铜<bold>/</bold>钢复合管爆炸焊接数值模拟及边界效应

杨海娟; 刘翠荣; 张文斌; 李岩; Yang Haijuan; Liu Cuirong; Zhang Wenbin; Li Yan

网刊加载中。。。

使用Chrome浏览器效果最佳，继续浏览，你可能不会看到最佳的展示效果，

确定继续浏览么?

复制成功，请在其他浏览器进行阅读

Numerical Simulation and Boundary Effect of Explosive Welding of Copper/Steel Composite Pipe PDF

- ORCID：
Yang Haijuan ¹
- ORCID：
Liu Cuirong ^1,2
- ORCID：
Zhang Wenbin ¹
- ORCID：
Li Yan ^1,2
✉

1. School of Material Science and Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China； 2. Modern College of Humanities and Sciences, Shanxi Normal University, Linfen 041000, China

Updated：2024-04-23

DOI：10.12442/j.issn.1002-185X.E20230019

Abstract

With copper/steel composite pipe as research object, two-dimensional numerical simulation of explosive welding process was conducted through AUTODYN finite element software with SPH and ALE methods. The dynamic welding process and boundary effect were analyzed, and the explosive welding tests of copper/steel composite pipe were conducted. Results indicate that under the action of detonation waves, the composite pipe obliquely collides with the base pipe. The pressure in the collision zone remains stable at the order of 10⁷ kPa, and a plastic deformation band appears near the collision zone. The shear stresses have opposite directions on the base pipe and composite pipe, and the interface morphology changes from straight line to wavy shape with the propagation of explosion wave. This result is consistent with the actual interface morphology of the T2/316L bimetal composite pipe in experiments, indicating that this finite element model can effectively simulate the explosive welding process of bimetal composite pipe. During the numerical simulation process, the dynamic parameter values at the edges are all smaller than the normal values, leading to boundary effects. Increasing the length of composite pipe and explosive can eliminate the boundary effect.

Keywords

explosive welding; numerical simulation; dynamic parameter; boundary effect

Explosive welding of metals involves metal physics, explosion, and welding technique, which can achieve high-quality solid metallurgical combination of different metal pipe combinations. Currently, explosive welding technique can achieve welding of similar or different metals and alloys of more than 260 types, which has been widely used in the engineering field^[

1–3]. Numerical simulation is a convenient method to investigate the effect of process parameters during explosive welding process, therefore reducing the experiment cost^{[Reference 4

Baidu Scholar}4]. Miao et al^{[Reference 5

Baidu Scholar}5] found that the Lagrangian method is more concise than most modeling methods, and the SPH-FEM coupling method requires much longer simulation calculation time than other methods. The collision velocity obtained by different algorithms has the error of 0.9%–5.3% from the theoretical calculation values. Cao et al^{[Reference 6

Baidu Scholar}6] used the LS-DYNA software with ALE method to effectively simulate the composite process of the underwater explosion of bimetal pipe, but the waveform of the bonding interface could not be obtained. Ding et al^{[Reference 7

Baidu Scholar}7] proposed the dynamic self-constrained explosive welding of copper/steel bimetal pipes without outer film and analyzed the mechanical balance of the self-constrained process with three-dimensional numerical simulation, thus eliminating the requirements of explosive welding of composite pipes on the mold.

In the actual production, the edges of products manufactured by explosive welding may be unwelded or torn, namely the explosive welding boundary effects, which affects the quality of welding products and wastes metal material. Zhang et al^[

8] prepared Q235/T2 composite pipe and 1060/T2 composite rod in a single test by new dolly-type explosive welding method, but the welding quality of the resultant top area of 1060/T2 composite rod was inferior. Miao et al^{[Reference 9–11}9–11] found that although the severity of explosive welding boundary effect is different by changing the types of cladding plates and explosives, the boundary effect exists in all cases. The lower the ultimate tensile strength of cladding plates or the higher the explosive detonation speed, the more serious the boundary effect phenomenon. The existence of sparse waves in explosives causes the boundary effects. However, the methods to eliminate the boundary effect of composite pipes are rarely investigated.

