Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms

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Study of internal pressure strength of the titaniumsteel composite tube based on yield and shear failure mechanisms Deng Kuanhai a,**, Li Jialian b, Li Bin c, Pen Lin b, Liu Wanying c, Lin Yuanhua a,* a

State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University), Chengdu, Sichuan 610500, China b Pangang Group Research Institute Co., Ltd., Chengdu, Sichuan, 610303, China c School of Material Science and Engineering (Sichuan University), Chengdu, Sichuan, 610000, China

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abstract

Article history:

Combining the high mechanical strength of carbon steel with the excellent corrosion resis-

Received 13 June 2018

tance of titanium, titanium-steel composite tubing, which consists of an inner tube made of

Received in revised form

titanium (Ti) and an outer tube made of carbon steel, is not only an ideal material for the oil

26 November 2018

and gas pipelines system, but also has huge application prospects in the oil and gas industry

Accepted 27 November 2018

[1,2]. However, the yield and shear failure of the titanium-steel composite tube occurs easily

Available online xxx

under internal pressure due to its own structural features, especially concerning shear failure. Hence, based on the elastic-plastic theory, a mechanical model capable of calculating

Keywords:

internal pressure strength of the Ti-steel composite tube prepared by metallurgical bonding

Titanium-steel composite tube

has been established by combining the yield failure mechanism and the shear failure

Internal pressure strength

mechanism. The corresponding design methods of internal pressure strength have been

Mechanical model

proposed respectively, for users and manufacturers. The effects of the inner pipe wall

Yield failure

thickness, the radius-thickness ratio of the outer pipe, the elastic modulus, and the bonding

Shear failure

strength and bonding rate of the Ti-steel composite tube on internal pressure strength have

Bonding strength

been analysed. According to the national standard, design drawings for selecting Ti-steel composite tubes under different internal pressures have been presented for users. The accuracy and reliability of this model are verified by comparing the results with the API/ISO standard. These research results can provide an important reference for manufacturing, strength design and specification optimization of Ti-steel composite tubing. © 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.

Introduction The corrosive environment that oil and gas pipelines are exposed to becomes more and more serious in deep and ultra-

deep wells with high levels of CO2, H2S and sulfur [3e5]. The electrochemical corrosion, pitting and sulfide stress cracking caused by CO2 and H2S occurs frequently in China [6e9] during oil and gas transportation, which poses a threat to the safety

* Corresponding author. ** Corresponding author. E-mail addresses: [email protected] (D. Kuanhai), [email protected] (L. Yuanhua). https://doi.org/10.1016/j.ijhydene.2018.11.201 0360-3199/© 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved. Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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and life of the oil and gas pipelines. In order to solve these problems, many anti-corrosion technologies have been proposed such as corrosion inhibitors, plastic internal coating and corrosion-resistant materials [1,2,10e13]. Analysis indicates that the bimetal composite tube, which consists of a base layer of low carbon steel and a layer of corrosionresistant cladding material is an economic and reliable anticorrosion technology [2,14,15], and has broad application prospects in the transportation of oil and gas with corrosive mediums [16e18]. Up to now, the mechanical bonding technology (such as hydraulic expansion and cold-drawing) [14,19,20] and metallurgical bonding technology (roll bonding and diffusion bonding processes) [21e24] have been used to manufacture bimetal composite tubes. These composite tubes can be divided into two categories according to the inner-liner of the pipe made of different corrosion-resistant materials. The first category is a bimetal composite tube with the pipe's inner-liner made of corrosion-resistant alloy [18], such as stainless-steel composite tubing, and the other is titanium-steel composite tubing with an inner pipe liner made of pure titanium [2]. It is well-known that the bonding strength of the bimetal composite tube is a key consideration during the practical application process. Studies show that the bonding strength of the bimetal composite tube obtained by mechanical bonding technology is very low, not more than 10 MPa [25,26], and interface failure can be easily caused by the thermal load and harmful residual contact pressure, thereby limiting its practical application in the oil and gas industry to a great extent [27]. The stainless-steel composite tube is also susceptible to pitting, which becomes especially hazardous when pitting penetrates the cladding layer and reaches the base metal [18]. On the contrary, the titanium-steel composite tubes combine the excellent corrosion resistance of titanium with desirable mechanical properties (high strength, high toughness) and the lower cost of low carbon steel. Further, the excellent metallurgical interface can be obtained by economical and environmentally friendly roll bonding technology [27] so that the maximum bonding strength can reach 250 MPa [2]. As a result, the titanium-steel composite tube which exhibits excellent overall properties is likely to be the next-generation of mainstream compositing and be embraced by the oil and gas industry. Data from the Chinese oil and gas fields [28e31] shows that the pressure of oil-gas gathering and transportation can be divided into three grades: high pressure (10e25 MPa), medium-pressure (1.6e10 MPa) and low pressure (less than 1.6 MPa). Consequently, it is particularly important to design the internal pressure strength and technology parameters of titanium-steel composite tubing for users and manufacturers under those different pressure grades. The calculation of internal pressure strength is one of the key factors in titaniumsteel composite tube design and is more complicated than conventional single tubes because its special structural features are remarkably different from conventional single tubes [32,33], especially the mechanical properties (elastic modulus and yield strength) and stress distribution. The design and mechanical properties (shear strength and bearing capacity) of composite material (porous composite tube, concrete composites, steel-concrete composite beams)

has been investigated by many researchers [34,35], and a number of studies on shear strength prediction were conducted, based on several factors, by theoretical models and numerical analyses [36e40]. The effects of synthesis conditions and microstructures of composite materials (NiO-YSZ and Ni-YSZ cermet) on performance of nano-composite ceramic membranes have been investigated previously [41,42]. Those research achievements build a strong foundation for this work. At present, the studies on the internal pressure strength of titanium-steel composite tubing obtained by metallurgical bonding technology have rarely been reported, and there is no internationally accepted standard which can calculate the internal pressure strength of the tubing, so some users and manufacturers blindly design titanium-steel composite tubing by adopting the international standards of the single tube [43], which frequently results in material waste or interface failure of the composite tubing. Hence, in this present work, a mechanical model capable of computing the internal pressure strength of titanium-steel composite tubing has been established based on the yield failure and shear failure mechanisms and the bonding mechanisms of Ti-steel composite tubing. The effects of various internal pressure strength factors have been analysed. According to the national standards, the design drawings for selecting Ti-steel composite tubing under different internal pressures have been presented for users of Ti-steel composite tubes. Research results can provide an important theoretical basis for the manufacture, strength design and specification optimization of Ti-steel composite tubing.

