wave velocity measurements lab #1

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South Dakota State University ErBrookings SD 57007

ME-492 Non-Destructive Testing

Laboratory Report

Wave Velocity Measurements

Laboratory No.1

Written by: Eric S. Krage Class Section 01

Instructor: Dr. Jikai Du Date Performed: 09/14/2012


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Abstract:

The longitudinal and shear wave velocity are measured in a standard as well as anunknown sample using an Olympus Omni Scan MX. A standard calibration block was used tofind how to test various ways to improve the velocity measurement. We found to it to be mostaccurate to measure over multiple waveforms to divide the human error. Calculations forlongitudinal and sh ear wave velocities using Youngs modulus coupled with Poissons ratiodefines the properties of the unknown material which proved the unknown material to besteel. The depths of three holes were determined in another sample within 5% error.


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Table of Contents

Abstract .. a

List of Figures, Tablees and Experimental Apparatus . 1

Introduction .2

Experimental Procedure .... 2

Experimental Results and Analysis...9

Interpretation of Results and Discussion .9

Conclusion .10

References and Appendix .. 12


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List of Figures

Figure 1: Aluminum 7075- T6 calibration block ..2

Figure 2: Steel 0.297 thick 1 dia. Unknown modulus 2

Figure 3: Steel bloc with holes 10.71, 17.53, and 23.89mm from left to right respectively .. 3

Figure 4: Calibration block signal analysis for the longitudinal wave transducer .. 4

Figure 5: Multiple signal averaging of the 0.50 aluminum block (Longitudinal Wave Transducer) 4

Figure 6: Trend line of thickness vs. time of calibration block 6

Figure 7: Shear Wave Transducer on 0.500 thick position of the aluminum calibration block 7

List of Tables

Table1: Cali bration block @ 0.500 thick longitudinal wave transducer 5

Table 2: Calibration block trend line (Longitudinal Wave Transducer) 5

Table 3: calibration Block 0.500 thick (Shear Wave Transducer) .. 7

Table 4: Steel slug (Longitudinal Wave Transducer) . 8

Table 5: Steel Slug (Shear Wave transducer)

Table 6: Steel block hole depth measurements ..

Table 7: Wave Velocity Measurements of Steel Slug and Mechanical Properties ..11

Apparatus

OriginPro 8 graphing utility Shear Wave Piezo operating frequency 5MHz Longitudinal Wave Piezo operating frequency 3.5 MHz Olympus Omni Scan MX Digital calipers


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Introduction

The goal of this experiment is to become proficient in the procedures for measuring thevelocity of longitudinal and shear waves in media.

Sample Description

There were three different samples analyzed for this laboratory procedure.

Aluminum Calibration Block:

The block had five steps that were marked in increasing increments of 0.100 inches from left toright. The aluminum used was 7075-T6. Figure 1 is a picture of that block used.

Figure 1: Aluminum 7075-T6 calibration block

Steel Unknown Disk:

The steel disk was 0.297 in. and a 1 in. diameter which is represented in Figure 2.

Figure 2: Steel 0.297 thick 1 dia. Unknown modulus.


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Aluminum Block with 3 holes at varying depth:

The aluminum block had three holes drilled at different depths as shown in Figure 3. Thethickness of the block was 0.625 and a height of 4. With hole depths of 10.71, 17.53, and23.89mm measured from the top and left to right respectively.

Figure 3: Steel bloc with holes 10.71, 17.53, and 23.89mm from left to right respectively

Experimental Parameters

Using the Olympus Omni Scan MX the shear and longitudinal wave transducers were used at5MHz and 3.5MHz respectively. Using a digital caliper we verified the thickness of the blocksample step block, round block, and block with holes in them. The caliper was then used tomeasure the depth of the holes in the block to check the modulus of the block itself.

Aluminum Calibration Block Velocity Measurements.

Using the longitudinal wave transducer with the frequency set to 3.5MHz we measure the timeit took to travel through the block on four of the five thicknesses of the calibration block. Themeasurements in Table 1 were done on the 0.5 step as seen in F igure 1. The time readings

were done between two signal beginnings as seen in Figure 4 and averaged over multiplewaveforms Figure 5. Calculating the longitudinal wave velocity using C = 2* (d/T) which yieldsthe wave velocity to be 2.44*10 7 m/s.


