# Numerical Study on the Explosive Separation of Pyrotechnic Cutter

Authors: Shihui Xiong; Yaokun Ye; Yanhua Li; Yuquan Wen
Journal: Shock and Vibration
 (2019)

---

## Abstract

Pyrotechnic cutters are widely used in the wrapping-band connecting structures of carrier rockets. In this article, a three-dimensional (3D) finite element model of a pyrotechnic cutter is proposed to determine the influence of the explosive dynamic fracture process and the cutter blade acceleration distance on the cutting effect, using AUTODYN finite element simulation software. Numerical simulations of the cutting process reveal that the initial shear speed, the maximal speed, and the speed at which the cutter connects the rod increase linearly with increasing distance between the cutter blade and the cutting board. As the distance increases, the difference between the initial cutting speed and the maximal speed of the cutter gradually decreases and effectively disappears for a distance of 8.5 mm. At this time, the acceleration effect of the gunpowder gas on the cutter is nearly maximal. When the distance between the cutter and the connecting rod is less than 7.5 mm, the cutting time decreases significantly with increasing spacing. For distances between 7.5 mm and 8.5 mm, the distance has little effect on the cutting time as it increases. There is a small increase in the cutting time, and it can be seen that there is an optimal distance between the cutter and the cutting board during the cutting process. The cutting effect is the strongest for this distance. For the cutter studied in this article, the optimal distance was 7.5 mm. In addition, numerical studies were also performed by varying the maximal cutting diameter of the connecting rod of the pyrotechnic cutter. The discrepancy between the simulation results and actual test data was under 10%, and the simulation result for the cut state of the connecting rod was also consistent with the test result. The simulation results in this article can deepen the understanding of the action mechanism and process of the pyrotechnic cutter and reveal the maximal cutting diameter of the connecting rod of the pyrotechnic cutter under different charging conditions. This provides a reference for future cutter design optimization.


---

## Body

## 1. Introduction

The stage separation of carrier rockets, the section separation of spacecraft cabins, and the separation of spacecraft hatch covers, all require extensive use of connection/unlocking-type separating pyrotechnic devices. In these pyrotechnic devices, the separation target is originally composed of two separate parts, which are connected together by a pyrotechnic device before action. When separation is required, the pyrotechnic device is unlocked to unlock the connection. Such products mainly include explosive bolts, explosive nuts, unlocking bolts, separating nuts, pyrotechnic cutters, and wrapping-band separating devices [1]. Of these, pyrotechnic cutters are used for cutting high-strength ropes, cables, pipes, and various metal rods. In this approach, the front end of a piston is made into a shape of a cutter blade and gains impulse by the drive from the gas combustion to cut both metallic and nonmetallic materials. When used as a separating device, the cutter mainly functions by cutting the connecting bolts, providing an alternative to unlocking bolts. Pyrotechnic cutters are advantageous for the following reasons: (1) they allow the separation structures to be connected by ordinary bolts, not requiring weakening treatment; (2) their bearing capacity is high; (3) they achieve unlocking by cutting the bolt from the middle; (4) their performance is not affected by the installation conditions, such as the bolt preload force; and (5) after the cutting work is completed, the gas is completely sealed in the chamber, and no undesired products are generated. The key factors for the cutter are the design of the cutter blade and the control of the cutting capacity to ensure that the bolts can be completely cut. With improper design, complete cutting cannot be guaranteed, even if the internal pressure is high [2–5]. Currently, the research and development design efforts of pyrotechnic cutting devices are still based on experimental research, which cannot completely guarantee the safety and reliability of the product, in addition to the high cost and long design process. With the rapid development of computer technology, numerical simulation methods provide a new way for studying such issues. Shmuel et al. established a three-dimensional (3D) simulation model of a pyrotechnic cutter (using LS-DYNA finite element analysis software), simulated the action process of the pyrotechnic cutter, and conducted a contrast analysis of the action process of explosive cutting for different charging conditions and cutting structures [6–8]. Braud et al. established a mathematical model for the action of pyrotechnic devices such as pyrotechnic cutters and electric blast valves and analyzed the parameters affecting the action process [9–14]. Liu et al. analyzed the speed and acceleration of the cutter blade in the explosive cutting process using LS-DYNA, discussed the stress and strain changes and fracture characteristics of the typical fracture unit on the connecting rod, and analyzed the characteristics of the explosion impulse load and the structural response characteristics of the cutters at different stages [15, 16]. Wang et al. performed numerical simulations of the explosive cutting process using LS-DYNA and obtained 3D simulation results of the detonation wave propagation process of detonator charges, cutter blade motion, and cutting process of the metal rod [17].This article focuses on the influence of the explosive dynamic fracture process and the cutter blade acceleration distance of the pyrotechnic cutter on the cutting effect. Using pyrotechnic cutters as an example (which are commonly used in the wrapping band-type connecting structures of carrier rockets), a 3D finite element model of a pyrotechnic cutter was established using AUTODYN finite element simulation software, and the entire action process of the pyrotechnic cutter was numerically simulated. These simulation results can deepen the understanding of the action mechanism and process of the pyrotechnic cutter. In addition, they provide insights into the cutting limits of cutters under different charging conditions, which can be simulated using the proposed model, thus providing a reference for future cutter design optimization.


## 2. Structure and Working Principle of the Pyrotechnic Cutter

The pyrotechnic cutter is an actuating component of a hold-down and release device, and it consists of an igniter, a casing, a detonator, a shear pin, a sealing ring, a cutter, a cutting board, and an end cover, as shown in Figures1 and 2. The working process of the pyrotechnic cutter is as follows: (1) a charge is detonated by an electric detonator; (2) a large amount of high-temperature and high-pressure gas is generated to initiate the cutter blade motion; and (3) after moving for a certain distance, the cutter blade reaches a certain speed and gains considerable kinetic energy, resulting in its collision and penetration with the connecting rod, thereby fracturing the connecting rod. Once the connecting rod is fractured, the wrapping band is instantly released from the constraint of the pretightening force, thus unlocking the satellite-rocket connecting structure.Figure 1
Schematic of the pyrotechnic cutter.Figure 2
Real pyrotechnic cutter.This study mainly discusses the cutting and unlocking processes of the cutter. Under the premise that the basic composition is unchanged, various working conditions are considered, and numerical simulations are performed by varying some parameters, such as the spacing between the cutting board and the cutting edge. The assembly structure with different edge spacings is shown schematically in Figure3.Figure 3
Diagram of the spacing between the cutter blade and the cutting board.


## 3. Finite Element Modeling of the Pyrotechnic Cutter

### 3.1. Finite Element Model

This study uses AUTODYN to simulate the shear fracture of the pyrotechnic cutter. During modeling, the structure of the cutter is simplified, while the effective volume inside the combustion chamber is kept constant. Noncritical components (such as the igniter, sealing ring, end cover, and strap connecting piece) are omitted, and the energy produced by the ignition or explosion of the igniter and the detonator charge is converted into a primary charge (with a total converted energy of 84 mg PETN). The working space of the burner chamber and the separating mechanism of the cutter are both inclined through the chambers. Belonging to a nonaxisymmetric structure, the space is semisectioned into the left and right symmetry planes to simplify the calculation model, following which the finite element mesh is divided to establish a half finite element model. The final simplified finite element model is shown in Figure4. Therefore, the simplified pyrotechnic cutter model consists of a casing, main charge, a shear pin, a cutter, a cutting board, and an air domain; of these, the air domain covers all areas through which the explosive fluid may flow.Figure 4
Finite element division effect diagram of the simplified model. (a) Model of the pyrotechnic cutter. (b) Detonation point.
(a)
(b)


