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Experimental and numerical studies on the deformation and tearing of X70 pipelines subjected to localized blast loading
Thin-Walled Structures 107 (2016) 156–168
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Experimental and numerical studies on the deformation and tearing of X70 pipelines subjected to localized blast loading Kejian Song a, Yuan Long a, Chong Ji a,n, Fuyin Gao a, Hailong Chen b a
Engineering Institute of Engineering Corps, PLA University of Science and Technology, Nanjing, 210007, China State Key Laboratory for Disaster Prevention & Mitigation of Explosion & Impact, College of Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China
b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 September 2015 Received in revised form 2 February 2016 Accepted 7 March 2016
The dynamic response of X70 grade steel pipeline under localized blast loading is studied by experimental and numerical investigations. The steel pipelines with large diameter and high grade are concerned in the paper. The influences of the explosive mass, contact area and wall thickness on the deformation/failure mechanisms of the X70 pipelines were investigated. The post-failure motion of the fragment was also observed during the experiment. Four different failure modes were observed during the experiment namely Mode I, Mode II, Mode IIIa and Mode IIIb. The features of each mode are analyzed concretely. Results revealed that the deflection and damage level of pipeline increased with the increase of explosive mass and contact area. The wall thickness plays an important role on the damage and postfailure motion. Numerical simulations based on the experimental results were conducted. The damage process, midpoint deflection, pressure distribution, energy changes and the post-failure fragment velocities were analyzed. The results of numerical simulations show good correlation with the experiments & 2016 Elsevier Ltd. All rights reserved.
Keywords: Blast load X70 pipeline Contact explosion Failure mode Post-failure motion
1. Introduction Large-diameter, high-pressure gas transmission pipelines have been used more and more widely all over the world. With the development of the pipeline network, safety and maintenance become an important task. Terrorism and military operations could increase the potential for structures to be subjected to explosions. Some pipeline structures might be subjected to explosive loads during their service life. So, the behavior of the pipeline during and after being subjected to blast loading is important to understand. For the past few decades, numerous theoretical and experimental studies on structures such as beams and plates subjected to blast loading have been published. Menkes and Opat [1] firstly studied the dynamic failure of beams experimentally for blast loaded alloy 6062 T6 beams. Jones [2] studied the problem analytically using a rigid plastic material model. Three failure modes were identified for the beams: Mode Ⅰ-large permanent displacement deflections or damage without any material rupture; Mode Ⅱ-tensile rupture at supports; Mode Ⅲ-transverse shear failure at supports. Teeling Smith and Nurick [3] were the first to identify n
Corresponding author. E-mail address: [email protected] (C. Ji).
http://dx.doi.org/10.1016/j.tws.2016.03.010 0263-8231/& 2016 Elsevier Ltd. All rights reserved.
and report the three failure modes for circular plates subjected to uniformly distributed pressure impulses. Ref. [4] presented a theoretical method of analysis for mass impacts, dynamic pressure pulses and impulsive velocity or blast loadings on circular, square and rectangular plate for the idealization of a rigid, perfectly plastic material, and simple equations were also presented to predict the maximum permanent transverse displacements. Several authors such as Gupta N.K. [5], Jones N. [6], Henchie T.F. [7], Karagiozova D. [8] have presented experimental and theoretical results of blast loaded structures. Bambach [9] and Jama H.H. [10] reported the investigation of steel square hollow sections subjected to transverse blast loads. Some other authors have focus on petalling and post-failure response of structures subjected to blast loading [11–14]. Although experimental and analytical methods have been used extensively in the literatures, numerical analyses can not be ignored because they can provide valuable information on the details of the response of structural members with more complex material properties. Recently three commercial numerical codes, namely, ABAQUS, LS-DYNA and AUTODYN have been used extensively in the modeling of blast-loaded structures [15–17]. Numerous attempts have been made using commercially available software packages to model the large inelastic deformation or complete failure of the structure subjected to blast loading [18– 22]. These simulations have compared well with the experiments.
K. Song et al. / Thin-Walled Structures 107 (2016) 156–168
Table 1 The chemical compositions of steel X70 (wt%) Elements Contents Elements Contents
C 0.051 Mo 0.21
Si 0.20 Ni 0.14
Mn 1.56 Nb 0.045
P 0.014 V 0.032
S 0.0029 Ti 0.016
Cr 0.026 Cu 0.18
157
the blast fragment was also recorded. Numerical simulations of these impact scenarios, identical to the experiments were performed using the commercial finite element code LS-DYNA, and the results obtained were compared with the experimental data. The experiments are generally well reproduced and the key phenomena are well captured by the computer simulations.
2. Experimental research Table 2 Mechanical properties.
2.1. Material properties
Yield strength ss/MPa Tensile strength sb/ MPa
Elongation (%) Ratio of ss/sb
575
42
687
Front Zone
0.84
The steel used is a Chinese-made pipeline steel in grade X70. The wall thicknesses of pipes are 14.6 mm and 26.4 mm, respectively. The diameter of the pipeline is 1.016 m, which is the same size as the pipelines used in serve. The chemical compositions of the pipelines are shown in Table 1. The steel is in hot rolling state and the microstructure is composed of ferrite and pearlite. The ordinary mechanical properties are shown in Table 2.
TNT Charge 2.2. Experimental setup
X70 Pipeline
Back Zone
Soil Ground
Fig. 1. Sketches of experiment setup.
The above researches mainly focus on small-diameter and ordinary steel materials. For large-diameter and high grade steel pipeline, they may display different damage pattern when subjected to blast loading. However, researches on this subject are difficult to find. Post-failure motion of the blast fragment is very important in the dynamic analysis of the structure, but it has hitherto been difficult to predict due to the fact that the material properties at the moment of tearing are difficult to quantify. The study presents experimental research of X70 grade steel pipeline with diameter 1.016 m subjected to localized blast loading, and numerical simulations thereof. Four kinds of failure modes are observed during the experiment. Post-failure motion of
Sketches of the experiment setup are shown in Fig. 1. The experiments were conducted in the field test site. The X70 pipelines were placed on the ground. The impulsive loading was created by the detonation of TNT explosive. The charge was placed at the top center of the pipe. During the experimental study, the mass of charge was varied from 0.4 kg from 10.0 kg to achieve different impulses. The explosive has a density of 1.61 g/cm3, a detonation velocity of 6950 m/s, and a CJ energy per unit volume of 6.74 106 kJ/m3. All charges were initiated at top center end using an electrical detonator and a 15 g C4 booster. For each test, explosion mass, permanent displacement and the final deformed shape profile were recorded. Previous studies defined three failure modes that were observed in uniformly blast-loaded beams: large inelastic deformation (Mode I), tensile tearing at the boundary (Mode II), and shearing at the supports (Mode III). The failure modes reported for locally loaded pipelines were similar to those observed for locally loaded plates, the main difference being an additional capping mode (that is, thinning and tearing of a central fragment, or ‘cap’). Fragments, referred to as caps, were produced from surface at higher impulses due to tearing of a central ring of material. The pipe failure mode can be subdivided on the basis of experimental observations by Mode I: Large inelastic response with thinning in the central area; Mode II: Large inelastic response with thinning in the central area and spallation in the inner area;
Table 3 Experimental specimens and deformation results. Test no.
