# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 1 Introduction
This latter included a preliminary study to assess the stress tensor at the first and the last engaged threads of the connection, and the Dang Van criterion was then used to calculate the fatigue strength. Although the use of a purely elastic constitutive law, the authors suggested that the eventual elastic-plastic behavior of the most stressed thread roots during the cyclic loading should be investigated. This last proposal can be accomplished following two different methods: the first would employ FE simulations while the second would make use of closed-form expressions as the Neuber rule or the Zarka rule [21]. Other analyses of the threaded connection [22; 23] were also carried out on the drill collar, where the connection is clearly the weakest point given that the pipe body has the same inner and outer diameters of the threaded zone. In ref. [23] it was highlighted the strong influence of the make-up load on the mean and on the alternating stress of the FET of the pin because a high make-up torque led to a later contact loss so, given that this thread generally experiences the maximum bending load, a lower alternating stress. Careful monitoring of the make-up operation is recommended for fatigue initiation prediction. After these studies related to the connection, some geometric optimizations were discussed in order to reduce the stress concentration factors of this region, as in [14; 15; 16; 24; 25], and in ref. [26] it was proposed to generate, through an over-make-up torque, a controlled compressive state at the most stressed zone of the connection. The various mentioned stress concentrations can be crucial for the fatigue strength, which is the main cause of failure for drill pipes, as stated in refs. [4; 18; 27; 28; 29; 30]. In addition to this, the vibration of the drill string can result in further fatigue damage, and there are three principal mechanisms of vibration: bit bounce (axial), stick/slip (torsional), and lateral (bending). Various approaches can be used to analytically model the dynamic behavior, in ref. [31] the differential quadrature method was used, in ref. [32] a model that included axial and torsional drill string dynamics and the damping of the structure was performed to investigate the stick-slips vibrations, while in ref. [33] a three-DOF model was used to study the torsional vibrations of drill strings. The vibration analysis can be crucial for long drill strings, given that the natural frequency of axial vibration can be close to that of the heave motion, as shown in ref. [34]. In order to reduce the torsional oscillations of the drill strings, the use of Multiple Scales LindstedtPoincare method was used to design an optimum damper in ref. [35], whereas in ref. [36] an optimized Linear-quadratic-Gaussian control was accurately designed. In order to experimentally characterize the fatigue strength of drill pipes, it is possible to perform quasi-static tests, as shown in refs. [37; 38], whereas in ref. [39] two kinds of resonant fatigue test benches were presented. The first is suitable to test short regions of heavy sections, such as drill collars, and it employs two couples of counter-rotating eccentric masses, providing an in-plane alternating bending on the tested samples. The second is generally used to test long tubular specimens as drill pipes by means of a single rotating eccentric mass at one end, along with two fixed masses at both ends. The rotation of the eccentric mass provides a rotating bending, which in principle, is quite small according to a quasi-static analysis. However, in both kinds of these test rigs, the eccentric masses rotate at a frequency near (but lower) than that corresponding to the first natural frequency of the structure. These two proposed resonant test rigs were able to reproduce a fully alternating load (\(R=-1\)), so the mean stress was null. The second idea of the resonant fatigue test was also applied in other research regarding pipes, as in refs. [40; 41; 42; 43].