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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
09:35 Jun-25-2018
Reflection transmission formula at incident angles.

Krautkramer publish a graphical description of the various amplitudes of interface transmitted and reflected shear and transverse ultrasound at various angles of incidence. Can anyone supply the formulas for signal amplitude associated with these graphical presentations?

 
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Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
16:03 Jun-25-2018
Re: Reflection transmission formula at incident angles.
In Reply to George Crowe at 09:35 Jun-25-2018 (Opening).

George, the equations used in Krautkramer for the transmittance and reflection curves are provided at the beginning of Appendix F in the Krautkramer book; Ultrasonic Testing of Materials (I am using the 3rd English edition). To calculate the echo-transmittance curves, Krautkramer (in Section 2.4 of that book) states that you simply multiply the transmittance in one direction by the transmittance in the other.
Another source of the equations can be seen in geophysics using the Zoeppritz equations (in the form of a matrix) see: https://en.wikipedia.org/wiki/Zoeppritz_equations.
Do you have a copy of the Krautkramer book?

 
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J.B.
J.B.
15:44 Jun-26-2018
Re: Reflection transmission formula at incident angles.
In Reply to Ed Ginzel at 16:03 Jun-25-2018 .

I wonder if it is a legal copy of the fourth edition, which is available here, but it is still posted:
http://allaboutmetallurgy.com/wp/wp-content/uploads/2017/02/Ultrasonic-Testing-of-Materials.pdf

 
 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
19:23 Jul-09-2018
Re: Reflection transmission formula at incident angles.
In Reply to Ed Ginzel at 16:03 Jun-25-2018 .

Hi Ed, Sorry for the tardy reply I have been on vacation for three weeks. Thank you for your response. Yes, I do have the 4th edition. I am principally trying to establish an approach to minimise losses and maximise longitudinal wave transmissions for a project at a 'refracted' angle of 22 degrees +/- 5.0 degrees into steel. I cannot see why I cannot just produce a 22-degree steel shoe for the probe and accept transmission loss through the couplant rather than have accompanying shear waves in the product when using acrylic plastic for the shoe. Anyway I was going to look at the maths to see if there were objective calculations I could examine

 
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Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
21:34 Jul-09-2018
Re: Reflection transmission formula at incident angles.
In Reply to George Crowe at 19:23 Jul-09-2018 .

zoom image
George, if it is just a matter of getting a good L-mode into steel, then I suspect a steel wedge is the optimum option. I have attached an image of a Civa model I did using your information. I placed a 10mm diameter 5MHz probe on a Rexolite wedge that has an incident angle suitable to refract a 22° L-mode and then I modelled the situation using a steel wedge (i.e. 22° and no refraction). In the models, I had Civa compute the shear component as well. You can see a weak shear component in both cases.
I then used the steel wedge as the Reference beam. This normalises the results to the reference and we see that there is about a 19dB drop in the pressure when using the Rexolite plastic wedge as compared to the steel wedge.
This is perhaps a bit more convenient than calculating the echo transmittance values in that it represents the effect of a divergent beam crossing boundaries. I made no provision to account for attenuation in the steel nor in the Rexolite so this is just indicating the transmission differences.
 
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Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
21:37 Jul-09-2018
Re: Reflection transmission formula at incident angles.
In Reply to George Crowe at 19:23 Jul-09-2018 .

zoom image
Here is a better image in that I labelled the wedges and beams
 
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Mark
,
Zambia, Joined Jun 2016, 49

Mark

,
Zambia,
Joined Jun 2016
49
07:23 Jul-10-2018
Re: Reflection transmission formula at incident angles.
In Reply to Ed Ginzel at 21:37 Jul-09-2018 .

Hi Ed,
Correct me if I'm wrong but That means the steel wedges will produce low beam attenuation. I think practically there will be more difference .To transmit ultrasound from steel to steel with couplant is very difficult.I think Civa calculated beam transmission without coplant.

 
 Reply 
 
Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
13:59 Jul-10-2018
Re: Reflection transmission formula at incident angles.
In Reply to Mark at 07:23 Jul-10-2018 .

Mark, very good practical observation!!
Indeed, the model does not consider the coupling in the way it actually works. In order to verify your concern I placed a steel step wedge on an old 25mm thick V2 block and coupled the probe to the step wedge and step wedge to the 25mm block using a coupling gel. The A-scan indicated only multiples of the step wedge and I could not get a delayed response from the 25mm block with the added step wedge thickness. When I placed a variety of plastics on the 25mm block I could see the 25mm thickness after the delay line interface signal.

So George, in spite of my earlier model, it would seem that a steel wedge is not the solution due to the high reflection at the coupling boundary.
Thanks Mark.