### 3.2. Material Model

#### 3.2.1. Explosive Material

The main charge used in this study is common PETN, with a charging density of 0.88 g/cm3. To simulate the explosive performance of the charge, the Jones–Wilkins–Lee (JWL) state equation is used in its standard form [18]:(1)P=A1−ωR1Ve−R1v+B1−ωR2Ve−R2v+ωE0V. Here, P and V denote the pressure and the relative specific volume of the detonation product, respectively; E0 is the internal energy; and A, B, R1, R2, and ω are empirical parameters. The material parameters of PETN are listed in Table 1, and the material structural parameters were from the AUTODYN material library [18].Table 1
Material parameters of PETN.
Parameters
Value
ρ
0 (g/cm3)
0.88
A (GPa)
348.62
B (GPa)
11.288
R
1
7.0
R
2
2.0
w
0.24
DCJ (m/s)
5170
PCJ (GPa)
6.2
E
0 (kJ/m3)
5.025 × 106


#### 3.2.2. Structure Material

The casing of the pyrotechnic cutter is made of steel (4340), the shear pin is made of aluminum (2024), the cutter blade and the cutting board are made of V250, and the connecting rod adopts Ti6%Al4%V.To describe the relationship between the pressure and the volume of the structure material under impact, the equation of state (EOS) of the structure material is described with shock EOS, which is an EOS in the form of Mie–Gruneisen, with shock Hugoniot as a reference:(2)P−PH=γve−eH. Here, P is the pressure, γ is the Gruneisen constant, v is the specific volume, and e is the specific internal energy. The subscript H denotes the shock Hugoniot, which is defined as the trajectory of all vibration states for each material. Here, Shock EOS requires P-ν Hugoniot, which can be obtained from U-u Hugoniot, or the relationship between vibration and particle speed:(3)U=C0+su,where C0 and s are empirical parameters.The materials of the shear pin (2024 aluminum), cutter blade (V250) and cutting board (V250), the shell material (steel 4340) and the connecting rod material (Ti6%Al4%V), and the Johnson–Cook constitutive model are used to simulate the dynamic response behavior under explosion and mechanical impact. This model defines the flow stress as the strain rate, a function of an equivalent plastic strain and temperature. The dynamic flow stress is expressed as follows:(4)σ=σ0+Bεn+1+Clnε˙ε˙0+1−T−TrTm−Trm,where σ is the flow pressure, σ0 is the static yield stress, B is the constant of hardening, ε is the strain, n is the hardening index, C is the constant of strain rate, ε˙ is the strain rate, ε˙0 is the reference strain rate, T is the temperature, Tr is the reference temperature, Tm is the melting point, and m is the thermal softening index.The failure of the casing and the connecting rod is described using the Johnson–Cook failure model. The calculated damage parameterD is based on damage accumulation and is given as follows:(5)D=∑Δεpεf,where D is the damage to the material element and Δεp is the increment of the accumulated plastic strain. On the other hand, εf is the accumulated plastic strain from stress triaxiality, temperature, and strain rate and is defined as follows:(6)εf=D1+D2eD3σ∗1+D4lnε˙ε˙01+D5T−TrTm−Tr,where εf is the failure strain; σ∗ is the ratio of the average stress to the equivalent stress; and D1, D2, D3, D4, and D5 are constants. The other parameters are the same as those used in the Johnson–Cook force model. A failure occurs when the fracture parameter D reaches the value of 1.In this study, the instantaneous geometric strain erosion model is used for 2024 aluminum and V250 to prevent a large distortion of Lagrangian elements. By adjusting the model based on the comparison of the test results, the erosion strain was eventually determined to be 2.0. The simulation results are similar to the test results.All of the material structural parameters were from the AUTODYN material library, and their specific values are listed in Tables2–5 [19–22].Table 2
Material parameters of 4340 stainless steel.
Shock EOS
Johnson–Cook strength model
Johnson–Cook failure model
ρ
0 (g/cm3)
7.83
σ
0 (GPa)
0.792
D
1
0.05
γ
1.77
B (GPa)
0.51
D
2
3.44
C
0 (m/s)
3382
n
0.26
D
3
2.12
S
1
1.812
C
0.014
D
4
0.002
T
r (K)
300
m
1.03
D
5
0.61
C
p (J/kg·K)
477
T
m (K)
1793
Erosion criterion
ε
˙
0 (1) s
1.0
Type
FailureTable 3
Material parameters of Ti6%Al4%V.
Shock EOS
Johnson–Cook strength model
Johnson–Cook failure model
ρ
0 (g/cm3)
4.419
σ
0 (GPa)
41.9
D
1
−0.09
γ
1.23
B (GPa)
1.092
D
2
0.25
C
0 (m/s)
5130
n
0.93
D
3
−0.5
S
1
1.028
C
0.014
D
4
0.014
T
r (K)
300
m
1.1
D
5
3.87
C
p (J/kg·K)
525
T
m (K)
1878
Erosion criterion
ε
˙
0 (1) s
1.0
Type
FailureTable 4
Material parameters of V250 stainless steel.
Shock EOS
Johnson–Cook strength model
ρ
0 (g/cm3)
2.785
Y (GPa)
0.26
γ
2.00
Y
max (GPa)
0.76
C
0 (m/s)
5328
β
381
S
1
1.338
n
0.185
T
r (K)
300
G
p
′
1.8647
C
p (J/kg·K)
863
G
T
′ (kPa/K)
−17620
Y
p
′
0.01695
T
melt (K)
1220
Geometric strain
2.5Table 5
Material parameters of 2024-T4 aluminum.
Shock EOS
Johnson–Cook strength model
ρ
0 (g/cm3)
2.785
Y (GPa)
0.26
γ
2.00
Y
max(GPa)
0.76
C
0 (m/s)
5328
β
381
S
1
1.338
n
0.185
T
r (K)
300
G
p
′
1.8647
C
p (J/kg·K)
863
G
T
′ (kPa/K)
−17620
Y
p
′
0.01695
T
melt (K)
1220
Geometric strain
0.7


#### 3.2.3. Air Model

The air in the Euler grid is described by the ideal gas state equation:(7)P=γ−1ρE,where γ is the adiabatic exponent (for the ideal gas, γ=1.4), ρ is the density (the initial density of air is 0.001225 g/cm3), and E is the gas specific thermodynamic energy (the initial value E0 is 2.068 × 105 J/kg).


### 3.3. Boundary Conditions and Other Settings

Euler–Lagrange coupling analysis was used for this model. For the Euler part, outflow boundary conditions were used for the boundaries except the symmetry plane; for the Lagrange part, fixed boundaries were used for the casing and the cutting board. Transmit boundary conditions were used for the both ends of the connecting rod. The static friction coefficient was 0.13, and the dynamic friction coefficient was 0.12 between different parts. The maximal energy error to ensure the energy conservation in AUTODYN was set to 0.05.


## 3.1. Finite Element Model

This study uses AUTODYN to simulate the shear fracture of the pyrotechnic cutter. During modeling, the structure of the cutter is simplified, while the effective volume inside the combustion chamber is kept constant. Noncritical components (such as the igniter, sealing ring, end cover, and strap connecting piece) are omitted, and the energy produced by the ignition or explosion of the igniter and the detonator charge is converted into a primary charge (with a total converted energy of 84 mg PETN). The working space of the burner chamber and the separating mechanism of the cutter are both inclined through the chambers. Belonging to a nonaxisymmetric structure, the space is semisectioned into the left and right symmetry planes to simplify the calculation model, following which the finite element mesh is divided to establish a half finite element model. The final simplified finite element model is shown in Figure4. Therefore, the simplified pyrotechnic cutter model consists of a casing, main charge, a shear pin, a cutter, a cutting board, and an air domain; of these, the air domain covers all areas through which the explosive fluid may flow.Figure 4
Finite element division effect diagram of the simplified model. (a) Model of the pyrotechnic cutter. (b) Detonation point.
(a)
(b)


