An Experimental Study on Mechanical properties of P110S under Dynamic Loads

Oil country tubular goods (OCTG) may develop plastic bending, fracture and fatigue failure during the service due to dynamic loads, such as perforation impacts and fluid-induced vibration. This paper was to evaluate strength safety of OCTG under dynamic loading. To gain key parameters of the dynamic constitutive model of materials represented by Johnson-cook. An axial tensile test of the common P110S and an experiment on its mechanical properties under high strain rate were carried out for the first time. The yield limit of P110S under static loads was 775MPa, which was 2.2% higher than the nominal value (758MPa). The ultimate strength was 835MPa and the yield ratio was 1.08. Since it often requires the yield ratio higher than 1.2 5, the P110S had slightly poor tenacity. Under the strain rates of 500s-1 and 1000s-1, the yield limits of P110S were 15.5% and 41.4% higher than the static measured values. The dynamic loading experiments of P110S under the strain rates of 500s−1 and 1000s−1 were corresponding to the fluid-induced vibration of columns and perforation i mpacts-induced vibration of columns, respectively. Dynamic factor of P110S was determined according to engineering habits. According to conversion and contrast analysis on increment of yield limit under dynamic loading, the final strengths were decreased by 4.5% and 8.6%, respe ctively. Moreover, key parameters of the Johnson-cook dynamic constitutive model of P110S material were determined through experiments for the first time. They could provide key para meters of constitutive model for accurate finite element simulation analysis under dynamic loa ds.

Abstract.Oil country tubular goods (OCTG) may develop plastic bending, fracture and fatigue failure during the service due to dynamic loads, such as perforation impacts and fluid-induced vibration. This paper was to evaluate strength safety of OCTG under dynamic loading. To gain key parameters of the dynamic constitutive model of materials represented by Johnson-cook . a n axial tensile test of the common P110S and an experiment on its mechanical properties under high strain rate were carried out for the first time. The yield limit of P110S under static loads was 775MPa, which was 2.2% higher than the nominal value (758MPa). The ultimate strength was 835MPa and the yield ratio was 1.08. Since it often requires the yield ratio higher than 1.2 5, the P110S had slightly poor tenacity. Under the strain rates of 500s-1 and 1000s-1, the yield limits of P110S were 15.5% and 41.4% higher than the static measured values. The dynamic lo ading experiments of P110S under the strain rates of 500 s -1 and 1000s -1 were corresponding to the fluid-induced vibration of columns and perforation i mpacts-induced vibration of columns, respectively. Dynamic factor of P110S was determined a ccording to engineering habits. According to conversion and contrast analysis on increment of yield limit under dynamic loading, the final strengths were decreased by 4.5% and 8.6%, respe ctively. Moreover, key parameters of the Johnson-cook dynamic constitutive model of P110S material were determined through experiments for the first time. They could provide key para meters of constitutive model for accurate finite element simulation analysis under dynamic loa ds.

