细观结构参量对推进剂力学性能影响的数值研究

乌布力艾散•麦麦提图尔荪; 吴艳青; 侯晓; 王宁

doi:10.13801/j.cnki.fhclxb.20210708.001

细观结构参量对推进剂力学性能影响的数值研究

doi: 10.13801/j.cnki.fhclxb.20210708.001

1.
北京理工大学　爆炸科学与技术国家重点实验室，北京 100081
2.
北京理工大学　宇航学院，北京 100081
3.
湖北航天化学技术研究所　航天化学动力技术重点实验室，襄阳 441003

基金项目: 国家自然科学基金(11872119)

详细信息

通讯作者:
吴艳青，博士，教授，博士生导师，研究方向为高能炸药及推进剂细观力学　 E-mail：wuyqing@bit.edu.cn

中图分类号: V512; TB330.1
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出版历程
- 收稿日期: 2021-05-17
- 修回日期: 2021-06-25
- 录用日期: 2021-06-29
- 网络出版日期: 2021-07-08
- 刊出日期: 2022-06-01

Numerical investigations on mesoscopic structure parameters affecting mechanical responses of propellant

1.
State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China
2.
School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
3.
Science and Technology on Aerospace Chemical Power Laboratory, Hubei Institute of Aerospace Chemotechnology, Xiangfan 441003, China

摘要

摘要: 为了更好地理解并预测复合固体推进剂组分、界面对其宏观力学性能的影响，在细观层次上建立了考虑界面和颗粒形貌的代表性体积单元(Representative volume elements，RVE)计算模型，通过引入内聚力模型(Cohesive zone model，CZM)研究了界面刚度、强度及最大失效位移对推进剂力学性能的影响，并对比分析了颗粒形貌与界面对其力学性能的贡献。研究结果表明：界面刚度为0.004~400 MPa/mm时，推进剂初始模量从0.67 MPa提升到3.67 MPa；界面强度从0.05 MPa提高至30 MPa时，推进剂拉伸强度从0.15 MPa 提高到了0.76 MPa，即界面刚度增加对推进剂初始模量的提高有限，而界面强度对其拉伸强度的提高非常显著；然而，较高的界面强度可能导致细观结构出现“损伤局部化”，从而降低延伸率。相对于界面对推进剂实际力学性能的提升，颗粒级配、形状的作用显得较小，说明界面是决定推进剂拉伸性能的主要因素之一。最后基于以上分析结果，对另一种推进剂在不同应力下的蠕变性能进行了预测，发现蠕变断裂时间的对数与恒定应力满足线性关系。
- 复合固体推进剂 /
- 界面脱湿 /
- 细观模型 /
- 蠕变 /
- 内聚力模型
Abstract: A computational representative volume element (RVE) framework considering interface, as well as particle morphology, was adopted to provide a better understanding and prediction of the existing links between the behaviors of contents, interface and the macroscopic mechanical responses of composite solid propellants. A cohesive zone model (CZM) was taken into account to study the significance of interface stiffness, strength and critical displacement, along with the relative contribution of particle morphology and interface, on the macroscopic mechanical properties of the propellant. Results indicate that the initial modulus of propellant increases from 0.67 MPa to 3.67 MPa as the interface stiffness varies between 0.004 MPa/mm and 400 MPa/mm, while the tensile strength of propellant increases from 0.15 MPa to 0.76 MPa when the interface strength changes from 0.05 MPa to 30 MPa, which implies that an increase in the interface stiffness has a limited improvement over the initial modulus of the propellant. In comparison, the interface strength improves its tensile strength remarkably. However, higher interfacial strength may lead to “damage localization” in the microstructure, thus reducing the elongation of propellant. The different behaviors observed on macroscopic view are rather due to interface than to the morphology of particles; all of the results exhibit that the interface is one of the major determining factors affecting the tensile properties of the propellant. Finally, based on the previous analyses, the creep behaviors of another propellant were predicted under various stress levels. It is found that the logarithm of creep rupture time is linear with constant stress.
- composite solid propellants /
- interface debonding /
- mesoscale model /
- creep behavior /
- cohesive zone model

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图 1 由3个参数定义的纯法向(或纯切向)双线性内聚力单元模型示意图

Figure 1. Traction-separation behavior of a cohesive element for a purely normal (or purely tangent) displacement defined by 3 parameters