## 3.2. Material Model

### 3.2.1. Explosive Material

The main charge used in this study is common PETN, with a charging density of 0.88 g/cm3. To simulate the explosive performance of the charge, the Jones–Wilkins–Lee (JWL) state equation is used in its standard form [18]:(1)P=A1−ωR1Ve−R1v+B1−ωR2Ve−R2v+ωE0V. Here, P and V denote the pressure and the relative specific volume of the detonation product, respectively; E0 is the internal energy; and A, B, R1, R2, and ω are empirical parameters. The material parameters of PETN are listed in Table 1, and the material structural parameters were from the AUTODYN material library [18].Table 1
Material parameters of PETN.
Parameters
Value
ρ
0 (g/cm3)
0.88
A (GPa)
348.62
B (GPa)
11.288
R
1
7.0
R
2
2.0
w
0.24
DCJ (m/s)
5170
PCJ (GPa)
6.2
E
0 (kJ/m3)
5.025 × 106


### 3.2.2. Structure Material

The casing of the pyrotechnic cutter is made of steel (4340), the shear pin is made of aluminum (2024), the cutter blade and the cutting board are made of V250, and the connecting rod adopts Ti6%Al4%V.To describe the relationship between the pressure and the volume of the structure material under impact, the equation of state (EOS) of the structure material is described with shock EOS, which is an EOS in the form of Mie–Gruneisen, with shock Hugoniot as a reference:(2)P−PH=γve−eH. Here, P is the pressure, γ is the Gruneisen constant, v is the specific volume, and e is the specific internal energy. The subscript H denotes the shock Hugoniot, which is defined as the trajectory of all vibration states for each material. Here, Shock EOS requires P-ν Hugoniot, which can be obtained from U-u Hugoniot, or the relationship between vibration and particle speed:(3)U=C0+su,where C0 and s are empirical parameters.The materials of the shear pin (2024 aluminum), cutter blade (V250) and cutting board (V250), the shell material (steel 4340) and the connecting rod material (Ti6%Al4%V), and the Johnson–Cook constitutive model are used to simulate the dynamic response behavior under explosion and mechanical impact. This model defines the flow stress as the strain rate, a function of an equivalent plastic strain and temperature. The dynamic flow stress is expressed as follows:(4)σ=σ0+Bεn+1+Clnε˙ε˙0+1−T−TrTm−Trm,where σ is the flow pressure, σ0 is the static yield stress, B is the constant of hardening, ε is the strain, n is the hardening index, C is the constant of strain rate, ε˙ is the strain rate, ε˙0 is the reference strain rate, T is the temperature, Tr is the reference temperature, Tm is the melting point, and m is the thermal softening index.The failure of the casing and the connecting rod is described using the Johnson–Cook failure model. The calculated damage parameterD is based on damage accumulation and is given as follows:(5)D=∑Δεpεf,where D is the damage to the material element and Δεp is the increment of the accumulated plastic strain. On the other hand, εf is the accumulated plastic strain from stress triaxiality, temperature, and strain rate and is defined as follows:(6)εf=D1+D2eD3σ∗1+D4lnε˙ε˙01+D5T−TrTm−Tr,where εf is the failure strain; σ∗ is the ratio of the average stress to the equivalent stress; and D1, D2, D3, D4, and D5 are constants. The other parameters are the same as those used in the Johnson–Cook force model. A failure occurs when the fracture parameter D reaches the value of 1.In this study, the instantaneous geometric strain erosion model is used for 2024 aluminum and V250 to prevent a large distortion of Lagrangian elements. By adjusting the model based on the comparison of the test results, the erosion strain was eventually determined to be 2.0. The simulation results are similar to the test results.All of the material structural parameters were from the AUTODYN material library, and their specific values are listed in Tables2–5 [19–22].Table 2
Material parameters of 4340 stainless steel.
Shock EOS
Johnson–Cook strength model
Johnson–Cook failure model
ρ
0 (g/cm3)
7.83
σ
0 (GPa)
0.792
D
1
0.05
γ
1.77
B (GPa)
0.51
D
2
3.44
C
0 (m/s)
3382
n
0.26
D
3
2.12
S
1
1.812
C
0.014
D
4
0.002
T
r (K)
300
m
1.03
D
5
0.61
C
p (J/kg·K)
477
T
m (K)
1793
Erosion criterion
ε
˙
0 (1) s
1.0
Type
FailureTable 3
Material parameters of Ti6%Al4%V.
Shock EOS
Johnson–Cook strength model
Johnson–Cook failure model
ρ
0 (g/cm3)
4.419
σ
0 (GPa)
41.9
D
1
−0.09
γ
1.23
B (GPa)
1.092
D
2
0.25
C
0 (m/s)
5130
n
0.93
D
3
−0.5
S
1
1.028
C
0.014
D
4
0.014
T
r (K)
300
m
1.1
D
5
3.87
C
p (J/kg·K)
525
T
m (K)
1878
Erosion criterion
ε
˙
0 (1) s
1.0
Type
FailureTable 4
Material parameters of V250 stainless steel.
Shock EOS
Johnson–Cook strength model
ρ
0 (g/cm3)
2.785
Y (GPa)
0.26
γ
2.00
Y
max (GPa)
0.76
C
0 (m/s)
5328
β
381
S
1
1.338
n
0.185
T
r (K)
300
G
p
′
1.8647
C
p (J/kg·K)
863
G
T
′ (kPa/K)
−17620
Y
p
′
0.01695
T
melt (K)
1220
Geometric strain
2.5Table 5
Material parameters of 2024-T4 aluminum.
Shock EOS
Johnson–Cook strength model
ρ
0 (g/cm3)
2.785
Y (GPa)
0.26
γ
2.00
Y
max(GPa)
0.76
C
0 (m/s)
5328
β
381
S
1
1.338
n
0.185
T
r (K)
300
G
p
′
1.8647
C
p (J/kg·K)
863
G
T
′ (kPa/K)
−17620
Y
p
′
0.01695
T
melt (K)
1220
Geometric strain
0.7


### 3.2.3. Air Model

The air in the Euler grid is described by the ideal gas state equation:(7)P=γ−1ρE,where γ is the adiabatic exponent (for the ideal gas, γ=1.4), ρ is the density (the initial density of air is 0.001225 g/cm3), and E is the gas specific thermodynamic energy (the initial value E0 is 2.068 × 105 J/kg).


## 3.2.1. Explosive Material

The main charge used in this study is common PETN, with a charging density of 0.88 g/cm3. To simulate the explosive performance of the charge, the Jones–Wilkins–Lee (JWL) state equation is used in its standard form [18]:(1)P=A1−ωR1Ve−R1v+B1−ωR2Ve−R2v+ωE0V. Here, P and V denote the pressure and the relative specific volume of the detonation product, respectively; E0 is the internal energy; and A, B, R1, R2, and ω are empirical parameters. The material parameters of PETN are listed in Table 1, and the material structural parameters were from the AUTODYN material library [18].Table 1
Material parameters of PETN.
Parameters
Value
ρ
0 (g/cm3)
0.88
A (GPa)
348.62
B (GPa)
11.288
R
1
7.0
R
2
2.0
w
0.24
DCJ (m/s)
5170
PCJ (GPa)
6.2
E
0 (kJ/m3)
5.025 × 106


