Strength limit of titanium alloy drill pipe under combined tension and torsion load

With a focus on the issue of drill pipe failure brought on by the interaction of tension and torsion in deep and ultra-deep wells, the yield limit curve of the pipe body and joints under the combination of tension and torsion was drawn. According to the practice of DNV-RP-F201, it was investigated how temperature affected drill pipe strength. The findings demonstrate that as temperature increases, both yield and tensile strength decrease linearly, and the decreasing range gradually decreases when temperature exceeds 140°C, and yield strength decreases by 31.91% in 140°C. Under the conditions of the same yield strength and outer diameter, the larger the thickness of the drill pipe body is, the higher its tensile strength and torsional strength are. The resulting yield limit curve covers a wider range. As the temperature increases, the yield limit elliptic curves of titanium alloy drill pipes with various wall thicknesses gradually shrink. This work presents the foundation for the strength research of titanium alloy drill pipe under tension and torsion load.


Introduction
As the technology for petroleum exploration and development has advanced, drill pipe is affected by tensile and torsion combined load and other factors in deep and ultra-deep wells.The main failure modes are corrosion fatigue and pipe body piercing [1][2][3].During the stuck freeing operations at the oil field, the drill pipe is lifted and twisted, and subjected to the interaction of tension and torque, which significantly raises the failure risk.Relevant studies show that the majority of drill pipe failures occur under the combined action of tension and torsion [4].Besides, drill pipe strength deteriorates as the temperature rises.How to quantitatively evaluate the strength limit under tension and torsion combined load is extremely important for drilling safety, especially for deep and ultra-deep wells.Therefore, drilling safety and efficiency are mostly dependent on the drill pipe material and strength limit under combined tension and torsion loads.
Santus et al. [5] investigated two techniques for aluminum body and steel tool joint and compared the torsional strength.Smith et al. [6] studied the modeling and analysis of titanium drill string in drilling programs.Two design criteria are used, including margin of overpull and hydraulic performance.Koji and Toshikiko [7] describe the feature of the parameter, which will affect the high-strength drill pipe's fatigue strength.Zhao et al. [8] investigated the fracture performance of a cracked body under the combination of tension and torque by numerical simulation.Lian et al. [9] processed stress and strain at different times according to the methods in micromechanics.
As an alternative to steel drill pipe, titanium alloy drill pipe has characteristics of low density, small elastic modulus and well corrosion resistance [10].Its use in petroleum exploration and development will become more widespread as the price of titanium alloy continues to drop and processing and manufacturing technology advances [11][12][13][14].Wang et al. [15] analyzed the mechanical qualities of TC4 titanium alloy.To explore the strength limit of drill pipe more accurately under tensile and torsion combined load, the author conducted laboratory tests, drew a yield limit curve of pipe body and joint under tensile and torsion combined load, and examined how temperature and thickness affected the drill pipe's mechanical characteristics.

Study on the strength limit under tensile and torsion combined load
During the actual operation of the drill pipe, the working torque should be lower than the upper torque.The yield limit curve under tension-torsion combined loading can be used to evaluate the performance of the drill pipe.In the curve, the horizontal coordinate is torque and the vertical coordinate is tension, as shown in Figure 1.9), and British units are used here.
The impact of temperature on the drill pipe strength is depicted in Figure 2. The temperature of 140 ℃ is a critical value.Before and after 140℃, both yield strength and tensile strength decrease linearly as temperature increases.At the temperature of 140℃, the yield strength decreases by 172.8 MPa and tensile strength decreases by 148.8 MPa.When the temperature rises to 200℃, the yield strength decreases by 31.91%.

Effect of temperature on drill pipe strength
For φ127×9.19 mm drill pipe (105 ksi), the tensile strength, torsional strength, internal pressure strength, and exterior extrusion strength as a function of working temperature are depicted in Figure 3.

Effect of temperature on mechanical properties under tensile and torsion combined loading
Combined with Formula (9) and Formula (10), the drill pipe's tensile strength under torque is determined by taking into account how temperature affects the yield strength.For drill pipe with a yield strength of 105 ksi and outer diameter of φ127 mm, three kinds of wall thicknesses of 7.52 mm, 9.19 mm and 12.7 mm were selected for calculation, as shown in Figures 4-6.If the yield strength and outside diameter are the same, the greater the thickness of the drill pipe is, the higher the tensile strength and torsional strength are, and the wider the envelope range of the yield limit curve formed is.As temperature increases, the yield limit elliptic curves of drill pipe gradually shrink, indicating that the safety factor is lower when it works in high temperature environment.Figure 6 Yield limit curve (12.7 mm).

Conclusion
(1) The temperature of 140℃ is a critical value.Before and after 140℃, the strength of titanium alloy drill pipe material decreases linearly as temperature increases.When the temperature rises from 20℃ to 140℃, the yield strength and tensile strength decrease by 172.8 MPa and 148.8 MPa, respectively.When the temperature exceeds 140℃, the decreasing range gradually decreases, and the yield strength decreases by 31.91% at 200℃.
(2) For drill pipe with a yield strength of 105 ksi, the greater the thickness of the drill pipe is, the higher the tensile and torsional strength is, and the wider the envelope range of the formed yield limit curve is.The yield limit elliptic curves of titanium alloy drill pipe gradually shrink as temperature increases.
(3) Further research can focus on the experimental analysis of titanium alloy drill pipe's mechanical qualities, to verify the applicability of titanium alloy drill pipe and evaluate the operational difference between steel and titanium alloy drill pipe.

Figure 1 .
Figure 1.Yield limit curve of drill pipe under tension and torsion combined loading.The calculation formulas of each parameter in the figure are shown in Formulas (1)-(9), and British units are used here.

Figure 2 .
Figure 2. Effect of temperature on yield strength and tensile strength of titanium alloy.

Figure 3 .
Figure 3.Effect of temperature on titanium alloy drill pipe strength.(a) Strength of extension; (b) Torsional strength; (c) Internal pressure strength; (d) Collapse resistance strength.As the working temperature increases, tensile strength, torsional strength, internal compressive strength, and external extrusion strength of the drill pipe body decrease linearly.Therefore, the operation of a downhole drill pipe should consider how temperature affects drill pipe strength.Tensile strength reduces from 2465 kN to 2263 kN when temperature increases from 20 °C to 200 °C.Torsional strength was reduced from 43 kN•m to 29 kN•m; the internal compressive strength was reduced from 92 MPa to 62.5 MPa; the extrusion strength was reduced from 74 MPa to 55 MPa.
Ta represents buckling torque, i.e., tool joint torque before tensile stress loading, ft•lbs; TDH represents downhole torque, ft•lbs; P1 represents male joint yield tension, lbs; P0 represents Ta Tension required for shoulder separation of drill pipe joint after loading, lbs; PT4T2 represents Ta Tension required for male joint yield after loading, lbs; PT3T2 represents TDH Tension required for male joint yield after loading, lbs; T1 represents female buckle torsion strength, ft•lbs; T2 represents buckle torsion strength, ft•lbs; T3 represents Additional loading torque resulting in separation of drill pipe joints, ft•lbs; T4 represents shoulder separation torque, ft•lbs; PQ represents Tensile strength of drill pipe body under torque, lbs.Temperature will affect the strength of the titanium alloy drill pipe.According to DNV-RP-F201, the strength reduction of titanium alloy drill pipe under high temperatures can be expressed as follows: 3. Effect of temperature on yield strength