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- since 1996 -
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George Crowe
Consultant, AEROSPACE NDT
Self Employed, United Kingdom, Joined May 2013, 30

George Crowe

Consultant, AEROSPACE NDT
Self Employed,
United Kingdom,
Joined May 2013
30
16:24 Nov-02-2018
First Critical Angle of reflection Formula

Can anyone let me have the velocity formula for first critical angle of reflection? (Not Refraction)

 Reply

Kelly G.
Kelly G.
19:21 Nov-02-2018
Re: First Critical Angle of reflection Formula
In Reply to George Crowe at 16:24 Nov-02-2018 (Opening).

I am a student, a newbie in this field, and am curious as well. I looked over my notes briefly and was under the impression the velocity was given or determined by the type of material being used and the type of wave. For instance, if I was using steel it would be .230 u/s for compression wave but if I was using a shear wave it is half this amount. If I am wrong or this is not your answer to your problem then I am interested in the velocity formula as well.

 Reply

Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1286

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1286
19:56 Nov-02-2018
Re: First Critical Angle of reflection Formula
In Reply to George Crowe at 16:24 Nov-02-2018 (Opening).

George, I THINK you are asking about a shear mode impinging on a free boundary and mode converting. I have attached a figure conveying what I think you are asking. If so, it is just the arc-sin of the ratio of the incident shear velocity over the reflected (mode-converted) compression velocity.
 Reply

George Crowe
Consultant, AEROSPACE NDT
Self Employed, United Kingdom, Joined May 2013, 30

George Crowe

Consultant, AEROSPACE NDT
Self Employed,
United Kingdom,
Joined May 2013
30
20:11 Nov-02-2018
Re: First Critical Angle of reflection Formula
In Reply to Ed Ginzel at 19:56 Nov-02-2018 .

Hi Ed, Probably not explained myself well. We understand refraction but do not appear to address total reflection angles of incidence. Take a steel X to steel Y interface coupled by a water interface with an incident compressional angle A degrees in steel X. As A increases from 0 degrees, there comes an angle of incidence where the compressional beam totally reflects and no energy enters the water and therefore cannot enter the steel Y.

This phenomena is commonly discussed in optics but not in ultrasonics. I am looking for the related formula?

 Reply

Mario Talarico
NDT Inspector,
Italy, Joined May 2010, 423

Mario Talarico

NDT Inspector,
Italy,
Joined May 2010
423
20:23 Nov-02-2018
Re: First Critical Angle of reflection Formula
In Reply to George Crowe at 20:11 Nov-02-2018 .

George,
by imposing 90 ° to the angle of refraction of the shear wave in Snell's equation we obtain the limit incidence angle, beyond which there is no longer a refracted wave but only reflection. If you mean this.
If the interface is water-solid we only have longitudinal wave type reflection; in the solid-solid case the reflection is mixed, that is both longitudinal wave and shear (for angles both follow the snell law).
greetings
mario

 Reply

Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1286

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1286
22:22 Nov-02-2018
Re: First Critical Angle of reflection Formula
In Reply to George Crowe at 20:11 Nov-02-2018 .

George, I tried to imagine the situation so I could model it in Civa. I made 2 blocks of steel with a 2mm water gap. When the initial beam is incident at about 13° we can get both S and L modes in the steel.
The S-mode will reflect and mode convert at the water gap. But the L mode will reflect, mode-convert and also transmit because the slower velocity in water produces a negative refraction. There will be another reflection of the L-mode at the water/steel interface and also a very weak transmitted L mode into the steel below the gap. Since I used the same steel on both sides of the gap, the angle of the reflected and transmitted L modes are equal. But I do not see how these conditions can generate a glancing L mode from a direct incident L-mode at the gap. The S mode, however, COULD reach an angle less than 90° incidence on the steel/water interface and mode convert the reflected L mode at a glancing angle. Continued increase of the incident S mode angle would not add any more to the L mode but I suspect could begin to increase the proportion of energy being transferred to Rayleigh mode. Or perhaps more accurately at a liquid/solid interface this would be called a Scholte wave.
As we move into the "imaginary numbers realm" someone with better wave-mechanics mathematics will have to explain it for you. Civa is as good as I can get.
 Reply

George Crowe
Consultant, AEROSPACE NDT
Self Employed, United Kingdom, Joined May 2013, 30

George Crowe

Consultant, AEROSPACE NDT
Self Employed,
United Kingdom,
Joined May 2013
30
10:14 Nov-03-2018
Re: First Critical Angle of reflection Formula
In Reply to Ed Ginzel at 22:22 Nov-02-2018 .

