目的 针对航空透明件在高速冲击载荷下失效预测困难的问题,构建能够准确描述聚甲基丙烯酸甲酯（PMMA）高速冲击的失效模型,为透明件的抗冲击设计与安全评估提供理论依据。方法 基于分离式霍普金森压杆（SHPB）实验获取PMMA在高应变率下的应力-应变曲线,并据此标定DSGZ本构模型参数;在Abaqus中通过VUMAT子程序实现本构关系,并引入等效链段伸长量与静水应力耦合的失效判据（λfmax=1.155,pc=80 MPa）描述材料失效行为。进一步开展直径8 mm钢球弹丸正入射冲击PMMA平板实验,获取破坏形貌、弹丸残余速度及损伤直径等关键响应指标,并建立对应的仿真模型,对不同冲击工况下的侵彻过程进行模拟验证。结果 SHPB仿真结果表明,DSGZ本构模型能够较好地再现PMMA在高应变率下的动态力学响应;弹丸侵彻仿真结果表明,所建立的损伤模型在破坏形貌、损伤区域分布及失效模式方面与实验观测具有良好的一致性。在定量指标上,弹丸残余速度的平均相对误差为6.06%,损伤直径的平均相对误差为2.16%。结论 所提出的联合等效链段伸长量与静水应力的失效判据能够有效描述PMMA在高速冲击条件下的失效行为。
Abstract
To address the difficulty in predicting the failure of aerospace transparent components under high-velocity impact loading, the work aims to establish a failure model capable of accurately describing the high-velocity impact behavior of polymethyl methacrylate (PMMA), providing a theoretical basis for the impact-resistant design and safety evaluation of transparent structures. Split Hopkinson Pressure Bar (SHPB) experiments were conducted to obtain the stress-strain curves of PMMA at high strain rates, based on which the parameters of the DSGZ constitutive model were calibrated. The constitutive relation was implemented in Abaqus through a VUMAT subroutine, and a failure criterion coupling the equivalent chain stretch with hydrostatic pressure (λfmax=1.155, pc=80 MPa) was introduced to describe material failure. Furthermore, normal impact experiments of an 8 mm diameter steel spherical projectile on PMMA plates were carried out to obtain key response indicators, including failure morphology, residual projectile velocity, and damage diameter. Corresponding numerical simulation models were established to reproduce the penetration process under different impact conditions. The SHPB simulation results indicated that the DSGZ constitutive model could effectively reproduce the dynamic mechanical response of PMMA at high strain rates. The projectile penetration simulations showed good agreement with the experimental observations in terms of failure morphology, damage distribution, and failure modes. Quantitatively, the average relative errors of the residual projectile velocity and the damage diameter were 6.06% and 2.16%, respectively. The proposed failure criterion, coupling the equivalent chain stretch and hydrostatic pressure, is capable of effectively describing the failure behavior of PMMA under high-velocity impact conditions.
关键词
PMMA /
弹丸侵彻 /
SHPB /
失效模型 /
有限元仿真
Key words
PMMA /
projectile penetration /
SHPB /
failure model /
finite element simulation
{{custom_sec.title}}
{{custom_sec.title}}
{{custom_sec.content}}
参考文献
[1] WANG X, CHEN S R, XU J J, et al.Comparative Study on the Water Droplet Erosion Behavior between Stretched and Casted Aeronautical PMMA[J]. International Journal of Impact Engineering, 2024, 183: 104806.
[2] WANG X, XU J J, CHEN S R, et al.Damage Behavior and Assessment of Aeronautical PMMA Subjected to High-Velocity Water-Jet Impact[J]. Wear, 2023, 534: 205145.
[3] KANG C X, PENG L, LI Y T, et al.Mechanical Performance of Structural Polymethyl Methacrylate Joints at Different Temperatures[J]. Polymers, 2024, 16(23): 3243.
[4] GAO G, HUANG Y, ZENG S Q, et al.Transparent and Hard TiO2/Au Electromagnetic Shielding Antireflection Coatings on Aircraft Canopy PMMA Organic Glass[J]. Applied Surface Science, 2024, 658: 159830.
[5] 芮涵钦, 崔浩, 于泽宗, 等. 航空透明件边缘连接结构的失效行为分析[J/OL]. 材料工程,1-13(2025-03- 19)[2026-09-09]. https://link.cnki.net/urliid/11.1800.tb.20250319.1032.002.
RUI H Q, CUI H, YU Z Z, et al. Failure Behavior Analysis Of Edge Attachment Structure Of Aviation Transparency[J/OL]. Journal of Materials Engineering, 1-13 (2025-03-19) [2026-09-09]. https://link.cnki.net/urliid/11.1800.tb.20250319.1032.002.
[6] LI Z, LAMBROS J.Strain Rate Effects on the Thermomechanical Behavior of Polymers[J]. International Journal of Solids and Structures, 2001, 38(20): 3549-3562.
[7] SIVIOUR C R.High Strain Rate Characterization of Polymers[C]//AIP Conference Proceedings, 2017, 1793: 060029.