Wall thickness (cm)
Mass of explosive (kg)
Contact area
Deformation range Front zone
1 2 3 4 5 6 7 8 9
1.46 2.62 2.62 2.62 1.46 2.62 1.46 2.62 2.62
0.2 0.4 0.8 1.4 3 3 5 5 10
10 cm 5 cm 10 cm 10 cm 10 cm 10 cm 10 cm 10 cm 20 cm 15 cm 20 cm 15 cm 20 cm 20 cm 25 cm 20 cm 25 cm 20 cm
2.3 cm 3.5 cm 5.3 cm 5.9 cm 23 cm 28 cm 23 cm 16 cm 32 cm 28 cm 29 cm 21 cm 29 cm 21 cm
Failure mode Back zone
20 cm 16 cm 27 cm 23 cm 25 cm 20 cm 31 cm 24 cm
Mode Mode Mode Mode Mode Mode Mode Mode Mode
I response I response II response II response IIIb response IIIa response IIIb response IIIa response IIIb response
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Q=0.2 kg δ=1.46 cm
Local pitting
Bulge deformation
Mode I Outer surface
Inner surface Fig. 2. Deformation of the pipeline with wall thickness 1.46 cm under 0.2 kg TNT.
Q=0.4 kg δ=2.62 cm Bulge deformation Local pitting
Mode I Outer surface
Inner surface Fig. 3. Deformation of the pipeline with wall thickness 2.62 cm under 0.4 kg TNT.
0.0
0
-1
-1.0
Deflection (cm)
Deflection (cm)
-0.5
-1.5 -2.0 -2.5 Inner surface Outer surface
-3.0 -3.5 0
1
2
3
4
Distance from impact mid-point (cm) Fig. 4. The measured profiles of the pipeline in Test.1.
Mode IIIa: Complete tearing in the central area (also known as ‘capping’ failure) and mode I response on back face. Mode IIIb: Complete tearing in the central area and the blast fragment perforation back face. During the experiment the fragment travelled from the front face toward the back face. Table 3 contains a summary of the localized blast test results,
-2
-3
-4
Inner surface Outer surface
-5
-6 0
1
2
3
4
5
Distance from impact mid-point (cm) Fig. 5. The measured profiles of the pipeline in Test.2.
with explosion mass, deformation range and failure mode listed for each experiment. 2.3. Experimental observations and discussion 2.3.1. Failure Mode I When the explosive mass is small, the pipeline displays failure Mode I, which is large inelastic response with thinning in the
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Q=0.8 kg δ=2.62 cm
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Spallation
Local pitting
Mode II Outer surface
Inner surface Fig. 6. Damage of the pipeline with wall thickness 2.62 cm under 0.8 kg TNT.
Q=1.4 kg δ=2.62 cm
Local pitting
Spallation
Mode II Outer surface
Inner surface Fig. 7. Damage of the pipeline with wall thickness 2.62 cm under 1.4 kg TNT.
central area. Selected photographs that demonstrate the failure characteristics of the pipeline are shown in Figs. 2–3. Fig. 2 shows the results of the pipeline with wall thickness 1.46 cm subjected to 0.2 kg TNT. A local pitting and a bulge are formed on the outer and inner surface of the pipeline, respectively. The pitted regions are approximately the same size as the contact area. The measured profile of the pipeline in this test is shown in Fig. 4. It is found that the maximum deformation of the outer surface is 2.2 cm. Fig. 3 shows the results of the pipeline with wall thickness 2.62 cm subjected to 0.4 kg TNT. Similar phenomenon can be seen compared with test 1. The measured profile of this test is shown in Fig. 5. The maximum deformation of the outer surface is 3.4 cm. 2.3.2. Failure Mode II With the increase of the explosive mass, the level of deformation and damage increased. And the failure mode of the pipeline transitioned from Mode I to Mode II. When the X70 steel pipeline subjected to 0.8 kg TNT explosive, the outer surface of the pipeline undergoes large inelastic response with thinning in the central area, while the inner surface displayed spallation mechanism, as shown in Fig. 6. When the mass of the explosive increased to 1.4 kg, the pipeline still remained Mode II, but has a
little difference with 0.8 kg TNT explosive. Fig. 7 shows the top view of a localized failure of X70 pipeline. A local pitting with larger areas was formed on the outer surface after testing. And also we can see clearly that a macroscopic crack emerged in the center region. 2.3.3. Failure Mode IIIa Fig. 8 shows the failure mode of X70 pipeline with wall thickness 2.62 cm subjected to 3 kg TNT explosive. It is clearly seen that both the outer surface and the inner surface of the pipeline tore completely in the center region. The pipeline failed catastrophically. A crevasse with dimension of about 23 cm 16 cm was formed at the front zone. The edge of the crevasse was quite tidy because of the adiabatic shearing failure of the pipeline. It is also evident that the macroscopic cracks emerged on the outer surface and grew along the direction toward the corner. A piece of fragment was produced from the eroded material of the front zone during the experiment as shown in Fig. 8. The fragment travelled from the front zone to the back zone and impacted the back surface at last, leaving a local pitting on it. The similar phenomenon can be seen in Fig. 9 for the explosive mass 5 kg and wall thickness 2.62 cm. The dimension of the rectangle hole is 29 cm 21 cm.
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Complete tearing in the central area of the front zone
Q=3 kg δ=2.62 cm
Fragment
Local pitting on the back zone
Fig. 8. Damage of the pipeline with wall thickness 2.62 cm under 3 kg TNT.
The mass and the velocity of the fragment were larger than Fig. 8, and a local pitting with dimension 25 cm 20 cm is formed on the back zone. 2.3.4. Failure Mode IIIb When subjected to 3 kg TNT explosive with wall thickness 1.46 cm, the X70 pipeline exhibits Mode IIIb. Both the front zone and the back zone tore completely in the center region. Selected photographs that demonstrate the failure characteristics are shown in Fig. 10. From the photographs we can see that a rectangle crevasse with dimension 23 cm 28 cm was formed on the front zone. Four cracks with length of 10 cm were formed at the four corners. Under the impact of the blast loading, the inner surface of the front zone tore in a “petalling” fashion with numbers of petals. A crevasse with dimension 20 cm 16 cm was also formed on the back zone because of the fragment produced from the front zone. The fragment shown in Fig. 10 underwent large inelastic deformation in the center region with buckling on the end sides. When the explosive mass increased to 5 kg, similar phenomenon can be observed shown in Fig. 11. Fig. 12 shows photographs of X70 pipeline with wall thickness 2.56 cm subjected to 10 kg TNT explosive. From the figures we can
see that six macroscopic cracks emerged on the edge of the front crevasse. The front zone of the pipeline underwent adiabatic shearing failure, and a big piece of fragment was produced. Then the back zone of the pipeline was penetrated by the fragment.