Introduction
Oil country tubular goods (OCTG) are easy to develop breakage and bending of columns during the service due to the dynamic loads from perforation impacts and fluids, which have attracted high research attentions in the world [1][2][3] . Gilat A et al. [4] developed a new experimental device that can measure the full-field deformation and temperature on sample surface in the high-speed tensile test. Gilat A et al. [5] measured strain and strain rates in compressive and tensile separation Hopkinson experiments by using the commercial image software and two digital high-speed cameras. Baumann C et al. [6] and Baumann C E et al. [7] calculated the instantaneous pressures of perforation fluid and the gun body by the computer software developed by Schlumberger, and predicted deformations, speeds, accelerations and stresses of tubular columns and downhole tools in the perforation segment. Some foreign companies (e.g. Schlumberger) took the perforation pressure analysis and measurement technologies as the core confidentialities. They only offered Chinese oil fields limited single well technological services rather than software and instrument. In addition, feasibility and applicability of associated studies still have to be further confirmed. All of these studies viewed OCTG as an integral bar, but overlooked influences of mechanical attributes and dynamic performances of OCTG on its overall stress.
In material sciences, studies concerning mechanical properties of materials under dynamic loads mainly focused on dynamic responses of high-energy and high-strength protective metals of ships and warships to explosive blast [8][9] . They concluded that changes of strain rate and deformation temperatures influenced rheological stress of H13 steel significantly, and evident dynamic softening was developed, thus getting relevant parameters of Johnson-Cook model. Lindholm et al [10] described the development of high-speed torsion testing machine as well as strength related with copper strain rate under strong shear strain. The acquired test technologies and data were applied in ballistics and machining. Although there were many experiments on P110 materials, they mainly focused on static mechanical properties of P110 materials with different Cr contents as well as their resistances to CO 2 and H 2 S corrosion behaviors. No experimental studies on P110S under dynamic loads have been available yet.
In a word, P110S was collected and processed into standard specimens for the standard tensile experiments. These experiments quantified the dynamic factor and increment of yield strength of the material under dynamic loads, gained key parameters of the dynamic Johnson-cook constitutive model and improved analysis precision of safety coefficient of columns under dynamic loads. Stress and strain values were mean of two groups of specimens. Hence, the stress-strain curves of P110S under static loads were gained. Material samples were collected on the same OCTG and processed into 15 Ф5mm×h5mm solid cylinder samples. These cylinder samples were used in 15 groups of experiments on impact strain rates under 500s -1 and 1000s -1 , thus getting stress-strain curves under different high strain rates. Later, key parameters of the dynamic Johnson-cook constitutive model were determined by analyzing increment of yield strength and comprehensive dynamic load of P110S under high strain rates. Research conclusions could provide references to analyze strength safety of OCTG under dynamic loads.

Experimental analysis on stress-strain curves of P110S
Standard regulations on the size of tensile specimens were proposed for accurate comparison of properties of different materials. In this experiment, tensile specimens adopted the rectangular sections. According to requirements in internal standards of GB/T228-2002 and GB/P7314-1987, specimens shall meet the Eq.(1): (1) where L 0 is length of specimens (mm) and S 0 is the sectional area of rectangular specimens (mm2).
A total of 4 groups of specimens with different specifications were prepared (Figurea 1). The sectional area was 19.05×9.19 mm 2 and the calculated L 0 was approximately equal to 150 mm. The clamping parts at two ends were 10 mm, respectively. The total length of specimens was 170 mm. The static tensile experiment of P110S was accomplished on the axial tensile testing machine. To increase experimental accuracy and avoid errors brought by contingency of experimental data, four groups of same experiments were carried out. A total of 3,906 groups of data were recorded and extracted from each group of experiments. Some data are listed in Table 1. Mean values of four groups of experimental data were collected to draw the stress-strain curves of P110S ( Figure 2 and Figure 3). Obviously, the yield limit of P110S was 775 MPa, which was 2.2% higher than the nominal value (758 MPa). The ultimate strength was  b =835MPa and the yield ratio was  b / s =835/775=1.08With considerations to tenacity requirements of steel materials, it generally requires the yield ratio to be higher than 1.25 (GB50204-2002), indicating the slightly poor tenacity of P110S. Therefore, P110S is easier to develop "brittle failure" in actual working conditions.   It is mainly used to test mechanical properties of metal materials under high strain rates of 10 2 ～ 10 4 /s. Air pressure-driving bar impacted the input bar at a certain speed, thus generate compressive stress pulse in the input bar. When this compressive stress pulse was propagated into the contact surface between input bar and samples, some stress impulses were reflected to the input bar, while the rest transmitted to specimens. Impact loads were applied onto specimens until the failure. Incidence, reflected and transmitted pulse voltage signals were measured by strain gages pasted on the input bar and transmission bar, and then converted into strain signals. Subsequently, stress, strain and strain rate of specimens were acquired according to the one-dimensional stress wave theory [11] :  Considering vibrations of tubular columns caused by perforation impacts and fluids, the strain rate ranged between 500s -1 and 1000s -1 . To avoid error caused by contingency of single experimental data, three specimens were set as one group and the acquired experimental data were the mean values. 2,166 groups of experimental data were recorded to improve experimental accuracy. Some data are listed in Table 2.
The stress-strain curves under different strain rates were drawn by using data (Figure 6). Clearly, two curves overlapped basically under the dynamic strain rate of 500s -1 . The mean yield limit ( s ) of P110S was 895MPa, which was 15.5% higher than the static measured value (775MPa). The ultimate strength ( b ) was 990MPa, which was 18.6% higher than the static measured value. Under 1000s -1 dynamic strain rate, three curves overlapped basically. The mean  s of P110S was 1,096MPa, which was 41.4% higher than the static measured value (775MPa).  b was 1,201MPa, which 43.8% was higher than the static measured value.
With respect to the stress-strain state, P110S belongs to the metal plastic flow under thermal activation mechanism when the strain rate is lower than 10,000S -1 . The stain rate and temperature follow the Arrheinus equation [10] :   Table 3. With consideration to both situations, the upper limit of The dynamic loading experiment of P110S under the strain rate of 500s -1 tested the tubular column vibration induced by fluid. The increase coefficient of yield limit and dynamic factor were measured 1.155 and 1.200, respectively. Therefore, strength was decreased by 4.5% compared with that under static loads. The dynamic loading experiment of P110S under the strain rate of 1000s -1 tested the column vibration induced by perforation impacts. The increase coefficient of yield limit and dynamic factor were measured 1.414 and 1.50, respectively. This implied that strength was 8.6% lower than that under static loads.