Copper, as a traditional thermal conductive rolling material, has been widely used in the metallurgy, power, and chemical industries. Stainless steel has the advantages of fine corrosion resistance, high strength, good fatigue resistance, good pressure resistance, and relatively low cost. Therefore, the copper/stainless steel composite pipes have wide application prospects due to their high thermal conductivity, fine corrosion resistance, and good mechanical strength. Based on AUTODYN software, a two-dimensional explosive welding model of copper/steel bimetal pipe was established through SPH and ALE algorithms in this research to simulate and analyze the explosive welding process of copper/steel composite pipe. The process parameters, such as velocity, pressure, and effective plastic strain, were discussed, and the simulated and experimental interface morphologies were compared to verify the accuracy of numerical simulation. Normally, the explosive welding causes boundary effect. In this research, the length of the composite pipe and explosive was increased to decrease the boundary effect. Numerical simulation and corresponding analyses of this new model were conducted, and the boundary effect of the composite pipe was studied.

1 Numerical Simulation of Explosive Welding

1.1 Model

The calculation process of explosive welding of copper/stainless steel pipe was simulated by AUTODYN software. Combined with the physical process of explosive welding, the two-dimensional model used SPH method to effectively and accurately simulate the steel pipe and copper pipe, avoiding the grid distortion. ALE method was used to simulate the explosives and moulds. ALE method could adaptively adjust and maintain high-quality grids, which was suitable for fluid structure coupling problems^[

12]. The initiation point was set at the center of the explosive edge; 14 gauge points were spaced with equal distances between the lower surface of the composite pipe and the upper surface of the base pipe, as shown in Fig.1. Table 1 lists the geometric parameters of the two-dimensional model. The spacing between the composite pipe and the base pipe was 0.6 mm. The particle size in SPH method was crucial. If the particle size was too large, the model could not accurately simulate the wave interface. If the particle size was too small, the computational cost was high and the material stiffness reduced^{[Reference 4

Baidu Scholar}4]. In this research, the particle size was 15 μm in SPH method. The model contained 52 000 particles. The ALE grid size was 0.1 mm, and the unit system in the model was mm-mg-ms.

Fig.1 Two-dimensional model of explosive welding of T2/316L composite pipe

Table 1 Geometry parameters of two-dimensional model of explosive welding for T2/316L composite pipe (mm)

Material	Length	Height
316L	30	0.4
T2	30	0.4
ANFO	30	2.8
Mould	30	3.0

1.2 Explosive model and state equation

Jones Wilkins Lee (JWL) state equation was selected as the state equation of explosives, which is a semi-empirical state equation without detonation products by chemical reaction. This state equation could accurately describe the process of expansion-driven work produced by detonation^[

13]. JWL state equation is shown in Eq.(1), as follows:

P = A (1 - \frac{ω}{R_{1} V}) e^{- R_{1} V} + B (1 - \frac{ω}{R_{2} V}) e^{- R_{2} V} + \frac{ω E_{0}}{V}

(1)

where P is the pressure of the detonation product; V is the

relative volume of the detonation product; E₀ is the initial specific internal energy; e is the initial internal energy; A, B, R₁, R₂, and ω are related parameters. The state equation can describe the relationship between various physical quantities (pressure, specific volume, temperature, internal energy) in the detonation system after explosion. Thus, it is often used in the explosive welding simulation. Combined with the theoretical value of explosive welding window^[

14], JWL state parameters of explosives are shown in Table 2.

Table 2 JWL state parameters of explosives

Relative volume of detonation product, V/m·s^-1	Density, ρ/kg·m^-3	Initial specific internal energy, E₀/GJ	A/GJ	B/GJ	R₁	R₂	ω
3750	900	2.48	49.46	1.89	3.91	1.11	0.33

1.3 Base and composite pipe models and state equation

Shock state equation is suitable to characterize the dynamic behavior of materials under severe deformation. Mie-Gruneisen state equation was selected to simulate the steel pipe and copper pipe and to describe the basic relationship between particle velocity and impact velocity of SPH algorithm. The expression of this state equation^[

