12 R. W. L. Fong and J. Patrick -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 22 Circumference: 41.183 mm Circumference: 41.183 mm (contiguous) Tube Circumference: 41.183 mm Strain: -0.00 % (e) Fig. 2.4 Two sets of twin lasers measurement system: (a) twin lasers 1 and 3 at Q1 and Q3: on duty (while orthogonal twin lasers 2 and 4 at Q2 and Q4: off duty; (b) twin lasers 2 and 4 at Q2 and Q4: on duty (while orthogonal twin lasers 1 & 3 at Q1 and Q3: off duty; (c) profiles measured by lasers 1 & 3; (d) profiles measured by lasers 2 & 4; and (e) analyzed complete profile of tube circumference obtained from the 4 orthogonal lasers 9. All four lines are organized into a contiguous string of (x–y) data points to calculate the tube circumference at that given time. This instantaneous tube circumference (ci) is obtained by summing all the lengths between all two adjacent data points in the entire contiguous string of data points (Fig. 2.4e). 10. The instantaneous tube circumference (ci) is used to calculate the tube hoop strain using the relation given earlier (Fig. 2.4e). 2.3.1 Example of Analysis of a Fuel Sheath Biaxial Burst Specimen As mentioned earlier, the ability to scan the sample at different axial locations during the burst test provide a useful means to be now able to extract the maximum strain rate corresponding to where the maximum bulge (ballooning) strain is occurring on the tube as it progressively deforms to rupture. This measurement technique generates precise information on the onset event of metal instability and deformation behavior. In addition, since this four-laser measurement technique can capture the entire profile of the tube circumference, there is no ambiguity to discern whether or not the maximum diametral strain would have been captured. Figure 2.6 presents an example of analysis using the four-laser measurement technique where the tube is scanned all around the tube circumference at each different axial location on the tube by sliding all four lasers a short distance up and down (above and below) the Zr-tab which is used as reference position marker. From experience, the spot-welded Zr-tab is placed on the tube at a location fairly near where the maximum (bulge) ballooning is be expected to occur. The photograph shown on the left hand side of Fig. 2.6 shows the Zr-tab on the fuel sheath burst sample. On the right-hand side of the same figure are the results of analysis of the tube circumference (with no distorted circumferential profile) for the locations just above and below the Zr-tab for two cases. In Case A, the lasers moved upward, and Case B when the lasers returned and moved downward. At the Zr-tab locations, the laser scan results show the tube circumferential profile to be distorted, thus providing an indication of the reference marker location on the tube. Figure 2.7 shows some results of the four-laser measurement of the full tube circumference of a fuel sheath sample during a ballooning test to burst. The snapshot photographs taken from the video camera show the axial location of the laser scan on the tube relative to the location of the Zr-tab reference marker.
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