THE UNIVERSITY OF ADELAIDE

THE SCHOOL OF MECHANICAL ENGINEERING

FRACTURE MECHANICS

LAB CLASS 3

Mason Said

A1192868

2013

Unstable crack growth velocity in PMMA

Methodology and Results

1. Calibration of grid

Using the grid image captured at the beginning of the experiment, the image was imported into MATLAB in order to measure the x distance of the grid in pixels.

The MATLAB code used is as follows:

A=imread('calibration_0.jpg');image(A)[X,Y]=ginput(2)

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Figure 1: Calibration grid

Note: x and y axes are in ‘pixels’.

X =

1.0e+002 *

0.619377880184332

5.084262672811059

Therefore, the x distance measured over 7 squares is:

7 xsquare=508.43−61.94=446.40 pixels

xsquare=446.407

=63.78 pixels

Since the actual distance of 1 square is 5 mm, then the calibration factor for each pixel is:

CalibrationFactor= 563.78

=0.0784mm / pixel

2. Measuring crack length distance

Using the MATLAB code above, the crack lengths for each image were measured and recorded.

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Figure 2: Test specimen at the first time interval

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Figure 3: Test specimen at the 7th time interval

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Figure 4: Test specimen at the 35th time interval (final interval)

The crack lengths were then calibrated to actual real-life values in millimetres.

3. Calculating crack path velocities

The crack length distances were then recorded in increments. The differences (or increments) in crack length distances were divided by a time interval of 0.0001 seconds, thus producing the crack path velocity values for each increment in millimetres per second. The crack path velocity is the slope of the curve in the crack length distance vs time plot.

Table 1: Results of the crack length distances and the crack path velocities over each interval

x-distance (pixels)

Crack path distance after calibration factor (mm)

Crack path distance increments (mm)

Crack path velocity (mm/s)

Time (seconds)

0 0 0 0 0.00014.99 0.391216 0.391216 3912.16 0.0002

188.15 14.75096 14.35974 143597.4 0.0003200.12 15.68941 0.938448 9384.48 0.0004206.61 16.19822 0.508816 5088.16 0.0005208.61 16.35502 0.1568 1568 0.0006214.6 16.82464 0.469616 4696.16 0.0007

217.59 17.05906 0.234416 2344.16 0.0008221.08 17.33267 0.273616 2736.16 0.0009222.08 17.41107 0.0784 784 0.001224.58 17.60707 0.196 1960 0.0011224.58 17.60707 0 0 0.0012224.58 17.60707 0 0 0.0013224.58 17.60707 0 0 0.0014224.58 17.60707 0 0 0.0015225.58 17.68547 0.0784 784 0.0016228.07 17.88069 0.195216 1952.16 0.0017228.07 17.88069 0 0 0.0018231.07 18.11589 0.2352 2352 0.0019232.56 18.2327 0.116816 1168.16 0.002232.56 18.2327 0 0 0.0021232.56 18.2327 0 0 0.0022233.06 18.2719 0.0392 392 0.0023233.06 18.2719 0 0 0.0024233.06 18.2719 0 0 0.0025233.06 18.2719 0 0 0.0026234.06 18.3503 0.0784 784 0.0027234.06 18.3503 0 0 0.0028234.06 18.3503 0 0 0.0029234.06 18.3503 0 0 0.003235.06 18.4287 0.0784 784 0.0031

236.56 18.5463 0.1176 1176 0.0032236.56 18.5463 0 0 0.0033239.46 18.77366 0.22736 2273.6 0.0034246.76 19.34598 0.57232 5723.2 0.0035

0 5 10 15 20 25 30 35 400

5

10

15

20

25

Crack length

Series2

Time (in seconds)

Crac

k pa

th d

istan

ce (m

m)

Figure 5: Crack path distance vs time of fractured specimen

0 5 10 15 20 25 30 35 400

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40000

60000

80000

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Crack Path Velocity

Series2

Time * 0.0001 (seconds)

Crac

k Pa

th V

eloc

ity (m

m/s

)

Figure 6: Crack path velocities vs time of fractured specimen

Analysis

The PMMA experiences a very high mode 1 load, where the specimen fractures at the crack tip. The PMMA specimen shows a rapid crack growth over a time interval of 1/10000 of a second, at the 0.0003 second interval. The specimen suffered a dynamic fracture, where the static loading created from the heavy weight rig forced the specimen to exceed its dynamic fracture initiation toughness, thus resulting in a rapid crack growth after initiation. Since a majority of the crack path velocities are recorded over 500 mm/sec, then the rapid crack propagation is a result of unstable crack growth.