2 Non-contact Measurement of Strains Using Two Orthogonal Sets of Twin “Blue” Lasers 11 Once the sample is readied, a burst test comprises the following steps. 1. Apply a prescribed controlled constant axial load on the sample using the tensile machine. This allows a prescribed biaxial stress state to be imposed on the tube sample (e.g., to simulate a “closed-end” type of burst test where the axial stress is half the hoop stress – i.e., axial-to-hoop stress ratio of 0.5). 2. Enable all the controllers, vis-à-vis, (a) four lasers, (b) two slides, (c) PID temperature feedback for AC power supply, (d) video cameras, and (e) LABVIEW data acquisition and control system (programmed to control alternating trigger cycling duty of the two orthogonal set of twin lasers, and controlling motorized needle valves for the sample pressuring gas feed and bleed system). 3. Start the slides which holds the four lasers to move repeatedly up and down to scan the sample to a set distance above and below the spot-welded Zr tab. If desired, the slides can be set at a fixed (stationary) axial location to scan the sample. 4. Start the LABVIEW program. 5. Heat the sample using PID controls to prescribed test conditions. The prescribed test conditions can be a simple single creep test (at a desired constant temperature) or staged creep test (multiple steps of different constant temperatures), a ramped pressure, or a ramped temperature test condition. 6. Once the test is completed, allow the sample to cool to room temperature then obtain laser scans on the burst sample at various axial locations and at the maximum ruptured diameter location, before removing the sample for ex situ post-test examination. 7. Disable all controllers, and close out the LABVIEW program. 2.3 Analysis The analysis of displacement data collected by the four lasers at a given time is processed using a MATLAB routine which we have developed to determine the full circumference of the tube that is used to calculate the hoop strain. The hoop strain is calculated using the following relation: hoop strain (%) =(ci−co) ×100/co,where ci =instantaneous tube circumference and co =original (initial) tube circumference. The value for total circumferential elongation (TCE) is obtained using the relation: TCE (%) =(cf−co) ×100/co, where cf =final tube circumference and co =original (initial) tube circumference. Figure 2.4 illustrates an example of an alternating duty cycle of the two sets of twin lasers (laser 1 and 3 and laser 2 and 4), the individual displacement profiles measured, and the analyzed tube circumference determined using the MATLAB routine. Using an alternating duty cycle as shown in Fig. 2.4a, b, we have found that this measurement technique clearly eliminates crossover speckle interference originating from immediate adjacent (orthogonal) lasers. With the twin lasers 1 and 3 (diametrically opposite each other) operated from the same Keyence controller, the displacement profile of laser 1 is flipped about its y-axis and has positive values for y-displacement, and for laser 3, the profile is not flipped about its y-axis but has negative values for the y-displacement (Fig. 2.4c). The characteristics of the y-displacement profiles and orientations produced by the lasers as configured in the Keyence control operation have been verified with scans made on a four-sided calibration block with distinctly different profiles machined on each of the four faces. Similarly, for the twin lasers 2 and 4 which operated using a different Keyence controller, the y-displacement profiles and orientations produced are of the same characteristics as those generated by the twin lasers 1 and 3 (Fig. 2.4d). To determine the tube full circumference at a given time (Fig. 2.4e), the MATLAB routine follows the steps below to process the displacement profiles generated by the four lasers. Figure 2.5 illustrates the process step (1–8) listed below. 1. Flip the scan line (raw x–y data) about the y-axis for laser 1 and laser 2 (Step 1). 2. Trim “out-of-range” (y-displacement) data points, and remove excess data points at both tails if the length of the line is too long (Step 2). 3. Level the trimmed line to be parallel to the x-axis (Step 3). 4. Translate the levelled line with its mid-point centered on the centerline axis and its y-value corrected by adjustment to the untested tube radius (Step 4). 5. Rotate the line to the respective quadrant (e.g., laser 1 line to quadrant 1, and so on) (Step 5). 6. Fit a circle to the line to find the center x–y coordinates and the radius of the fitted circle. Using the known diameter of the tube before test, the levelled line is adjusted by calibrating to the known radius of the untested tube (Step 6). 7. Using the fitted center coordinates, the line is translated to the origin (0, 0) to be coincident with the axis of the tube, to be in the sample coordinates system (Step 7). 8. Trim each line along the x and y axes so that the line is solely contained within its respective quadrant (Step 8).
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