## 3.2.2. Structure Material

The casing of the pyrotechnic cutter is made of steel (4340), the shear pin is made of aluminum (2024), the cutter blade and the cutting board are made of V250, and the connecting rod adopts Ti6%Al4%V.To describe the relationship between the pressure and the volume of the structure material under impact, the equation of state (EOS) of the structure material is described with shock EOS, which is an EOS in the form of Mie–Gruneisen, with shock Hugoniot as a reference:(2)P−PH=γve−eH. Here, P is the pressure, γ is the Gruneisen constant, v is the specific volume, and e is the specific internal energy. The subscript H denotes the shock Hugoniot, which is defined as the trajectory of all vibration states for each material. Here, Shock EOS requires P-ν Hugoniot, which can be obtained from U-u Hugoniot, or the relationship between vibration and particle speed:(3)U=C0+su,where C0 and s are empirical parameters.The materials of the shear pin (2024 aluminum), cutter blade (V250) and cutting board (V250), the shell material (steel 4340) and the connecting rod material (Ti6%Al4%V), and the Johnson–Cook constitutive model are used to simulate the dynamic response behavior under explosion and mechanical impact. This model defines the flow stress as the strain rate, a function of an equivalent plastic strain and temperature. The dynamic flow stress is expressed as follows:(4)σ=σ0+Bεn+1+Clnε˙ε˙0+1−T−TrTm−Trm,where σ is the flow pressure, σ0 is the static yield stress, B is the constant of hardening, ε is the strain, n is the hardening index, C is the constant of strain rate, ε˙ is the strain rate, ε˙0 is the reference strain rate, T is the temperature, Tr is the reference temperature, Tm is the melting point, and m is the thermal softening index.The failure of the casing and the connecting rod is described using the Johnson–Cook failure model. The calculated damage parameterD is based on damage accumulation and is given as follows:(5)D=∑Δεpεf,where D is the damage to the material element and Δεp is the increment of the accumulated plastic strain. On the other hand, εf is the accumulated plastic strain from stress triaxiality, temperature, and strain rate and is defined as follows:(6)εf=D1+D2eD3σ∗1+D4lnε˙ε˙01+D5T−TrTm−Tr,where εf is the failure strain; σ∗ is the ratio of the average stress to the equivalent stress; and D1, D2, D3, D4, and D5 are constants. The other parameters are the same as those used in the Johnson–Cook force model. A failure occurs when the fracture parameter D reaches the value of 1.In this study, the instantaneous geometric strain erosion model is used for 2024 aluminum and V250 to prevent a large distortion of Lagrangian elements. By adjusting the model based on the comparison of the test results, the erosion strain was eventually determined to be 2.0. The simulation results are similar to the test results.All of the material structural parameters were from the AUTODYN material library, and their specific values are listed in Tables2–5 [19–22].Table 2
Material parameters of 4340 stainless steel.
Shock EOS
Johnson–Cook strength model
Johnson–Cook failure model
ρ
0 (g/cm3)
7.83
σ
0 (GPa)
0.792
D
1
0.05
γ
1.77
B (GPa)
0.51
D
2
3.44
C
0 (m/s)
3382
n
0.26
D
3
2.12
S
1
1.812
C
0.014
D
4
0.002
T
r (K)
300
m
1.03
D
5
0.61
C
p (J/kg·K)
477
T
m (K)
1793
Erosion criterion
ε
˙
0 (1) s
1.0
Type
FailureTable 3
Material parameters of Ti6%Al4%V.
Shock EOS
Johnson–Cook strength model
Johnson–Cook failure model
ρ
0 (g/cm3)
4.419
σ
0 (GPa)
41.9
D
1
−0.09
γ
1.23
B (GPa)
1.092
D
2
0.25
C
0 (m/s)
5130
n
0.93
D
3
−0.5
S
1
1.028
C
0.014
D
4
0.014
T
r (K)
300
m
1.1
D
5
3.87
C
p (J/kg·K)
525
T
m (K)
1878
Erosion criterion
ε
˙
0 (1) s
1.0
Type
FailureTable 4
Material parameters of V250 stainless steel.
Shock EOS
Johnson–Cook strength model
ρ
0 (g/cm3)
2.785
Y (GPa)
0.26
γ
2.00
Y
max (GPa)
0.76
C
0 (m/s)
5328
β
381
S
1
1.338
n
0.185
T
r (K)
300
G
p
′
1.8647
C
p (J/kg·K)
863
G
T
′ (kPa/K)
−17620
Y
p
′
0.01695
T
melt (K)
1220
Geometric strain
2.5Table 5
Material parameters of 2024-T4 aluminum.
Shock EOS
Johnson–Cook strength model
ρ
0 (g/cm3)
2.785
Y (GPa)
0.26
γ
2.00
Y
max(GPa)
0.76
C
0 (m/s)
5328
β
381
S
1
1.338
n
0.185
T
r (K)
300
G
p
′
1.8647
C
p (J/kg·K)
863
G
T
′ (kPa/K)
−17620
Y
p
′
0.01695
T
melt (K)
1220
Geometric strain
0.7


## 3.2.3. Air Model

The air in the Euler grid is described by the ideal gas state equation:(7)P=γ−1ρE,where γ is the adiabatic exponent (for the ideal gas, γ=1.4), ρ is the density (the initial density of air is 0.001225 g/cm3), and E is the gas specific thermodynamic energy (the initial value E0 is 2.068 × 105 J/kg).


## 3.3. Boundary Conditions and Other Settings

Euler–Lagrange coupling analysis was used for this model. For the Euler part, outflow boundary conditions were used for the boundaries except the symmetry plane; for the Lagrange part, fixed boundaries were used for the casing and the cutting board. Transmit boundary conditions were used for the both ends of the connecting rod. The static friction coefficient was 0.13, and the dynamic friction coefficient was 0.12 between different parts. The maximal energy error to ensure the energy conservation in AUTODYN was set to 0.05.


## 4. Calculation Results and Analysis

With the above AUTODYN analysis program, the cutting process of the pyrotechnic cutter for different spacings between the cutter blade and the cutting board and the maximal cutting diameter of the connecting rod were numerically simulated. The calculation results are as follows.


### 4.1. Working Process of the Pyrotechnic Cutter

Taking the case in which the spacing between the cutter blade and the cutting board was 6.5 mm and the diameter of the connecting rod was 5 mm as an example, the cutter was subjected to a series of actions, from ignition to the completion of cutting. The pressure contours for each component during the action of the pyrotechnic cutter are shown in Figure5.Figure 5
Pressure contours for the pyrotechnic cutter during its actuation. (a) 0.001 ms (b) 0.004 ms. (c) 0.028 ms (d) 0.078 ms. (e) 0.144 ms. (f) 0.198 ms.
(a)
(b)
(c)
(d)
(e)
(f)After the main charge is detonated by the igniter, high-temperature gas is continuously released into the combustion chamber, and the energy and the substance diffuse throughout the entire Euler field and finally fill the entire space; consequently, a strong detonation wave and a shock wave are generated in the chamber, as shown in Figure5(a). With the continuous increase in the pressure that is applied to the inner wall of the chamber and the end face of the cutter blade, as shown in Figure 5(b), the cutter blade moves under the action of the gas pressure and cuts down the shear pin, as shown in Figure 5(c). As the cutter blade continuously advances under the pressure, it contacts the connecting rod and presses it onto the cutting board, as shown in Figure 5(d). Then, the cutting board and the edge of the cutting blade act together to cut the connecting rod from both sides, until the connecting rod is completely fractured, as shown in Figure 5(e). The cutter blade gradually stops moving after contacting the cutting board, as shown in Figure 5(f).To analyze the collision between the cutter blade and the connecting rod and the fracture process of the connecting rod, the pressure variation of the cutter blade’s end face and the speed variation of the cutter blade’s centroid were studied, with the cutter blade as the study object, and the results are shown in Figure6.Figure 6
Simulation results of the pyrotechnic cutter, for the connection diameter of 5 mm and the spacing of 6.5 mm. (a) Pressure history of the cutter blade’s end face. (b) Velocity history of the cutter blade. (c) Acceleration history of the cutter blade.
(a)
(b)
(c)The pressure in the chamber of the pyrotechnic cutter reaches a peak value of 1.53 GPa∼0.002 ms following the main charge detonation; then, the pressure drops sharply, and a secondary peak of 0.66 GPa appears 0.006 ms after it enters the oscillation mode. At 0.007 ms, when the cutter blade starts cutting the shear pin, the pressure applied onto the end face of the cutter blade is ∼0.38 GPa; then, the pressure oscillates below 0.30 GPa with a small amplitude, as shown in Figure6(a). Under the instantaneous detonation of the explosive, the axial acceleration of the cutter increases rapidly, and the cutter starts to move from rest, as shown in section AB in Figures 6(b) and 6(c). At point B, the cutting speed of the cutter is 10.07 m/s, the acceleration is 5.96 × 105 g, and the time is 0.003 ms. Then, the pressure starts to fall back and oscillate, and the cutter continues to accelerate under the pressure. However, owing to the existence of the shear pin, the motion of the cutter is blocked, and the acceleration decreases rapidly, as shown in the BC section of Figure 6(c), so that the shear pin breaks at point C. After the cutting pin breaks, owing to the reduction in the resistance, the cutting knife gradually increases under the action of the gunpowder gas, as shown in the CD section of Figure 6(c). As the gunpowder gas pressure stabilizes, the acceleration of the cutter also tends to be flat and stable, as shown in the DE section of Figure 6(c). At point E, the cutter is in contact with the connecting rod. After that, owing to the obstruction of the connecting rod, the cutter’s acceleration gradually decreases, as shown in the EG section of Figure 6(c), where the cutter’s acceleration at point F is reduced to 0, at which point, the cutter’s speed reaches a maximum of 49.52 m/s. Subsequently, the cutter speed gradually decreases. After point G, the cutter begins to cut the connecting rod. During the cutting process, the cutter accelerates the vibration up and down, near zero. The cutter’s speed stabilizes, as shown in the GH sections of Figures 6(b) and 6(c). After the contact between the cutter’s H point and the cutting board is established, the cutter’s acceleration gradually decreases, the cutter’s speed decreases rapidly, and the cutter eventually stops, as shown in Figures 6(b) and 6(c).