3. Material constitutive models 3.1. Material model for X70 steel To be able to describe the various phenomena taking place during contact explosion, it is necessary to characterise the behavior of materials under explosion-generated high strain rate loading conditions. The tube steel is modeled by the Johnson-Cook material model [23], which is suitable to model the strength behavior of materials subjected to large strains, high strain rates and high temperatures. The model defines the yield stress sy as Table 4
σy = [A + B(ε¯ p)n][1 + C ln ε*̇ ][1 − (T *)m]
(1)
where A, B, C, n and m are the material parameters determined by experiments. ε̇* is the dimensionless effective strain rate for and T *
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161
Complete tearing in the central area of the front zone
Q=5 kg δ=2.62 cm
Fragment
Local pitting on the back zone Fig. 9. Damage of the pipeline with wall thickness 2.62 cm under 5 kg TNT.
is the homologous temperature which is defined by
T* =
T − Troom Tmelt − Troom
(2)
In Eq. (2), Troom and Tmelt are the room and melting temperatures, respectively. In the fracture analysis, Johnson-Cook fracture model is used. The model is based on the concept of cumulative damage, and it can take account of the loading history that may involve variations in strain rate, temperature and pressure. The damage parameter D is defined by
D=
∑ Δϵ/ϵf
(3)
where Δϵ is the increment of effective strain caused by the tensile load and εf is the effective fracture strain in the instantaneous conditions. Fracture occurs, when D ¼1. The effective fracture strain is assumed to be the function of strain rate, temperature and pressure in the form
εf = [D1 + D2expD3σ *][1 + D4 ln ε*̇ ][1 + D5T *]
(4)
where σ * is the dimensionless pressure-stress ratio defined as
σ * = σm/σ¯ where σm is the mean stress normalised by the effective stress, σ¯ is the effective stress, and D1, D2, D3, D4 and D5 are the material parameters. The material constants adopted here are based on the typical data for X70 steel. 3.2. Material model for high explosive and air High explosives (TNT) are typically modeled by using the JonesWilkins-Lee (JWL) EOS, which models the pressure generated by chemical energy in an explosion. It can be written in the form
p = A1(1 −
ω −R1v ω −R2v ωe )e + B1(1 − )e + R1v R2v v
(5)
where p is the hydrostatic pressure; v is the specific volume, e is internal specific energy. The values of constants A1, R1, B2, R2, ω for many common explosives have been determined from dynamic experiments. In the present simulation, for a TNT explosive charge, C1, R1, C2, R2, and ω are 3.712 105MPa, 4.15, 3.231 103 MPa, 0.9, 0.35, respectively. In the numerical model, air is modeled by an ideal gas EOS, which is one of the simplest forms of EOS. The pressure is related
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Complete tearing in the central area of the front zone
Q=3 kg δ=1.46 cm
Fragment produced in the expriment
Penetration hole of the back zone
Fig. 10. Damage of the pipeline with wall thickness 1.46 cm under 3 kg TNT.
to the energy by
p = (γ − 1)ρe
(6)
where γ is a constant, ρ is air density and e is the specific internal energy. In the simulation, air density, ρ ¼ 1.225 kg/m3 and γ ¼1.4. The air initial internal energy is assumed to be 2.068 105 kJ/kg.
boundary. According to the different failure modes observed in the experiment, we develop a series of numerical analysis to further study these phenomenons in the following paper. In order to demonstrate the validity of the numerical method adopted, the comparisons between simulation results and experimental observations are also needed in the paper.
4. Numerical simulation
4.1. Mode I response
Numerical analyses were carried out using the commercial finite element code LS-DYNA. The test results on X70 pipeline under dynamic pressure loading were compared with the numerical results in order to validate the accuracy and reliability of the numerical model. The geometry of the quarter symmetry finite element models as implemented in the element code are given in Fig. 13. A convergence study is conducted to determine the optimal number of elements in each of the model. In the simulation, the steel pipe is modeled using a Lagrange mesh, in which the coordinates move with the material; while the air and high explosive are modeled by the Euler mesh, in which the grid is fixed and material flows through it. At the Euler-Lagrange interface, interaction is considered. The Lagrange mesh imposes a geometric constraint on the Euler mesh, while the Euler mesh provides a pressure boundary to the Lagrange mesh. The boundary condition of the Euler mesh is set as an outflow
Fig. 14 shows the representative failure process of X70 pipeline with wall thickness 2.62 cm subjected to 0.4 kg TNT explosive. When the shock wave impacts on the pipeline, the front zone of the pipeline is subjected to a large stress with plastic deformation. In order to measure pressure distribution of the explosive shock wave on the surface of the pipeline, a number of measuring points are selected and shown in Fig. 15. Fig. 16 shows the pressure-time curves obtained at different points. The peak pressures at these points are listed in Table 5. From the table we can see that the maximum value is captured at element B, with a value of 2.82 GPa. The peak pressures measured at element A, C, D are a little smaller, which are 2.59 GPa, 1.98 GPa, 2.07 GPa, respectively. The simulation results shows that, a local pitting is formed on the outer surface of the front zone, the final deformation amount of the middle point is 3.19 cm. While a bulge is formed on the inner surface, with a final deformation value 2.62 cm. Comparison
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Q=5 kg δ=1.46 cm
163
Complete tearing in the central area of the front zone
Penetration hole of the back zone
Fig. 11. Damage of the pipeline with wall thickness 1.46 cm under 5 kg TNT.
Tearing holes of the front zone Fragment
Q=10 kg δ=2.62 cm
Tearing holes of the back zone Fig. 12. Damage of the pipeline with wall thickness 2.62 cm under 10 kg TNT.
Table 4 Parameters for John-Cook model of X70 pipeline.
Air Explosive
Elasticity and density Density
Steel pipe
Yield stress, strain hardening
Poisson’s ratio Young’s modulus
ρ (kg/m3) μ 7850 0.3
Ep (GPa) 210
A (MPa) 560
B (MPa) 510
n 0.48
Fig. 13. Finite element model.
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(a) t=25 us
(b) t=105 us
(c) t=180 us
(d) t=490us
Fig. 14. Deformation process of steel pipe under 0.4 kg TNT explosion.
Table 5 Pressure distributions on the pipeline under different explosive mass Explosive mass (kg)
0.4 0.8 3
Peak pressure (GPa) A
B
C
D
2.59 3.36 3.18
2.82 4.42 5.04
1.98 2.86 2.32
2.07 0.67 0.98
between numerical simulation and the experiment are shown in Table 6 Comparison between numerical simulation and experiment of Test.2.
Element B
Element C
d1 d2 h1 h2
Element D
Element A
(cm) (cm) (cm) (cm)
Numerical simulation
Experiment
Error (%)
3.19 2.62 9.95 10.43
3.40 2.49 10.42 10.83
6.2 þ 5.2 4.5 3.7
d1 denotes the maximum deformation on the outer surface; d2 denotes the maximum deformation on the inner surface; as shown in Fig. 17, h1 and h2 denote the length of local pitting on the axial and circumferential direction, respectively.
Table 6 and Fig. 17. From the table and figures we can see that the simulation agrees well with the experiment. Fig. 15. Location of the chosen elements on the pipeline.
4.2. Mode II response 3.0 2.5
Element A Element B Element C Element D
Pressure (GPa)
2.0 1.5 1.0 0.5 0.0 -0.5 0
20
40
60
80
100
Time (us) Fig. 16. Pressure–time curves of elements A, B, C and D.
120
Fig. 18 shows the failure process of pipeline with wall thickness 2.62 cm subjected to 0.8 kg TNT explosive. From the figures we can see that the front zone of the pipeline undergoes large inelastic deformation under the impacts of shock wave. At the time t¼240 μs, the phenomenon of spallation comes out on the inner face of the front zone, and a number of fragments are formed at the same time. We choose four elements with the same locations in Fig.15 to measure the pressure distributions on the pipeline. The results are listed in Table 5. The peak pressure at the location of A, B, C and D are 3.36 GPa, 4.42 GPa, 2.86 GPa and 0.67 GPa, respectively. The finite element analysis shows that a local pitting with depth 5.88 cm is formed on the outer surface of the front zone. A phenomenon of spallation is formed on the inner surface. Comparison between numerical simulation and the experiment are shown in Table 7. The numerical simulation agrees well with the experiment.