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Figure 4: Calibration block signal analysis for the longitudinal wave transducer

Figure 5: Multiple signal averaging of the 0.50 aluminum block (Longitudinal Wave Transducer)


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Table1: Calibration block @ 0.500 thick longitudinal wave transducer

Trial T1 (us) T2 (us) T (us)

1 4.16 8.32 4.16

2 12.34 16.43 4.09

3 20.77 24.82 4.05

4 Wave Form Average (4) 4.18 20.53 4.09

Average time to travel 0.500 4.10

Calibration Trend Line (Longitudinal Wave Transducer) Table 2 shows the time readings that were taken between two consecutive signal peaks atdifferent steps or thicknesses of the aluminum calibration block. This calibration line will givethe capability to be able to compare the calibration block thickness with unknown thickness.Figure 6 show the trend line of the calibration block using the longitudinal wave transducer.

Table 2: Calibration block trend line (Longitudinal Wave Transducer)

Depth (inches) T (us)

0.100 0.83

0.200 1.64

0.300 2.49

0.400 3.26

0.500 4.10


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0.0 0.2 0.4 0.6

1

2

3

4

T i m e

( u s

)

Thickness (inches)

Equation y = a + Adj. R-Sq 0.9997

Valu StandardTime Interce 0.0 0.02062Time Slope 8.1 0.06218

Figure 6: Trend line of thickness vs. time of calibration block

Signal Measurement of Shear Wave Transducer

The shear wave transducer was calibrated for wave speed on the 0.500 thick location of thealuminum calibration block. Figure 7 represents the signal measurements of the shear wavetransducer note that to get a good signal force needs to be applied down on the transducer totranslate the vibrational energy into the medium. Tables 3 give us the average time of the sheartransducer velocity in the aluminum calibration standard. The shear wave velocity wascalculated C = 2* ( d/ T) = 2.70*10 4 m/s.

The shear wave transducer velocity was found to be c T = 0.107 in./us. Comparing with TableE.1-1 the shear wave velocity c T= 3.14 mm/us, which converts to 0.123 in./us. The differencebetween these numbers is 13.7%. The large error in the shear transducer is most likely due topoor coupling between the material and the transducer as well as human error.


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Figure 7: Shear Wave Transducer on 0.500 thick position of the aluminum calibration block

Table 3: calibration Block 0.500 thick (Shear Wave Transducer)

Trial T1 (us) T2 (us) T (us)

1 9.87 14.55 4.68

2 9.76 14.49 4.73

3 9.81 14.52 4.71

Average 4.71

Wave Velocity Measurements of Steel Slug

The thickness of the steel round specimen was measured with a digital caliper to be 0.297. Thethickness measurement was used for all the following calculations. See Figure 2 for furtherdescription of specimen. The longitudinal wave velocity was examined and data Table 4 shows


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that the longitudinal wave velocity c = 2* (d/T) = 5.79*10 3 m/s. The shear wave velocity wascalculated to be c = 3.26*10 3m/s data is shown in Table 5.

Table 4: Steel slug (Longitudinal Wave Transducer)

Trial T (us)

1 2.54

2 2.61

3 2.64

Average 2.597

Table 5: Steel Slug (Shear Wave transducer)

Trial T (us)

1 4.66

2 4.61

3 4.63

Average 4.633

Steel Block Hole Depth Measurements Using Longitudinal Wave Transducer

The longitudinal wave transducer was used for all of the elements on the steel specimen withholes. Firs the wave velocity was found in this medium. Three time readings were taken foreach hole of different depth and averaged. See Figure 3 for sample image. Please see Table 6

for the three readings.

Table 6: Steel block hole depth measurements

Hole Number Time (us) Depth Calculated Depth Measured %Difference

1 3.53 11.33 10.70 mm 6.8


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2 5.31 17.04 17.53mm 1.4

3 7.60 24.39 23.89mm 1.03

Hole depth velocity measurements (Longitudinal Wave Transducer)

Results Analysis

Aluminum Calibration Block Velocity Measurements

Using the longitudinal wave transducer the first two techniques are similar to one another withan average of 0.244 mm/us. Table E.1-1 p.401 shows a wave speed c L=6.27 mm/us which isequivalent to c L=0.2469 mm/us.

