基于细观结构的复合固体推进剂含损伤黏弹性本构模型

doi:10.12382/bgxb.2022.0747

摘要/Abstract

摘要：

复合固体推进剂的宏观力学性能与其细观组分及损伤密切相关,基于复合固体推进剂变形过程中细观结构的演化,开发复合固体推进剂含孔洞损伤的宏细观本构模型。该模型考虑了推进剂温度和应变率的相关性,并能够描述推进剂拉伸和压缩状态下不同的力学响应。通过不同温度和不同应变率下的拉伸和压缩试验,验证本构模型的有效性。基于有限元分析软件提供的用户材料子程序接口UMAT,对非线性黏弹性本构模型进行二次开发,并应用于低温点火工况下药柱结构完整性分析,结果表明药柱在低温点火条件下安全系数为2.56,结构完整性满足要求。与基于Prony级数的线性黏弹性本构模型进行对比分析,表明新建立的本构模型能够更准确地进行复合固体推进剂药柱的结构分析。

关键词: 复合固体推进剂, 非线性黏弹性, 本构模型, 低温点火, 结构完整性

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

中图分类号:

V435

王贵军, 吴艳青, 侯晓, 黄风雷. 基于细观结构的复合固体推进剂含损伤黏弹性本构模型[J]. 兵工学报, 2023, 44(12): 3696-3706.

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.

图/表 20

图1 固体推进剂典型细观结构

Fig.1 Typical solid propellant mesostructure

图2 本构模型参数拟合

Fig.2 Parameter fitting of constitutive model

图3 拉伸情况下本构模型预测结果与试验数据对比

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

图4 推进剂SEM图像

Fig.4 SEM image of propellant

图5 压缩情况下本构模型预测结果与试验数据对比

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

表1 本构模型参数

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

表1 本构模型参数

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

图6 温度转换因子与温度关系

Fig.6 Temperature conversion factor vs. temperature

图7 推进剂293.15K下的应力松弛曲线

Fig.7 Stress relaxation curve of propellant at 293.15K

图8 拉伸状态下两种模型对比

Fig.8 Comparison of two models under tension

图9 压缩状态下两种模型对比

Fig.9 Comparison of two models under compression

图10 有限元网格模型

Fig.10 Mesh of finite element model

表2 材料性能参数

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

图11 加载条件

Fig.11 Load conditions

图12 温度-内压联合载荷下药柱应力场

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

图13 温度-内压联合载荷下药柱应变场

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

图14 内孔表面应变沿L1线变化

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

图15 位置A处应变随时间变化

Fig.15 Strain vs. time at position A

图16 温度载荷下位置A处应变率随时间变化

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

图17 内压载荷下位置A处应变率随时间变化曲线

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

图18 孔隙率沿L1线变化曲线

Fig.18 Variation curve of porosity along L1 line

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