T_c—Interface strength; ${\delta _{\rm{0}} }$—Displacement at damage initiation; ${\delta _{\rm{f}} } $—Interface critical displacement; K—Interface stiffness; $\varGamma $—Interface fracture energy

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图 2 网格映射法随机颗粒填充原理示意图

Figure 2. Schematic diagram of mesh projection particles randomly dispersed in a matrix

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图 3 考虑小颗粒填充的HTPB推进剂细观模型(76.1vol%)

Figure 3. Packing microstructure of HTPB propellant with small particles (76.1vol%)

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图 4 黏合剂及复合基体在准静态单轴加载-卸载应力-应变曲线

Figure 4. Stress-strain curves of binder and composite matrix under quasi-static loading-unloading

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图 5 HTPB推进剂应力-应变曲线对比 (◆表示计算不收敛)

Figure 5. Comparison between experimental and numerical stress-strain curves of HTPB propellant (◆Indicates the simulation divergence)

S—Area; S₀—Initial area

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图 6 HTPB推进剂代表性体积单元(RVE)变形及应力分布

Figure 6. Deformation and stress distribution in representative volume element (RVE) of HTPB propellant

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图 7 HTPB推进剂初始模量随界面刚度K变化预估

Figure 7. Estimates of the Young's modulus of HTPB propellant with different interface stiffness

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图 8 HTPB推进剂拉伸强度随界面强度变化预估

Figure 8. Tensile strength estimation of HTPB propellant with different interface strength

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图 9 HTPB推进剂拉伸强度随界面最大失效位移的变化

Figure 9. Tensile strength estimation of HTPB propellant with various interface critical displacement

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图 10 不同界面断裂能条件下界面强度与最大失效位移对HTPB推进剂拉伸强度的影响

Figure 10. Interface strength and critical displacement contributions to the tensile strength of HTPB propellant under various interface fracture energies

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图 11 界面强度与HTPB推进剂强度的关系

Figure 11. Strength of HTPB propellant versus interface strength

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图 12 不同颗粒粒径分布HTPB推进剂RVE模型应力-应变曲线

Figure 12. Stress-strain responses of mesoscale RVE models of HTPB propellant with various particle size distributions

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图 13 HTPB推进剂中颗粒多边形随机填充流程示意图

Figure 13. Process of generation of a microstructure of HTPB propellant filled with randomly dispersed polygons

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图 14 HTPB推进剂中圆形或多边形颗粒填充细观模型应力-应变曲线

Figure 14. Stress-strain responses of HTPB propellant microstructures filled with disks or polygons

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图 15 HTPB推进剂应变为0.14及0.25时圆形(上)及多边形(下)细观模型界面损伤演化

Figure 15. Interface damage evolution of HTPB propellant RVEs filled with disks (top) and polygon (bottom) at 0.14 and 0.25 strain

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图 16 不同应力载荷水平下NEPE推进剂蠕变性能预测

Figure 16. Prediction of creep behaviors of NEPE propellant under various constant stress

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图 17 硝酸酯增塑聚醚 (NEPE)推进剂恒定应力与对数时间关系

Figure 17. Constant stress versus logarithmic time of nitrate ester plasticized polyether (NEPE) propellant

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表 1 丁羟 (HTPB)黏合剂材料模型参数

Table 1. Material parameters for the constitutive phases of hydroxyl-terminated polybutadiene (HTPB) binder

Parameter	${\mu _1}$/MPa	${\alpha _1}$	${\mu _2}$/MPa	${\alpha _2}$	${\mu _3}$/MPa	${\alpha _3}$	$\nu $
Value	0.0202	−1.584	0.0246	−1.584	0.0189	1.9898	0.495
Parameter	${m_\infty }$	${m_1}$	${m_2}$	${m_3}$	${\tau _1}$/s	${\tau _2}$/s	${\tau _3}$/s
Value	0.556	0.064	0.184	0.1966	614.53	24.5	37.03
Notes: ${\mu _1},{\mu _2},{\mu _3},{\alpha _1},{\alpha _2},{\alpha _3}$—Ogden constants; ${m_\infty },{m_1},{m_2},{m_3}$—Prony series; ${\tau _1},{\tau _2},{\tau _3}$—Relaxation times; $\nu $—Poisson’s ratio.

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表 2 颗粒力学模型参数

Table 2. Particles mechanical properties

Particle	Elastic modulus/GPa	Poisson’s ratio
AP	19.5	0.25
Al	68.3	0.33
Note: AP—Ammonium perchlorate.