Study on internal pressure strength of Ti-steel composite tubing Stress and stain analysis under internal pressure Ti-steel composite tubes with desirable interfacial bonding properties, consisting of inner tubes made of pure titanium and outer tubes made of carbon steel, have been successfully fabricated by roll bonding technology [21,22], as shown in Fig. 1. The shear strength between the inner tube (defined as Ti-lined tube) and the outer pipe (defined as base tube) can reach up to at least 100 MPa (the maximum can reach 250 MPa) due to the metallurgical bonding [2]. The mechanical analysis of long thick-walled composite tubing under internal pressure is one of the axisymmetric plane stress problems. The mechanical model of a Ti-steel composite tube under internal pressure (Pi) is shown in Fig. 1. In Fig. 1a shows the inside radius (mm) of a Ti-lined tube; (b) is the radius (mm) of the interface between the inner and outer tube, with r being the radius (mm) at any location in the composite tube; and (c) is the outside radius (mm) of the base tube, with t representing the wall thickness (mm) of the composite tube, and tb being the wall thickness (mm) of the base tube, and tc the wall thickness (mm) of the Ti-lined tube. It can be seen from Fig. 1 that Pi is the internal pressure on the inner wall of the Ti-lined tube, and Pc is the interface pressure (MPa) caused by Pi on the inner wall of the base tube and the outer wall of the Ti-lined tube.

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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Fig. 1 e Mechanical model of Ti-steel composite tube under internal pressure. (a) Ti-steel composite tube (b) Ti-lined tube (inner tube) (c) Base tube (Outer tube).

In order to study the internal pressure strength of composite tubing, the stress and strain of the inner and outer tubes need to be analysed separately under internal pressure because the inner tube (Ti-lined tube) of the composite tube is considered a thin-walled tube with low elastic modulus, and the outer pipe is a thick-walled tube with high elastic modulus. Hence, the stress and strain of the outer tube is analysed based on the principle of a thick-walled cylinder, and the stress and strain of the outer tube is analysed based on the principle of a thin-walled cylinder. According to the mechanical model, the internal pressure (Pi) and interface pressure (Pc) are applied to the inner and outer wall of the inner tube, respectively, as shown in Fig. 1b, and only the interface pressure (Pc) is applied to the inner wall of the outer tube, as shown in Fig. 1c.

According to Fig. 1b, the Ti-lined tube is subjected to internal pressure (Pi) and interface pressure (Pc). Based on the lame formula [44], the stress component of the inner pipe caused by internal pressure and interface pressure can be obtained:

(1)

where srT is the radial stress component (MPa) of the inner pipe; sqT is the circumferential stress component (MPa) of the inner pipe; a and b are the inner radius and interface radius (mm) between the inner and outer tube, respectively; and Pi and Pc are the internal pressure and interface pressure (MPa), respectively. The radial stress (srT) is much smaller than the circumferential stress (sqT) because the wall thickness of the Ti-lined tube is much smaller than the inside radius (a) and the radiusthickness ratio (tc/a) is far less than 1. Hence, the radial stress (srT) can be neglected. By Eq. (1), the stress component of the inner pipe can be simplified as follows:

(2)

By Eq. (2) and the physical equation of a plane stress problem, the strain component of the inner tube can be obtained.

8 < εrT ¼ 0 εrT ¼ ðsrT  n1T sqT Þ=E1  / a  εqT ¼ ðsqT  n1 srT Þ=E1 : εqT ¼ pi  pc E 1 tc

(3)

where εrT and εqT are the radial strain and circumferential strain of inner the tube, respectively; and E1 is the elastic modulus of inner tube (GPa). Substituting Eq. (3) into a geometric equation under the polar coordinate system gives: εqT ¼

Stress and strain analysis of inner tube

    2    8 1 a2 > 2 b 2 > s ¼   1 p þ b a 1  pc > rT i < r2 r2 b2  a2        2 > > 1 a2 > 2 b 2 : sqT ¼ þ 1 p  b a 1 þ p c i r2 r2 b2  a2

8 2 2 8 < b r z1 < sr ¼ 0  / a  2  a 2 2 :a b  a ¼ : sq ¼ pi  pc t c 2tc

 urT 1 vuqT ra  þ /urT ¼ rεqT ¼ pi  pc r vq E1 tc r

(4)

where urT is the radius displacement (mm) of the inner tube.

