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

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Discussion Overview

The discussion focuses on the relationship between induced voltage (V) and semicircular area (A) in a conductive flat plate with notches subjected to a fixed alternating magnetic field. Participants explore the generalized scaling law represented by the equation V2/V1 = (A2/A1)^b, specifically seeking to determine the conditions and factors that influence the exponent b, including drive frequency, conductivity, plate thickness, and coil Q factor.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • The original poster (OP) reports observing b values of approximately 0.4 for far-side notches and 1.6 for near-side notches.
  • Some participants request additional details about the test setup, including diagrams, frequencies used, and the specific geometry being analyzed.
  • One participant suggests that the exponent b may be related to the ratio of standard depth of penetration (d) to thickness (t), proposing a relationship of b ~ (t/d)^3.
  • There is a mention of achieving consistent power law regression fits with R2 values of .99 or better, although the implications of this are not fully explored.
  • The OP indicates that the investigation is motivated by the need to estimate flaw depths and assess risks in aerospace applications, where eddy current testing is being considered as a replacement for traditional methods.

Areas of Agreement / Disagreement

Participants have not reached a consensus on the exact nature of the relationship governing exponent b, and multiple viewpoints regarding the factors influencing it remain. There is ongoing clarification and inquiry about the experimental setup and motivations behind the investigation.

Contextual Notes

Participants have noted the need for clearer details regarding the test instrumentation and setup, as well as the specific frequencies used in the analysis. The discussion reflects a dependency on various assumptions related to the geometry and conditions of the experiment.

sgtnichols
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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?

1000008376.webp

1000008377.webp

Resources:

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

Formulas: https://www.eddycurrent.com/formulas
 
Last edited by a moderator:
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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?

sgtnichols said:
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.
 
berkeman said:
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.
 
1000007787.webp
 
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.
 
berkeman said:
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).
 
Last edited:
sgtnichols said:
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.
 
1000008383.webp

1000008384.webp
 

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