15–16] is shown in Eq.(2–6), as follows:

p = p_{H} + Γ_{ρ} (e - e_{H})

(2)

with

Γ_{ρ} = Γ_{0} ρ_{0}

(3)

p_{H} = \frac{ρ_{0} c_{0}^{2} μ (1 + μ)}{1 - (s - 1) μ^{2}}

(4)

e_{H} = \frac{p_{H} μ}{2 ρ_{0} (1 + μ)}

(5)

μ = \frac{ρ}{ρ_{0}} - 1

(6)

where Γ₀ is the Gruneisen coefficient; Γ_ρ is a constant; ρ₀ and ρ are the initial density and current density of the material, respectively; p and p_H are the material impact pressure and current pressure, respectively; e_H is the material impact internal energy; μ is the compression ratio; s is the material constant; c₀ is the volume sound velocity of the material. The parameters of the Mie-Gruneisen material model used in this research are shown in Table 3.

Table 3 Mie-Gruneisen material model parameters

Material	Gruneisen coefficient, Γ₀	Volumetric sound velocity, c₀/m·s^-1	Constant, s	Initial temperature, T_r/K
316L	2.17	4569	1.49	300
T2	1.99	3940	1.49	294

Johnson-Cook constitutive equation can accurately describe the relationship between stress and strain and that between strain rate and temperature under large deformation. Thus, Eq.(7) was selected to simulate the constitutive equation of copper pipe and steel pipe, as follows^[

17]:

σ = (A + B ε_{p}^{n}) (1 + C l n ε_{p}^{*}) (1 - T^{* m})

(7)

where σ is flow stress for Von Mises; A is the initial yield stress; B is the hardening constant; ε_p is the equivalent plastic strain; $ε_{p}^{*} = \frac{ε_{p}}{ε_{0}}$ is the equivalent plastic strain rate; n is the hardening index; C is the strain rate constant; m is the thermal softening index; $T^{*} = \frac{T - T_{r o o m}}{T_{m e l t} - T_{r o o m}}$ is a dimensionless temperature; T_melt and T_room represent the melting temperature of the material and room temperature, respectively. The Johnson-Cook material model parameters are shown in Table 4.

Table 4 Johnson-Cook material model parameters

Material

Density,

ρ/kg·m^-3

Initial yield

stress, A/MPa

Hardening

constant, B/MPa

Hardening

index, n

Strain rate

constant, C

Thermal softening

index, m

Melting temperature,

T_melt/K

316L

7980

280

1250

0.76

0.021

0.82

1680

Mould

8930

7896

350

292

275

0.31

0.36

0.025

0.022

1.09

1356

1811

2 Results and Discussion

2.1 Explosive welding process

Fig.2 shows the explosive welding process of copper/steel composite pipe (the explosive and mold parts are hidden), which is similar to the welding process of clad plate^[

12]. The composite pipe is accelerated to bend under the action of explosives, then collides with the base pipe, and ultimately forms a composite material. The inner diameter becomes larger under the action of explosives.

Fig.2 Simulated explosive welding process: (a) 0 ms, (b) 2.73×10^-3 ms, (c) 6.15×10^-3 ms, and (d) 8.96×10^-3 ms

2.2 Velocity distribution

Fig.3a shows the interface morphology of explosive welding model. Fig.3b shows the relationship between Y velocity and time of the composite pipe in the model. Fig.3c₁–3c₆ show the interface waveforms of the regions in Fig.3a. In the numerical simulation, the Y velocity of the base pipe determines the collision velocity between the composite pipe and the base pipe, as well as the waveform formation during interface bonding. According to Fig.3b, the feature point 1 is at the starting position. In the beginning, the explosive energy is insufficient, resulting in the lower velocity of production and no binding occurs at the interface, as shown in Fig.3c₁.

