According to Ohms Law, the voltage is the product of current and resistance.
i.e., V = I x R
Where V = Voltage in volts, I = Current in Amps and R = Resistance in Ohms
Phase Angle and Impedance
Phase angle is expressed as follows:
TanΦ = XL/R
Where Φ = Phase Angle in degrees, XL = Inductive Reactance in ohms and R = Resistance in ohms.
Impedance is defined as follows:
Where Z = Impedance in ohms, R = Resistance in ohms and XL = Reactance in ohms.
Magnetic Permeability and Relative Magnetic Permeability
Magnetic permeability is the ratio between magnetic flux density and magnetizing force.
i.e., μ =B/H
Where μ = Magnetic Permeability in Henries per meter (mu), B = Magnetic Flux Density in Tesla, H = Magnetizing Force in Amps/meter.
Relative magnetic permeability is expressed as follows:
μ r = μ/ μo
Where μr = Relative magnetic permeability (mu) and μo = Magnetic permeability of free space (Henries per meter = 1.257 * 10-6). μr = 1 for non-ferrous materials.
Conductivity and Resistivity
Conductivity and resistivity is related as follows:
Where σ = Conductivity (sigma) and ρ =Resistivity (rho). Conductivity can be quantified in Siemens per m (S/m) or in Aerospace NDT in % lACS (International Annealed Copper Standard). One Siemen is the inverse of an ohm. Another common unit used for conductivity measurement is Siemen per cm (S/cm).
Resistance and Conductivity
Resistance can be defined as follows:
R = l/Aσ or R = ρl/A
Where R = the resistance of a uniform cross section conductor in ohms (Ω), l = the length of the conductor in the same linear units as the conductivity or resistivity is quantified, A=Cross Sectional area, σ = conductivity in S/m and ρ = Resistivity in Ωm.
Standard Depth of Penetration
Standard depth of penetration is given as follows:
Where δ = standard depth of penetration in m; f = frequency (Hz); μ = Magnetic Permeability (Henries per meter); and σ = conductivity in S/m.
The influence of frequency and conductivity on standard depth of penetration is illustrated in Figure 1.
Figure 1. Influence of frequency and conductivity on standard depth of penetration.
Current Density Change with Depth
The change in current density with depth is expressed as follows:
Where Jx = Current Density at distance x below the surface (amps/m2); J0 = Current Density at the surface (amps/m2); e = the base of the natural logarithm (Euler's number) = 2.71828; x = Distance below the surface; and δ = standard depth of penetration in meters.
Depth of Penetration and Probe Size
Smith et al have introduced the idea of spatial frequency.
Where D = the effective diameter of the probe field in meters, limiting the depth of penetration to D/4. The probe effective diameter is considered to be infinite in the usual equation.
Phase change with Depth
Phase change with depth is expressed as follows:
θ = 57.3x/δ
Where, θ = Phase lag (degrees); 57.3 = 1 radian expressed in degrees; x = Distance below the surface; and δ = standard depth of penetration.
The change in phase and current density with depth of penetration is depicted in Figure 2.
Figure 2. Phase and current density change with depth of penetration.
Frequency is expressed as follows:
Where f = frequency (Hz); x= material thickness in meters; μ = Magnetic Permeability (Henries per meter); and σ = conductivity in S/m.
Conductivity of some common non-ferrous metals is listed in Table 1:
Table 1. Conductivity of Some Common Non-Ferrous Metals
|Types and/or Description
||Conductivity % lACS
||Mega Siemen per m (MSm-1)
|Pure Aluminium (A1)
|Aluminium Alloy 1100-0
|Aluminium Alloy 1100-H18
|Aluminium Alloy 2024-0
|Aluminium Alloy 2024-T4
|Nickel and Alloys
|Nickel - (Pure) (Ni)
|Nickel - (Wrought)
|Nickel - (Dura) 301
|Stainless Steel Type 420
|Stainless Steel Type 403, 410 & 416
|St Steel Type 430, 430-F, 434 & & 436
|Stainless Steel Type 405 & 409
|Stainless Steel Type 442
|99.995% Min (Vacuum Cast Pure Copper) (Cu)
|C10100 99.99% Min
|C10200 99.95% Cu+Ag
|C10400, C10500 & C10700 +0.5 to 0.15% Ag
|C10300 +0.001 to 0.005% P
|Brass 95% Cu + 5% Zn
|95.7% Cu + 4.3% Ti
|C34000 65% Cu; 34%Zn
|C85200 (Yellow Brass)
|C86200 (Manganese Bronze)
|Cobalt (Co) (99.8% Pure)
|Cobalt (Co) (Pure)
|Lead Alloy +0.07% Ca
|Lead Alloy +0.07% Ca +0.7% Sn
|Molybodenum (Hard Drawn)
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