14 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: 1779 Tube Circumference: 41.183 mm Strain: 2.31 % -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1809 Tube Circumference: 41.183 mm Strain: 3.07 % Laser moving up Laser moving down Zr-tab Thermocouple Fuel Sheath Sample Thermocouple Top Bottom Edge of Zr-tab Edge of Zr-tab -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1778 Tube Circumference: 41.183 mm Strain: 1.33 % -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1769 Tube Circumference: 41.183 mm Strain: 6.02 % -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1768 Tube Circumference: 41.183 mm Strain: 2.73 % -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1810 Tube Circumference: 41.183 mm Strain: 3.37 % -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1819 Tube Circumference: 41.183 mm Strain: 1.76 % -15 -10 -5 0 5 10 15 X-position (mm) -15 -10 -5 0 5 10 15 Q1 Q3 Q2 Q4 Specimen #3: Row: 1820 Tube Circumference: 41.183 mm Strain: 2.68 % Distorted profiles Distorted profiles Case A Case B t = 177.9 s t = 177.8 s t = 176.9 s t = 176.8 s t = 180.9 s t = 181.0 s t = 181.9 s t = 182.0 s Fig. 2.6 Example of four-laser measurements of tube circumference at different axial location on the fuel sheath burst sample In Fig. 2.7b, the tube was further heated to 700◦C, and a laser scan was made at a location on the tube just before it burst. The analyzed tube circumference showed that the tube ballooned extensively (>120% hoop strain) – shown in the plot below. The profile of the tube circumference indicated in the plot showed that the tube had ballooned uniformly. At high temperature uniform ballooning is usually expected, whereas at low temperatures or at high pressures, asymmetric (lopsided) deformation and burst can be expected. This translates to increasing the difference between the maximum and minimum diameter of the tube. As such, the measurement results could be affected or biased depending where the diameter measurement was taken. 2.3.2 Example of Analysis of a Dog-Bone Specimen A slightly different MATLAB routine is used for analysis of the laser data for a flat sample as it has a four-sided cross-section geometry. The displacement data collected by the four lasers in the width and thickness directions are used to compute the tensile axial strain in the specimen (i.e., along the loading direction). This MATLAB routine does not require the above Steps 6 and 7 (i.e., fitting a circle to the line profile and using the fitted center to translate the profile to the origin of the sample coordinates). These two processing steps are replaced by simply pre-determining the standoff distance of each laser sensor and calibrating the standoff value to translate the line profile that fits the sample dimension in sample coordinates. The following relation is used to calculate the true strain in each principal direction: εtrue =ln(l/lo), where l and lo are the instantaneous dimension and the original dimension in that direction, respectively. Assuming constant volume, the strain in
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