Fig.3 Simulated interface morphology of explosive welding process (a); relationship between Y velocity and time of different feature points (b); enlarged morphologies of unwelded area A (c₁), straight area B (c₂), wave area C (c₃), smooth wave area D (c₄), vortex wave area E (c₅), and straight area F (c₆) in Fig.3a

With the stable detonation of explosive, the interface presents a flat and straight interface in Fig.3c₂. The Y velocity increases sharply and the maximum value is 1420 m/s. Then, it decreases to about 80 m/s to maintain stability. The interface is transformed from the flat interface to the small wavy interface^[

18] (Fig.3c₃), the periodic smooth wavy interface (Fig.3c₄, wavelength of 0.16 mm, amplitude of 0.12 mm), and the vortex wavy interface (Fig.3c₅, wavelength of 0.27 mm, amplitude of 0.18 mm). Finally, under the action of the rarefaction wave of explosive^{[Reference 19

Baidu Scholar}19], the maximum velocity of feature point 7 is smaller than that at the middle position, and the interface becomes a straight interface again (Fig.3c₆).

2.3 Pressure distribution

When the composite pipe collides with the base pipe, huge pressure is generated at the collision point. During explosive welding of copper/steel composite pipe, the pressure distribution at 3.77×10^-3 ms is shown in Fig.4a. The maximum pressure occurs in the collision point area. The pressure-time curve of the characteristic points on the base composite pipe is shown in Fig.4b. The pressure at feature points 1 and 8 near the initiation point is extremely low. With propagating the detonation wave, the pressure at feature points 3 and 10 shows a pulse-like upward trend, and the pressure curves of these two points coincide, indicating the combination of the two impact points. Then, the pressure gradually decreases from peak to zero within 1.3×10^-3 ms^[

12].

Fig.4 Pressure distribution on copper/steel composite pipe at 3.77×10^-3 ms (a); relationship between pressure and time at feature points (b)

The pressure-time curve of the feature points in the middle part of the composite pipe shows the similar variation: the peak pressure value has the order of magnitudes of 10⁷ kPa. The collision pressure at the interface is much greater than the yield strength of the material. In the end, due to the sparse wave of the explosive, the pressure is relatively low.

2.4 Effective plastic strain and shear stress distribution

The materials near the interface produce serious plastic deformation during explosive welding, thus forming plastic deformation zone. A clear narrow plastic deformation band appears near the collision zone. The effective plastic strain cloud map at 3.77×10^-3 ms is shown in Fig.5a. The effective plastic strain curves of the feature points on the base pipe in the model are shown in Fig.5b. The feature points 5 and 12 undergo plastic deformation simultaneously, and their maximum deformation amount is 1.5 and 1.6, respectively. The plastic strain remains stable after reaching a certain value. Plastic deformation is usually irreversible, resulting in uneven surface. This phenomenon can ensure that the two metals can be successfully welded^[

4]. Severe plastic deformation is usually accompanied by the grain recrystallization and the formation of intermetallic compounds. However, due to restriction of AUTODYN software, the severe plastic deformation cannot be achieved in current simulations^{[Reference 12

Baidu Scholar}12].

Fig.5 Distribution of effective plastic strain at 3.77×10^-3 ms (a); relationship between effective plastic strain and time at different feature points (b)

The distribution cloud diagram of shear stress in copper/steel composite pipe at 3.77×10^-3 ms is shown in Fig.6. It can be seen that the shear stress on the composite pipe has opposite direction to that on the base pipe. The shear stress on the composite pipe is negative, whereas that on the base pipe is positive. The shear stress is unevenly distributed on the base pipe and composite pipe. Mousavi et al^[

21] found that the composite pipe can be achieved only when the base pipe is subjected to the opposite shear stress during the explosive welding. In addition, the material properties lead to the higher shear stress value of the composite pipe, compared with that on the base pipe^{[Reference 22

Baidu Scholar}22].

Fig.6 Shear stress nephogram of copper/steel composite pipe

2.5 Boundary effect of controlled explosive welding

Fig.7 shows the composite interfaces at the starting position and ending position after explosive welding. It can be seen that the composite pipe is tilted at the beginning, and the bonding interface at the end changes from the wavy interface to the flat surface. Based on the analysis of velocity and pressure, it can also be seen that these two parts of the composite pipe are not fully bonded, resulting in the boundary effect. Moreover, the boundary effect at the starting position is more severe than at the ending position. The existence of the boundary effect undoubtfully reduces the quality of the entire composite pipe, which not only causes material waste, but also requires additional operation procedures to remove the unbounded parts at the edges, thus increasing the manufacturing cost of the composite pipe.

