# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 4 Discussion  
The comparison of different connections and sizes put in evidence how the ratio between the section modulus of bending (namely \(\pi(D_{\text{ext}}^{4}-D_{\text{int}}^{4})/32D_{\text{ext}}\)), between connection, upset region, and pipe body, has a significant role in driving the position of fatigue crack initiation. It is worth noting that the modulus of bending depends on the cubic power of the external diameter, and also the internal one has a significant role. This justifies the employment of accurate instruments to obtain the true dimensions of the internal and external diameters. The fatigue crack is more prone to initiate at the connection, in particular at the FET of the pin, whenever the bending modulus at the connection is just slightly larger than that of the pipe body, and then the stress concentration at the thread root can be critical. On the contrary, the Wired Connection, which features a larger bending modulus, resulted in a safer condition than the pipe body, even with a passing-through hole, as evident in the present fatigue campaign. The trends of the bending moment, corresponding to the imposed amplitude stresses during the tests, for all kinds of the geometries investigated, are reported in Figures 13 and 14, along with the corresponding nominal bending stress amplitude at the various zones of the drill pipe, calculated with the beam theory. Points A, B and C are generally referred to the pipe body, the upset region and the connection region, respectively, while points A' and B' are the symmetric of A and B. In the Connection with 5-1/2\(\times\)0.415\" pipe body--Longer upset, point A is referred to the upset region, point B to the connection region and point C to the pipe body, while A' is the symmetric of A. It can be noticed that the Wired Connection drill pipes experience the highest value of the ratio between the maximum bending stress amplitude at the pipe body and the maximum nominal bending stress amplitude at the connection. This ratio is higher than three, mainly due to the much larger outer diameter at the connection. In ref. [55], the stress concentration factor for connection geometries, similar to the wired tool joint samples of this study, was calculated through a 3D FE model. The obtained values of the stress concentration factor fell into the range between two and three, so this can justify the failure at the pipe body instead of at the connection. The corrosion state of the pipe can play a significant role in steering the crack initiation. The Connection with 5-1/2\(\times\)0.415\" pipe body tested in the present fatigue campaign reported the fatigue initiation at the connection (pin FET). However, a similar connection was previously tested on connection specimens with corroded pipe bodies, and results are reported for a comparison in Figure 10, as previously discussed. Figure 12: (a) FE map of the axial stress of the Global model, (b) map of the axial stress of the Submodel, and (c) plot of the axial stress along the path realized through the hole. The failures of these former tests were observed at the pipe bodies since the connection surfaces were properly coated and then not affected by corrosion. On the contrary, the latter specimens reported an appreciably higher strength and failure at the connection instead of the pipe body. A longer upset was also tested, for comparison with respect to the standard geometry, in which the upset has a regular (short) length. An evident result was that the failure remained at the connection pin FET and approximately at the same fatigue life. Therefore, the main conclusion that can be formulated is that the longer upset manufacturing did not produce any detrimental effect on the material and its fatigue strength of the connection. Large-size specimens were also tested (6-5/8\(\times\)0.750\"). Among the specimens of this size category, two grades were investigated, namely 140 ksi and 165 ksi, which define the (minimum) yield strength.