Assignment 5-6 DIC LAB Ruben Stam - Assignment DIC LAB Strength of Ships MT Ruben Stam 5487552 3/9/ - Studeersnel (2024)

Assignment DIC LAB

Strength of Ships MT

Ruben Stam

5487552

3/9/

1. Assignment before the experiment

IMPORTANT: Note that you need to submit this assignment in order to attend the lab session. Please

be ready for a short discussion of your answers.

1) Read the material in reference [1].

2) Figures 1 and 2 below respectively show greyscale images of an object before and after motion. Figures 3

and 4 show the corresponding grey values. The grey values can be downloaded in tabulated form from

Brightspace in the file ‘Sec5Ques2_data.’ The object was subjected to a rigid body translation, but

random errors are present in the recorded greyscale values. Minimize the correlation function given by

Equation (1) in Section 2 to find out the displacement that has occurred. Use the subset shown by the

red box with size 4 x 4 in Figure 1 for this calculation.

Minimized correlation score: 0

Displacement:

Horizontaal: 1 naar links; Verticaal: 3 naar onder.

i ma ge before tra ns l a ti on i ma ge a fter tra ns l a ti on

68 ## ## ## ## 27 ## ## ## 39 ## 71 ## 50 33 ## ## 38 51 106

223 ## ## 42 ## 27 ## 74 ## ## ## 52 ## 42 65 ## 89 ## 0 153

212 30 75 ## ## ## 8 16 ## ## ## 0 ## 70 ## 94 90 40 36 42

20 ## 88 31 ## 42 3 ## ## 26 ## ## ## ## ## ## 4 ## ## 105

179 66 ## 67 ## 90 17 ## 59 ## 58 ## ## ## ## ## ## 37 ## 128

117 ## ## 19 ## 82 ## 63 56 56 ## 35 ## ## 10 88 62 38 ## 89

53 85 ## ## ## ## ## ## 26 ## ## 57 ## ## ## ## 19 ## ## 127

170 ## 77 ## ## ## ## ## 78 64 72 ## ## 31 27 6 15 18 94 0

86 ## ## 59 ## ## 53 ## 92 40 ## ## 0 ## ## 0 ## ## ## 33

77 ## ## 47 ## 79 ## ## 24 ## 41 ## 19 ## ## ## ## 19 ## 241

Totaal: Vierkantje: Nieuw totaal:

1840 1 2058 1892 2200 1869 1916 1783 1537

2 2290 2355 2449 2029 1979 1842 1648

3 2444 2421 2420 1965 1614 1787 1641

4 2524 2490 2502 2072 1808 2105 1974

5 2259 2101 2034 1522 1323 1685 1610

6 2096 1893 1691 1351 1325 1614 1605

7 1963 2110 1840 1703 1632 1662 1715

47524 2704 1E+05 841 5776 3249 91809

2E+05 3E+05 4E+05 35721 19321 4 36864

4E+05 3E+05 3E+05 15625 51076 2809 39601

5E+05 4E+05 4E+05 53824 1024 70225 17956

2E+05 68121 37636 101124 3E+05 24025 52900

65536 2809 22201 239121 3E+05 51076 55225

15129 72900 0 18769 43264 31684 15625

3) What are the advantages of using DIC compared to strain gauges for the experiment?

• It is a non-contact measurement technique.
• It can be used to quantify strains over the entire field of view using a post-processing technique,

thereby capturing strain differences very well.

4) A sketch of the plate is given below.

Figure: Test plate with point 1,2 and 3 indicated.

Point x-coordinate [mm] y-coordinate [mm]

1 0 0

2 50 80

3 - 20 - 200

5) Assuming a yield strength of 235 MPa and that the primary mechanism of force transfer is pure shear

between the attachment strips and the plate, calculate the maximum force and the corresponding number

of discs that the can be applied such that there is a safety factor of two from yielding.

Stress in pure shear at yielding:

𝜎𝑣𝑚 = √(

####### 1

2 ) (𝜎 11 − 𝜎 22 ) + 3 ∗ 𝜎 11

𝜎 11 =

####### 1

####### √ 3

∗ 235 = 135. 7 𝑀𝑃𝑎

Applied force at yielding:

𝐹 = 𝜏 ∗ 𝐴

𝐴 = 60 𝑚𝑚 ∗ 6 𝑚𝑚 ∗ 2 = 0. 00072 𝑚^ 2

𝐹 = 97. 7 𝑘𝑁

Maximum force with a safety factor of two:

𝐹 =

####### 97. 7

####### 2

= 48. 8 𝑘𝑁

Number of discs:

48. 8 ∗

####### 1000

2452. 5 = 19. 89 𝑑𝑖𝑠𝑐𝑠 = 20 𝑑𝑖𝑠𝑐𝑠

6) Explain what would happen to the measured strains if you use 2-D DIC and move a rigid body toward the

camera during a DIC measurement.

De ‘strains’ worden groter, omdat ze fout gemeten worden t.o. referentiepunt.

7) Explain what happens if some of the pixels were saturated (i. pure white) in 2-D DIC. (Note that drawing a

small graphic may be informative).

Zogenaamde ‘whitepots’ geven dan errors. Er is geen verschil meer tussen de gemeten waarde, omdat de

pixels ‘te’ saturated zijn. Hierdoor heb je dus geen resultaat meer van je 2-D DIC, want het beeld dat je

krijgt is niet heel veel meer op te zien behalve dat het overbelicht is.

8) Read the assignment in Section 6 so you are prepared to collect the relevant data.

6. Assignment after the experiment

1) What subset size did you use? 27 pixels

2) What distance between grid points did you use? 25 pixels

3) What is your resolution in pixels/mm? 3 pixels/mm

4) Plot the normal stresses acting in the y-direction at the cross-section y = 0 when the plate is

loaded by the number of discs calculated in question 5) of the pre-lab assignment. Attach the

plot in your submission.

7) Find the eigenvalues of the stress tensors of points 1, 2 and 3 found above.

Point 1:

𝜆 1 = 7. 2

𝜆 2 = − 1. 36

Point 2:

𝜆 1 = 187. 1

𝜆 2 = − 17. 8

Point 3:

𝜆 1 = 31. 2

𝜆 2 = − 268. 1

8) Construct Mohr’s circles of stress for points 1, 2, and 3, for the same level of

loading as considered in question 6). For each of these points, find the

direction of principal stresses, and provide sketches to illustrate the direction

and magnitude of the principal stresses. Compare the eigenvalues in 7) and

the principal stresses obtained in 8), and comment on the comparison.

Point 1

The Circle of Mohr:

𝜆 1 = 7. 2

𝜆 2 = − 1. 36

Point 2

The Circle of Mohr:

𝜆 1 = 187. 1

𝜆 2 = − 17. 8

Point 3

The Circle of Mohr:

𝜆 1 = 31. 2

𝜆 2 = − 268. 1

Bij punt 3 zijn de eigenwaarden en principal stresses nagenoeg hetzelfde, wat mij de bedoeling

lijkt. Bij de punten 1 en 2 zit hier echter meer marge tussen. Namelijk, bij punt 2 ligt één

principal stress redelijk dichtbij een van de eigenwaarde en wijkt de andere redelijk af.

Ditzelfde geldt voor punt 1.