Fig.7 Boundary effect at starting position (a) and ending position (b)

The boundary effect is caused by not only the insufficient energy generated by explosive detonation at the initial stage and ending stage, but also the effect of explosive rarefaction wave. To eliminate the boundary effect, the composite pipe, explosive length (extending of 5 mm at both ends), explosive initiation position, and other unchanged model parameters should be added into the original model, as shown in Fig.8a. The simulation results of this method at the edges are shown in Fig.8b–8c. Compared with Fig.7, it can be seen that this method can avoid the generation of boundary effect, and good combination of pipes can be achieved at the edge of base pipe.

Fig.8 Boundary effect in extended copper/steel composite pipe model: (a) overall model; (b) starting position; (c) ending position

The properties of the extended model are shown in Fig.9. It can be seen that the Y velocities at feature points 1 and 7 at the edge increase to 820 and 950 m/s, respectively, and the order of magnitudes of the pressure is 10⁷ kPa. Compared with Fig.3 and Fig.4, it can be seen that the pressure value at the edge greatly increases, which is similar to that at the middle feature points. These results indicate that the combination energy at the edge increases and the edge is well combined, eliminating the boundary effect.

Fig.9 Relationship of Y velocity (a) and pressure (b) with time of different feature points

3 Experiment

To conduct the explosive welding experiment of copper/steel composite pipe, the geometric parameters of copper/steel composite pipe are 10 times larger than those of the numerical simulation parameters, as shown in Table 5. Ammonium oil explosive with density of 900 kg/m³ and detonation velocity of 3750 m/s was selected for edge center initiation. Fig.10a shows the welded composite pipe. The wire cutting method is used to cut the composite pipes A, B, and C at three positions. The cut samples are shown in Fig.10c, and each sample has the size of 10 mm×5 mm×8 mm. Grind and polish the sample, and observe the interface morphology of the sample under a VHX-2000 ultra depth of field three-dimensional microscope.

Table 5 Base pipe parameters (mm)

Material	Length	Inside diameter	Thickness
316L	300	28	4
T2	300	48	4

Fig.10 Appearances of copper/steel composite pipe: (a) side appearance; (b) cross-section appearance; (c) longitudinal-section appearance

The detailed waveform at area A–C in Fig.10a is shown in Fig.11a–11c, respectively. The smooth wave length in Fig.11b is 203 μm and the amplitude is 59 μm. The vortex wave length in Fig.11c is 227 μm and the amplitude is 75 μm. Compared with the simulated interface morphologies in Fig.3, in the initial stage of explosion, the junction surface is flat, and the periodic smooth waves and vortex waves are formed with the detonation of explosives proceeding^[

23]. The simulated and experimental shapes of the junction surface are consistent, which verifies the accuracy of the numerical model of explosive welding.

Fig.11 Interface morphologies of waveform at area A (a), area B (b), and area C (c) in Fig.10a

4 Conclusions

1) Under the action of explosive detonation waves, the copper/steel composite pipe is accelerated and collides obliquely with the base pipe. When the explosive explodes stably, the pressure is at the order of magnitude of 10⁷ kPa, which is much greater than the dynamic yield strength of copper and steel materials. A clear narrow plastic deformation band appears near the collision zone, and the shear stresses on the base and composite pipes have opposite directions.

2) The velocity, pressure, and effective plastic deformation at the initial position and end position of the explosion are all lower than the normal values. Besides, boundary effect exists in the explosive welding. The boundary effect can be eliminated by extending the composite pipe and explosive, which increases the binding energy at the edge.

3) The established numerical model of explosive welding is reasonable and reliable to simulate the explosive welding process of copper/steel bimetal pipe. In the simulation, the interface morphology changes from straight line to wave shape with the propagation of the explosion wave, which is consistent with the actual interface morphology of the T2/316L bimetal composite pipe after explosive welding.