Hi Ed, Thank you for your detailed response. Let me first say I much appreciate what you do here on this forum. Sharing your knowledge, not only for me but for many others as well.
May I further impose on you to use Civa with a 68-degree longitudinal incidence only in the first steel to water interface? I am interested to see what longitudinal energy if any, enters the second steel after the water gap.
I am experimenting practically to locate cross-drilled holes in the second steel after the water gap with a steel 'shoe' on an L probe (The first steel) angled at 68 degrees to give the same 68 degrees L beam in the second steel. In theory, I would expect to obtain a far stronger compressional wave in the second steel then using say an acrylic shoe below the first critical angle of incidence as mode conversion in minimised.

 Reply

Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1286

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1286
21:01 Nov-03-2018
Re: First Critical Angle of reflection Formula
In Reply to George Crowe at 10:14 Nov-03-2018 .

George, Attached is a model that may help explain some of the problem. I made a steel wedge with incident angle at 68° on steel and the 2mm watergap to another steel portion (5MHz 10mm diameter element). To get a feel for the losses at boundaries I placed a 3mm diameter SDH centred 2.5mm in the steel above the gap and another centred 4.5mm in the steel below the gap.
A B-scan over the surface such that the 68° L mode intersects each of the SDHs indicates that the upper hole is the largest response (0dB reference) and the response from the lower hole is 53dB lower.
It will be quite a noisy signal too. There could be multiple reflections from the upper hole that rattle between the upper and lower steel boundaries.
 Reply

Mario Talarico
NDT Inspector,
Italy, Joined May 2010, 423

Mario Talarico

NDT Inspector,
Italy,
Joined May 2010
423
09:51 Nov-05-2018
Re: First Critical Angle of reflection Formula
In Reply to Ed Ginzel at 21:01 Nov-03-2018 .

George,
I misunderstood your post. I do not know how, at the beginning I thought that your request was focused on everything that comes back in reflection between the first and second medium, when there is nothing in refraction. After Ed's simulations I realized that in your second post the request was clearly formulated but for some reason I had continued to keep this initial strangeness in my mind. I apologize for going off topic, what might have been avoided.
Ed, I associate myself so much with the beautiful words of George.
Greetings
Mario

 Reply

George Crowe
Consultant, AEROSPACE NDT
Self Employed, United Kingdom, Joined May 2013, 30

George Crowe

Consultant, AEROSPACE NDT
Self Employed,
United Kingdom,
Joined May 2013
30
19:02 Nov-05-2018
Re: First Critical Angle of reflection Formula
In Reply to Ed Ginzel at 21:01 Nov-03-2018 .

Ed, It would appear from the Civa simulation that there probably are a lot of reflective losses not shown in the first steel wedge and a much more reduced longitudinal wave in the second steel than apparent from the simulation. As Civa suggests -53dB. But this assumes no losses at the wedge interface. This reinforces the reasons the poor result I had with a physical experiment using a 68-degree steel wedge and an oil couplant. I may be better advised to produce the 68-degree compressional wave in the second steel using an acrylic wedge and live with an accompanying strong shear wave losses producing multiple return echoes. My target is normal to a 68 degreee compressional beam a through a further wetted interface and I can make the path length to coincide with the near field distance at the target interface to maximise compressional transmission. The shear wave noise is being removed by signal processing so my main issue is how well the processor works once I have achieved maximum transmission at the target!
Thank you again for your interest and support.

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