Determination of parameters of the Johnson-Cook model of P110S under high dynamic strain rate
The Johnson-cook thermoviscoplasticity dynamic constitutive model which is constructed based on abundant practical experiences is applicable to a large range, especially metal materials represented by steel. It can reflect the dynamic constitutive relations of metals under large strain, high strain rate and high-temperature loading. The flow stress of Johnson-Cook can be expressed as [12] : (4) where  P is the equivalent plastic strain.  1 is the equivalent plastic strain rate when =1. T* is the relative temperature and . Items in the first brackets are influencing factors of strain and items in the second brackets are influencing factors of strain rate. Items in the third brackets are influencing factors of ambient temperature. T  is the reference temperature, which is determined the room temperature 293K in this test. T m is the temperature at melting point of OCTG, which is set 1800K. A, B, N, C and m are five key material constants of the model. Key parameters of the Johnson-Cook model of P110S are gained in the experiment under high dynamic strain rate (Table 4).

Conclusions and suggestions
In this paper, an axial tensile experiment ofΦ88.9×6.45 mm P110S under static loads and an experiment on its mechanical properties under high strain rate are carried out successively. On this basis, the overall mechanical properties of P110S are analyzed. Some major conclusions could be drawn.
(1) The first stress-strain curve of P110S which is one of the widely used OCTG in onshore oil fields in China is carried out, which provides the first-handed data concerning axial tensile mechanical properties of OCTG. The dynamic performance of P110S under high dynamic strain rate is performed by using the Hopkinson pressure bar system. Therefore, the first-handed experimental data on stress-strain relationship of P110S under dynamic loads are acquired.
(2) The yield limit of P110S is 775MPa, which is slightly (2.2%) higher than the nominal value 7 1234567890''"" MTMCE IOP Publishing IOP Conf. Series: Materials Science and Engineering 392 (2018) 062020 doi:10.1088/1757-899X/392/6/062020 (758MPa), indicating the qualified strength of P110S. The ultimate strength is 835MPa and the yield ratio is 1.08, which is lower than the requirements of steel tenacity (yield ratio >1.25). This reflects the slightly poor tenacity of P110S and it is easy to develop "brittle failure".
(3) Under the dynamic strain rate of 500s -1 , the yield limit ( s ) of P110S is 15.5% higher than the static measured value. Under the dynamic strain rate of 1000s -1 ,  s of P110S is 41.4% higher than the static measured value.
(4) The dynamic load experiment of P110S under the dynamic strain rate of 500s -1 tests tubular column vibration induced by fluid and strength of P110S is 4.5% lower. The dynamic load experiment of P110S under the dynamic strain rate of 1000s -1 tests tubular column vibration induced by perforation impacts and the strength of P110S is decreased by 8.6%. (5) Seven key parameters of the Johnson-cook dynamic constitutive model are acquired by experiments for the first time. The first Johnson-cook dynamic constitutive model of P110S is constructed. These can provide references to increase strength safety analysis accuracy of tubular columns under dynamic loads.