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Numerical simulation
165
Numerical simulation
Inner surface
Outer surface
Experiment
Experiment Fig. 17. Comparison between numerical simulation and experiment.
(a) t=25 us
(b) t=240 us
(c) t=485 us
(d) t=800 us
Fig. 18. Deformation and damage process of steel pipe under 0.8 kg TNT explosion.
Table 7 Comparison between numerical simulation and experiment of Test.3.
d3 (cm) h3 (cm) h4 (cm)
Numerical simulation
Experiment
Error (%)
5.88 11.85 14.77
6.06 12.44 13.85
3.0 4.7 þ6.6
d3 denotes the maximum deformation on the outer surface of the pipeline; h3 and h4 denote the length of local pitting on the axial and circumferential direction, respectively.
4.3. Mode IIIa response Fig. 19 shows the process of X70 pipeline with wall thickness 2.62 cm subjected to 3 kg TNT explosive. From the figures we can
see that a large piece of fragment was formed on the front zone after the shock wave impacts on the pipeline. The fragment then travels from the front zone to the back zone and causes a local pitting on it. Fig. 20 shows the velocity–time curves of the fragment. The figure reveals that at the initial stage, the center element of the fragment has the largest velocity, while the edge element has the smallest one. At about 400 μs, the total fragment reaches to the velocity of 406 cm/s. At the time 2350 μs, the fragment reaches to the back zone and impacts the pipeline. Finally, with the increase of time, the velocity of the fragment decrease to zero. The finite element analysis shows that a rectangle hole is formed in the front zone. And four cracks appear at the four corners of the hole. The dimensions of the penetration hole and the fragment are shown in Fig. 21. Comparison between numerical
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(a) t=55 us
(b) t=200 us
(c) t=2340 us
(d) t=3200us
Fig. 19. Deformation and damage process of 2.62 cm thickness pipeline under 3 kg TNT.
100
Table 8 Comparison between numerical simulation and experiment of Test.6
0
Velocity (m/s)
-100
h5 (cm) h6 (cm) l1 (cm) l2 (cm) M1 (kg)
-200 -300
Numerical simulation
Experiment
Error (%)
15.4 22.8 21.7 12.8 6.51
16.1 23.2 22.9 12.3 6.93
3.1 1.7 4.8 4.1 6.1
As shown in Fig. 21, h5 and h6 denote the length of local pitting on the circumferential and axial direction, respectively; l1 and l2 denote the length and the width of the fragment, respectively; M1 denotes the mass of the fragment.
-400 -500 Center element Element between center and edge Edge element
-600 -700 0
500
1000
1500
2000
2500
3000
3500
Time (us) Fig. 20. Velocity–time curves of the fragment.
simulation and the experiment are shown in Table 8. The results show that the two agree well with each other. 4.4. Mode IIIb response Fig. 22 shows the process of X70 pipeline with wall thickness 1.46 cm subjected to 3 kg TNT explosive. From the figures we can see that a large piece of fragment was formed after the shock
wave impacts on the front zone. The fragment then travels from the front zone to the back zone and causes a penetration hole on the pipeline. The velocity distribution of the fragment at different location is shown in Fig. 23. From the figure we can see that the fragment velocities at the front zone of the pipeline in Test.7 are similar with those in Test.6. The center element has the largest velocity and the edge element has the smallest one. At the back zone of Test.7, the center element, the edge element and element between center and edge have almost the same velocity. The numerical results show that a rectangle hole was formed on the front zone. Four cracks appear at four corners. Comparison between numerical simulation and the experiment are shown in Table 9 and Fig. 24. The two results agree well with each other.
l1 h6 h5
l2
Fig. 21. The dimensions of the penetration hole and the fragment.
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(a) 35 us
(b) 200 us
(c) 1680 us
167
(d) 2680 us
Fig. 22. Deformation and damage process of 1.46 cm thickness pipeline under 3 kg TNT.
5. Conclusions
Center element Element between center and edge Edge element
1200
Velocity (m/s)
1000
800
600
400
200
0
Test.6
Front zone of Test.7 Back zone of Test.7
Fig. 23. Velocity distribution of the fragment at different location. Table 9 Comparison between numerical simulation and experiment of Test.5.
h7 (cm) h8 (cm) l3 (cm) l4 (cm) M2 (kg)
Numerical simulation
Experiment
Error (%)
22.1 28.8 24.2 5.9 5.9
23.3 27.8 23.6 6.4 5.5
5.2 þ3.6 þ2.5 7.8 þ7.3
As shown in Fig. 24, h7 and h8 denote the length of local pitting on the circumferential and axial direction, respectively; l3 and l4 denote the length and the width of the fragment, respectively; M2 denotes the mass of the fragment.
This paper presents the experimental observations from an extensive series of localized blast tests on X70 pipeline. Numerical models developed in LS-DYNA and validated against the experimental results provide further understanding of the large-diameter and high grade steel pipeline subjected to blast loading. Based on the results of this investigation the following conclusions are drawn. Four failure modes of X70 pipeline are observed during the experiments. The results indicate that wall thickness and charge mass play an important role in the deformation process of the pipeline. The deformation range has large relationship with the contact area. When the explosive mass is small, the pipeline undergoes inelastic deformation. When the mass of the explosive is large enough, the pipeline displays adiabatic shearing failure. Postfailure motion of the pipeline is also observed. The fragment formed during the experiment has large kinetic energy and may cause the tearing of the back zone. The results of numerical simulations show good correlation with the experiments for the deformation profiles and midpoint deflection. The energy curves are recorded and the results show that the internal energy is a key factor leading to the deformation and damage of the pipeline. The post-failure fragment velocities are also recorded and analyzed. The stable velocity of the fragment can reach to 400–568 m/s. The fragment with large kinetic energy can cause the tearing of the pipeline.
h8 h7
Numerical simulation
Experiment
Fig. 24. Comparison between numerical simulation and experiment of Test.5.
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Acknowledgments The work described in this paper is financially supported by the National Natural Science Foundation of China under Grant number 11102233. The authors would like to gratefully acknowledge this support.
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[11] G.N. Nurick, G.C. Shave, The deformation and tearing of thin square plates subjected to impulsive loads—an experimental study, Int. J. Impact Eng. 18 (1) (1996) 99–116. [12] N. Jones, M. Alves, Post-severance analysis of impulsively loaded beams, Int. J. Solids Struct. 41 (22–23) (2004) 6441–6463. [13] V.R. Ikkurthi, S. Chaturvedi, Use of different damage models for simulating impact-driven spallation in metal plates, Int. J. Impact Eng. 30 (2004) 274–301. [14] V.H. Balden, G.N. Nurick, Numerical simulation of the post-failure motion of steel plates subjected to blast loading, Int. J. Impact Eng. 32 (2004) 14–34. [15] Kim Chung, S. Yuen, G.N. Nurick, Experimental and numerical studies on the response of quadrangular stiffened plates – Part I- subjected to uniform blast load, Int. J. Impact Eng. 31 (1) (2005) 55–83. [16] D. Karagiozova, G.N. Nurick, G.S. Langdon, Behaviour of sandwich panels subjected to intense air blast – Part 2: numerical simulation, Compos. Struct. 91 (4) (2009) 442–450. [17] A.C. Jacinto, R.D. Ambrosini, R.F. Danesi, Experimental and computational analysis of plates under air blast loading, Int. J. Impact Eng. 25 (10) (2001) 927–947. [18] D. Karagiozova, G.N. Nurick, S. Chung Kim Yuen, Energy absorption of aluminium alloy circular and square tubes under anaxial explosive load, ThinWalled Struct. 43 (6) (2005) 956–982. [19] M.D. Theobald, G.N. Nurick, Numerical investigation of the response of sandwich-type panels using thin-walled tubes subject to blast loads, Int. J. Impact Eng. 34 (1) (2007) 134–156. [20] T. Krauthammer, C.K. Ku, Hybrid computational approach for the analysis of blast resistant connections, Comput. Struct. 61 (5) (1996) 831–843. [21] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strainrates, temperatures and pressures, Eng. Fract. Mech. 21 (1) (1985) 31–48. [22] H.H. Jama, M.R. Bambach, G.N. Nurick, Numerical modeling of square tubular steel beams subjected to transverse blast loads, Thin-walled Struct. 47 (1) (2009) 1523–1534. [23] G.R. Johnson, W.H. Cook, Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures, Eng. Fract. Mech. 21 (1) (1985) 31–48.