Stress and strain analysis of the inner tube The base tube (outer tube) of the Ti-steel composite tube is subjected to interface pressure Pc under internal pressure, as shown in Fig. 1c. Similarly, based on the lame formula and a physical and geometric equation, the stress component and strain component of the outer tube can be obtained.    2 8 b2 c > >  1 pc > srb ¼  2 2 2 > < c b r    2 > > > b2 c > : sqb ¼ 2 þ 1 pc c  b2 r2   8 1 b2 c2 > > > εrb ¼ E pc c2  b2 ð1  n2 Þ  r2 ð1 þ n2 Þ > 2 > > > > > >   < 1 b2 c2 Þ þ ð1 þ n Þ ð1  n εqb ¼ pc 2 2 2 > E2 c  b2 r2 > > > > > >   > 2 > c2 > : urb ¼ rεqb ¼ 1 pc b rð1  n2 Þ þ ð1 þ n2 Þ 2 2 E2 c  b r

(5)

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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where srb and sqb are the radial stress and circumferential stress (MPa) of base tube, respectively; εrb and εqb are the radial strain and circumferential strain of the base tube, respectively; urb is the radial displacement of the base tube (mm); and E2 is the elastic modulus of the base tube (GPa). According to continuity of deformation along the radial direction, the radial displacement of the inner tube is equal to the radial displacement of the outer tube at the interface between the inner and outer tube before the plastic deformation of the Ti-steel composite tube occurs under internal pressure. Hence, Eq. (6) can be obtained. ðurT Þr¼b ¼ ðurb Þr¼b

(6)

Substituting Eqs. (4) and (5) into Eq. (6) gives:    ab  1 b2 c2 bð1  n2 Þ þ ð1 þ n2 Þ pi  pc ¼ pc 2 2 E1 tc E2 c  b b

(7)

By transforming the plane stress problem into a plane strain problem, the relationship between interface pressure (Pc) and internal pressure (Pi) can be obtained.where

  8 E ¼ E1 1  n21 ; > < 1

elastic modulus to the outer tube's elastic modulus, namely dE ¼ E1/E2. In general, the ratio (dE ¼ E1/E2) applies to three situations. One is dE ¼ 1, when the elastic modulus of the inner tube is equal to that of the outer tube. Another is dE > 1, when the elastic modulus of the inner tube is larger than that of the outer tube, and the third is dE < 1, when the elastic modulus of the inner tube is smaller than that of the outer tube. Based on Eqs. (11) and (13), the radial and circumferential stress distributions of one bimetal composite tube (including a stainless steel composite tube and a Ti-steel composite tube) with a different elastic modulus ratio (dE ¼ 0.5, 1.0, 1.5) under 10 MPa can be obtained, as shown in Fig. 2. It can be seen from Fig. 2a that the radial stress is much lower than the circumferential stress under different elastic modulus ratios so that it is less harmful to bimetal composite tubes than circumferential stress is. The radial stress decreases with the increasing elastic modulus ratio (dE), and the maximum radial stress is reached at the interface. It can be seen from Fig. 2b that the circumferential stress increases gradually from the inner wall to the outer wall when

  1  n22 ; n2 ¼ n2 =ð1  n2 Þ    pi a 1  n21 c2  b2 E2 >

 2    2     : pc ¼ 2 2 E1 ðb  aÞ ð1 þ n2 Þn2 c  b þ 1  n2 c þ b2 þ a c2  b2 1  n21 E2 E2 ¼ E2

  8  a 1  n21 c2  b2 ¼ A1 > > > > b  a ¼ A2 <   ð1 þ n2 Þn2 c2  b2 ¼ A3   2  > 2 2 > 1  n c þ b ¼ A4 > >  :  2 2 2  a c  b 1  n21 ¼ A5

(9)

From Eqs. (8) and (9), Eq. (10) can be obtained: pc ¼

pi A1 E2 E1 A2 ½A3 þ A4  þ E2 A5

(10)

From Eqs. (2) and (10), the stress component of the Ti-lined inner tube can be obtained: 8 < srT ¼ 0 : sqT ¼

 a  pi  pi B ba

(11)

where B ¼ A1 =½ðE1 =E2 ÞA2 ðA3 þ A4 Þ þ A5 

(12)

From Eqs. (5) and (10), the stress component of the base tube (outer tube) can be obtained:   2 8 b2 c > >  1 pi B > srb ¼  2 2 2 < c b r   2 > > b2 c > : sqb ¼ 2 þ 1 pi B 2 2 c b r

(13)

Stress distribution of Ti-steel composite tube E1 and E2 represent the elastic moduli of the inner and outer tube, respectively. dE is defined as the ratio of the inner tube's

(8)

the elastic modulus ratio (dE) is equal to 0.5. It is noted that the circumferential stress increases sharply at the interface. As a result, the circumferential stress difference between the inner wall of the outer tube and the outer wall of the inner tube reaches a peak, meanwhile, when the maximum circumferential stress of the outer tube is reached, it easily gives rise to yield failure of the base tube and especially to shear failure of the interface. The circumferential stress decreases gradually from the inner wall to the outer wall when the elastic modulus ratio (dE) is equal to 1.5. On the contrary, the circumferential stress decreases sharply at the interface, which easily gives rise to shear failure of the interface. The circumferential stress is almost continuous from the inner wall to the outer wall of the composite tube when the elastic modulus ratio (dE) is equal to 1.0, which is less harmful to the composite tube compared to the other two situations (dE > 1 and dE < 1). In other words, the shear failure of the interface of the composite tube happens easily whether the elastic modulus ratio is larger than, or less than 1. What is worse is that both the shear failure of the interface and the yield failure of the base tube are likely to occur under internal pressure when the elastic modulus ratio is less than 1. It is well-known that the elastic modulus (E1) is smaller in the Ti-lined tube of Ti-steel composite than the elastic modulus (E2) of the base tube (carbon steel), and the elastic modulus ratio (dE) of the Ti-steel composite tube is less than 1, which can easily cause both shear failure and yield failure of the base tube. As a result, it is of great importance to study the internal pressure strength of the Ti-steel composite tube to improve the manufacturing techniques and the internal pressure strength design. In addition, according to Fig. 2b, the shear failure probability of

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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Fig. 2 e Stress distribution of a titanium-steel composite tube. (a) Radial stress (b) Conferential stress.

the Ti-steel composite tube with a similar elastic modulus of both the inner and outer tube can be decreased to some extent by weakening the abrupt change of circumferential stress at the interface.