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表 3 HTPB推进剂基本组分及尺寸

Table 3. Components and dimensions of HTPB propellant

Component	HTPB	AP(Large particles)	AP(Small particles)	Al	Auxiliary
Density/(g·cm^-³)	0.9	1.95	1.95	2.70	−
Mass fraction/wt%	8	36.92	32.58	18.5	4
Volume fraction/vol%	23.9	34	30	12.1	Treated as binder
Diameter/μm	−	100-300	20	10	−

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表 4 HTPB推进剂力学性能随界面性能变化关系

Table 4. Mechanical responses of HTPB propellant varying with interface properties

Order	Matrix	1	2	3	4	5	6	7	8	9	10	11	Without interface
Condition		With T_c=0.45 MPa, ${\delta _{\rm{f}}}$=0.06 mm
Interface stiffness K/(MPa·mm^-1)		0.004	4	20	40	100	200	300	400	4000	10000	16000	19500
Initial modulus E/MPa	0.28	0.67	1.12	1.98	2.50	3.10	3.45	3.60	3.67	3.90	3.96	3.97	4.00
Condition		With K=400 MPa/mm, ${\delta _{\rm{f}}}$=0.06 mm
Interface strength/MPa		0.05	0.1	0.2	0.3	0.45	0.6	0.75	1	2	3	30	300
Tensile strength/MPa		0.15	0.17	0.21	0.27	0.34	0.40	0.46	0.55	0.73	0.76	0.764	0.83

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表 5 不同HTPB推进剂RVE颗粒粒径分布

Table 5. Particle size distributions of different RVEs of HTPB propellant

Type	S₀	S₁		S₂
Diameter/μm	100-300	100	200	200	300
Volume fraction/vol%	34	10	24	10	24
Sum of particles	48	80		25
Notes: S₁—Model with minimum mean particle size; S₂—Model with the largest average particle size.

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表 6 NEPE推进剂在不同应力下蠕变模拟结果

Table 6. Simulation results of creep of NEPE propellant at various stress

Time/s	Creep strain	Constant stress/MPa
Exceeded 60000	0.063	0.05
Exceeded 60000	0.128	0.1
56903	0.489	0.3
36772	0.540	0.4
18297	0.553	0.5
5203	0.728	0.6
1624	0.630	0.7

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参考文献(42)