Contents lists available at ScienceDirect
Thin-Walled Structures journal homepage: www.elsevier.com/locate/tws
Experimental and numerical studies on the deformation and tearing of X70 pipelines subjected to localized blast loading Kejian Song a, Yuan Long a, Chong Ji a,n, Fuyin Gao a, Hailong Chen b a
Engineering Institute of Engineering Corps, PLA University of Science and Technology, Nanjing, 210007, China State Key Laboratory for Disaster Prevention & Mitigation of Explosion & Impact, College of Defense Engineering, PLA University of Science and Technology, Nanjing 210007, China
b
art ic l e i nf o
a b s t r a c t
Article history: Received 23 September 2015 Received in revised form 2 February 2016 Accepted 7 March 2016
The dynamic response of X70 grade steel pipeline under localized blast loading is studied by experimental and numerical investigations. The steel pipelines with large diameter and high grade are concerned in the paper. The influences of the explosive mass, contact area and wall thickness on the deformation/failure mechanisms of the X70 pipelines were investigated. The post-failure motion of the fragment was also observed during the experiment. Four different failure modes were observed during the experiment namely Mode I, Mode II, Mode IIIa and Mode IIIb. The features of each mode are analyzed concretely. Results revealed that the deflection and damage level of pipeline increased with the increase of explosive mass and contact area. The wall thickness plays an important role on the damage and postfailure motion. Numerical simulations based on the experimental results were conducted. The damage process, midpoint deflection, pressure distribution, energy changes and the post-failure fragment velocities were analyzed. The results of numerical simulations show good correlation with the experiments & 2016 Elsevier Ltd. All rights reserved.
Keywords: Blast load X70 pipeline Contact explosion Failure mode Post-failure motion
1. Introduction Large-diameter, high-pressure gas transmission pipelines have been used more and more widely all over the world. With the development of the pipeline network, safety and maintenance become an important task. Terrorism and military operations could increase the potential for structures to be subjected to explosions. Some pipeline structures might be subjected to explosive loads during their service life. So, the behavior of the pipeline during and after being subjected to blast loading is important to understand. For the past few decades, numerous theoretical and experimental studies on structures such as beams and plates subjected to blast loading have been published. Menkes and Opat [1] firstly studied the dynamic failure of beams experimentally for blast loaded alloy 6062 T6 beams. Jones [2] studied the problem analytically using a rigid plastic material model. Three failure modes were identified for the beams: Mode Ⅰ-large permanent displacement deflections or damage without any material rupture; Mode Ⅱ-tensile rupture at supports; Mode Ⅲ-transverse shear failure at supports. Teeling Smith and Nurick [3] were the first to identify n
Corresponding author. E-mail address: [email protected] (C. Ji).
http://dx.doi.org/10.1016/j.tws.2016.03.010 0263-8231/& 2016 Elsevier Ltd. All rights reserved.
and report the three failure modes for circular plates subjected to uniformly distributed pressure impulses. Ref. [4] presented a theoretical method of analysis for mass impacts, dynamic pressure pulses and impulsive velocity or blast loadings on circular, square and rectangular plate for the idealization of a rigid, perfectly plastic material, and simple equations were also presented to predict the maximum permanent transverse displacements. Several authors such as Gupta N.K. [5], Jones N. [6], Henchie T.F. [7], Karagiozova D. [8] have presented experimental and theoretical results of blast loaded structures. Bambach [9] and Jama H.H. [10] reported the investigation of steel square hollow sections subjected to transverse blast loads. Some other authors have focus on petalling and post-failure response of structures subjected to blast loading [11–14]. Although experimental and analytical methods have been used extensively in the literatures, numerical analyses can not be ignored because they can provide valuable information on the details of the response of structural members with more complex material properties. Recently three commercial numerical codes, namely, ABAQUS, LS-DYNA and AUTODYN have been used extensively in the modeling of blast-loaded structures [15–17]. Numerous attempts have been made using commercially available software packages to model the large inelastic deformation or complete failure of the structure subjected to blast loading [18– 22]. These simulations have compared well with the experiments.
K. Song et al. / Thin-Walled Structures 107 (2016) 156–168
Table 1 The chemical compositions of steel X70 (wt%) Elements Contents Elements Contents
C 0.051 Mo 0.21
Si 0.20 Ni 0.14
Mn 1.56 Nb 0.045
P 0.014 V 0.032
S 0.0029 Ti 0.016
Cr 0.026 Cu 0.18
157
the blast fragment was also recorded. Numerical simulations of these impact scenarios, identical to the experiments were performed using the commercial finite element code LS-DYNA, and the results obtained were compared with the experimental data. The experiments are generally well reproduced and the key phenomena are well captured by the computer simulations.
2. Experimental research Table 2 Mechanical properties.
2.1. Material properties
Yield strength ss/MPa Tensile strength sb/ MPa
Elongation (%) Ratio of ss/sb
575
42
687
Front Zone
0.84
The steel used is a Chinese-made pipeline steel in grade X70. The wall thicknesses of pipes are 14.6 mm and 26.4 mm, respectively. The diameter of the pipeline is 1.016 m, which is the same size as the pipelines used in serve. The chemical compositions of the pipelines are shown in Table 1. The steel is in hot rolling state and the microstructure is composed of ferrite and pearlite. The ordinary mechanical properties are shown in Table 2.
TNT Charge 2.2. Experimental setup
X70 Pipeline
Back Zone
Soil Ground
Fig. 1. Sketches of experiment setup.