Equation for internal pressure strength of a Ti-steel composite tube The elastic modulus of an inner tube made of titanium (TA1) is about 105 GPa, and the elastic modulus of an outer tube made of carbon steel is 210 GPa. Hence, the elastic modulus ratio (dE) is 0.5. Based on previous analysis, it is known that both the shear failure of the interface and the yield failure of the base tube of the Ti-steel composite tube ((dE ¼ 0.5) can occur under internal pressure. As a result, corresponding calculation equations are presented in this paper based on the shear failure mechanism and the yield failure mechanism.

Internal pressure strength based on shear failure mechanism Although the bonding strength of Ti-steel composite tubes can reach up to at least 100 MPa by metallurgical bonding technology, the shear failure of the interface between the inner and outer tube is still easily caused by the abrupt change of circumferential stress at the interface due to the different elastic moduli. According to the shear failure mechanism, it is known that the shear failure of the interface will occur when the circumferential stress difference (sqb  sqT ) reaches the bonding strength of the Ti-steel composite tube, which may cause delamination or cracking of the Ti-steel composite tube. According to the elastic modulus ratio of the Ti-lined tube (E1 ¼ 105 GPa) and the outer carbon steel tube (E2 ¼ 210 GPa), it can be understood from Fig. 2b that the circumferential stress of the outer tube is much larger than that of the inner tube. Based on the shear failure mechanism and from Eqs. (11) and (13), the equation for calculating the internal pressure strength (Pic1) of the Ti-steel composite tube can be obtained.

sqb  sqT

  8 lsJ c2  b2 ðb  aÞ > >    p ¼ > ic1 > ðb  aÞðc2 þ b2 B  a c2  b2 ð1  BÞ > > > > > > > B ¼ A1 =½ðE1 =E2 ÞA2 ðA3 þ A4 Þ þ A5  > > >   2  > 2 2 > > > A1 ¼ a 1  n 1 c  b > > > 2 > A 3 ¼ ð1 þ n2 Þn2 c  b > > > >    > 2 2 2 > > > A4 ¼ 1  n2 c þ b > >    > > > A5 ¼ a c2  b2 1  n21 > > > > > > A  DA : l¼ A (14)

where Pic1 is the internal pressure strength (MPa) of the Tisteel composite tube based on the shear failure mechanism; sJ is the specified bonding strength (MPa) of the Ti-steel composite tube; a is the inside radius (mm) of the Ti-lined tube; b is the interface radius (mm); c is the outer radius (mm) of the Ti-steel composite tube; l is the bonding rate between the inner and outer tube; A is the area of interface (mm2) between the inner and outer tube; and DA is the unbonded area (mm2) of the interface. The internal pressure strength (Pic1) of the Ti-steel composite tube based on the shear failure mechanism can be calculated by Eq. (14), and then the interface pressure (Pc1) can be obtained with Eq. (10). The yield failure of the Ti-lined tube and the outer carbon steel tube could still occur under the internal pressure strength (Pic1) obtained from Eq. (14) and the interface pressure (Pc1) obtained from Eq. (10). Hence, in order to guarantee the safety of Ti-steel composite in use, sufficient yield strength of the Ti-lined tube and the outer carbon steel tube is required and needs to be determined according to the internal pressure strength (Pic1) and the interface pressure (Pc1). Based on the internal pressure strength (Pic1) and corresponding interface pressure (Pc1), the minimum required yield strength of the Ti-lined tube and the base tube can be determined using Eqs. (11),(13) and (14) with the Von Mises yield criterion.

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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8 pic1 a > > > ssi ¼ ðb  aÞ ð1  BÞ; Minimum yield strength of Ti  lined tube < pffiffiffi 2 > > > sy ¼ 3c Bpic1  ; Minimum yield strength of base tube : ðc2  b2 (15) where ssi is the required minimum yield strength (MPa) of the Ti-lined tube; sy is the required minimum yield strength (MPa) of the base tube (outer carbon steel tube).

Internal pressure strength based on yield failure mechanism Fig. 2 shows that the yield failure of the base tube can occur in the internal wall under internal pressure because the elastic modulus (E1 ¼ 105 GPa) of the Ti-lined tube is smaller than the elastic modulus (E2 ¼ 210 GPa) of the base tube. Based on the yield failure mechanism and Von Mises yield criterion, the internal pressure strength of the Ti-steel composite tube can be obtained by Eq. (13). 8  ðc2  b2 sy > > > pffiffiffi 2 p ic2 ¼ > > > 3Bc > > > > > B ¼ A =½ðE 1 1 =E2 ÞA2 ðA3 þ A4 Þ þ A5  > > >    > > > A ¼ a 1  n21 c2  b2 < 1 2 jsrb  sqb j ¼ pffiffiffisy / A2 ¼ b  a > 3 > > >   > > A3 ¼ ð1 þ n2 Þn2 c2  b2 > > > > > > A ¼ 1  n2 c2 þ b2  > 4 > 2 > > >    : A5 ¼ a c2  b2 1  n21

(16)

where Pic2 is the internal pressure strength (MPa) of the Tisteel composite tube based on the yield failure mechanism; and sy is the specified yield strength (MPa) of outer carbon steel tube. According to Eq. (16), the internal pressure strength (Pic2) based on the yield failure mechanism can be obtained, and the corresponding interface pressure (Pc2) can be obtained under the internal pressure Pic2 found using Eq. (10). Similarly, the shear failure of the interface could still occur too under the critical internal pressure (Pic2) obtained with Eq. (16), and the yield failure of the Ti-lined tube could also happen under that critical internal pressure (Pic2) and interface pressure (Pc2). Hence, in order to guarantee the safety of Ti-steel composite in use, the sufficient bonding strength of the interface and the yield strength of the Ti-lined tube are required and need to be determined according to that internal pressure strength (Pic2) and interface pressure (Pc2). Based on that internal pressure strength (Pic2) and corresponding interface pressure (Pc2), the required minimum bonding strength of the interface and the yield strength of the Ti-lined tube can be obtained by Eqs. (11), (14) and (16) and the Von Mises yield criterion.

where Pic2 and Pc2 are the internal pressure strength of the Tisteel composite tube and the interface pressure based on the yield failure mechanism (MPa); ssi is the required minimum yield strength (MPa) of the Ti-lined tube; and sJ-min is the required minimum bonding strength (MPa) of the interface.

