HYPERELASTIC CONSTITUTIVE MODEL FOR SHORT FIBER REINFORCED EPDM INHIBITOR FILM
-
摘要: 短纤维增强三元乙丙橡胶（EPDM）包覆薄膜用于一种新型缠绕包覆工艺，主要解决复杂构型自由装填药柱外表面可靠性包覆问题.为了描述其在固体火箭发动机工作过程中产生的大变形、非线性和各向异性等力学行为，根据纤维增强复合材料连续介质力学理论，提出了各向异性超弹性本构模型.该模型中单位体积的应变能函数被解耦成两部分：表征各向同性的橡胶基体应变能和表征各向异性的纤维拉伸应变能，通过引入纤维方向对纤维应变能进行修正，给出了通过单轴拉伸、偏轴拉伸实验数据获取模型参数的具体方法.研究结果表明，该模型能够很好地预测材料在纤维方向0°~45°时的各向异性力学特性，并将预测结果与实验数据对比，误差在5%以下.所建立的各向异性超弹性本构模型准确性高、易于实现数值开发，在一定程度上能够为固体火箭发动机的装药结构完整性分析提供理论依据.Abstract: Short fiber reinforced EPDM inhibitor film is used for a new winding coating process, which is mainly to solve the reliable problem in free loading solid rocket grains with complicated structure. Based on fiber reinforced continuum mechanics theory, a simple anisotropic hyperelastic constitutive model is proposed to describe their large deformation, highly non-linear and strongly anisotorpic mechanical behaviors in the work process of solid rocket motor. The unitvolume strain energy function is decomposed into two parts:representing the strain energy from isotropic rubber matrix and anisotropic fiber tensile deformation. By introducing fiber direction to modify fiber strain energy, the specific method of obtaining model parameters by uniaxial and off-axis tension data is presented.Results show that it is highly suitable to characterize their anisotropic mechanical behaviors in the fiber direction from 0° to 45° and the error is less than 5% compared with experimental data. It is concluded that the proposed model is highly accurate and easy to achieve numerical development, which can provide theoretical basis for the structural integrity analysis of solid rocket motor.
-
Key words:
- EPDM /
- inhibitor /
- anisotropic /
- hyperelastic /
- constitutive model
-
图 5 短纤维增强EPDM单轴拉伸变形
Figure 5. Uniaxial tensile deformation of short fiber reinforced EPDM
-
[1] 汪建丽, 王红丽, 熊治荣等.三元乙丙橡胶绝热层在固体火箭发动机中的应用.宇航材料工艺, 2009, 39(2):12-14 http://www.cnki.com.cn/Article/CJFDTOTAL-YHCG200902002.htmWang Jianli, Wang Hongli, Xiong Zhirong, et al. EPDM rubber insulation applied in solid rocket motor. Aerospace Materials and Technology, 2009, 39(2):12-14(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YHCG200902002.htm [2] 许进升, 鞠玉涛, 周长省等.模数对药柱热应力的影响.弹道学报, 2011(3):74-78 http://www.cnki.com.cn/Article/CJFDTOTAL-DDXB201103016.htmXu Jinsheng, Ju Yutao, Zhou Changsheng, et al. Influence of modulus on thermal stress of grain. Journal of Ballistics, 2011(3):74-78(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-DDXB201103016.htm [3] 赵付彬. 短纤维增强氯丁橡胶基复合材料结构与力学性能研究. [硕士论文]. 青岛: 青岛科技大学, 2012Zhao Fubin. Study on the structure and mechanical properties of short fiber reinforced rubber composite.[Master Thesis]. Qingdao:Qingdao University of Science and Technology, 2012(in Chinese) [4] 董金平, 张志强.基于横观各向同性超弹性理论的短纤维增强橡胶本构模型的建立与应用.计算力学学报, 2016, 33(2):231-237 http://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201602014.htmDong Jinping, Zhang Zhiqiang. Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory. Chinese Journal of Computa-tional Mechanics, 2016, 33(2):231-237(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-JSJG201602014.htm [5] 张少实.复合材料与粘弹性力学.第二版.