# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 2 Materials and Methods
### Calibration of the Strain Gauges and Laser Signal Set Up  
The main signal to control during the tests was the alternating stress at a point of the pin or at a point of the box close to the connection edge. These two values would nominally be the same, but some differences generally occurred for experimental reasons or geometry inaccuracies. For this reason, the controlled quantity during the tests was the average between the alternating stresses at the pin and box strain gauges' locations. Therefore, the calibration of the strain gauges was crucial in order to record reliable values of the stresses. During this operation, the static load was applied through a hydraulic actuator, and the load cell at the end of the actuator was previously calibrated. The positions of the applied load and of the supports were accurately recorded, and the three strain gauges to be calibrated were set at the pin, at the box, and at the connection, as shown in Figure 3a. Once the static load was applied, the voltage signals of the strain gauges were recorded, and the ratios between the stresses, calculated through the beam theory, and the voltages were evaluated and recorded. These ratios are indeed the conversion factors to be employed during the test, and this was repeated for each sample of the testing campaign. It might be argued that the stress calculated with the beam theory at the connection did not accurately represent the state of stress at this location. However, as explained below, the strain gauge at the connection was not considered as the stress reference of the tests. Nevertheless, it could be employed in case of failure of both the strain gauges at the pin and at the box. The procedure for applying the strain gauges is shown in Figure 3b-d. Given the pulsating load during the tests, the electric wires of the strain gauges were subjected to a push-pull load; thus, in order to enhance their fatigue lives, the fixing process required particular attention. As shown in Figure 3b, they were initially mounted loose, forming an omega shape. Then the strain gauges were glued to the samples using a Teflon tape with a layer of neoprene, which allowed us to uniformly distribute the pressure, during the glue curing, with a thin sheet of metal and two magnets. After that, the two layers of Teflon and neoprene were removed, and a slice of HBM ABM75 was employed, as shown in Figure 3d, to avoid large vibrations of the electric wires during the test. Despite these precautions to avoid the rupture of the electric wires, sometimes the signal had a failure after a certain percentage of the test duration, mainly due to the fatigue of the strain gauge grid. In order to reliably continue the test, the controlled signal was switched on a strain gauge not damaged or on a laser. The measures of the internal and external diameters at the locations of the strain gauges were of fundamental importance in order to perform the correct stress calculations during the strain gauges calibrations. As concerns the internal diameter, a comparator rod was conceived and produced, as shown in Figure 4. The measurement with the internal diameter rod comparator required three steps: first, it was inserted to reach the strain-gauge position; second, through a leverage system, the two adjustable side contacts were pushed until the internal diameter was reached. Then, the diameter span was registered, the comparator was extracted, and the desired measure was finally obtained with a caliper. According to Figure 4c, the alternative way was to cut the samples in correspondence with the strain gauges' locations and to measure the internal diameter, as done for the samples of the second kind of geometry. This operation could only be done at the end of the tests and required a more onerous set-up and a back-calculation of the actual stresses applied during the test. The external diameters were simply measured through the employment of a caliper.