration (in or mm)

Phase Lag Example Calculation

More on Phase Lag

When electrical conductivity (S/m) is known.

$\theta=57.3x\sqrt{\pi f\mu_{r}\sigma}$

Where:

$\theta$ = Phase Lag (degrees)

x = Distance Below Surface (m)

$\pi$ = 3.14

f = Test Frequency (Hz)

$\mu$_r = Relative Magnetic Permeability

$\sigma$ = Electrical Conductivity (Siemens/m)

When electrical conductivity (%IACS) is known.

In mm: $\theta\approx\frac{x\sqrt{f\mu_{r}\sigma}}{11.54}$ 

In inches: $\theta\approx2.2x\sqrt{f\mu_{r}\sigma}$

Where:

$\theta$ = Phase Lag (degrees)

x = Distance Below Surface (mm)

f = Test Frequency (Hz)

$\mu$_r = Relative Magnetic Permeability (dimensionless)

$\sigma$ = Electrical Conductivity (%IACS)

When electrical resistivity (mohm-cm) is known.

In mm: $\theta\approx1.15x\sqrt{\frac{f\mu_{r}}{\rho}}$

In inches: $\theta\approx28.94x\sqrt{\frac{f\mu_{r}}{\rho}}$

Where:

$\theta$ = Phase Lag (degrees)

x = Distance Below Surface (inch)

$\rho$ = Electrical Resistivity (mohm-cm)

f = Test Frequency (Hz)

$\mu$_r = Relative Magnetic Permeability (dimensionless)

When measuring resistivity or conductivity, the thickness of the material should be at least 3 times the depth of penetration to minimize material thickness effects

$t\geq3\delta$

$$Where:

t = Material Thickness

$\delta$ = Standard Depth of Penetration

Selecting a frequency that produces a standard depth of penetration that exceeds the material thickness by 25% will produce a phase angle of approximately 90^o between the liftoff signal and the material thickness change signal.

$1.25t=\delta$

$$ or

$t=0.8\delta$

Defect Detection

A test frequency that puts the standard depth of penetration at about the expected depth of the defect will provide good phase separation between the defect and liftoff signals.

$\delta=\text{Defect Depth}$

Nonconductive Coating Thickness Measurement 

To minimize effects from the base metal the highest practical frequency should be used.