Design method for internal pressure strength of Ti-steel composite tube Design method for manufacturer of Ti-steel composite tube Manufacturers not only want to design and manufacture economic and applicable Ti-steel composite tubing according to users’ requirements and practical working conditions, but also seek to minimize manufacturing costs and maximize benefits on the basis of guaranteeing the material safety of composite tubes. For that purpose, based on different steel grades and manufacturing technologies, two methods have been proposed to design Ti-steel composite tubing according to the equation of internal pressure strength presented in this paper, as follows. (1) If the steel grade (yield strength sy of material) of the base tube is defined in advance, the internal pressure strength of the Ti-steel composite tube should be designed by Eq. (16) based on the yield failure mechanism, and then the required minimum yield strength of the Ti-lined tube and the required minimum bonding strength of the interface, determined by Eq. (17). Finally, the optimal Ti-lined tube and manufacturing technology of Ti-steel composite tubing as well as corresponding geometric parameters are determined. (2) If the bonding strength (sJ) of the interface (manufacturing technology of Ti-steel composite tube) is defined in advance, the internal pressure strength of the Ti-steel composite tube should be designed by Eq. (14) based on the shear failure mechanism, after which the required minimum yield strength (ssi) of the Ti-lined tube and the required minimum yield strength (sy) of the base tube (outer carbon steel tube) can be determined by Eq. (15). Finally, the optimal Ti-lined tube, the base tube, and the corresponding geometric parameters are determined.

Design method for user of the Ti-steel composite tube Similarly, users of Ti-steel composite tubing (such as transportation company for oil and gas) also want to design economic and applicable Ti-steel composite tubes according to the technological parameters (including geometry size and mechanical properties) of manufacturers, the practical working pressure, and maximization of cost savings on the

8 pic2 a > s ¼ ð1  BÞ; Minimum yield strength of Ti  lined tube > < si ðb  aÞ   2 2 > > : sJmin ¼ pic2 c þ b B  a ð1  BÞ ; Minimum bonding strength 2 2 ba l c b

(17)

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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basis of guaranteeing material safety. As such, based on different steel grades and technological parameters, one method to design Ti-steel composite tubing has been proposed according to the equation of internal pressure strength presented in this paper, as follows. Firstly, based on the shear failure mechanism, the internal pressure strength (Pci1) of the Ti-steel composite tube should be designed by Eq. (14) according to the bonding strength (sJ) from the manufacturer and the practical working pressure. Secondly, based on the yield failure mechanism, the internal pressure strength (Pci2) of the Ti-steel composite tube should be designed by Eq. (16) according to the particular steel grade/ yield strength (such as X52/360 MPa and X60/415 MPa) of the base tube from the manufacturer and the practical working pressure. Thirdly, the internal pressure strengths (Pci1 and Pci2) should be compared, based on different failure mechanisms. Finally, the smaller of Pci1 and Pci2 should be selected as the internal pressure strength design of the Ti-steel composite tube.

Analysis of internal pressure strength of the Tisteel composite tube From the mechanical model presented in this paper it is known that the internal pressure strength of the Ti-steel composite tube is related to the geometrical parameters (such as wall thickness and radius-thickness ratio) and mechanical parameters (such as elastic modulus, steel grade/ yield strength of material, bonding strength, and bonding rate). Hence, the effects of those factors on internal pressure strength are analysed through the examples presented in the following sections.

Effect of wall thickness of Ti-lined tube on internal pressure strength Based on the shear failure mechanism, the internal pressure strengths of the Ti-steel composite tube with different thicknesses of the Ti-lined walls and six kinds of typical bonding

7

strengths (sJ ¼ 120 MPa, sJ ¼ 150 MPa, sJ ¼ 180 MPa、 sJ ¼ 200 MPa, sJ ¼ 220 MPa and sJ ¼ 250 MPa) have been calculated by Eq. (14). The radius-thickness ratio (Do/tb) of the base tube is 29.67, the elastic modulus ratio (E1/E2) of the inner and outer tube is 0.5, and the Poisson's ratio of the inner and outer tube is 0.3. The relationship between the internal pressure strength and the wall thickness of the Ti-lined tube under different bonding strengths is shown in Fig. 3a. It can be seen that the internal pressure slightly increases in a linear way with the increasing wall thickness of the Ti-lined tube under the same bonding strength, and it also increases with the increasing bonding strength under the same wall thickness. Hence, there are two methods to improve the internal pressure strength of the Ti-steel composite tube with a large enough margin of material yield strengths (ssi and sy) for the inner and outer tube. One method is to increase the wall thickness of the inner tube appropriately, and the other method is to increase the bonding strength. It is noted that the best method can be selected for maximum benefits according to the manufacturing technology and actual working conditions. Similarly, based on the yield failure mechanism, the internal pressure strengths of Ti-steel composite tube with different wall thickness of Ti-lined tube and six kinds of frequently-used steel grade/yield strengths (X60/415 MPa, X65/450 MPa, X70/485 MPa, X80/552 MPa, X90/620 MPa, and X100/690 MPa) of base tube have been calculated using Eq. (16). The radius-thickness ratio (Do/tb) of the base tube is 35.6, the elastic modulus ratio (E1/E2) of the inner and outer tube is 0.5, and the Poisson's ratio of the inner and outer tube is 0.3. The relationship between the internal pressure strength and the thickness of Ti-lined tube wall under different steel grade/yield strengths is shown in Fig. 3b. It can be seen that the steel grade/yield strength of the base tube has a great impact on the internal pressure strength, and the internal pressure strength increases with the increasing steel grade under the same radius-thickness ratio. The internal pressure strength also increases linearly with the increasing thickness of the Ti-lined tube wall. Hence, if the yield strength of the Tilined tube and the bonding strength of the interface have a big