北京:机械工业出版社, 2005Zhang Shaoshi. Composite Materials and Viscoelastic Mechanics. Second edition. Beijing:China Machine Press, 2005(in Chinese) [6] Begley MR, Creton C, Mcmeeking RM. The elastostatic plane strain mode Ⅰ crack tip stress and displacement fields in a generalized linear neo-Hookean elastomer. Journal of the Mechanics & Physics of Solids, 2015, 84:21-38 https://www.researchgate.net/publication/280974594_The_elastostatic_plane_strain_mode_I_crack_tip_stress_and_displacement_Fields_in_a_generalized_linear_neo-Hookean_elastomer [7] Yeoh OH. Some forms of the strain energy function for rubber. Rubber Chemistry & Technology, 1993, 66(5):754-771 https://www.researchgate.net/publication/271350510_Some_Forms_of_the_Strain_Energy_Function_for_Rubber [8] Holzapfel GA, Gasser TC. A viscoelastic model for fiber-reinforced composites at finite strains:Continuum basis, computational aspects and applications. Computer Methods in Applied Mechanics & Engineering, 2001, 190(34):4379-4403 https://www.researchgate.net/publication/222835905_A_viscoelastic_model_for_fiber-reinforced_composites_at_finite_stains_Continuum_basis_computational_aspects_and_applications [9] Ehret AE. On a molecular statistical basis for Ogden's model for rubber elasticity. Journal of the Mechanics & Physics of Solids, 2015, 78:249-268 https://www.researchgate.net/publication/272200496_On_a_molecular_statistical_basis_for_Ogden's_model_of_rubber_elasticity [10] Pierce DM, Trobin W, Raya JG, et al. DT-MRI based computation of collagen fiber deformation in human articular cartilage:a feasibility study. Annals of Biomedical Engineering, 2010, 38(7):2447-2463 doi: 10.1007/s10439-010-9990-9 [11] Peng XQ, Guo ZY, Moran B. An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus. Journal of Applied Mechanics, 2006, 73(5):815-824 doi: 10.1115/1.2069987 [12] 郭国栋, 彭雄奇, 赵宁.一种考虑剪切作用的各向异性超弹性本构模型.力学学报, 2013, 45(3):451-455 http://lxxb.cstam.org.cn/CN/abstract/abstract143942.shtmlGuo Guodong, Peng Xiongqi, Zhao Ning. An anisotropic hyperelastic constitutive model with shear interaction for cord-rubber tire composites. Chinese Journal of Theoretical and Applied Mechanics, 2013, 45(3):451-455(in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract143942.shtml [13] 孙书蕾, 毛建良, 彭雄奇.考虑纤维弯曲刚度的橡胶-帘线复合材料各向异性超弹性本构模型.应用数学和力学, 2014, 35(5):471-477 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201405001.htmSun Shulei, Mao Jianliang, Peng Xiongqi. An anisotropic hyperelastic constitutive model with fiber bending stiffness for cordrubber composites. Applied Mathematics and Mechanics, 2014, 35(5):471-477(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201405001.htm [14] 张必超, 彭雄奇, 黄小双.考虑双拉耦合的复合材料编织物非正交本构模型.应用数学和力学, 2016, 37(3):227-234 http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201603001.htmZhang Bichao, Peng Xiongqi, Huang Xiaoshuang. A nonorthogonal constitutive model for woven composites involving biaxial tension coupling. Applied Mathematics and Mechanics, 2016, 37(3):227-234(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-YYSX201603001.htm [15] 黄小双, 彭雄奇, 张必超.帘线/橡胶复合材料各向异性黏-超弹性本构模型.力学学报, 2016, 48(1):140-145 http://lxxb.cstam.org.cn/CN/abstract/abstract145565.shtmlHuang Xiaoshuang, Peng Xiongqi, Zhang Bichao. An anisotropic visco-hyperelastic constitutive model for cord-rubber composites. Chinese Journal of Theoretical and Applied Mechanics, 2016, 48(1):140-145(in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract145565.shtml [16] 张中水, 陈雄, 周清春, 等.EPDM绝热层的粘超弹本构模型.固体火箭技术, 2015(2):273-277 http://www.cnki.com.cn/Article/CJFDTOTAL-GTHJ201502023.htmZhang Zhongshui, Chen Xiong, Zhou Qing chun, et al. A visco-hyperelastic constitutive model for EPDM insulation. Journal of Solid Rocket Technology, 2015(2):273-277(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-GTHJ201502023.htm [17] 余家泉, 陈雄, 周长省等. EPDM薄膜橡胶包覆材料的粘-超弹本构模型研究.推进技术, 2015(3):465-470 http://www.cnki.com.cn/Article/CJFDTOTAL-TJJS201503021.htmYu Jiaquan, Chen Xiong, Zhou Changsheng, et al. Visco-hyperelastic constitutive model for filmy EPDM inhibitor. Journal of Propulsion Technology, 2015(3):465-470(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-TJJS201503021.htm [18] Jing J, Xu JS, Zhang ZS, et al. Rate-dependent compressive behavior of EPDM insulation:experimental and constitutive analysis. Mechanics of Materials, 2016, 96:30-38 doi: 10.1016/j.mechmat.2016.02.003 [19] 杨晓红, 许进升, 孙俊丽等.