Research on the Viscoelastic Constitutive Model of Composite Solid Propellant Containing Damage Based on Mesostructure

doi:10.12382/bgxb.2022.0747

Abstract

Abstract:

The macroscopic mechanical properties of composite solid propellant are inseparably linked to its mesoscopic components and damage. A macro and mesoscopic constitutive model of composite solid propellant with void damage was developed based on the evolution of the mesostructure during the deformation process of composite solid propellants. The model takes into account the dependence of propellant temperature and strain rate, and is able to describe the different mechanical responses of propellant in tension and compression. The validity of the constitutive model is verified by tensile and compressive tests at different temperatures and strain rates. The macro and mesoscopic constitutive model is re-developed based on the user material subroutine interface UMAT provided by the finite element software, and applied to the structural integrity analysis of grain under low temperature ignition conditions, indicating that the safety factor of grain under low-temperature ignition conditions is 2.56, and the structural integrity of grain meets the requirements. Finally, compared with the linear viscoelastic constitutive model based on Prony series, the proposed constitutive model can be used to more accurately analyze the structure of composite solid propellant grains.

Key words: composite solid propellant, nonlinear viscoelasticity, constitutive model, low temperature ignition, structural integrity

CLC Number:

V435

WANG Guijun, WU Yanqing, HOU Xiao, HUANG Fenglei. Research on the Viscoelastic Constitutive Model of Composite Solid Propellant Containing Damage Based on Mesostructure[J]. Acta Armamentarii, 2023, 44(12): 3696-3706.

Figures/Tables 20

Fig.1 Typical solid propellant mesostructure

Fig.2 Parameter fitting of constitutive model

Fig.3 Comparison of the prediction results of constitutive model with the experimental data under tension

Fig.4 SEM image of propellant

Fig.5 Comparison between the prediction results of constitutive model and the experimental data under compression

Table 1 Constitutive model parameters

参数	数值	参数	数值
f₀	0.01	H₀/MPa	0.2
ρ₀	0.715	ε_o	1.0
ρ_N	0.615	n	0.3
s_N	0.5/0.8	R₀	5.0
ε_N	0.2/0.3	m	0
k₀	180.65	σ₀/MPa	10.0
k₁	-4.55	$ε · 0$ /s^-1	1.0
k₂	0.128	A	0.1
k₃	125.42	B	7.5
k₄	-3.11	p	7.0
k₅	0.125	q	1.0

Table 1 Constitutive model parameters

参数	数值	参数	数值
f₀	0.01	H₀/MPa	0.2
ρ₀	0.715	ε_o	1.0
ρ_N	0.615	n	0.3
s_N	0.5/0.8	R₀	5.0
ε_N	0.2/0.3	m	0
k₀	180.65	σ₀/MPa	10.0
k₁	-4.55	$ε · 0$ /s^-1	1.0
k₂	0.128	A	0.1
k₃	125.42	B	7.5
k₄	-3.11	p	7.0
k₅	0.125	q	1.0

Fig.6 Temperature conversion factor vs. temperature

Fig.7 Stress relaxation curve of propellant at 293.15K

Fig.8 Comparison of two models under tension

Fig.9 Comparison of two models under compression

Fig.10 Mesh of finite element model

Table 2 Material performance parameters

参数	壳体	衬层	药柱
密度/(kg·m^-3)	7810	1100	1750
弹性模量/MPa	206840	0.8
泊松比	0.31	0.495
热导率/ (mW·mm^-1·K^-1)	46.88	0.25	0.51
比热容/(mJ·t^-1·K^-1)	531.72×10⁶	1.7×10⁹	1.25×10⁹
热膨胀系数/K^-1	0.11×10^-4	1×10^-4	1.43×10^-4