References

Zheng Yuanmou. Explosive Welding and Explosive Composite Materials[M]. Beijing: Defense Industry Press, 2017: 13 (in Chinese) [Baidu Scholar]

Findik F. Materials and Design[J], 2011, 32: 1081 [Baidu Scholar]

Xu Zuxi. Explosive Welded Composite Pipe[D]. Wuhan: Wuhan University of Science and Technology, 2018 (in Chinese) [Baidu Scholar]

Sun Z R, Shi C G, Xu F et al. Materials and Design[J], 2020, 191: 108630 [Baidu Scholar]

Miao Guanghong, Hu Yu, Ai Jiuying et al. Transactions of the China Welding Institution[J], 2022, 43(12): 64 (in Chinese) [Baidu Scholar]

Cao Jianbin, Zhang Zhousuo. Transactions of the China Welding Institution[J], 2018, 39(2): 61 (in Chinese) [Baidu Scholar]

Ding Long, Xu Junfeng, Ma Honghao et al. Journal of Materials Research and Technology[J], 2023, 24: 7229 [Baidu Scholar]

Zhang Lingyun, Ma Honghao, Shen Zhaowu et al. Transactions of the China Welding Institution[J], 2021, 42(5): 1 (in Chinese) [Baidu Scholar]

Miao Guanghong, Ai Jiuying, Hu Yu et al. Transactions of the China Welding Institution[J], 2021, 42(9): 61 (in Chinese) [Baidu Scholar]

Miao Guanghong, Ma Leiming, Ai Jiuying. Ordnance Materials Science and Engineering[J], 2020, 43(3): 7 (in Chinese) [Baidu Scholar]

Miao Guanghong, Li Liang, Jiang Xiangyang et al. Chinese Journal of Energetic Materials[J], 2017, 25(9): 762 (in Chinese) [Baidu Scholar]

Li Y, Liu C R, Yu H B et al. Metals[J], 2017, 7(10): 407 [Baidu Scholar]

Wang Yanjin, Zhang Shudao, Li Hua et al. Acta Physica [Baidu Scholar]

Sinica[J], 2016, 65(10): 106401 (in Chinese) [Baidu Scholar]

Li Xiaojie, Yang Wenbin, Xi Jinyi et al. Explosive Materials[J], 1999, 28(3): 22 (in Chinese) [Baidu Scholar]

Wang X, Zheng Y Y, Liu H X et al. Materials and Design[J], 2012, 35: 210 [Baidu Scholar]

Mojżeszko M, Perzyński K, Sionkowski M et al. Archives of Metallurgy and Materials[J]. 2020, 65(2): 707 [Baidu Scholar]

Wu X M, Shi C G, Gao L et al. Rare Metal Materials and Engineering[J], 2023, 52(4): 1272 [Baidu Scholar]

Bi Z X, Li X J, Wu Y et al. Rare Metal Materials and Engineering[J], 2022, 51(10): 3611 [Baidu Scholar]

Wang Li. Study on Hydraulic Explosion Welding of Bimetal Composite Pipe[D]. Taiyuan: North University of China, 2018 (in Chinese) [Baidu Scholar]

Li Yan, Li Yanbiao, Liu Cuirong et al. Welding & Joining[J], 2021, 579(9): 10 (in Chinese) [Baidu Scholar]

Mousavi A A L, Hassani S T S. Journal of the Mechanics and Physics of Solids[J], 2005, 53(11): 2501 [Baidu Scholar]

Miao Guanghong, Ai Jiuying, Ma Leiming et al. Transactions of the China Welding Institution[J], 2020, 41(8): 5562 (in Chinese) [Baidu Scholar]

Wu Xiaoming, Shi Changgen, Fang Zhongxing et al. Rare Metal Materials and Engineering[J], 2022, 51(1): 286 (in Chinese) [Baidu Scholar]

首页

期刊简介

编委会

投稿指南

过刊浏览

联系我们

English

Numerical Simulation and Boundary Effect of Explosive Welding of Copper/Steel Composite Pipe PDF

Abstract

Keywords