The above researches mainly focus on small-diameter and ordinary steel materials. For large-diameter and high grade steel pipeline, they may display different damage pattern when subjected to blast loading. However, researches on this subject are difficult to find. Post-failure motion of the blast fragment is very important in the dynamic analysis of the structure, but it has hitherto been difficult to predict due to the fact that the material properties at the moment of tearing are difficult to quantify. The study presents experimental research of X70 grade steel pipeline with diameter 1.016 m subjected to localized blast loading, and numerical simulations thereof. Four kinds of failure modes are observed during the experiment. Post-failure motion of
Sketches of the experiment setup are shown in Fig. 1. The experiments were conducted in the field test site. The X70 pipelines were placed on the ground. The impulsive loading was created by the detonation of TNT explosive. The charge was placed at the top center of the pipe. During the experimental study, the mass of charge was varied from 0.4 kg from 10.0 kg to achieve different impulses. The explosive has a density of 1.61 g/cm3, a detonation velocity of 6950 m/s, and a CJ energy per unit volume of 6.74 106 kJ/m3. All charges were initiated at top center end using an electrical detonator and a 15 g C4 booster. For each test, explosion mass, permanent displacement and the final deformed shape profile were recorded. Previous studies defined three failure modes that were observed in uniformly blast-loaded beams: large inelastic deformation (Mode I), tensile tearing at the boundary (Mode II), and shearing at the supports (Mode III). The failure modes reported for locally loaded pipelines were similar to those observed for locally loaded plates, the main difference being an additional capping mode (that is, thinning and tearing of a central fragment, or ‘cap’). Fragments, referred to as caps, were produced from surface at higher impulses due to tearing of a central ring of material. The pipe failure mode can be subdivided on the basis of experimental observations by Mode I: Large inelastic response with thinning in the central area; Mode II: Large inelastic response with thinning in the central area and spallation in the inner area;
Table 3 Experimental specimens and deformation results. Test no.
Wall thickness (cm)
Mass of explosive (kg)
Contact area
Deformation range Front zone
1 2 3 4 5 6 7 8 9
1.46 2.62 2.62 2.62 1.46 2.62 1.46 2.62 2.62
0.2 0.4 0.8 1.4 3 3 5 5 10
10 cm 5 cm 10 cm 10 cm 10 cm 10 cm 10 cm 10 cm 20 cm 15 cm 20 cm 15 cm 20 cm 20 cm 25 cm 20 cm 25 cm 20 cm
2.3 cm 3.5 cm 5.3 cm 5.9 cm 23 cm 28 cm 23 cm 16 cm 32 cm 28 cm 29 cm 21 cm 29 cm 21 cm
Failure mode Back zone
20 cm 16 cm 27 cm 23 cm 25 cm 20 cm 31 cm 24 cm
Mode Mode Mode Mode Mode Mode Mode Mode Mode
I response I response II response II response IIIb response IIIa response IIIb response IIIa response IIIb response
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Q=0.2 kg δ=1.46 cm
Local pitting
Bulge deformation
Mode I Outer surface
Inner surface Fig. 2. Deformation of the pipeline with wall thickness 1.46 cm under 0.2 kg TNT.
Q=0.4 kg δ=2.62 cm Bulge deformation Local pitting
Mode I Outer surface
Inner surface Fig. 3. Deformation of the pipeline with wall thickness 2.62 cm under 0.4 kg TNT.
0.0
0
-1
-1.0
Deflection (cm)
Deflection (cm)
-0.5
-1.5 -2.0 -2.5 Inner surface Outer surface
-3.0 -3.5 0
1
2
3
4
Distance from impact mid-point (cm) Fig. 4. The measured profiles of the pipeline in Test.1.
Mode IIIa: Complete tearing in the central area (also known as ‘capping’ failure) and mode I response on back face. Mode IIIb: Complete tearing in the central area and the blast fragment perforation back face. During the experiment the fragment travelled from the front face toward the back face. Table 3 contains a summary of the localized blast test results,
-2
-3
-4
Inner surface Outer surface
-5
-6 0
1
2
3
4
5
Distance from impact mid-point (cm) Fig. 5. The measured profiles of the pipeline in Test.2.
with explosion mass, deformation range and failure mode listed for each experiment. 2.3. Experimental observations and discussion 2.3.1. Failure Mode I When the explosive mass is small, the pipeline displays failure Mode I, which is large inelastic response with thinning in the
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Q=0.8 kg δ=2.62 cm
159
Spallation
Local pitting
Mode II Outer surface
Inner surface Fig. 6. Damage of the pipeline with wall thickness 2.62 cm under 0.8 kg TNT.
Q=1.4 kg δ=2.62 cm
Local pitting
Spallation
Mode II Outer surface
Inner surface Fig. 7. Damage of the pipeline with wall thickness 2.62 cm under 1.4 kg TNT.
central area. Selected photographs that demonstrate the failure characteristics of the pipeline are shown in Figs. 2–3. Fig. 2 shows the results of the pipeline with wall thickness 1.46 cm subjected to 0.2 kg TNT. A local pitting and a bulge are formed on the outer and inner surface of the pipeline, respectively. The pitted regions are approximately the same size as the contact area. The measured profile of the pipeline in this test is shown in Fig. 4. It is found that the maximum deformation of the outer surface is 2.2 cm. Fig. 3 shows the results of the pipeline with wall thickness 2.62 cm subjected to 0.4 kg TNT. Similar phenomenon can be seen compared with test 1. The measured profile of this test is shown in Fig. 5. The maximum deformation of the outer surface is 3.4 cm. 2.3.2. Failure Mode II With the increase of the explosive mass, the level of deformation and damage increased. And the failure mode of the pipeline transitioned from Mode I to Mode II. When the X70 steel pipeline subjected to 0.8 kg TNT explosive, the outer surface of the pipeline undergoes large inelastic response with thinning in the central area, while the inner surface displayed spallation mechanism, as shown in Fig. 6. When the mass of the explosive increased to 1.4 kg, the pipeline still remained Mode II, but has a
little difference with 0.8 kg TNT explosive. Fig. 7 shows the top view of a localized failure of X70 pipeline. A local pitting with larger areas was formed on the outer surface after testing. And also we can see clearly that a macroscopic crack emerged in the center region. 2.3.3. Failure Mode IIIa Fig. 8 shows the failure mode of X70 pipeline with wall thickness 2.62 cm subjected to 3 kg TNT explosive. It is clearly seen that both the outer surface and the inner surface of the pipeline tore completely in the center region. The pipeline failed catastrophically. A crevasse with dimension of about 23 cm 16 cm was formed at the front zone. The edge of the crevasse was quite tidy because of the adiabatic shearing failure of the pipeline. It is also evident that the macroscopic cracks emerged on the outer surface and grew along the direction toward the corner. A piece of fragment was produced from the eroded material of the front zone during the experiment as shown in Fig. 8. The fragment travelled from the front zone to the back zone and impacted the back surface at last, leaving a local pitting on it. The similar phenomenon can be seen in Fig. 9 for the explosive mass 5 kg and wall thickness 2.62 cm. The dimension of the rectangle hole is 29 cm 21 cm.
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Complete tearing in the central area of the front zone
Q=3 kg δ=2.62 cm
Fragment
Local pitting on the back zone
Fig. 8. Damage of the pipeline with wall thickness 2.62 cm under 3 kg TNT.
The mass and the velocity of the fragment were larger than Fig. 8, and a local pitting with dimension 25 cm 20 cm is formed on the back zone. 2.3.4. Failure Mode IIIb When subjected to 3 kg TNT explosive with wall thickness 1.46 cm, the X70 pipeline exhibits Mode IIIb. Both the front zone and the back zone tore completely in the center region. Selected photographs that demonstrate the failure characteristics are shown in Fig. 10. From the photographs we can see that a rectangle crevasse with dimension 23 cm 28 cm was formed on the front zone. Four cracks with length of 10 cm were formed at the four corners. Under the impact of the blast loading, the inner surface of the front zone tore in a “petalling” fashion with numbers of petals. A crevasse with dimension 20 cm 16 cm was also formed on the back zone because of the fragment produced from the front zone. The fragment shown in Fig. 10 underwent large inelastic deformation in the center region with buckling on the end sides. When the explosive mass increased to 5 kg, similar phenomenon can be observed shown in Fig. 11. Fig. 12 shows photographs of X70 pipeline with wall thickness 2.56 cm subjected to 10 kg TNT explosive. From the figures we can
see that six macroscopic cracks emerged on the edge of the front crevasse. The front zone of the pipeline underwent adiabatic shearing failure, and a big piece of fragment was produced. Then the back zone of the pipeline was penetrated by the fragment.