[1]	孟红磊, 鞠玉涛. 含损伤非线性粘弹性本构模型及数值仿真应用[J]. 固体火箭技术, 2012, 35(6):764-768. MENG Honglei, JU Yutao. Nonlinear viscoelastic equation with cumulative damage and its application on numerical simulation[J]. Journal of solid Rocket Technology,2012,35(6):764-768(in Chinese).
[2]	HUI Li, JIN Shengxu, XIONG Chen, et al. Experimental investigation and modeling the compressive behavior of NEPE propellant under confining pressure[J]. Propellants, Explosives, Pyrotechnics,2021,46:1-14. doi: 10.1002/prep.202180101
[3]	封涛, 许进升, 范兴贵, 等. 考虑初始缺陷的HTPB推进剂粘超弹本构模型[J]. 含能材料, 2018, 26(4):316-322. doi: 10.11943/j.issn.1006-9941.2018.04.005 FENG Tao, XU Jinsheng, FAN Xinggui, et al. Visco-hyperelastic constitutive model of HTPB propellant considering initial defects[J]. Chinese Journal of Energetic Materials,2018,26(4):316-322(in Chinese). doi: 10.11943/j.issn.1006-9941.2018.04.005
[4]	CUI H, SHEN Z, LI H. A new constitutive equation for solid propellant with the effects of aging and viscoelastic Poisson's ratio[J]. Meccanica,2018,53:2393-2410.
[5]	WANG Z, QIANG H, WANG T, et al. A thermo-visco-hyperelastic constitutive model of HTPB propellant with damage at intermediate strain rates[J]. Mechanics of Time-Dependent Materials,2018,22:291-314.
[6]	MA H, SHEN Z, LI D. A viscoelastic constitutive model of composite propellant considering dewetting and strain-rate and its implementation[J]. Propellants Explosives Pyrotechnics,2019,44:759-768. doi: 10.1002/prep.201800264
[7]	XU F. Micromechanics approach to the study of constitutive response and fracture of solid propellant materials[D]. Illinois: University of Illinois at Urbana-Campaign, 2007.
[8]	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
[9]	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
[10]	YUN K S, PARK J B, JUNG G D, et al. Viscoelastic constitutive modeling of solid propellant with damage[J]. International Journal of Solids and Structures,2016,80:118-127. doi: 10.1016/j.ijsolstr.2015.10.028
[11]	XU J, CHEN X, WANG H, 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
[12]	LEI M, WANG J, CHENG J, et al. A constitutive model of the solid propellants considering the interface strength and dewetting[J]. Composites Science and Technology,2020,185:107893.1-107893.9.
[13]	RAE P J, GOLDREIN H T, PALMER S, et al. Quasi-static studies of the deformation and failure of -HMX based polymer bonded explosives[J]. Proceedings Mathematical Physical & Engineering Sciences,2002,458(2019):743-762.
[14]	常武军. 复合固体推进剂细观损伤及其数值仿真研究[D]. 南京: 南京理工大学, 2013. CHANG W J. Research on microstructural damage and its numerical simulation method for composite solid propellant[D]. Nanjing: Nanjing University of Science and Technology, 2013(in Chinese).
[15]	LI G, WANG Y, JIang A, et al. Micromechanical investigation of debonding processes in composite solid propellants[J]. Propellants Explosives Pyrotechnics,2017,43(7):642-649.
[16]	ZHI S J, BING S, ZHANG J W. Multiscale modeling of heterogeneous propellants from particle packing to grain failure using a surface-based cohesive approach[J]. Acta Mechanica Sinica,2012,28(3):746-759. doi: 10.1007/s10409-012-0058-y
[17]	封涛, 郑健, 许进升, 等. 复合固体推进剂细观结构建模及脱黏过程数值模拟[J]. 航空动力学报, 2018, 33(1):223-231. FENG Tao, ZHENG Jian, XU Jinsheng, et al. Mesoscopic structure modeling and numerical simulation of debonding process of composite solid propellants[J]. Journal of Aerospace Power,2018,33(1):223-231(in Chinese).
[18]	CHANG W, JU Y, HAN B, et al. Numerical simulation of particle/matrix interface failure in composite propellant[J]. Journal of China Ordnance,2012,8(3):146-153.
[19]	FRANCQUEVILLE F D, DIANI J, GILORMINI P, et al. Use of a micromechanical approach to understand the mechanical behavior of solid propellants[J]. Mechanics of Materials,2021,153:103656. doi: 10.1016/j.mechmat.2020.103656
[20]	FRANCQUEVILLE F D, GILORMINI P, DIANI J, et al. comparison of the finite strain macroscopic behavior and local damage of a soft matrix highly reinforced by spherical or polyhedral particles[J]. European Journal of Mechanics-A/Solids,2020,84:104070. doi: 10.1016/j.euromechsol.2020.104070
[21]	TAN H, LIU C, HUANG Y, et al. The cohesive law for the particle/matrix interfaces in high explosives[J]. Journal of the Mechanics and Physics of Solids,2005,53(8):1892-1917. doi: 10.1016/j.jmps.2005.01.009
[22]	李高春, 邢耀国, 戢治洪, 等. 复合固体推进剂细观界面脱粘有限元分析[J]. 复合材料学报, 2011, 28(3):229-235. LI G C, XING Y G, JI Z H, et al. Finite element analysis of microscale interfacial debonding in composite solid propellants[J]. Acta Materiae Compositae Sinica,2011,28(3):229-235(in Chinese).