Fig.11 Load conditions

Fig.12 Stress field of grain under combined temperature-internal pressure load

Fig.13 Strain field of grain under combined temperature-internal pressure load

Fig.14 Variation curve of inner hole surface strain along L1 line

Fig.15 Strain vs. time at position A

Fig.16 Strain rate vs. Time at position A under temperature load

Fig.17 Strain rate vs. time at position A under internal pressure load

Fig.18 Variation curve of porosity along L1 line

References 32

[1]	DOUGLASS H W, COLLINS J H, NOEL J S, et al. Solid propellant grain structural integrity analysis:NASA SP-8073[J]. Washington, DC, US:NASA Space Vehicle Design Criteria (Chemical Propulsion), 1973.
[2]	ZHOU D M, LIU X Y, SUI X, et al. Accelerated aging and structural integrity analysis approach to predict the service life of solid rocket motor[C]//Proceedings of the 51st AIAA/SAE/ASEE Joint Propulsion Conference.Orlando,FL, US:AIAA, 2015: 4240.
[3]	DENG B, TANG G J, SHEN Z B. Structural analysis of solid rocket motor grain with aging and damage effects[J]. Journal of Spacecraft and Rockets, 2015, 52(2): 331-339. doi: 10.2514/1.A32843 URL
[4]	WANG Z J, QIANG H F, WANG T J, et al. A thermovisco-hyperelastic constitutive model of HTPB propellant with damage at intermediate strain rates[J]. Mechanics of Time-Dependent Materials, 2018, 22(3): 291-314. doi: 10.1007/s11043-017-9357-9
[5]	CHYUAN S W. Dynamic analysis of solid propellant grains subjected to ignition pressurization loading[J]. Journal of Sound and Vibration, 2003, 268(3): 465-483. doi: 10.1016/S0022-460X(02)01554-7 URL
[6]	王佳奇, 贺绍飞, 申志彬, 等. 低温点火条件下药柱结构完整性分析与试验[J]. 固体火箭技术, 2019, 42(3):356-360.
	WANG J Q, HE S F, SHEN Z B, et al. Analysis and experiment on grain structural integrity under low temperature ignition[J]. Journal of Sound and Vibration, 2019, 42(3):356-360. (in Chinese)
[7]	WANG C G, TIAN W P. The influence factors of grain integrity under the internal pressure condition in SRM[J]. International Journal of Aerospace Engineering, 2021, 2021:5521455.
[8]	王哲君, 强洪夫, 王广, 等. 固体推进剂力学性能和本构模型的研究进展[J]. 含能材料, 2016, 24(4):403-416.
	WANG Z J, QIANG H F, WANG G, et al. Review on the mechanical properties and constitutive models of solid propellants[J]. Chinese Journal of Energetic Materials, 2016, 24(4):403-416. (in Chinese)
[9]	SCHAPERY R A. Analysis of damage growth in particulate composites using a work potential[J]. Composites Engineering, 1991, 1(3): 167-182. doi: 10.1016/0961-9526(91)90017-M URL
[10]	SCHAPERY R A. Nonlinear viscoelastic and viscoplastic constitutive equations with growing damage[J]. International Journal of Fracture, 1999, 97(1): 33-66. doi: 10.1023/A:1018695329398 URL
[11]	张建彬. 双基推进剂屈服准则及粘弹塑性本构模型研究[D]. 南京: 南京理工大学, 2013.
	ZHANG J B. Study on yield criteria and visco-elastoplastic constitutive model of the double-base propellant[D]. Nanjing: Nanjing University of Science and Technology, 2013. (in Chinese)
[12]	XU J S, CHEN X, WANG H L, et al. Thermo-damage-viscoelastic constitutive model of HTPB composite propellant[J]. International Journal of Solids and Structures, 2014, 51(18): 3209-3217. doi: 10.1016/j.ijsolstr.2014.05.024 URL
[13]	XU J S, HAN L, ZHENG J, et al. Finite element implementation of a thermo-damage-viscoelastic constitutive model for hydroxyl-terminated polybutadiene composite propellant[J]. Mechanics of Time-Dependent Materials, 2017, 21(4): 577-595. doi: 10.1007/s11043-017-9343-2 URL
[14]	MA H, SHEN Z B, LI D K. A viscoelastic constitutive model of composite propellant considering dewetting and strain‐rate and its implementation[J]. Propellants, Explosives, Pyrotechnics, 2019, 44(6): 759-768. doi: 10.1002/prep.v44.6 URL
[15]	ZHANG J F, ZHENG J, CHEN X, et al. A thermovisco-hyperelastic constitutive model of NEPE propellant over a large range of strain rates[J]. Journal of Engineering Materials and Technology, 2014, 136(3): 031002. doi: 10.1115/1.4027291 URL