Fig. 3 e Relationship between the internal pressure strength of the composite tube and the wall thickness of the Ti-lined tube. (a) Different bonding strengths (b) Different steel grades. Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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enough margin, the internal pressure strength of the Ti-steel composite tube can be improved by increasing the wall of Ti-lined tube or selecting a higher steel grade pipeline as the base tube. In a word, the wall thickness of the Ti-lined tube has less effect on the internal pressure strength than the bonding strength or steel grade. According to the specified manufacturing technology and practical working conditions, the design of the internal pressure strength can be improved based on Eqs. (14) and (16).

Effect of the radius-thickness ratio of the base tube on internal pressure strength Fig. 4a shows the relationship between the internal pressure strength of the Ti-steel composite tube with six kinds of bonding strengths and the radius-thickness ratio of the base tube. The elastic modulus ratio (E1/E2) is 0.5, the wall thickness (tc) of the Ti-lined tube is 2 mm, and Poisson's ratio is 0.3. It can be seen that both the radius-thickness ratio and the bonding strength have a great impact on the internal pressure strength, with the internal pressure strength decreasing nonlinearly with the increasing radius-thickness ratio. However, the internal pressure strength increases with the increasing bonding strength, but the effect of the bonding strength on the internal pressure strength is gradually weakened with the increasing radius-thickness ratio. For example, there is a 2.05 MPa increase in internal pressure strength for every 10 MPa of bonding strength for a Ti-steel composite tube with a radius-thickness ratio of 25, a 1.52 MPa increase in internal pressure strength for every 10 MPa increase in bonding strength for a Ti-steel composite tube with a radius-thickness ratio of 33, and a 1.09 MPa increase in internal pressure strength for every 10 MPa increase in bonding strength for a Ti-steel composite tube whose radius-thickness ratio is 45. Similarly, based on the yield failure mechanism, the internal pressure strengths of Ti-steel composite tubes with different radius-thickness ratios of base tubes and six kinds of frequently-used steel grade/yield strengths (X60/415 MPa,

X65/450 MPa, X70/485 MPa, X80/552 MPa, X90/620 MPa, and X100/690 MPa) of base tubes have been calculated by Eq. (16), and the relationship between the internal pressure strength and the radius-thickness ratio is shown in Fig. 4b. The thickness (tc) of the Ti-lined tube is 1 mm, the elastic modulus ratio (E1/E2) of the inner and outer tube is 0.5, and the Poisson's ratio of the inner and outer tube is 0.3. Fig. 4b shows that the increasing steel grade has a considerable impact of increasing the internal pressure strength, and decreasing it with an increasing radiusthickness ratio. The effect of steel grade on internal pressure strength is weakened gradually by increasing the Do/tb. For example, a 9.7 MPa increase in internal pressure strength for every 100 MPa increase in yield strength of the base tube for a Ti-steel composite tube whose radius-thickness ratio is 25, a 7.4 MPa increase in internal pressure strength for every 100 MPa increase in yield strength of the base tube for a Tisteel composite tube whose radius-thickness ratio is 33, and a 5.4 MPa increase in internal pressure strength for every 100 MPa increase in yield strength of the base tube for a Tisteel composite tube whose radius-thickness ratio is 45. Hence, in order to reduce costs, the internal pressure strength can be improved by selecting the radius-thickness ratio and the steel grade and by increasing the bonding strength in the design process. For manufacturers, they can choose the best method (decreasing radius-thickness ratio, increasing steel grade and bonding strength, or an overall consideration) according to their technological level. However, for users of the Ti-steel composite, they can choose the best method (decreasing radius-thickness ratio, increasing steel grade and bonding strength, or overall consideration) according to their practical working condition.

Effect of the elastic modulus ratio on internal pressure strength The relationship between the internal pressure strength of the Ti-steel composite tube (Do/tb ¼ 29.67, tc ¼ 2 mm, v1 ¼ v2 ¼ 0.3) with six bonding strengths (sJ ¼ 120 MPa, sJ ¼ 150 MPa,

Fig. 4 e Relationship between internal pressure strength of the composite tube and radius-thickness of the base tube. (a) Different bonding strengths (b) Different steel grades. Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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Fig. 5 e Relationship between internal pressure strength of composite tube and elastic modulus ratio. (a) Different bonding strengths (b) Different steel grades.

sJ ¼ 180 MPa, sJ ¼ 200 MPa, sJ ¼ 220 MPa and sJ ¼ 250 MPa) and the elastic modulus ratio (E1/E2) is obtained by Eq. (14), as shown in Fig. 5a. It can be seen that the elastic modulus ratio has a great impact on internal pressure strength, which increases nonlinearly with increases in the elastic modulus ratio (E1/E2). Similarly, the relationship between the internal pressure strength of the Ti-steel composite tube (Do/tb ¼ 35.6, tc ¼ 2 mm, v1 ¼ v2 ¼ 0.3) with six steel grades (X60/415 MPa, X65/450 MPa, X70/485 MPa, X80/552 MPa, X90/620 MPa, and X100/690 MPa) of base tube and the elastic modulus ratio (E1/E2) is obtained by Eq. (16), and is shown in Fig. 5b. It can be seen that the elastic modulus ratio has only a small impact on internal pressure strength, which only increases slightly with an increase in the elastic modulus ratio (E1/E2). Briefly, it can be seen from Fig. 5 that the elastic modulus of the inner and outer tube has an impact on internal pressure strength, and the greater the elastic modulus ratio is, the higher the internal pressure strength. For manufacturers, they can improve internal pressure strength by increasing the elastic modulus ratio of the inner and outer tube.