[8] DU Q H, LIU F Y, LEI Q.Numerical Simulation of PMMA Impact Based on the J-C Constitutive and Damage Models under Hydrostatic Pressure Loading[J]. Applied Sciences, 2023, 13(15): 8640.
[9] REZAEI M, AREZOO B, ZIAEI-RAD S.Redesign an Aircraft Windshield to Improve Its Mechanical Resistance Against Simultaneous Bird Impacts[J]. International Journal of Impact Engineering, 2024, 184: 104811.
[10] SUBRAMANIAM A, V B, B C, et al. Novel Ultra High Impact Strength Light Weight Transparent Polycarbonate Laminated Composite for Aviation and Defence[J]. Journal of Polymer Research, 2023, 30(11): 413.
[11] LIU Z X, SHENG J C, DU B, et al.Investigation on the Effects of Temperature and Strain Rate on Dynamic Tensile Fragmentation of PMMA Using a Novel Electromagnetic-Driven Composite Expansion Ring Test Setup[J]. Engineering Fracture Mechanics, 2025, 329: 111628.
[12] GEARING B P, ANAND L.On Modeling the Deformation and Fracture Response of Glassy Polymers Due to Shear-Yielding and Crazing[J]. International Journal of Solids and Structures, 2004, 41(11/12): 3125-3150.
[13] WANG J, XU Y J, ZHANG W H.Finite Element Simulation of PMMA Aircraft Windshield Against Bird Strike by Using a Rate and Temperature Dependent Nonlinear Viscoelastic Constitutive Model[J]. Composite Structures, 2014, 108: 21-30.
[14] BOYCE M C, PARKS D M, ARGON A S.Large Inelastic Deformation of Glassy Polymers. Part I: Rate Dependent Constitutive Model[J]. Mechanics of Materials, 1988, 7(1): 15-33.
[15] 苗春贺, 袁良柱, 陆建华, 等. 聚甲基丙烯酸甲酯的冲击破碎扩散特性[J]. 物理学报, 2022, 71(21): 292-300.
MIAO C H, YUAN L Z, LU J H, et al.Deformation Evolution and Diffusion Characteristics of Polymethyl Methacrylate under Impact Loading[J]. Acta Physica Sinica, 2022, 71(21): 292-300.
[16] CAO K, WANG Y, WANG Y.Experimental Investigation and Modeling of the Tension Behavior of Polycarbonate with Temperature Effects from Low to High Strain Rates[J]. International Journal of Solids and Structures, 2014, 51(13): 2539-2548.
[17] ZAÏRI F, NAÏT-ABDELAZIZ M, GLOAGUEN J M, et al. Modelling of the Elasto-Viscoplastic Damage Behaviour of Glassy Polymers[J]. International Journal of Plasticity, 2008, 24(6): 945-965.
[18] G’SELL C, JONAS J J. Determination of the Plastic Behaviour of Solid Polymers at Constant True Strain Rate[J]. Journal of Materials Science, 1979, 14(3): 583-591.
[19] G’SELL C, ALY-HELAL N A, JONAS J J. Effect of Stress Triaxiality on Neck Propagation during the Tensile Stretching of Solid Polymers[J]. Journal of Materials Science, 1983, 18(6): 1731-1742.
[20] JOHNSON G R, COOK W H.A Constitutive Model and Data for Metals Subjected to Large Strains, High Strain Rates and High Temperatures[C]//Proceedings of the 7th International Symposium on Ballistics, 1983: 541-547.
[21] DUAN Y, SAIGAL A, GREIF R, et al.A Uniform Phenomenological Constitutive Model for Glassy and Semicrystalline Polymers[J]. Polymer Engineering & Science, 2001, 41(8): 1322-1328.
[22] DUAN Y, SAIGAL A, GREIF R, et al.Analysis of Multiaxial Impact Behavior of Polymers[J]. Polymer Engineering & Science, 2002, 42(2): 395-402.
[23] DUAN Y, SAIGAL A, GREIF R, et al.Impact Behavior and Modeling of Engineering Polymers[J]. Polymer Engineering & Science, 2003, 43(1): 112-124.
[24] BERGSTRÖM J S, RIMNAC C M, KURTZ S M. Molecular Chain Stretch Is a Multiaxial Failure Criterion for Conventional and Highly Crosslinked UHMWPE[J]. Journal of Orthopaedic Research, 2005, 23(2): 367-375.
[25] DOROGOY A, RITTEL D, BRILL A.Experimentation and Modeling of Inclined Ballistic Impact in Thick Polycarbonate Plates[J]. International Journal of Impact Engineering, 2011, 38(10): 804-814.
[26] TORRES J P, FRONTINI P M. Mechanics of Polycarbonate in Biaxial Impact Loading[J]. International Journal of Solids and Structures, 2016, 85/86: 125-133.
PDF(11603 KB)
渝公网安备 50010702501719号 渝ICP备15012534号-4