3. Material constitutive models 3.1. Material model for X70 steel To be able to describe the various phenomena taking place during contact explosion, it is necessary to characterise the behavior of materials under explosion-generated high strain rate loading conditions. The tube steel is modeled by the Johnson-Cook material model [23], which is suitable to model the strength behavior of materials subjected to large strains, high strain rates and high temperatures. The model defines the yield stress sy as Table 4
σy = [A + B(ε¯ p)n][1 + C ln ε*̇ ][1 − (T *)m]
(1)
where A, B, C, n and m are the material parameters determined by experiments. ε̇* is the dimensionless effective strain rate for and T *
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161
Complete tearing in the central area of the front zone
Q=5 kg δ=2.62 cm
Fragment
Local pitting on the back zone Fig. 9. Damage of the pipeline with wall thickness 2.62 cm under 5 kg TNT.
is the homologous temperature which is defined by
T* =
T − Troom Tmelt − Troom
(2)
In Eq. (2), Troom and Tmelt are the room and melting temperatures, respectively. In the fracture analysis, Johnson-Cook fracture model is used. The model is based on the concept of cumulative damage, and it can take account of the loading history that may involve variations in strain rate, temperature and pressure. The damage parameter D is defined by
D=
∑ Δϵ/ϵf
(3)
where Δϵ is the increment of effective strain caused by the tensile load and εf is the effective fracture strain in the instantaneous conditions. Fracture occurs, when D ¼1. The effective fracture strain is assumed to be the function of strain rate, temperature and pressure in the form
εf = [D1 + D2expD3σ *][1 + D4 ln ε*̇ ][1 + D5T *]
(4)
where σ * is the dimensionless pressure-stress ratio defined as
σ * = σm/σ¯ where σm is the mean stress normalised by the effective stress, σ¯ is the effective stress, and D1, D2, D3, D4 and D5 are the material parameters. The material constants adopted here are based on the typical data for X70 steel. 3.2. Material model for high explosive and air High explosives (TNT) are typically modeled by using the JonesWilkins-Lee (JWL) EOS, which models the pressure generated by chemical energy in an explosion. It can be written in the form
p = A1(1 −
ω −R1v ω −R2v ωe )e + B1(1 − )e + R1v R2v v
(5)
where p is the hydrostatic pressure; v is the specific volume, e is internal specific energy. The values of constants A1, R1, B2, R2, ω for many common explosives have been determined from dynamic experiments. In the present simulation, for a TNT explosive charge, C1, R1, C2, R2, and ω are 3.712 105MPa, 4.15, 3.231 103 MPa, 0.9, 0.35, respectively. In the numerical model, air is modeled by an ideal gas EOS, which is one of the simplest forms of EOS. The pressure is related
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Complete tearing in the central area of the front zone
Q=3 kg δ=1.46 cm
Fragment produced in the expriment
Penetration hole of the back zone
Fig. 10. Damage of the pipeline with wall thickness 1.46 cm under 3 kg TNT.
to the energy by
p = (γ − 1)ρe
(6)
where γ is a constant, ρ is air density and e is the specific internal energy. In the simulation, air density, ρ ¼ 1.225 kg/m3 and γ ¼1.4. The air initial internal energy is assumed to be 2.068 105 kJ/kg.
boundary. According to the different failure modes observed in the experiment, we develop a series of numerical analysis to further study these phenomenons in the following paper. In order to demonstrate the validity of the numerical method adopted, the comparisons between simulation results and experimental observations are also needed in the paper.
4. Numerical simulation
4.1. Mode I response
Numerical analyses were carried out using the commercial finite element code LS-DYNA. The test results on X70 pipeline under dynamic pressure loading were compared with the numerical results in order to validate the accuracy and reliability of the numerical model. The geometry of the quarter symmetry finite element models as implemented in the element code are given in Fig. 13. A convergence study is conducted to determine the optimal number of elements in each of the model. In the simulation, the steel pipe is modeled using a Lagrange mesh, in which the coordinates move with the material; while the air and high explosive are modeled by the Euler mesh, in which the grid is fixed and material flows through it. At the Euler-Lagrange interface, interaction is considered. The Lagrange mesh imposes a geometric constraint on the Euler mesh, while the Euler mesh provides a pressure boundary to the Lagrange mesh. The boundary condition of the Euler mesh is set as an outflow
Fig. 14 shows the representative failure process of X70 pipeline with wall thickness 2.62 cm subjected to 0.4 kg TNT explosive. When the shock wave impacts on the pipeline, the front zone of the pipeline is subjected to a large stress with plastic deformation. In order to measure pressure distribution of the explosive shock wave on the surface of the pipeline, a number of measuring points are selected and shown in Fig. 15. Fig. 16 shows the pressure-time curves obtained at different points. The peak pressures at these points are listed in Table 5. From the table we can see that the maximum value is captured at element B, with a value of 2.82 GPa. The peak pressures measured at element A, C, D are a little smaller, which are 2.59 GPa, 1.98 GPa, 2.07 GPa, respectively. The simulation results shows that, a local pitting is formed on the outer surface of the front zone, the final deformation amount of the middle point is 3.19 cm. While a bulge is formed on the inner surface, with a final deformation value 2.62 cm. Comparison
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Q=5 kg δ=1.46 cm
163
Complete tearing in the central area of the front zone
Penetration hole of the back zone
Fig. 11. Damage of the pipeline with wall thickness 1.46 cm under 5 kg TNT.
Tearing holes of the front zone Fragment
Q=10 kg δ=2.62 cm
Tearing holes of the back zone Fig. 12. Damage of the pipeline with wall thickness 2.62 cm under 10 kg TNT.
Table 4 Parameters for John-Cook model of X70 pipeline.
Air Explosive
Elasticity and density Density
Steel pipe
Yield stress, strain hardening
Poisson’s ratio Young’s modulus
ρ (kg/m3) μ 7850 0.3
Ep (GPa) 210
A (MPa) 560
B (MPa) 510
n 0.48
Fig. 13. Finite element model.
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(a) t=25 us
(b) t=105 us
(c) t=180 us
(d) t=490us
Fig. 14. Deformation process of steel pipe under 0.4 kg TNT explosion.
Table 5 Pressure distributions on the pipeline under different explosive mass Explosive mass (kg)
0.4 0.8 3
Peak pressure (GPa) A
B
C
D
2.59 3.36 3.18
2.82 4.42 5.04
1.98 2.86 2.32
2.07 0.67 0.98
between numerical simulation and the experiment are shown in Table 6 Comparison between numerical simulation and experiment of Test.2.
Element B
Element C
d1 d2 h1 h2
Element D
Element A
(cm) (cm) (cm) (cm)
Numerical simulation
Experiment
Error (%)
3.19 2.62 9.95 10.43
3.40 2.49 10.42 10.83
6.2 þ 5.2 4.5 3.7
d1 denotes the maximum deformation on the outer surface; d2 denotes the maximum deformation on the inner surface; as shown in Fig. 17, h1 and h2 denote the length of local pitting on the axial and circumferential direction, respectively.