[23]	RUIZE H, CHANDRA P, VIKAS T, et al. Experimentally-validated mesoscale modeling of the coupled mechanical-thermal response of AP–HTPB energetic material under dynamic loading[J]. International Journal of Fracture,2016,203:277-298.
[24]	PRAKASH C, GUNDUZ I E, OSKAY C, et al. Effect of interface chemistry and strain rate on particle-matrix delamination in an energetic material[J]. Engineering Fracture Mechanics,2018,191:46-64.
[25]	PRAKASH C. Effect of interface chemical composition on the high strain rate dependent mechanical behavior of an energetic material[D]. West Lafayette: Purdue University, 2019.
[26]	YILMAZER U, FARRIS R J. Finite element formulation for modeling particle debonding in reinforced elastomers subjected to finite deformations[J]. Journal of Applied Polymer Science,1983,28:3280-3369. doi: 10.1016/j.cma.2006.06.008
[27]	NGO D, PARK K, PAULINO G H, et al. On the constitutive relation of materials with microstructure using a potential-based cohesive model for interface interaction[J]. Engineering Fracture Mechanics,2010,77(7):1153-1174. doi: 10.1016/j.engfracmech.2010.01.007
[28]	TOULEMONDE P A, DIANI J, GILORMINI P, et al. On the account of a cohesive interface for modeling the behavior until break of highly filled elastomers[J]. Mechanics of Materials,2016,93:124-133.
[29]	LÓPEZ R, SALAZAR A, RODRÍGUEZ J. Fatigue crack propagation behaviour of carboxyl-terminated polybutadiene solid rocket propellants[J]. International Jour-nal of Fracture,2020,223(1):3-15.
[30]	GAO Y F, BOWER A F. A simple technique for avoiding convergence problems in finite element simulations of crack nucleation and growth on cohesive interfaces[J]. Modelling & Simulation in Materials Science & Engineering,2004,12(3):453.
[31]	FRANCQUEVILLE F D, GILORMINI P, DIANI J, et al. Relationship between local damage and macroscopic response of soft materials highly reinforced by monodispersed particles[J]. Mechanics of Materials,2020,146:103408. doi: 10.1016/j.mechmat.2020.103408
[32]	FRANCQUEVILLE F D, GILORMINI P, DIANI J. Representative volume elements for the simulation of isotropic composites highly filled with monosized spheres[J]. International Journal of Solids and Structures,2019,158:277-286. doi: 10.1016/j.ijsolstr.2018.09.013
[33]	张镇国, 侯晓, 郜婕, 等. 一种高颗粒填充率丁羟推进剂二维细观模型生成方法[J]. 复合材料学报, 2019, 36(10):2302-2307. ZHANG Z G, HOU X, GAO J, etal. A method of generating two-dimensional mesoscopic model for hydroxyl-terminated polybutadiene propellant with high particle volume fraction[J]. Acta Materiae Compositae Sinica,2019,36(10):2302-2307(in Chinese).
[34]	MORALEDA J, SEGURADO J, LLORCA J. Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach[J]. Journal of the Mechanics and Physics of Solids,2009,57(9):1596-1613. doi: 10.1016/j.jmps.2009.05.007
[35]	乌布力艾散·麦麦提图尔荪, 葛超, 董永香, 等. 基于Al/PTFE真实细观特性统计模型的宏观力学性能模拟[J]. 复合材料学报, 2016, 33(11):2528-2536. MAIMAITITUERSUN W, GE C, DONG Y X, et al. Simulation on mechanical properties of Al/PTFE based on mesoscopic statistical model[J]. Acta Materiae Compositae Sinica,2016,33(11):2528-2536(in Chinese).
[36]	GE Chao, DONG Yongxiang, MAIMAITITUERSUN Wubuliaisan, et al. Microscale simulation on mechanical properties of Al/PTFE composite based on real microstructures[J]. Materials,2016,9(7):590. doi: 10.3390/ma9070590
[37]	SONG W, LIU H, NING J. Tensile property and crack propagation behavior of tungsten alloys[J]. International Journal of Modern Physics B,2011,24(11):1475-1492.
[38]	SMIT R J M, BREKELMANS W A M, MEIJER H E H. Prediction of the mechanical behaviour of nonlinear heterogeneous systems by multi-level finite element modeling[J]. Computer Methods in Applied Mechanics and Engineering,1988,155(2):181-192.
[39]	LI S, SITNIKOVA E. Representative volume elements and unit cells—Concepts, theory, applications and implementation[M]. Amsterdam: Elsevier, 2019.
[40]	XIA Z, ZHANG Y, ELLYIN F. A unified periodical boundary conditions for representative volume elements of compo-sites and applications[J]. International Journal of Solids and Structures,2003,40:1907-1921. doi: 10.1016/S0020-7683(03)00024-6
[41]	TAN H, HUANG Y, LIU C, et al. The uniaxial tension of particulate composite materials with nonlinear interface debonding[J]. International Journal of Solids and Structures,2007,44(6):1809-1822. doi: 10.1016/j.ijsolstr.2006.09.004
[42]	赵玖玲, 强洪夫. 复合固体推进剂宏细观损伤机理[M]. 北京: 中国宇航出版社, 2014. ZHAO J L, QIANG H F. Macroscopic and microscopic damage mechanism of composite solid propellant[M]. Beijing: China Aerospace Publishing House, 2014(in Chinese).