### 4.2. Stress and Strain Analysis of the Fracture Part of the Connecting Rod

To analyze the fracture process of the connecting rod more accurately, nine typical units of gauge points were sequentially selected in the radial direction on the presection of the connecting rod and to analyze the stress and strain changes during the fracture, as shown in Figure7.Figure 7
Selection of gauge points of the connecting rod.After the cutter blade makes contact with the connecting rod as it moves continuously, the stress at the selected gauge points increases sharply, and the internal energy of the unit also increases sharply. When the yield limit is reached, the shearing action occurs. As a result, the connecting rod is separated from the presection. Because the unit disappears, the stress and internal energy of the selected unit decrease sharply and return to zero after the selected unit is completely cut, as shown in Figure8(a). The equivalent stress variation curve of the selected unit is identical to the internal energy variation curve, as shown in Figure 8(b). The pressure contours of the connecting rod in the cutting process are shown in Figure 9. At 0.050 ms, the cutter blade starts to make contact with the connecting rod, as shown in Figure 9(a). At 0.062 ms, the cutting board starts to exert a reaction force onto the connecting rod, as shown in Figure 9(b). Unit 14 on the connecting rod first reaches the failure strain at 0.076 ms, as shown in Figure 9(c), and unit 6 on the connecting rod reaches the failure strain at 0.090 ms, as shown in Figure 9(d). At 0.144 ms, unit 9 (the last one) reaches the failure strain, as Figure 9(e) shows. At 0.154 ms, the cutter is in contact with the cutting plate, to complete cutting of the connecting rod. The cutting state is shown in Figure 9(f). Therefore, the fracture process of the connecting rod first starts near the cutting board and then continues from both sides to the middle. The connecting rod incision is shown schematically in Figure 10. The phenomena observed in the simulation are basically consistent with those observed in the test data.Figure 8
Stress, energy, and damage histories on impair slot. (a) von Mises stress and (b) INT.ENERGY.
(a)
(b)Figure 9
Pressure contours of the connecting rod. (a) 0.050 ms. (b) 0.062 ms. (c) 0.076 ms. (d) 0.090 ms. (e) 0.148 ms. (f) 0.154 ms.
(a)
(b)
(c)
(d)
(e)
(f)Figure 10
Photograph of a real cut of a connecting rod.


### 4.3. Influence of the Spacing between the Cutter Blade and the Cutting Board

To quantify the effect of the spacing between the cutter blade and the cutting board on the cutting effect of the pyrotechnic cutter, a numerical simulation of the dynamic cutting process of the pyrotechnic cutter (connecting rod diameter of 5 mm). This was performed for the case in which the distance between the cutter blade and the cutting board was 5.5, 6.5, 7.5, and 8.5 mm. Estimates of the maximal cutting diameter of the connecting rod were also obtained using these simulations.


#### 4.3.1. Numerical Simulation Results for the Cutter Blade Motion

The numerical simulation results for the pyrotechnic cutter, for a connecting rod of diameter 5 mm and different spacings between the cutter blade and the cutting board (5.5, 6.5, 7.5, and 8.5 mm), are listed in Table6. The change curves of the acceleration and velocity of the cutter, for different spacing values, are shown in Figures 11(a) and 11(b).Table 6
Numerical simulation results for a pyrotechnic cutter with a connecting rod with the diameter of 5 mm for different spacing values.
Spacing (mm)
Diameter of connecting rod (mm)
Cutting start timeT (ms)
Cutting start velocityV (m/s)
Cutting completion timet (ms)
Cutting completion velocityV (m/s)
5.5
5
0.023
34.79
0.160
30.06
6.5
5
0.050
46.64
0.153
43.31
7.5
5
0.068
57.89
0.149
49.64
8.5
5
0.086
63.34
0.163
55.32Figure 11
(a) Velocity of the cutter blade for different spacing values. (b) Acceleration of the cutter blade for different spacing values. (c) Relationship between initial speed and completion speed and spacing during cutting. (d) Cutting time of the connecting rod vs. the spacing.
(a)
(b)
(c)
(d)As can be seen from Figure11(a), because the cutter has the same amount of charge for different spacing values, the acceleration of the cutter is virtually the same during the ABCDE stage in Figure 5(c), before the cutter touches the connecting rod. However, the duration of the DE phase is different. With increasing spacing, the duration of the DE phase increases, and the cutter speed increases, as shown in Figure 11(b). Comparisons of the cutter’s initial cutting speed, maximal speed, and completion speed, for different spacing values, are shown in Figure 11(c). As the distance between the cutter and the cutting plate increases, the cutter’s initial shear speed, maximal speed, and speed at the completion of the cutting of the connecting rod increase linearly. Furthermore, the difference between the initial cutting speed of the cutter and its maximal speed decreases gradually with increasing spacing; the peak values are obtained for the spacing of 8.5 mm. This suggests that the acceleration effect of the gunpowder gas on the cutter is close to maximal for the distance of 8.5 mm. Comparing the cutting time results (Figure 11(d)), it can be seen that for the spacing under 7.5 mm, the cutting time decreases significantly as the spacing increases. For spacings in the 7.5–8.5 mm range, the spacing has little effect on the cutting time; increasing the spacing increases the cutting time by a very small amount. Thus, there is an optimal distance between the cutter and the cutting plate during the action of the cutter; for this distance, the cutting effect is the strongest. For the cutter selected in this study, such optimal spacing was determined to be 7.5 mm.


