High-precision numerical modeling of the projectile launch and failure mechanism analysis of projectile-borne components

doi:10.1007/s10483-025-3254-9

Abstract

Abstract:

As core components of precision-guided projectiles, projectile-borne components are highly susceptible to failure or even damage in complex high-overload environments, thereby significantly compromising launch reliability and safety. However, accurately characterizing the mechanical behavior of propellants remains challenging due to the limitations in the current internal ballistic theory and the constraints of large-scale artillery firing experiments. This complicates the high-precision numerical modeling of projectile launch, and obstructs investigations into the failure mechanisms of projectile-borne components. Therefore, this paper identifies propellant parameters using the computational inverse method under uncertainty, further establishes high-precision numerical models of projectile launch, and explores the failure mechanisms of projectile-borne components in complex high-overload environments. First, a projectile launching experiment is meticulously designed and executed to obtain the breech pressure and muzzle velocity. Then, a general simulation model is built, and the powder burn model is used to simulate the ignition and combustion. Subsequently, the propellant parameters are effectively identified with the computational inverse method by the combination of the experiments and simulations. A high-precision numerical model of projectile launch is modified with the parameters validated by another experiment, and the high-overload characteristics during projectile launch are thoroughly analyzed based on this model. Finally, the high-overload characteristics of projectile-borne components are analyzed to elucidate the stress variation laws and to reveal the failure mechanisms influenced by time and spatial locations. This research provides an effective method for perfectly identifying propellant parameters and building high-precision numerical models of projectile launch. Additionally, it provides significant guidance for the anti-high overload design and analysis of projectile-borne components.

Key words: projectile-borne component, high-overload environment, propellant parameter identification, computational inverse technique, failure mechanism

2010 MSC Number:

Xindan GUO, Qiming LIU, Xu HAN, Tao LI, Bin'an JIANG, Canwei CAI. High-precision numerical modeling of the projectile launch and failure mechanism analysis of projectile-borne components. Applied Mathematics and Mechanics (English Edition), 2025, 46(5): 885-906.

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Figures/Tables 30

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Table 1

Material properties of the projectile"

Name	Value	Unit	Name	Value	Unit
Density	$7.7 × 103$	kg/m³	Specific heat	465.0	J/(kg · K)
Bulk modulus	$2.0 × 108$	kPa	Yield stress	$8.27 × 105$	kPa
Shear modulus	$8.0 × 107$	kPa	Melting temperature	1 811	K
Hardening constant	$2.75 × 105$	kPa	Hardening exponent	0.36
Strain rate constant	0.022		Thermal softening exponent	1.03

Table 1

Table 2

Material properties of the projectile band"

Name	Value	Unit	Name	Value	Unit
Density	$8.45 × 103$	kg/m³	Gruneisen coefficient	2.04
Parameter $C$	$3.73 × 103$	m/s	Parameter $S$	1.434

Table 2

Table 3

Fig. 6

Table 4

Ranges of the propellant parameters in the powder burn model"

Parameter	$G R$	$C 1$	$a$	$n$
Description	Reaction growth constant	Ignition front velocity coefficient	Burn rate coefficient	Burn rate exponent
Range	[0.1, 0.3]	[40, 60]	[0.5, 0.9]	[0.7, 1.2]

Table 4

Fig. 7

Fig. 8

Table 5

Comparison of the recognition results based on the PEM-INT and MCS methods"

Statistical moment		MCS	PEM-INT	Relative error/%
Burn rate coefficient $a$	$μ 1$	0.653 8	0.650 0	0.58
Burn rate coefficient $a$	$σ 1$	0.048 7	0.050 0	2.67
Burn rate exponent $n$	$μ 2$	0.934 2	0.949 5	1.64
Burn rate exponent $n$	$σ 2$	0.043 2	0.049 5	14.58

Table 5

Fig. 9

Table 6

Material properties of the propellant"

Name	Value	Unit	Name	Value	Unit
Density	$1.86 × 103$	kg/m³	Reference temperature	293	K
Bulk modulus	$1.35 × 107$	kPa	Thermal conductivity	0	J/(kg ·K)
Specific heat	0	J/(kg · K)	Reaction growth constant	0.23	mm^-1
Specific energy	$1.0 × 106$	kJ/m³	Reaction growth exponent	0.5
Parameter $D$	1.003 3		Burn rate coefficient	0.650 0
Yield stress	$2.0 × 103$	kPa	Burn rate exponent	0.954 5
Shear modulus	$1.38 × 106$	kPa	Ignition front velocity coefficient	40.37	m/s

Table 6

Fig. 10

Table 7

Comparative results between simulations and experiments"

Variable	Experiment 1	Vacuum model		Air model		Band model
Variable	Experiment 1	Value	Error/%	Value	Error/%	Value	Error/%
Time/ms	11.25	11.00	2.22	11.10	1.33	11.90	5.78
Pressure/MPa	241.03	254.72	5.68	255.62	6.05	234.95	2.52
Velocity/ $(m ⋅ s − 1)$	693	664	4.18	661	4.62	640	7.65
Variable	Experiment 2	Vacuum model		Air model		Band model
Variable	Experiment 2	Value	Error/%	Value	Error/%	Value	Error/%
Time/ms	12.83	12.80	0.23	12.90	0.55	12.12	5.53
Pressure/MPa	194.33	197.31	1.53	197.19	1.47	190.11	2.17
Velocity/ $(m ⋅ s − 1)$	664	604	9.04	603	9.19	587	11.60

Table 7

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Table 8

The material properties of each part in the finite element model where ABS denotes acrylonitrile-butadiene-styrene"

Part name	Material	Density/(kg · m^-3)	Elastic modulus/kPa	Poisson's ratio
Projectile body	Steel	$7.86 × 103$	$2.00 × 108$	0.27
Inner cylinder	Aluminum	$2.71 × 103$	$6.90 × 107$	0.33
Fixed bearing	Aluminum	$2.71 × 103$	$6.90 × 107$	0.33
PCB	Epoxy resin^[41]	$1.97 × 103$	$1.40 × 107$	0.18
Optical lens	Optical glass^[42-43]	$2.54 × 103$	$8.13 × 107$	0.21
Lens housings	ABS plastic	$2.30 × 103$	$2.28 × 106$	0.39
Buffer assembly	Cushion rubber^[44]	$1.35 × 103$	–	0.50

Table 8

Fig. 17

Fig. 18

Fig. 19

Fig. 20

Fig. 21

Table 9

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Friction coefficient	Spatial location				Time/ms
Friction coefficient	Center (0%–25%)	Near-center (25%–50%)	Near-edge (50%–75%)	Edge (75%–100%)	Time/ms
0.05	Moderate	Moderate	Low	High	7.5–15.0, 25–30
0.10	Low	Moderate	Moderate	High	5.0–15.0, 25–30
0.15	Low	Moderate	High	High	7.5–15.0, 25–30
0.20	High	Moderate	High	High	7.5–15.0, 25–30
0.25	High	High	High	High	7.5–17.5, 25–30
0.30	High	High	High	High	7.5–17.5, 25–30