# Resonant Fatigue Tests on Drill Pipe Connections with Different Geometries and Sizes
## 1 Introduction  
Drill pipes are the main components of a drill string, which is the long tubular structure that connects the drilling bit to the rig. The dimensions of the rotary drilling elements are defined by the American Petroleum Institute (API) standard [1]. Drill strings can be used for oil exploration, but they can also be employed for scientific drillings, as utilized by JAMSTEC on the drilling-equipped science vessel Chikyu. As described in refs. [2, 3], these long tubular elements can serve to investigate the most active earthquake zones near the Japanese coasts. The two mating parts of a drill pipe, named, respectively, the \"pin\" and the \"box\" tool joints, are connected through a conical threaded connection with single or double shoulder seal faces. The connection zone is characterized by a larger external diameter and a smaller internal diameter with respect to the pipe body. An intermediate region (upset) is required to provide the attachment, generally realized through a friction welding process, between the pipe body and each tool joint to smooth the stress distribution at the transition from the threaded zone to the pipe body. A drill pipe is so generally composed of three parts: the connection, the upset, and the pipe body. As resumed in ref. [4], in drill pipes there are some stress concentration points, which can be classified as:  
* Surface irregularities,
* Section variation at the upset,
* Corrosion pitting,
* Stress concentrations at the threaded region. The surface irregularities can be caused by inappropriate handling with the gripping systems or by slip-cuts. In refs. [5, 6] the stress concentration effects caused by the die-markson the static and fatigue failures were investigated. Alternatively, the upset zone can be a potential point of cracking in a drill pipe. In ref. [7], the erosion caused by the drilling fluid on the internal upset was examined using the CFD software FLUENT 13.0 to obtain the shear stress and the pressure at the contact between the fluid and the upset in order to investigate the flow erosion. In ref. [8], a stress analysis of the upset region was conducted through an FE software, and a geometric optimization of this zone was proposed. In ref. [9], an FE simulation of the upset region was developed trying to understand which are the geometric features with the most impact on the stress distribution of the upset region. The authors eventually developed an optimized geometry for the upset region of the 5\" connection according to the API drill pipe standard [1]. Corrosion pitting is generally caused by the removal of the internal coating caused by the drilling fluid, which exerts an erosive impact. This issue was investigated in ref. [10], where it was stated that the irregularities of the internal surface and the employment of a material with a low resistance to corrosion could have a significant impact on failure due to corrosion. The threaded connection zone of the drill pipe received great interest from the researchers. In ref. [11], FE simulations were carried out, showing that the maximum stress concentration factor occurred at the root of the first engaged thread (FET) of the pin and at the last engaged thread (LET) of the box. The simulations aimed to reproduce the pre-load, the axial load, and the bending load caused by the dog-leg imposed bending, which severely deteriorate the fatigue strength of the drill pipe [12]. In ref. [11], fractographic observations of the failed drill pipes were also included, showing that the crack nucleated at the first thread root of the pin and propagated through the wall of the tool joint. Several other research papers showed that the first and the last engaged threads of the pin and the box, respectively, are potential sites of failure [13; 14; 15; 16; 17; 18; 19]. In ref. [20], a method to predict the fatigue life of the threaded connection of drill string was proposed.