#### 4.3.2. Numerical Simulation Results for the Maximal Cutting Diameter of the Connecting Rod

In these studies, the spacing between the cutter blade and the cutting board was 6.5 and 7.5 mm. Numerical simulation results for a cutter and connecting rods with different diameters are listed in Table7.Table 7
Numerical simulation results for the maximal cutting diameter of the connecting rod of the pyrotechnic cutter.
Spacing (mm)
Diameter of connecting rod (mm)
Cutting start timeT (ms)
Cutting start velocityV (m/s)
Cutting completion timet (ms)
Cutting completion velocityV (m/s)
6.5
5
0.050
46.64
0.153
43.31
5.5
0.036
41.13
0.169
36.42
5.7
0.032
38.75
0.172
33.89
6
0.023
35.76
—
7.5
5
0.068
57.89
0.149
49.64
5.5
0.058
53.82
0.165
45.82
5.7
0.054
51.65
0.184
33.23
6
0.050
46.60
—From the simulation results, cutting for the connecting rod with a diameter of 5.7 mm can be completed when the spacing between the cutter blade and the cutting board is 6.5 and 7.5 mm, while cutting cannot be completed for the connecting rod with a diameter of 6 mm. The speed curves and displacement curves of the cutter blade are shown. According to Figures12(a) and 12(b), for the connecting rod with a diameter of 6 mm, the cutting depth of the cutter blade is 4.35 and 5.12 mm, respectively, when the spacing is 6.5 and 7.5 mm. Therefore, the shear depth can be increased by increasing the spacing between the cutter blade and the cutting board.Figure 12
Cutter blade velocity and displacement, vs. time, for the spacing values of 6.5 mm and 7.5 mm, and for the connecting rod’s diameter of 6 mm. (a) Cutter blade velocity vs. time (b) Cutter displacement vs. time.
(a)
(b)


### 4.4. Test Verification

Pyrotechnic cutters with spacing values between the cutter blade and the cutting board of 6.5 and 7.5 mm were installed using connecting rods with different diameters. Then, an ignition test was performed at normal temperature, using the dual-initiation method, to determine the cutting effects of the connecting rod on the cutter. The test site was as shown in Figure13, and the test results are listed in Table 8.Figure 13
Pyrotechnic cutter test site. (a) Test site. (b) Before action. (c) After action.
(a)
(b)
(c)Table 8
Test results for the explosive cutting device.
No.
Spacing (mm)
Diameter of connecting rod (mm)
Function
1
6.5
4.5
Success in cutting
2
6.5
4.5
Success in cutting
3
6.5
4.5
Success in cutting
4
6.5
5
Success in cutting
5
6.5
5
Success in cutting
6
6.5
5
Success in cutting
7
6.5
5.3
Success in cutting
8
6.5
5.3
Success in cutting
9
6.5
5.3
Success in cutting
10
6.5
5.5
Failure in cutting
11
6.5
5.5
Failure in cutting
12
6.5
5.5
Failure in cutting
13
7.5
4.5
Success in cutting
14
7.5
4.5
Success in cutting
15
7.5
4.5
Success in cutting
16
6.5
5
Success in cutting
17
7.5
5
Success in cutting
18
7.5
5
Success in cutting
19
7.5
5.3
Success in cutting
20
7.5
5.3
Success in cutting
21
7.5
5.3
Success in cutting
22
7.5
5.5
Success in cutting
23
7.5
5.5
Failure in cutting
24
7.5
5.5
Failure in cuttingAccording to the test results, the maximal cutting diameter of the pyrotechnic cutter for the cutting rod was 5.3 mm, which was obtained when the spacing between the cutter blade and the cutting board was 6.5 or 7.5 mm. The discrepancy with simulation results was 7.5%, suggesting that the present simulation setup is effective, may be used to describe the explosive cutting process of the pyrotechnic cutter, and can provide a reference for the design and optimization of pyrotechnic cutters. The main possible reasons for the deviation of this model are that the influence of the sealing ring on the resistance of the cutting tool was neglected in the model, and there is a certain deviation between the material failure characteristics in the model and those of the actual material.


## 4.1. Working Process of the Pyrotechnic Cutter

Taking the case in which the spacing between the cutter blade and the cutting board was 6.5 mm and the diameter of the connecting rod was 5 mm as an example, the cutter was subjected to a series of actions, from ignition to the completion of cutting. The pressure contours for each component during the action of the pyrotechnic cutter are shown in Figure5.Figure 5
Pressure contours for the pyrotechnic cutter during its actuation. (a) 0.001 ms (b) 0.004 ms. (c) 0.028 ms (d) 0.078 ms. (e) 0.144 ms. (f) 0.198 ms.
(a)
(b)
(c)
(d)
(e)
(f)After the main charge is detonated by the igniter, high-temperature gas is continuously released into the combustion chamber, and the energy and the substance diffuse throughout the entire Euler field and finally fill the entire space; consequently, a strong detonation wave and a shock wave are generated in the chamber, as shown in Figure5(a). With the continuous increase in the pressure that is applied to the inner wall of the chamber and the end face of the cutter blade, as shown in Figure 5(b), the cutter blade moves under the action of the gas pressure and cuts down the shear pin, as shown in Figure 5(c). As the cutter blade continuously advances under the pressure, it contacts the connecting rod and presses it onto the cutting board, as shown in Figure 5(d). Then, the cutting board and the edge of the cutting blade act together to cut the connecting rod from both sides, until the connecting rod is completely fractured, as shown in Figure 5(e). The cutter blade gradually stops moving after contacting the cutting board, as shown in Figure 5(f).To analyze the collision between the cutter blade and the connecting rod and the fracture process of the connecting rod, the pressure variation of the cutter blade’s end face and the speed variation of the cutter blade’s centroid were studied, with the cutter blade as the study object, and the results are shown in Figure6.Figure 6
Simulation results of the pyrotechnic cutter, for the connection diameter of 5 mm and the spacing of 6.5 mm. (a) Pressure history of the cutter blade’s end face. (b) Velocity history of the cutter blade. (c) Acceleration history of the cutter blade.
(a)
(b)
(c)The pressure in the chamber of the pyrotechnic cutter reaches a peak value of 1.53 GPa∼0.002 ms following the main charge detonation; then, the pressure drops sharply, and a secondary peak of 0.66 GPa appears 0.006 ms after it enters the oscillation mode. At 0.007 ms, when the cutter blade starts cutting the shear pin, the pressure applied onto the end face of the cutter blade is ∼0.38 GPa; then, the pressure oscillates below 0.30 GPa with a small amplitude, as shown in Figure6(a). Under the instantaneous detonation of the explosive, the axial acceleration of the cutter increases rapidly, and the cutter starts to move from rest, as shown in section AB in Figures 6(b) and 6(c). At point B, the cutting speed of the cutter is 10.07 m/s, the acceleration is 5.96 × 105 g, and the time is 0.003 ms. Then, the pressure starts to fall back and oscillate, and the cutter continues to accelerate under the pressure. However, owing to the existence of the shear pin, the motion of the cutter is blocked, and the acceleration decreases rapidly, as shown in the BC section of Figure 6(c), so that the shear pin breaks at point C. After the cutting pin breaks, owing to the reduction in the resistance, the cutting knife gradually increases under the action of the gunpowder gas, as shown in the CD section of Figure 6(c). As the gunpowder gas pressure stabilizes, the acceleration of the cutter also tends to be flat and stable, as shown in the DE section of Figure 6(c). At point E, the cutter is in contact with the connecting rod. After that, owing to the obstruction of the connecting rod, the cutter’s acceleration gradually decreases, as shown in the EG section of Figure 6(c), where the cutter’s acceleration at point F is reduced to 0, at which point, the cutter’s speed reaches a maximum of 49.52 m/s. Subsequently, the cutter speed gradually decreases. After point G, the cutter begins to cut the connecting rod. During the cutting process, the cutter accelerates the vibration up and down, near zero. The cutter’s speed stabilizes, as shown in the GH sections of Figures 6(b) and 6(c). After the contact between the cutter’s H point and the cutting board is established, the cutter’s acceleration gradually decreases, the cutter’s speed decreases rapidly, and the cutter eventually stops, as shown in Figures 6(b) and 6(c).