三元乙丙材料粘超弹本构模型研究.兵工学报, 2014, 35(8):1205-1209 http://www.cnki.com.cn/Article/CJFDTOTAL-BIGO201408011.htmYang Xiaohong, Xu Jinsheng, Sun Junli, et al. Research on visco-hyperelastic constitutive model of EPDM. Acta Armamentarii, 2014, 35(8):1205-1209(in Chinese) http://www.cnki.com.cn/Article/CJFDTOTAL-BIGO201408011.htm [20] Spencer AJM. Continuum theory of the mechanics of fiberreinforced composites. Journal of Applied Mechanics, 1984, 53(1):233 [21] Ciarlrtta P, Izzo I, Micera S, et al. Stiffening by fiber reinforcement in soft materials:a hyperelastic theory at large strains and its application. Journal of the Mechanical Behavior of Biomedical Materials, 2011, 4(7):1359-1368 doi: 10.1016/j.jmbbm.2011.05.006 [22] Horgan CO. The remarkable Gent constitutive model for hyperelastic materials. International Journal of Non-Linear Mechanics, 2015, 68:9-16 doi: 10.1016/j.ijnonlinmec.2014.05.010 [23] 王宇, 彭雄奇.腰椎椎间植骨融合有限元分析.力学学报, 2011, 43(2):381-389 http://lxxb.cstam.org.cn/CN/abstract/abstract141997.shtmlWang Yu, Peng Xiongqi. Finite element analysis on lumbar interbody fusion. Chinese Journal of Theoretical and Applied Mechanics, 2011, 43(2):381-389(in Chinese) http://lxxb.cstam.org.cn/CN/abstract/abstract141997.shtml [24] Seki W, Fukahori Y, Iseda Y, et al. A large deformation finite element analysis for multilayer elastomeric bearings. Rubber Chemistry and Technology, 1987, 60(5):856-869 doi: 10.5254/1.3536160 [25] Holzapfel GA. Nonlinear solid mechanics:A continuum approach for engineering science. Meccanica, 2002, 37(4):489-490 http://www.academia.edu/25107340/Nonlinear_Solid_Mechanics_A_Continuum_Approach_for_Engineering_Science [26] Zhurov AI, Evans SL, Holt CA, et al. A nonlinear compressible transversely-isotropic viscohyperelastic constitutive model of the periodontal ligament//Proceedings of ASME, 2008 International Mechanical Engineering Congress and Exposition, 2008:707-719 [27] Merodio J, Ogden RW. Mechanical response of fiber reinforced incompressible non-linearly elastic solids. International Journal of Non-Linear Mechanics, 2005, 40(s 2-3):213-227 https://www.researchgate.net/publication/40704018_Mechanical_response_of_fiber-reinforced_incompressible_non-linearly_elastic_solids [28] Qiu GY, Pence TJ. Loss of ellipticity in plane deformation of a simple directionally reinforced incompressible nonlinearly elastic solid. Journal of Elasticity, 1997, 49(1):31-63 doi: 10.1023/A:1007441804480 [29] Brown LW, Smith LM. A simple transversely isotropic hyperelastic constitutive model suitable for finite element analysis of fiber reinforced elastomers. Journal of Engineering Materials and Technology, 2011, 133(2):307-314 https://www.researchgate.net/publication/274438882_A_Simple_Transversely_Isotropic_Hyperelastic_Constitutive_Model_Suitable_for_Finite_Element_Analysis_of_Fiber_Reinforced_Elastomers [30] Jiang Y, Wang Y, Peng X. A visco-hyperelastic constitutive model for human spine ligaments. Cell Biochemistry and Biophysics, 2015, 71(2):1147-1156 doi: 10.1007/s12013-014-0322-9 [31] Peng XQ, Guo ZY, Du TL, et al. A simple anisotropic hyperelastic constitutive model for textile fabrics with application to forming simulation. Composites, 2013, 52(52):275-281 https://www.researchgate.net/publication/257546035_A_simple_anisotropic_hyperelastic_constitutive_model_for_textile_fabrics_with_application_to_forming_simulation -
下载:
点击查看大图
图(10)
计量
- 文章访问数: 1397
- HTML全文浏览量: 168
- PDF下载量: 587
- 被引次数: 0
