# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 2 Materials and Methods
### Types and Geometries of the Tested Specimens  
Five types of geometries were tested by means of the introduced test rig, and their technical drawings are reported in Figures 7 and 8, while the nominal diameters of the various sections of the drill pipes are reported in Figure 9. The nomenclature of the investigated geometries refers to the nominal external diameter and the wall thickness of the pipe body. The first type of geometry was named as Connection with 5-1/2\(\times\)0.415\" pipe body, and it presented either a regular upset or a longer upset as explained in Figure 7a,b. The second type of geometry, named Wired Connection with 5\(\times\)0.374\" pipe body, presented an internal hole to accommodate a wire sensor, while the third type of geometry was named Connection with 6-5/8\(\times\)0.750\" pipe body. Finally, the fourth type of geometry was a pipe specimen 6-5/8\(\times\)0.750\", for which the test was focused just on the pipe body instead of the connection region. In Figures 7 and 8, the positions of the supports, determined through the FE analysis explained in Section 2.1, and the positions of the strain-gauges are reported. The strain-gauges were not always applied to the pipe body of the drill-pipe as in Figure 7a,b, but at the (pin and box) upset regions instead. This last accommodation of the strain gauges was motivated by the fact that there was not a pipe body zone on one half of the longer upset samples, so the strain gauges were both located at the upset region  
Figure 5: (**a**) Control scheme to explain the driving of the test rig, (**b**) electronic devices employed during the tests.  
for uniformity. The third type of geometry presented a heavier section than the other two types with a connection zone. This had an effect on the value of the first natural frequency. Additional fixed masses were thus applied to lower the natural frequency of the structure, as shown in Figure 8. The measured external and internal diameters differ from the nominal values; for example, for a sample belonging to the category Wired Connection with \(5\times 0.374\)\" pipe body, the measured external diameter resulted equal to \(D_{\text{ext}}=127.8\) mm, whereas the measured internal diameter was equal to \(D_{\text{int}}=105.8\) mm. In the case of the wired samples, all the measured diameters resulted in a smaller value of the measured internal diameter than the nominal value and a bigger value of the external diameter than the nominal value. The samples of the first kind of geometry were made of AISI 4340 steel, those of the second kind were made of S135 steel grade, with a yield stress of \(S_{\text{Y}}=135\) ksi, and those of the third and fourth kinds of geometry were made of Z140 steel or UD165 steel grades, corresponding to a yield stress of \(S_{\text{Y}}=140\) ksi and \(S_{\text{Y}}=165\) ksi, respectively. The reported values of the yield stress are the minimum guaranteed during the tests.  
Figure 6: (**a**) Qualitative trend of the stresses during the tests at the pin, at the box and the connection strain gauge locations, (**b**) qualitative trend of the horizontal and vertical displacements obtained by the laser sensors and (**c**) saved stress and displacement amplitudes during one of the tests along the accumulated number of cycles.  
Figure 7: (**a**) Connection with 5-1/2\(\times\)0.415” pipe body—Regular upset, (**b**) Connection with 5-1/2\(\times\)0.415”—Longer upset, (**c**) Wired Connection with 5\(\times\)0.374” pipe body.  
Figure 8: (**a**) Connection with 6-5/8\(\times\)0.750” pipe body, UD165, (**b**) Connection with 6-5/8\(\times\)0.750” pipe body, Z140, (**c**) Pipe specimen 6-5/8” Z140 and UD165 and application of additional masses to both the connection and the pipe specimens for lowering the first natural frequency.