## 4.2. Stress and Strain Analysis of the Fracture Part of the Connecting Rod

To analyze the fracture process of the connecting rod more accurately, nine typical units of gauge points were sequentially selected in the radial direction on the presection of the connecting rod and to analyze the stress and strain changes during the fracture, as shown in Figure7.Figure 7
Selection of gauge points of the connecting rod.After the cutter blade makes contact with the connecting rod as it moves continuously, the stress at the selected gauge points increases sharply, and the internal energy of the unit also increases sharply. When the yield limit is reached, the shearing action occurs. As a result, the connecting rod is separated from the presection. Because the unit disappears, the stress and internal energy of the selected unit decrease sharply and return to zero after the selected unit is completely cut, as shown in Figure8(a). The equivalent stress variation curve of the selected unit is identical to the internal energy variation curve, as shown in Figure 8(b). The pressure contours of the connecting rod in the cutting process are shown in Figure 9. At 0.050 ms, the cutter blade starts to make contact with the connecting rod, as shown in Figure 9(a). At 0.062 ms, the cutting board starts to exert a reaction force onto the connecting rod, as shown in Figure 9(b). Unit 14 on the connecting rod first reaches the failure strain at 0.076 ms, as shown in Figure 9(c), and unit 6 on the connecting rod reaches the failure strain at 0.090 ms, as shown in Figure 9(d). At 0.144 ms, unit 9 (the last one) reaches the failure strain, as Figure 9(e) shows. At 0.154 ms, the cutter is in contact with the cutting plate, to complete cutting of the connecting rod. The cutting state is shown in Figure 9(f). Therefore, the fracture process of the connecting rod first starts near the cutting board and then continues from both sides to the middle. The connecting rod incision is shown schematically in Figure 10. The phenomena observed in the simulation are basically consistent with those observed in the test data.Figure 8
Stress, energy, and damage histories on impair slot. (a) von Mises stress and (b) INT.ENERGY.
(a)
(b)Figure 9
Pressure contours of the connecting rod. (a) 0.050 ms. (b) 0.062 ms. (c) 0.076 ms. (d) 0.090 ms. (e) 0.148 ms. (f) 0.154 ms.
(a)
(b)
(c)
(d)
(e)
(f)Figure 10
Photograph of a real cut of a connecting rod.


## 4.3. Influence of the Spacing between the Cutter Blade and the Cutting Board

To quantify the effect of the spacing between the cutter blade and the cutting board on the cutting effect of the pyrotechnic cutter, a numerical simulation of the dynamic cutting process of the pyrotechnic cutter (connecting rod diameter of 5 mm). This was performed for the case in which the distance between the cutter blade and the cutting board was 5.5, 6.5, 7.5, and 8.5 mm. Estimates of the maximal cutting diameter of the connecting rod were also obtained using these simulations.


### 4.3.1. Numerical Simulation Results for the Cutter Blade Motion

The numerical simulation results for the pyrotechnic cutter, for a connecting rod of diameter 5 mm and different spacings between the cutter blade and the cutting board (5.5, 6.5, 7.5, and 8.5 mm), are listed in Table6. The change curves of the acceleration and velocity of the cutter, for different spacing values, are shown in Figures 11(a) and 11(b).Table 6
Numerical simulation results for a pyrotechnic cutter with a connecting rod with the diameter of 5 mm for different spacing values.
Spacing (mm)
Diameter of connecting rod (mm)
Cutting start timeT (ms)
Cutting start velocityV (m/s)
Cutting completion timet (ms)
Cutting completion velocityV (m/s)
5.5
5
0.023
34.79
0.160
30.06
6.5
5
0.050
46.64
0.153
43.31
7.5
5
0.068
57.89
0.149
49.64
8.5
5
0.086
63.34
0.163
55.32Figure 11
(a) Velocity of the cutter blade for different spacing values. (b) Acceleration of the cutter blade for different spacing values. (c) Relationship between initial speed and completion speed and spacing during cutting. (d) Cutting time of the connecting rod vs. the spacing.
(a)
(b)
(c)
(d)As can be seen from Figure11(a), because the cutter has the same amount of charge for different spacing values, the acceleration of the cutter is virtually the same during the ABCDE stage in Figure 5(c), before the cutter touches the connecting rod. However, the duration of the DE phase is different. With increasing spacing, the duration of the DE phase increases, and the cutter speed increases, as shown in Figure 11(b). Comparisons of the cutter’s initial cutting speed, maximal speed, and completion speed, for different spacing values, are shown in Figure 11(c). As the distance between the cutter and the cutting plate increases, the cutter’s initial shear speed, maximal speed, and speed at the completion of the cutting of the connecting rod increase linearly. Furthermore, the difference between the initial cutting speed of the cutter and its maximal speed decreases gradually with increasing spacing; the peak values are obtained for the spacing of 8.5 mm. This suggests that the acceleration effect of the gunpowder gas on the cutter is close to maximal for the distance of 8.5 mm. Comparing the cutting time results (Figure 11(d)), it can be seen that for the spacing under 7.5 mm, the cutting time decreases significantly as the spacing increases. For spacings in the 7.5–8.5 mm range, the spacing has little effect on the cutting time; increasing the spacing increases the cutting time by a very small amount. Thus, there is an optimal distance between the cutter and the cutting plate during the action of the cutter; for this distance, the cutting effect is the strongest. For the cutter selected in this study, such optimal spacing was determined to be 7.5 mm.


### 4.3.2. Numerical Simulation Results for the Maximal Cutting Diameter of the Connecting Rod

In these studies, the spacing between the cutter blade and the cutting board was 6.5 and 7.5 mm. Numerical simulation results for a cutter and connecting rods with different diameters are listed in Table7.Table 7
Numerical simulation results for the maximal cutting diameter of the connecting rod of the pyrotechnic cutter.
Spacing (mm)
Diameter of connecting rod (mm)
Cutting start timeT (ms)
Cutting start velocityV (m/s)
Cutting completion timet (ms)
Cutting completion velocityV (m/s)
6.5
5
0.050
46.64
0.153
43.31
5.5
0.036
41.13
0.169
36.42
5.7
0.032
38.75
0.172
33.89
6
0.023
35.76
—
7.5
5
0.068
57.89
0.149
49.64
5.5
0.058
53.82
0.165
45.82
5.7
0.054
51.65
0.184
33.23
6
0.050
46.60
—From the simulation results, cutting for the connecting rod with a diameter of 5.7 mm can be completed when the spacing between the cutter blade and the cutting board is 6.5 and 7.5 mm, while cutting cannot be completed for the connecting rod with a diameter of 6 mm. The speed curves and displacement curves of the cutter blade are shown. According to Figures12(a) and 12(b), for the connecting rod with a diameter of 6 mm, the cutting depth of the cutter blade is 4.35 and 5.12 mm, respectively, when the spacing is 6.5 and 7.5 mm. Therefore, the shear depth can be increased by increasing the spacing between the cutter blade and the cutting board.Figure 12
Cutter blade velocity and displacement, vs. time, for the spacing values of 6.5 mm and 7.5 mm, and for the connecting rod’s diameter of 6 mm. (a) Cutter blade velocity vs. time (b) Cutter displacement vs. time.
(a)
(b)