Effect of bonding rate on internal pressure strength The internal pressure strengths of Ti-steel composite with different interface bonding rates are obtained by Eq. (14), and the calculation results and corresponding parameters are shown in Table 1. Based on Table 1, the relationship between

internal pressure strength and bonding rate (l) can be obtained, as shown in Fig. 6. It can be seen from Fig. 6 that the internal pressure strength is in proportion to the bonding rate (l), which increases sharply with the increasing bonding rate. Calculations show that 2.5 MPa decreases in internal pressure strength occur for every 10% decrease in bonding rate, indicating that the bonding rate has a significant impact on internal pressure strength. Hence, in order to guarantee the Ti-steel composite safety, it is necessary to improve the bonding rate of the interface by strictly controlling of manufacture process.

Numerical comparison with API/ISO standard In order to validate the new mechanical model of internal pressure strength, the calculation results of the new model (Eq. (16) proposed in this paper, based on the yield failure mechanism, have been compared with the calculation results of the new API/ISO model [43], as shown in Fig. 7 and Table 2. The Ti-steel composite tube consists of API 5L B pipeline (base tube) and TA1 (Ti-lined tube). The yield strength of the base tube and Ti-lined tube is 245 MPa and 275 MPa, respectively, the elastic modulus ratio (E1/E2) of the inner and outer tube is 0.5, and their Poisson's ratio is 0.3. In Table 2, Pi is the internal pressure strength of the Ti-steel composite tube by Eq. (16), Pio is the internal pressure strength of the single base tube by Eq. (16), and PISO is the internal pressure strength of the single base tube by the API/ISO model.

Table 1 e Internal pressure strength of Ti-X70 pipeline steel composite tube under different bonding rate. Outer tube

Inner tube

Do/mm

tb/mm

tc/mm

E1/E2

sJ/MPa

l/%

Pci1/MPa

X70 485 MPa

TA1 275 MPa

178

6

2

0.5

150

100 95 90 85 80 75

25.48 24.21 22.93 21.66 20.38 19.11

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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the internal pressure strength of the Ti-lined composite tube can be improved by 0.5 mm. As a result, the mechanical model presented in this paper is accurate and reasonable, and can be used to design internal pressure strength of Ti-steel composite tubing for users and manufacturers according to the actual technology level and working conditions.

Specification optimization and design drawing of Ti-steel composite tube

Fig. 6 e Relationship between IPS and bonding rate.

Based on the industrial standard [2,45,46] and manufacturer (Ansteel Group Corporation), the bonding strength is larger than 140 MPa, and 196 MPa is the typical and frequently-used bonding strength. Hence, based on the previous design method and industrial standard, and from the pressures of oil-gas gathering and transportation [28e31], design drawings have been presented which can be used to select TA1-X52 pipeline steel composite tubing (including size and thickness) for users of composite tubes under different internal pressures (5 MPa, 10 MPa, 15 MPa, 20 MPa, 25 MPa and 30 MPa), as shown in Fig. 8 (with the specific design parameters presented in Appendix 1). In these design drawings, the thickness of the Ti-lined tube ranges from 0.5 mm to 3.0 mm, and the outer diameter ranges from 127 mm to 244 mm, which is convenient for users of TA1-X52 pipeline steel composite tubes.

Discussion

Fig. 7 e Comparison between this model and API/ISO.

Table 2 and Fig. 7 show that the internal pressure strengths of the base tube calculated by this model are very close to the calculation results of the API/ISO model, with only slightly higher results than those of the API/ISO model. The main reason for this difference is that this model considered the effect of radial stress on internal pressure strength whereas the API/ISO model did not. In addition, internal pressure strength (Pi) of the Ti-steel composite tube is slightly larger than that of the single base tube, the main reason being that

Firstly, it is well known that the bonding/shear strength of composite materials plays a very important role in its bearing capacity and practical application [36e40]. Secondly, based on stress distribution and failure mechanisms of composite tubes, the circumferential stress of the composite tube is discontinuously distributed due to the elasticity modulus difference between the inner tube (lined tube) and the outer tube (carbon steel tube) under internal pressure. Therefore, in practical application, additional shear stress may occur at the bi-metallic interface position and cause shear failure [32], especially for the titanium-steel composite tube with a huge elasticity modulus difference between the inner and outer tube. Thirdly, the stress distribution is closely related to the elasticity modulus and geometric parameters of the inner and outer tube. For the Ti-steel composite tube (elastic modulus ratio dE ¼ E1/E2 < 1), the yield failure could occur at the bimetallic interface. However, for the other composite tube (elastic modulus ratio dE ¼ E1/E2 > 1), the yield failure could

Table 2 e Comparison between calculation results of this model and the API/ISO model. sy (MPa) 245

tc (mm)

Do (mm)

tb (mm)

Do/tb

pic (MPa)

pico (MPa)

PISO (MPa)

0.5

219.1 219.1 219.1 219.1 219.1 219.1 219.1

4.5 5.0 5.5 6.0 6.5 7.0 7.5

48 44 40 36 34 31 29

11.84 13.34 14.36 15.74 16.95 18.17 19.38

11.12 12.52 13.72 14.88 16.22 17.26 18.45

10.58 11.78 12.99 14.21 15.43 16.66 17.88

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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Fig. 8 e Design drawing for selecting TA1-X52 pipeline steel composite tube under different internal pressure. (a) Wall thickness of inner pipe TA1 tc ¼ 0.5 mm (b) Wall thickness of inner pipe TA1 tc ¼ 1.0 mm, (c) Wall thickness of inner pipe TA1 tc ¼ 1.5 mm (d) Wall thickness of inner pipe TA1 tc ¼ 2.0 mm, (e) Wall thickness of inner pipe TA1 tc ¼ 2.5 mm (f) Wall thickness of inner pipe TA1 tc ¼ 3.0 mm.