2
 
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Philippe Rioux
R & D, Sonatest
Sonatest, Canada, Joined Jan 2015, 37

Philippe Rioux

R & D, Sonatest
Sonatest,
Canada,
Joined Jan 2015
37
14:30 Jul-10-2018
Re: Reflection transmission formula at incident angles.
In Reply to Ed Ginzel at 13:59 Jul-10-2018 .

Very good to know! I wonder why now CIVA does not consider the coupling layer... I suppose you have to create a thin water layer manually...?!

 
 Reply 
 
Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
14:42 Jul-10-2018
Re: Reflection transmission formula at incident angles.
In Reply to Ed Ginzel at 13:59 Jul-10-2018 .

On a related observation, I coupled the V2 block to the step wedge so I had 25mm of steel path prior to the step wedge. With that configuration I could see the step wedge with multiples after the first 25mm in steel. In fact, when the coupling layer thinned I set the 25mm backwall signal from the V2 block to 100% and observed the backwall from a 10mm step to be 80%. This suggested a high transmission was occurring. But when the soundpath in the delay block is too short, the multiples will interfere with observing the interface of the thicker sample (just as they would if using a plastic delay line that was too thin).
I am not sure if a 22° angle of incidence would adequately reduce the interface signal between a steel wedge and test piece to avoid multiples, but my second test suggests that a thick wedge on a thin test piece could provide a usable signal.

 
 Reply 
 
Mark
,
Zambia, Joined Jun 2016, 49

Mark

,
Zambia,
Joined Jun 2016
49
16:22 Jul-10-2018
Re: Reflection transmission formula at incident angles.
In Reply to George Crowe at 19:23 Jul-09-2018 .

Thanks Mr Ginzel for your information.
George I would suggest water wedge to reduce the wedge path attenuation. It need special housing design to inject the water between probe and material to be test.

 
 Reply 
 
Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
17:27 Jul-10-2018
Re: Reflection transmission formula at incident angles.
In Reply to Philippe Rioux at 14:30 Jul-10-2018 .

Philippe, I made a few more experiments in Civa to see how the interface at the coupling boundary would display. It appears that there is an assumption using a "wedge" model that there is no return signal internally from the wedge. This is probably not an issue for the angle beam inspections, but for a delay line (0°) the time in the delay line is critical to assessing the thickness that the probe can be used on.
Then I tried the equivalent for an immersion probe at 0° incidence on a plate. I can configure Civa to provide multiples from within the test piece, and of course I can see the first waterpath interface signal. But Civa does not then calculate the reflected waterpath for waterpath multiples. This would require a reflection off the element face and it seems that Civa only uses the element as a piezo source and does not use it as another "object" where a beam can reflect.

2
 
 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
10:31 Jul-11-2018
Re: Reflection transmission formula at incident angles.
In Reply to Ed Ginzel at 17:27 Jul-10-2018 .

Hi Ed,
I wonder if I could impose as discussions on this thread have digressed away from my immediate problem. I understand however the point and content of the discussions. My problem is which is the better option to achieve the maximum longitudinal beam intensity in steel at a transmitted angle of 22 degrees. My choices are:
a. using a steel wedge with a compressional beam directly at 22 degrees into the test material, accepting that there will be losses due to impedance mismatch reflection, or
b. using an acrylic plastic wedge below the first critical angle of refraction that produces a transmitted 22 degree refracted compressional beam, internal acrylic reflections due to impedance mismatch and transmitted unwanted shearwaves.

It would be great if I could identify the mathematical derivation of the solution?

 
 Reply 
 
Ed Ginzel
R & D, -
Materials Research Institute, Canada, Joined Nov 1998, 1274

Ed Ginzel

R & D, -
Materials Research Institute,
Canada,
Joined Nov 1998
1274
14:34 Jul-11-2018
Re: Reflection transmission formula at incident angles.
In Reply to George Crowe at 10:31 Jul-11-2018 .

George, I am not sure we have digressed too far from the initial problem. If we look at the geometry of placing a probe on a steel wedge (steel of identical acoustic properties to that being tested), the "ideal" condition you are suggesting has a 0° incidence of the beam on the steel-wedge. IF the steel wedge was perfectly coupled to the steel test piece (e.g. welded) it does not matter what angle the slope is relative to the test piece because the pulse moves past the steel-steel interface without refraction and, more importantly, without reflection. In the ideal case, there would be no loss as the pulse moved from steel to steel without changing direction. But Mark identified the practical issue of the couplant at the interface. This would redirect the pulse back into the wedge. Our plastic wedges have slower velocities than steel so the internal bounces take a relatively longer time to return to the element and in addition they have damping materials used to reduce/eliminate this unwanted signal. However, you will be hard pressed to eliminate the internal reflections with a steel wedge. The Civa model is probably a good indicator of the pressure you can transfer (i.e. steel is about 19dB more pressure than plastic). But you will need to consider the wedge design to allow a region of time unobstructed by internal echoes since the thin film of couplant does not allow a perfect transfer of pressure.

 
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