[16]	YANG L M, SHIM V P W, LIM C T. A visco-hyperelastic approach to modelling the constitutive behaviour of rubber[J]. International Journal of Impact Engineering, 2000, 24(6/7): 545-560. doi: 10.1016/S0734-743X(99)00044-5 URL
[17]	韩龙. 复合固体推进剂细观损伤机理及本构模型研究[D]. 南京: 南京理工大学, 2017.
	HAN L. Research on themesoscopic damage mechanism and nonlinear viscoelastic constitutive model of composite propellant[D]. Nanjing: Nanjing University of Science and Technology, 2017. (in Chinese)
[18]	LI T P, XU J S, HAN J L, et al. Effect of microstructure on micro-mechanical properties of composite solid propellant[J]. Micromachines, 2021, 12(11): 1378. doi: 10.3390/mi12111378 URL
[19]	乌布力艾散·麦麦提图尔荪, 吴艳青,侯晓,王宁.细观结构参量对推进剂力学性能影响的数值研究[J]. 复合材料学报, 2022, 39(6):2949-2961.
	MAIMAITITUERSUN W B L A S, WU Y Q, HOU X, et al. Numerical investigations on mesoscopic structure parameters affecting mechanical responses of propellant[J]. Acta Materiae Compositae Sinica, 2022, 39(6):2949-2961. (in Chinese)
[20]	VAN RAMSHORST M C J, et al.DI BENEDETTO G L, DUVALOIS W, Investigation of the Failure Mechanism of HTPB/AP/Al propellant by In-situ Uniaxial Tensile Experimentation in SEM[J]. Propellants, Explosives, Pyrotechnics, 2016, 41(4): 700-708. doi: 10.1002/prep.v41.4 URL
[21]	HOU Y F, XU J S, ZHOU C S, et al. Microstructural simulations of debonding, nucleation, and crack propagation in an HMX-MDB propellant[J]. Materials & Design, 2021, 207: 109854.
[22]	XU F, ARAVAS N, SOFRONIS P. Constitutive modeling of solid propellant materials with evolving microstructural damage[J]. Journal of the Mechanics and Physics of Solids, 2008, 56(5): 2050-2073. doi: 10.1016/j.jmps.2007.10.013 URL
[23]	HUR J, PARK J B, JUNG G D, et al. Enhancements on a micromechanical constitutive model of solid propellant[J]. International Journal of Solids and Structures, 2016, 87: 110-119. doi: 10.1016/j.ijsolstr.2016.02.025 URL
[24]	韩龙, 许进升, 周长省. 基体特性对HTPB推进剂力学性能的影响[J]. 航空动力学报, 2017, 32(10):2553-2560.
	HAN L, XU J S, ZHOU C S. Effect of matrix material properties on the mechanical behavior of HTPB composite propellant[J]. Journal of Aerospace Power, 2017, 32(10):2553-2560. (in Chinese)
[25]	CHU C C, NEEDLEMAN A. Void nucleation effects in biaxially stretched sheets[J]. Jounal of Engineering Materials and Technology, 1980, 102(3): 249-256.
[26]	李辉, 许进升, 周长省, 等. HTPB推进剂温度相关性失效准则[J]. 含能材料, 2018, 26(9):732-738.
	LI H, XU J S, ZHOU C S, et al. Failure criterion related to temperature for HTPB propellant[J]. Chinese Journal of Energetic Materials, 2018, 26(9):732-738. (in Chinese)
[27]	王鸿丽. 改性双基推进剂含损伤粘弹塑性本构模型及应用研究[D]. 南京: 南京理工大学, 2018.
	WANG H L. Research on visco-Elastic-plastic constitutive model with damage of modified double-base propellant and its application[D]. Nanjing: Nanjing University of Science and Technology, 2018. (in Chinese)
[28]	马赛尔. 复合推进剂高应变率力学性能及本构模型研究[D]. 南京: 南京理工大学, 2017.
	MA S E. Research on the mechanical properties and constitutive model of composite propellant[D]. Nanjing: Nanjing University of Science and Technology, 2017. (in Chinese)
[29]	程吉明. 预应变作用下复合固体推进剂损伤本构及应用研究[D]. 西安: 西北工业大学, 2019.
	CHENG J M. Damage constitutive model of composite solid propellant under prestrain and its application[D]. Xi’an: Northwestern Polytechnical University, 2019. (in Chinese)
[30]	刘梅, 高波, 董新刚, 等. 固体发动机药柱完整性失效的判据[J]. 固体火箭技术, 2018, 41(4):424-427,508.
	LIU M, GAO B, DONG X G, et al. Failure criterion of solid motors at ignition pressurization loading[J]. Journal of Solid Rocket Technology, 2018, 41(4):424-427,508. (in Chinese)
[31]	SHEN Z B, ZHANG L, LI Y F. Structural integrity analysis and experimental investigation for solid rocket motor grain subjected to low temperature ignition[C]//Proceedings of the 2019 7th Asia Conference on Mechanical and Materials Engineerin. Tokyo, Japan: EDP Sciences, 2019, 293: 04005.
[32]	宋仕雄. 低温点火状态下固体发动机药柱结构完整性分析[D]. 西安: 航天动力技术研究院, 2018.
	SONG S X. Structural integrity analysis of solid motor grain under low temperature ignition[D]. Xi’an:The 41st Institute of the Fourth Academy of CASC, 2018. (in Chinese)