## 4.3.1. Numerical Simulation Results for the Cutter Blade Motion

The numerical simulation results for the pyrotechnic cutter, for a connecting rod of diameter 5 mm and different spacings between the cutter blade and the cutting board (5.5, 6.5, 7.5, and 8.5 mm), are listed in Table6. The change curves of the acceleration and velocity of the cutter, for different spacing values, are shown in Figures 11(a) and 11(b).Table 6
Numerical simulation results for a pyrotechnic cutter with a connecting rod with the diameter of 5 mm for different spacing values.
Spacing (mm)
Diameter of connecting rod (mm)
Cutting start timeT (ms)
Cutting start velocityV (m/s)
Cutting completion timet (ms)
Cutting completion velocityV (m/s)
5.5
5
0.023
34.79
0.160
30.06
6.5
5
0.050
46.64
0.153
43.31
7.5
5
0.068
57.89
0.149
49.64
8.5
5
0.086
63.34
0.163
55.32Figure 11
(a) Velocity of the cutter blade for different spacing values. (b) Acceleration of the cutter blade for different spacing values. (c) Relationship between initial speed and completion speed and spacing during cutting. (d) Cutting time of the connecting rod vs. the spacing.
(a)
(b)
(c)
(d)As can be seen from Figure11(a), because the cutter has the same amount of charge for different spacing values, the acceleration of the cutter is virtually the same during the ABCDE stage in Figure 5(c), before the cutter touches the connecting rod. However, the duration of the DE phase is different. With increasing spacing, the duration of the DE phase increases, and the cutter speed increases, as shown in Figure 11(b). Comparisons of the cutter’s initial cutting speed, maximal speed, and completion speed, for different spacing values, are shown in Figure 11(c). As the distance between the cutter and the cutting plate increases, the cutter’s initial shear speed, maximal speed, and speed at the completion of the cutting of the connecting rod increase linearly. Furthermore, the difference between the initial cutting speed of the cutter and its maximal speed decreases gradually with increasing spacing; the peak values are obtained for the spacing of 8.5 mm. This suggests that the acceleration effect of the gunpowder gas on the cutter is close to maximal for the distance of 8.5 mm. Comparing the cutting time results (Figure 11(d)), it can be seen that for the spacing under 7.5 mm, the cutting time decreases significantly as the spacing increases. For spacings in the 7.5–8.5 mm range, the spacing has little effect on the cutting time; increasing the spacing increases the cutting time by a very small amount. Thus, there is an optimal distance between the cutter and the cutting plate during the action of the cutter; for this distance, the cutting effect is the strongest. For the cutter selected in this study, such optimal spacing was determined to be 7.5 mm.


## 4.3.2. Numerical Simulation Results for the Maximal Cutting Diameter of the Connecting Rod

In these studies, the spacing between the cutter blade and the cutting board was 6.5 and 7.5 mm. Numerical simulation results for a cutter and connecting rods with different diameters are listed in Table7.Table 7
Numerical simulation results for the maximal cutting diameter of the connecting rod of the pyrotechnic cutter.
Spacing (mm)
Diameter of connecting rod (mm)
Cutting start timeT (ms)
Cutting start velocityV (m/s)
Cutting completion timet (ms)
Cutting completion velocityV (m/s)
6.5
5
0.050
46.64
0.153
43.31
5.5
0.036
41.13
0.169
36.42
5.7
0.032
38.75
0.172
33.89
6
0.023
35.76
—
7.5
5
0.068
57.89
0.149
49.64
5.5
0.058
53.82
0.165
45.82
5.7
0.054
51.65
0.184
33.23
6
0.050
46.60
—From the simulation results, cutting for the connecting rod with a diameter of 5.7 mm can be completed when the spacing between the cutter blade and the cutting board is 6.5 and 7.5 mm, while cutting cannot be completed for the connecting rod with a diameter of 6 mm. The speed curves and displacement curves of the cutter blade are shown. According to Figures12(a) and 12(b), for the connecting rod with a diameter of 6 mm, the cutting depth of the cutter blade is 4.35 and 5.12 mm, respectively, when the spacing is 6.5 and 7.5 mm. Therefore, the shear depth can be increased by increasing the spacing between the cutter blade and the cutting board.Figure 12
Cutter blade velocity and displacement, vs. time, for the spacing values of 6.5 mm and 7.5 mm, and for the connecting rod’s diameter of 6 mm. (a) Cutter blade velocity vs. time (b) Cutter displacement vs. time.
(a)
(b)


## 4.4. Test Verification

Pyrotechnic cutters with spacing values between the cutter blade and the cutting board of 6.5 and 7.5 mm were installed using connecting rods with different diameters. Then, an ignition test was performed at normal temperature, using the dual-initiation method, to determine the cutting effects of the connecting rod on the cutter. The test site was as shown in Figure13, and the test results are listed in Table 8.Figure 13
Pyrotechnic cutter test site. (a) Test site. (b) Before action. (c) After action.
(a)
(b)
(c)Table 8
Test results for the explosive cutting device.
No.
Spacing (mm)
Diameter of connecting rod (mm)
Function
1
6.5
4.5
Success in cutting
2
6.5
4.5
Success in cutting
3
6.5
4.5
Success in cutting
4
6.5
5
Success in cutting
5
6.5
5
Success in cutting
6
6.5
5
Success in cutting
7
6.5
5.3
Success in cutting
8
6.5
5.3
Success in cutting
9
6.5
5.3
Success in cutting
10
6.5
5.5
Failure in cutting
11
6.5
5.5
Failure in cutting
12
6.5
5.5
Failure in cutting
13
7.5
4.5
Success in cutting
14
7.5
4.5
Success in cutting
15
7.5
4.5
Success in cutting
16
6.5
5
Success in cutting
17
7.5
5
Success in cutting
18
7.5
5
Success in cutting
19
7.5
5.3
Success in cutting
20
7.5
5.3
Success in cutting
21
7.5
5.3
Success in cutting
22
7.5
5.5
Success in cutting
23
7.5
5.5
Failure in cutting
24
7.5
5.5
Failure in cuttingAccording to the test results, the maximal cutting diameter of the pyrotechnic cutter for the cutting rod was 5.3 mm, which was obtained when the spacing between the cutter blade and the cutting board was 6.5 or 7.5 mm. The discrepancy with simulation results was 7.5%, suggesting that the present simulation setup is effective, may be used to describe the explosive cutting process of the pyrotechnic cutter, and can provide a reference for the design and optimization of pyrotechnic cutters. The main possible reasons for the deviation of this model are that the influence of the sealing ring on the resistance of the cutting tool was neglected in the model, and there is a certain deviation between the material failure characteristics in the model and those of the actual material.


## 5. Conclusion

In this article, a 3D finite element general calculation model of a pyrotechnic cutter was established. Using this model, the stress and energy variations of the failure unit of the fractured connecting rod upon explosion impulse were analyzed, and some curves were obtained, such as those that describe the internal pressure of the cutter and the dynamic parameters of the cutter blade. In addition, simulations were performed for different conditions, by adjusting parameters such as the spacing between the cutter blade and the cutting board, and the diameter of the connecting rod. Based on the data analysis, the following conclusions are made:(1)
The fracture of the connecting rod in the pyrotechnic cutter is achieved by the kinetic energy penetration of the cutter blade and the residual pressure of the detonation gas, and the fracture elastic-plastic transition occurs at the fracture of the joint.(2)
As the spacing between the cutter blade and the cutting board increases, the initial shear speed, maximal speed, and the speed at which the cutter connects to the rod all increase linearly. The acceleration effect of the gunpowder gas on the cutter is close to maximal for a distance of 8.5 mm. When the distance between the cutter and the connecting rod is less than 7.5 mm, the cutting time decreases significantly with increasing spacing. The cutting effect is the strongest for this distance. For the cutter studied in this article, the optimal distance was determined to be 7.5 mm.(3)
The limiting cutting diameter in the numerical simulations of the pyrotechnic cutter in the present work was 5.7 mm, and the test limiting cutting diameter was 5.3 mm; thus, the error was within 10%, and the simulation result of the cutting process of the connecting rod was consistent with the test result.The simulation method proposed in this article can comprehensively describe the physical and mechanical parameters of the entire dynamic fracture process of the connecting rod in the pyrotechnic cutter, revealing the dynamic behavior in the dynamic fracture process and deepening the understanding of the fracture mechanism of the pyrotechnic cutter. With this method, the influence of the spacing between the cutter blade and the cutting board on the cutting effect of the pyrotechnic cutter can also be analyzed. In addition, the maximal cutting diameter of the pyrotechnic cutter on the connecting rod can be simulated by using the model with different charging conditions. Therefore, the proposed framework can provide a reference for the future design and optimization of cutters.



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*Source: 2457854-2019-11-28.xml*