Table 6 and Fig. 17. From the table and figures we can see that the simulation agrees well with the experiment. Fig. 15. Location of the chosen elements on the pipeline.
4.2. Mode II response 3.0 2.5
Element A Element B Element C Element D
Pressure (GPa)
2.0 1.5 1.0 0.5 0.0 -0.5 0
20
40
60
80
100
Time (us) Fig. 16. Pressure–time curves of elements A, B, C and D.
120
Fig. 18 shows the failure process of pipeline with wall thickness 2.62 cm subjected to 0.8 kg TNT explosive. From the figures we can see that the front zone of the pipeline undergoes large inelastic deformation under the impacts of shock wave. At the time t¼240 μs, the phenomenon of spallation comes out on the inner face of the front zone, and a number of fragments are formed at the same time. We choose four elements with the same locations in Fig.15 to measure the pressure distributions on the pipeline. The results are listed in Table 5. The peak pressure at the location of A, B, C and D are 3.36 GPa, 4.42 GPa, 2.86 GPa and 0.67 GPa, respectively. The finite element analysis shows that a local pitting with depth 5.88 cm is formed on the outer surface of the front zone. A phenomenon of spallation is formed on the inner surface. Comparison between numerical simulation and the experiment are shown in Table 7. The numerical simulation agrees well with the experiment.
K. Song et al. / Thin-Walled Structures 107 (2016) 156–168
Numerical simulation
165
Numerical simulation
Inner surface
Outer surface
Experiment
Experiment Fig. 17. Comparison between numerical simulation and experiment.
(a) t=25 us
(b) t=240 us
(c) t=485 us
(d) t=800 us
Fig. 18. Deformation and damage process of steel pipe under 0.8 kg TNT explosion.
Table 7 Comparison between numerical simulation and experiment of Test.3.
d3 (cm) h3 (cm) h4 (cm)
Numerical simulation
Experiment
Error (%)
5.88 11.85 14.77
6.06 12.44 13.85
3.0 4.7 þ6.6
d3 denotes the maximum deformation on the outer surface of the pipeline; h3 and h4 denote the length of local pitting on the axial and circumferential direction, respectively.
4.3. Mode IIIa response Fig. 19 shows the process of X70 pipeline with wall thickness 2.62 cm subjected to 3 kg TNT explosive. From the figures we can
see that a large piece of fragment was formed on the front zone after the shock wave impacts on the pipeline. The fragment then travels from the front zone to the back zone and causes a local pitting on it. Fig. 20 shows the velocity–time curves of the fragment. The figure reveals that at the initial stage, the center element of the fragment has the largest velocity, while the edge element has the smallest one. At about 400 μs, the total fragment reaches to the velocity of 406 cm/s. At the time 2350 μs, the fragment reaches to the back zone and impacts the pipeline. Finally, with the increase of time, the velocity of the fragment decrease to zero. The finite element analysis shows that a rectangle hole is formed in the front zone. And four cracks appear at the four corners of the hole. The dimensions of the penetration hole and the fragment are shown in Fig. 21. Comparison between numerical
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(a) t=55 us
(b) t=200 us
(c) t=2340 us
(d) t=3200us
Fig. 19. Deformation and damage process of 2.62 cm thickness pipeline under 3 kg TNT.
100
Table 8 Comparison between numerical simulation and experiment of Test.6
0
Velocity (m/s)
-100
h5 (cm) h6 (cm) l1 (cm) l2 (cm) M1 (kg)
-200 -300
Numerical simulation
Experiment
Error (%)
15.4 22.8 21.7 12.8 6.51
16.1 23.2 22.9 12.3 6.93
3.1 1.7 4.8 4.1 6.1
As shown in Fig. 21, h5 and h6 denote the length of local pitting on the circumferential and axial direction, respectively; l1 and l2 denote the length and the width of the fragment, respectively; M1 denotes the mass of the fragment.
-400 -500 Center element Element between center and edge Edge element
-600 -700 0
500
1000
1500
2000
2500
3000
3500
Time (us) Fig. 20. Velocity–time curves of the fragment.
simulation and the experiment are shown in Table 8. The results show that the two agree well with each other. 4.4. Mode IIIb response Fig. 22 shows the process of X70 pipeline with wall thickness 1.46 cm subjected to 3 kg TNT explosive. From the figures we can see that a large piece of fragment was formed after the shock
wave impacts on the front zone. The fragment then travels from the front zone to the back zone and causes a penetration hole on the pipeline. The velocity distribution of the fragment at different location is shown in Fig. 23. From the figure we can see that the fragment velocities at the front zone of the pipeline in Test.7 are similar with those in Test.6. The center element has the largest velocity and the edge element has the smallest one. At the back zone of Test.7, the center element, the edge element and element between center and edge have almost the same velocity. The numerical results show that a rectangle hole was formed on the front zone. Four cracks appear at four corners. Comparison between numerical simulation and the experiment are shown in Table 9 and Fig. 24. The two results agree well with each other.
l1 h6 h5
l2
Fig. 21. The dimensions of the penetration hole and the fragment.
K. Song et al. / Thin-Walled Structures 107 (2016) 156–168
(a) 35 us
(b) 200 us
(c) 1680 us
167
(d) 2680 us
Fig. 22. Deformation and damage process of 1.46 cm thickness pipeline under 3 kg TNT.
5. Conclusions
Center element Element between center and edge Edge element
1200
Velocity (m/s)
1000
800
600
400
200
0
Test.6
Front zone of Test.7 Back zone of Test.7
Fig. 23. Velocity distribution of the fragment at different location. Table 9 Comparison between numerical simulation and experiment of Test.5.
h7 (cm) h8 (cm) l3 (cm) l4 (cm) M2 (kg)
Numerical simulation
Experiment
Error (%)
22.1 28.8 24.2 5.9 5.9
23.3 27.8 23.6 6.4 5.5
5.2 þ3.6 þ2.5 7.8 þ7.3
As shown in Fig. 24, h7 and h8 denote the length of local pitting on the circumferential and axial direction, respectively; l3 and l4 denote the length and the width of the fragment, respectively; M2 denotes the mass of the fragment.
This paper presents the experimental observations from an extensive series of localized blast tests on X70 pipeline. Numerical models developed in LS-DYNA and validated against the experimental results provide further understanding of the large-diameter and high grade steel pipeline subjected to blast loading. Based on the results of this investigation the following conclusions are drawn. Four failure modes of X70 pipeline are observed during the experiments. The results indicate that wall thickness and charge mass play an important role in the deformation process of the pipeline. The deformation range has large relationship with the contact area. When the explosive mass is small, the pipeline undergoes inelastic deformation. When the mass of the explosive is large enough, the pipeline displays adiabatic shearing failure. Postfailure motion of the pipeline is also observed. The fragment formed during the experiment has large kinetic energy and may cause the tearing of the back zone. The results of numerical simulations show good correlation with the experiments for the deformation profiles and midpoint deflection. The energy curves are recorded and the results show that the internal energy is a key factor leading to the deformation and damage of the pipeline. The post-failure fragment velocities are also recorded and analyzed. The stable velocity of the fragment can reach to 400–568 m/s. The fragment with large kinetic energy can cause the tearing of the pipeline.
h8 h7
Numerical simulation
Experiment
Fig. 24. Comparison between numerical simulation and experiment of Test.5.
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Acknowledgments The work described in this paper is financially supported by the National Natural Science Foundation of China under Grant number 11102233. The authors would like to gratefully acknowledge this support.
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