# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 3 Results  
The fatigue crack initiation regions are listed in Table 1 for each type of connection. The Connection specimens with 5-1/2\(\times\)0.415\" pipe body and the Connection with 6-5/8\(\times\)0.750\" pipe body, failed at the FET of the pin side, whereas the failure of the Wired Connection samples was located at the pipe body. The fatigue test results of each specimen are also reported in Table 1 in terms of the stress amplitude and the number of cycles to failure. As mentioned before, the strain gauges were placed on the upset zone for the Connection with 5-1/2\(\times\)0.415\" pipe body while at the pipe body for all the other geometries. The imposed amplitude stress in correspondence with the pipe body of the specimens was \(\sigma_{\text{a,ref}}=270\) MPa. In order to keep the same stress amplitude at the pipe body, the target stress to be imposed at the upset region was rescaled by means of the beam theory combined with the modal distribution of the bending moment. The numerical values of the stress amplitude presented in Table 1 are referred to the imposed alternating stress at the pipe body, about the connection samples with 6-5/8\(\times\)0.750\" pipe body, and to the stress at the upset region regarding the Connection with 5-1/2\(\times\)0.415\" pipe body. On the other hand, the values of the stress amplitude of the Wired Connection samples, reported in Table 1, substantially differ from the nominal \(\sigma_{\text{a,ref}}=270\) MPa because the measured values of the internal diameters obtained at the end of the tests were different from the nominal ones and, in addition to this, the locations of the fatigue cracks were not exactly in correspondence of the strain gauges positions. The bending moment at the initiation positions was lower than that at the strain gauges, so the material was expected to be not perfectly uniform; otherwise, the failure would have been obtained near the upset region where the load is higher. According to this, the bending moment acting on the section corresponding to the failure was obtained from that at the strain gauge location, and a rescale factor was calculated from the modal FE distribution of the bending moment. The fatigue strength data of the tested samples of all the geometries involved in this research, and that of the previous tests presented in ref. [43] (for comparison), are reported in Figure 10. In addition to the S-N data, fractographic images about the initiations and subsequent propagations of the cracks are shown in Figure 11 for all the drill pipe connection types involved in this research. An FE model was implemented to investigate the effect of the through hole on the structural strength of the Wired Connection, and the results are presented in Figure 12. As shown in this figure, a Global FE model was initially solved after applying a bending moment corresponding to one of the fatigue tests, while a fixed support was applied on the other side. A Submodel of the transaction region between the pipe body and the upset  
Figure 9: External and internal diameters of: (**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” and (**d**) Connection with 6-5/8\(\times\)0.750” pipe body. was then implemented, as shown in Figure 12b. Both the Global model and the Submodel exploited one plane of symmetry. The loading displacements then applied to the Submodel were obtained at the interface surfaces by interpolating the Global model. Both the Global and the Submodel maps of the axial stress, Figure 12a,b, show that the maximum is located far from the hole zone. The distribution of the axial stress obtained from the Submodel was extracted along a path on the hole's internal surface, and it is shown in Figure 12c where it is evident the absence of a high gradient stress concentration.