1 Comparing the two values yields a 1.1% difference betweenthe two values which is well within the experimental error. This error can be from human erroror resolution of the equipment to detect the signal more accurately.

Wave Velocity Measurements of Steel Slug

Using equation 1 we can calculate Youngs modulus of the unknown steel slug. Equation 2 willbe used to calculate the shear modulus of the sample and equation 3 will determine poisonsratio. To calculate Lames first constant we will solve equat ion 4 and to transform betweenthe two values c L and c T we will use equation 5 &6.

( ) * ( )+ (1)

Where E = Modulus of elasticity G = Shear Modulus = Lames constant

( ) Where = density (2)

( ) (3)

( ) * ( )+ (4)

(5)

(6)


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Steel Block Hole Depth Measurements Using Longitudinal Wave Transducer

The steel block with three holes Figure 3 depth was measured using the ultrasound technique.The holes measure depths were very accurate when comparing the caliper values with theultrasound values as shown in Table 6. The small observed error is most likely due to not beingdirectly over the center of the hole varying where the wave gets reflected from thus changingthe distance measured.

Summary / Conclusions

Through the experiment comparing the results with the standards there was little knownobserved error and all within standard experimental error. The wave velocity measurementimprovements can be made by measuring over multiple wave forms.

The properties of the steel were successfully measured with errors within the predicted errorbound of the given equations.

The depth measurement of the holes in the steel block was accurate. This method of ultrasound to detect holes and measure the depths of holes in a medium can be quantified asreliable and accurate.

Use of ultrasonic testing is clearly an advantageous method of non-destructive testing fordefects or use in other situations.

Question / Answer

1. Why would measuring the difference between the first and second backwall echo bemore accurate than between the main bang and the first backwall echo?The main bang is not concise leading to us not being able to clearly distinguish thebeginning of the signal. The first and second echoes are much more defined and able totell when the signal starts and ends to decrease measurement error.

2. Why would measuring the difference between a second and third backwall echosometimes be more accurate than between the first and second backwall echo?

The disadvantage of measuring the first and second backwall echo is that in thin sampleswaves are often very close together making it difficult to distinguish between the themand the main bang. Using the data from the second and third echo allows the wave to bemore developed and distinguishable and improving accuracy of measurement.

3. What are some suggestions on how to improve the accuracy of a velocitymeasurement? To improve the wave velocity calculations are to measure over multiple


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wave forms, improved detector resolution, eliminate background, and thicker material.By measuring over multiple waveforms you are minimizing the experimental error because it is divided among multiple elements. Through improving detector resolutionthe signal can be smoothed and the corresponding measuring points can be more easily

determined. If the sample was measured on a different backing to eliminatetransmission into the table in our case would eliminate noise and the signals would bemore distinguishable. The sample thickness being too small makes it difficult to tell thedifference between the signals if a single pulse were able to be generated and measured the reverberations from just that single pulse would improve the accuracy.

4. Calculate Youngs modulus, shear modulus, and Poissons ratio of the unknownmaterial. The values for Youngs modulus, shear modulus, and Poissons ratio can beseen in Table 7 below.

Table 7: Wave Velocity Measurements of Steel Slug and Mechanical Properties

E 201.4 * 10 9 Pa

G 82.47 * 10 9 Pa

0.27


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References

Rose, Joseph L. Ultrasonic Waves in Solid Media. Cambridge [ u.a.: Cambridge Univ. 2004]

2http://www.mxindustrial.com/index.php?route=product/product&product_id=294 Figure for

aluminum block

Appendix. N/A
http://www.mxindustrial.com/index.php?route=product/product&product_id=294http://www.mxindustrial.com/index.php?route=product/product&product_id=294http://www.mxindustrial.com/index.php?route=product/product&product_id=294http://www.mxindustrial.com/index.php?route=product/product&product_id=294

wave velocity measurements lab #1

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