140
5 An Electromagnetic Model for Anisotropic Media: Green’s Dyad for Plane-. . .
Table 5.3 Result of NLSE inversion of the sample function in Fig. 5.14
Φ
σ 11 /sensit
σ 22 /sensit
0.2301
598203/5.375(−2)
608706/6.222(−2)
when compared to those in Table 5.1 is not unexpected. The results, however, along
with the small sensitivity parameters, suggest that we have a good inversion that
gives a reliable estimate of σ 11 and σ 22 . (Keep in mind, however, that we have only
used a single sample function to draw this conclusion.)
5.4 Detectability of Flaws in Anisotropic Media: Application
to Ti64
In this section we will develop some simple models of notches in anisotropic Ti64.
In particular, we are interested in determining the effects of anisotropies on the
impedance response of a coil when scanned over a notch, and then using these
results as a basis for determining the effects that anisotropies can have on the
detectability of flaws.
Figure 5.15 illustrates the first model calculations. The host is isotropic with
a conductivity of σ = 6.04 × 10 5 S/m, which is typical of Ti64, and the two
anisotropic patches differ only in the exchange of σ 11 and σ 22 . The values shown
correspond to Ti64 with 6 mm symmetry. The notch is aligned along the 2-axis,
which is also the direction of the coil scan. The patch dimensions are 0.1 × 0.1 ×
0.02in, and the notch measures 0.01 × 0.06 × 0.02in.
Figure 5.16 shows the impedance-plane response at 2 MHz when the notch
is omitted from Fig. 5.15. This will be referred to as the ‘patch only’ response.
The labels ‘Top’ and ‘Bottom’ in Fig. 5.16 refer to the top and bottom models in
Fig. 5.15. The anisotropy of the patch makes a significant impact in the responses.
When we introduce the notch back into the two models, we get the impedanceplane response at 2 MHz shown in Fig. 5.17. It is clear, when comparing Figs. 5.16
and 5.17, that the ‘anisotropy’ induced by the 0.01 in-wide flaw dominates the
crystalline anisotropy of the host Ti64, in the sense that there is little difference
in the response when the notch is oriented along the 1-axis or 2-axis. When we
reduce the width of the flaw to 0.005 in, however, and redo the calculations, we get
the responses shown in Fig. 5.18. It is clear from this figure that the anisotropy of
the host plays a significant role in distinguishing the two responses. This suggests
that we will need to do a sensitivity study to determine the minimum detectable flaw
size when in the environment of a random crystalline anisotropy.
5 An Electromagnetic Model for Anisotropic Media: Green’s Dyad for Plane-. . .
Table 5.3 Result of NLSE inversion of the sample function in Fig. 5.14
Φ
σ 11 /sensit
σ 22 /sensit
0.2301
598203/5.375(−2)
608706/6.222(−2)
when compared to those in Table 5.1 is not unexpected. The results, however, along
with the small sensitivity parameters, suggest that we have a good inversion that
gives a reliable estimate of σ 11 and σ 22 . (Keep in mind, however, that we have only
used a single sample function to draw this conclusion.)
5.4 Detectability of Flaws in Anisotropic Media: Application
to Ti64
In this section we will develop some simple models of notches in anisotropic Ti64.
In particular, we are interested in determining the effects of anisotropies on the
impedance response of a coil when scanned over a notch, and then using these
results as a basis for determining the effects that anisotropies can have on the
detectability of flaws.
Figure 5.15 illustrates the first model calculations. The host is isotropic with
a conductivity of σ = 6.04 × 10 5 S/m, which is typical of Ti64, and the two
anisotropic patches differ only in the exchange of σ 11 and σ 22 . The values shown
correspond to Ti64 with 6 mm symmetry. The notch is aligned along the 2-axis,
which is also the direction of the coil scan. The patch dimensions are 0.1 × 0.1 ×
0.02in, and the notch measures 0.01 × 0.06 × 0.02in.
Figure 5.16 shows the impedance-plane response at 2 MHz when the notch
is omitted from Fig. 5.15. This will be referred to as the ‘patch only’ response.
The labels ‘Top’ and ‘Bottom’ in Fig. 5.16 refer to the top and bottom models in
Fig. 5.15. The anisotropy of the patch makes a significant impact in the responses.
When we introduce the notch back into the two models, we get the impedanceplane response at 2 MHz shown in Fig. 5.17. It is clear, when comparing Figs. 5.16
and 5.17, that the ‘anisotropy’ induced by the 0.01 in-wide flaw dominates the
crystalline anisotropy of the host Ti64, in the sense that there is little difference
in the response when the notch is oriented along the 1-axis or 2-axis. When we
reduce the width of the flaw to 0.005 in, however, and redo the calculations, we get
the responses shown in Fig. 5.18. It is clear from this figure that the anisotropy of
the host plays a significant role in distinguishing the two responses. This suggests
that we will need to do a sensitivity study to determine the minimum detectable flaw
size when in the environment of a random crystalline anisotropy.