What is Exponent b in Voltage-to-Area Flaw Relationships?

[sgtnichols]

TL;DR

What generalized equation can be found for exponent b from V2/V1 = (A2/A1)^b

[Mentor Note: Additional information has been added to this OP to address questions asked in subsequent replies below]

I'm analyzing the relationship between induced voltage (V) and semicircular area (A) in a conductive flat plate with notches in a fixed alternating magnetic field, specifically when the notches are located on the far surface (opposite the probe). The generalized scaling law I'm using is:

V2/V1 = (A2/A1)^b

In practice, for far-side notches, I consistently observe b values around 0.4, and 1.6 for near-side notches.

What generalized equation can be found for exponent b given the drive frequency, conductivity, plate thickness, coil Q factor, or other factors?

Resources:

Eddy Current Testing: https://www.nde-ed.org/NDETechniques/EddyCurrent/Instrumentation/ecinstruments.xhtml

Formulas: https://www.eddycurrent.com/formulas

 

[berkeman]

Welcome to PF.

Can you post some diagrams to describe the geometry you are asking about? Use the "Attach files" link below the Edit window to upload PDF or JPEG files.

What frequencies are you using in your analysis? Are the frequencies near resonance for the plate geometry?

TL;DR Summary: What generalized equation can be found for exponent b from V2/V1 = (A2/A1)^b

The generalized scaling law I'm using is:

V2/V1 = (A2/A1)^b

Where did this come from? Can you post a link for reference? Thanks.

 

[sgtnichols]

Welcome to PF.

Can you post some diagrams to describe the geometry you are asking about? Use the "Attach files" link below the Edit window to upload PDF or JPEG files.

What frequencies are you using in your analysis? Are the frequencies near resonance for the plate geometry?


Where did this come from? Can you post a link for reference? Thanks.

Power law regression fit. Consistent R2 of .99 or better.

 

[sgtnichols]

 

[berkeman]

Others may be able to decode what you are asking about, but I'm still pretty much in the dark so far.

Can you please state very clearly what you are asking about? Please give all details of your test setup, your test instrumentation (including frequencies), and what you are investigating with that setup. Schematics would also help.

What is motivating this investigation? What is the application? Thank you.

 

[sgtnichols]

Others may be able to decode what you are asking about, but I'm still pretty much in the dark so far.

Can you please state very clearly what you are asking about? Please give all details of your test setup, your test instrumentation (including frequencies), and what you are investigating with that setup. Schematics would also help.

What is motivating this investigation? What is the application? Thank you.

Hi Berkerman,

This is motivated by the need to estimate flaw depths and assess risks due to improper acceptance thresholds. Eddy current testing is a method gaining momentum in aerospace applications as a faster, cheaper, safer option for replacing radiography as a dominant method of volumetric weld flaw screening.

I just posted a few resources to the initial post which will help. I'll also follow up with an example. Initial thoughts are b may be proportionate to the standard depth of penetration (d) over thickness (t).

 

[sgtnichols]

TL;DR Summary: What generalized equation can be found for exponent b from V2/V1 = (A2/A1)^b

[Mentor Note: Additional information has been added to this OP to address questions asked in subsequent replies below]

I'm analyzing the relationship between induced voltage (V) and semicircular area (A) in a conductive flat plate with notches in a fixed alternating magnetic field, specifically when the notches are located on the far surface (opposite the probe). The generalized scaling law I'm using is:

V2/V1 = (A2/A1)^b

In practice, for far-side notches, I consistently observe b values around 0.4, and 1.6 for near-side notches.

What generalized equation can be found for exponent b given the drive frequency, conductivity, plate thickness, coil Q factor, or other factors?

View attachment 362177
View attachment 362178
Resources:

Eddy Current Testing: https://www.nde-ed.org/NDETechniques/EddyCurrent/Instrumentation/ecinstruments.xhtml

Formulas: https://www.eddycurrent.com/formulas

I initially suspect b ~ ( t / d)^3 where t relates to thickness and d is skin depth at the frequency and conductivity.

 

[sgtnichols]