Ohms Law
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:
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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:
σ =1/ρ
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:
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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.
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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:
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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.
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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.
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Figure 2. Phase and current density change with depth of penetration.
Frequency
Frequency is expressed as follows:
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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) |
| Aluminium |
| Pure Aluminium (A1) |
65.86% |
38.20 |
| Aluminium Alloy 1100-0 |
59.45% |
34.48 |
| Aluminium Alloy 1100-H18 |
57.47% |
33.33 |
| Aluminium Alloy 2024-0 |
50.71% |
29.41 |
| Aluminium Alloy 2024-T4 |
30.25% |
17.55 |
| Nickel and Alloys |
| Nickel - (Pure) (Ni) |
25.00% |
14. 50 |
| Nickel - (Wrought) |
18.00% |
10.44 |
| Nickel - (Dura) 301 |
4.06% |
2.35 |
| Monel 400 |
3.38% |
1.96 |
| Monel K-500 |
2.83% |
1.64 |
| Stainless Steels |
| Stainless Steel Type 420 |
3.13% |
1.82 |
| Stainless Steel Type 403, 410 & 416 |
3.02% |
1.75 |
| St Steel Type 430, 430-F, 434 & & 436 |
2.87% |
1.66 |
| Stainless Steel Type 405 & 409 |
2.83% |
1.64 |
| Stainless Steel Type 442 |
2.69% |
1.56 |
| Copper |
| 99.995% Min (Vacuum Cast Pure Copper) (Cu) |
102.00% |
59. 16 |
| C10100 99.99% Min |
101.00% |
58.58 |
| C10200 99.95% Cu+Ag |
100.00% |
58.00 |
| C10400, C10500 & C10700 +0.5 to 0.15% Ag |
100.00% |
58.00 |
| C10300 +0.001 to 0.005% P |
98.20% |
56.96 |
| Miscellaneous |
| Brass 95% Cu + 5% Zn |
55.00% |
31.90 |
| 95.7% Cu + 4.3% Ti |
10.00% |
5.80 |
| Barium (Ba) |
2.76% |
1.60 |
| Beryllium (Be) |
38.50% |
22.33 |
| C17300 Cu+Be+Pb |
22.00% |
12.76 |
| C34000 65% Cu; 34%Zn |
26.00% |
15.08 |
| C85200 (Yellow Brass) |
18.00% |
10.44 |
| C86200 (Manganese Bronze) |
7.50% |
4.35 |
| Cobalt (Co) (99.8% Pure) |
17.80% |
10.32 |
| Cobalt (Co) (Pure) |
27.60% |
16.01 |
| Lead Alloy +0.07% Ca |
7.91% |
4.59 |
| Lead Alloy +0.07% Ca +0.7% Sn |
7.87% |
4.56 |
| Molybodenum (Annealed) |
41.00% |
23.78 |
| Molybodenum (Hard Drawn) |
35.20% |
20.42 |
| Rhodium (Rh) |
38.20% |
22.16 |
| Rubidium (Rb) |
14.90% |
8.64 |
| Uranium (U) |
5.86% |
3.40 |
| Vanadium (Va) |
6.90% |
4.00 |
| Zircalloy2 |
2.40% |
1.39 |
| Zirconium (Zr) |
4.13% |
2.40 |
About Ether NDE
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