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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occur at the inner tube. Finally, for the Ti-steel composite tube, the general internal pressure strength is closely related to the elasticity modulus of the Ti-lined tube and its elastic deformation capacity, which could be improved with an increase of the elasticity modulus and elastic deformation capacity to some extent.

(3) The effects of the inner pipe wall thickness, the radiusthickness ratio of the outer pipe, the elastic modulus, and the bonding strength and bonding rate of the Tisteel composite tube on internal pressure strength have been analysed, and the correlations between those factors and internal pressure strength have been obtained.

Conclusions Acknowledgments (1) The failure mechanism of the Ti-steel composite tube prepared by metallurgical bonding under internal pressure has been determined based on its structural features and stress distribution, and the mechanical model that can calculate the internal pressure strength of the Ti-steel composite tube has been established based on the yield failure mechanism and shear failure mechanism, and its accuracy and reliability is verified by comparing the results with the API/ISO standard. (2) For users and manufacturers of Ti-steel composite tubes, the corresponding design method for internal pressure strength has been proposed based on the new mechanism model, by which the design drawings and specified design parameters used to select TA1-X52 pipeline steel composite tube for users have been presented under different pressures of oil-gas gathering and transportation.

Authors are thankful for the financial assistance provided by the National Natural Science Foundation of China (No. 51274170, No. 51774249).

Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.ijhydene.2018.11.201.

Appendix 1. for user of TA1-X52 pipeline steel composite tube

Table 1 e Design parameter of TA1-steel composite tube under specific internal pressure Pi Base tube API5L X52 (sy ¼ 360 MPa)

Ti-lined tube

sJ/MPa

Pi/MPa

Do/mm

tc/mm

tb/mm

TA1 (ssi ¼ 275 MPa)

196

10.00

127.00

0.50 1.00 0.50 1.00 0.50 1.00 0.50 1.00 0.50 1.00 1.50 0.50 1.00 1.50 0.50 1.00 1.50 0.50 1.00 1.50 0.50 1.00 1.50 0.50 1.00 1.50 2.00 0.50 1.00 1.50 2.00

1.29 1.03 1.45 1.18 1.79 1.53 1.91 1.65 2.10 1.84 1.58 2.41 2.15 1.89 2.72 2.46 2.21 2.07 1.81 1.54 2.31 2.04 1.77 2.83 2.57 2.30 2.03 3.01 2.74 2.47 2.21

139.70 168.28 177.80 193.70

219.10

244.50

API5L X52 (sy ¼ 360 MPa)

TA1 (ssi ¼ 275 MPa)

196

15.00

127.00

139.70

168.28

177.80

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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Table 1 e (continued ) Base tube

Ti-lined tube

sJ/MPa

Pi/MPa

Do/mm

tc/mm

tb/mm

193.70

0.50 1.00 1.50 2.00 0.50 1.00 1.50 2.00 2.50 0.50 1.00 1.50 2.00 2.50 0.50 1.00 1.50 2.00 0.50 1.00 1.50 2.00 0.50 1.00 1.50 2.00 2.50 0.50 1.00 1.50 2.00 2.50 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 0.50 1.00 1.50 2.00 2.50 0.50 1.00 1.50 2.00 2.50

3.30 3.03 2.77 2.50 3.77 3.50 3.23 2.97 2.70 4.23 3.99 3.70 3.44 3.18 2.87 2.59 2.32 2.04 3.17 2.92 2.63 2.36 3.89 3.43 3.34 3.07 2.79 4.12 3.85 3.62 3.30 3.03 4.51 4.24 3.97 3.69 3.42 3.15 5.14 4.87 4.59 4.32 4.05 3.77 5.76 5.49 5.23 4.95 4.70 4.40 3.68 3.4 3.12 2.83 4.06 3.8 3.51 3.23 2.95 4.95 4.68 4.4 4.13 3.85

219.10

244.50

API5L X52 (sy ¼ 360 MPa)

TA1 (ssi ¼ 275 MPa)

196

20.00

127.00

139.70

168.28

177.80

193.70

219.1

244.50

API5L X52 (sy ¼ 360 MPa)

TA1 (ssi ¼ 275 MPa)

196

25.00

127.00

139.70

168.28

(continued on next page)

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Table 1 e (continued ) Base tube

Ti-lined tube

sJ/MPa

Pi/MPa

Do/mm

tc/mm

tb/mm

177.80

0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00 0.50 1.00 1.50 2.00 2.50 3.00

5.25 4.97 4.7 4.41 4.13 3.85 5.74 5.46 5.2 4.91 4.63 4.35 6.55 6.25 5.98 5.7 5.42 5.14 7.33 7.04 6.77 6.5 6.23 5.95 4.49 4.20 3.92 3.63 3.34 4.96 4.68 4.40 4.11 3.82 3.53 6.03 5.75 5.47 5.18 4.90 4.60 6.40 6.12 5.82 5.55 5.25 4.96 7.00 6.70 6.42 6.14 5.85 5.58 7.94 7.66 7.38 7.09 6.80 6.52 8.89 8.61 8.34 8.04 7.76 7.48

193.70

219.1

244.50

API5L X52 (sy ¼ 360 MPa)

TA1 (ssi ¼ 275 MPa)

196

30.00

127.00

139.70

168.28

177.80

193.70

219.10

244.50

Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201

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Please cite this article as: Kuanhai D et al., Study of internal pressure strength of the titanium-steel composite tube based on yield and shear failure mechanisms, International Journal of Hydrogen Energy, https://doi.org/10.1016/j.ijhydene.2018.11.201