Constitutive Model of Flexible Composites for Rubber Track

doi:10.3969/j.issn.1000-1093.2020.09.003

Abstract

Abstract: The performance of rubber track is one of the key factors affecting the service life of tracked walking mechanism. In order to characterize the mechanical behavior of rubber track with large deformation, nonlinearity and anisotropy in the driving process, the test study of uniaxial tension of rubber-cord composites at different off-axis angles is carried out. The influence of cord off-axis angle on the mechanical properties of the composites is analyzed. A constitutive model involving interaction between rubber and cords is established. Based on the particle swarm optimization and Newton iteration method, an optimization algorithm for parameters fitting is proposed. The model parameters are obtained from the uniaxial tension data with cord off-axis angles of 90°, 0° and 15°. The uniaxial tension data with cord off-axis angles of 45° and 60° are predicted. The results show that the coefficients of determination, R², are 0.992 8 and 0.982 9, respectively. The proposed model is validated by comparing the numerical results with the uniaxial tension data. The maximum simulation error is about 10.86%, which further verifies the reliability and adaptability of the proposed model to finite element analysis.

Key words: rubbertrack, constitutivemodel, fiberreinforcedcomposite, anisotropy, hyperelastic

CLC Number:

TJ810.3⁺3

ZHAO Zihan, MU Xihui, DU Fengpo. Constitutive Model of Flexible Composites for Rubber Track[J]. Acta Armamentarii, 2020, 41(9): 1719-1726.

References 28

［1］	黄燕滨, 周科可, 巴国召, 等.沿海两栖车辆腐蚀现状及腐蚀综合控制技术[J].兵工学报,2016,37(7):1291-1298.HUANG Y B, ZHOU K K, BA G Z, et al. The corrosion status of amphibious vehicles along the coast and integrated corrosion control technology[J]. Acta Armamentarii, 2016,37(7):1291-1298.（in Chinese）
[2]	LEVIN V A, ZINGERMAN K M, VERSHININ A V, et al. Numerical analysis of effective mechanical properties of rubber-cord composites under finite strains[J]. Composite Structures, 2015,131:25-36.
[3]	REN J, ZHONG J L. The accurate prediction method of tension modulus for nylon cord/rubber composite material[J]. Applied Mechanics and Materials, 2014,575:115-120.
[4]	CHO J, EE S, JEONG H Y. Finite element analysis of a tire using an equivalent cord model[J]. Finite Elements in Analysis and Design, 2015,105:26-32.
[5]	陈洪月, 张坤, 李恩东. 钢丝绳芯橡胶输送带本构模型参数辨识与变化规律分析[J]. 振动与冲击, 2017,36(14):234-238.CHEN H Y, ZHANG K, LI E D. Parameter identification and analysis on the constitutive model of wire rope rubber conveyor belts[J]. Journal of Vibration and Shock, 2017,36(14):234-238.（in Chinese）
[6]	SPENCER A J M, SOLDATOS K P. Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness[J]. International Journal of Non-Linear Mechanics, 2007,42(2):355-368.
[7]	PENG X, GUO G, ZHAO N. An anisotropic hyperelastic constitutive model with shear interaction for cord-rubber composites[J]. Composites Science & Technology, 2013,78:69-74.
[8]	YANG H, YAO X F, YAN H, et al. Anisotropic hyper-viscoelastic behaviors of fabric reinforced rubber composites[J].Composite Structures, 2017,187:116-121.
[9]	YANG H, YAO X F, KE Y C, et al. Constitutive behaviors and mechanical characterizations of fabric reinforced rubber composites[J]. Composite Structures, 2016,152:117-123.
[10]	谈炳东, 许进升, 贾云飞, 等. 短纤维增强EPDM包覆薄膜超弹性本构模型[J]. 力学学报, 2017,49(2):317-323.TAN B D, XU J S, JIA Y F, et al. Hyperelastic constitutive model for short fiber rerinforced EPDM inhibitor film[J]. Chinese Journal of Theoretical and Applied Mecha- nics, 2017,49(2): 317-323.（in Chinese）
[11]	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[J]. 力学学报, 2016,48(1):140-145.HUANG X S, PENG X Q, ZHANG B C. An anisotropic visco-hyperelastic constitutive model for cord-rubber composites[J]. Chinese Journal of Theoretical and Applied Mechanics, 2016,48(1): 140-145.（in Chinese）
[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[J]. 力学学报, 2013,45(3):451-455.GUO G D, PENG X Q, ZHAO N. An anisotropic hyperelastic constitutive model with shear interaction for cord-rubber tire composites[J]. Chinese Journal of Theoretical and Applied Mecha-nics, 2013,45(3):451-455.（in Chinese）
[13]	刘海健, 崔海涛, 张宏建, 等.粒子分离器鼓包柔性复合材料的本构模型研究[J]. 推进技术,2019,40(8):1869-1875.LIU H J, CUI H T, ZHANG H J, et al. A constitutive model of flexible composites used in bump of particle separator[J].Journal of Propulsion Technology, 2019,40(8):1869-1875.（in Chinese）
[14]	PIOU D, PHELY O. Endless flexible track with reinforcing layers for all-terrain vehicles: US 7083242B2[P]. 2006-08-01.
[15]	FUJITA Y, MATSUO S. Rubber crawler having excellent straight driving property: US 7325888[P]. 2008-02-05.
[16]	MATSUO S. Structure of coreless crawler: US 7641292[P]. 2010-01-05.
[17]	FUKUSHIMA T, INOUE E, MITSUOKA M, et al. A simple rubber crawler model for studying fluctuation in crawler tension[J]. Engineering in Agriculture, Environment and Food, 2018,11(3):122-126.
[18]	葛晓雯, 侯捷建, 王立海.集材机可更换三角形履带转向动力学仿真分析[J]. 系统仿真学报,2017,29(2):360-367.GE X W, HOU J J, WANG L H. Steering dynamics simulation analysis of replaceable triangular track of skidder[J]. Journal of System Simulation, 2017,29(2):360-367.（in Chinese）
[19]	张滔,戴瑜,刘少军,等.深海履带式集矿机多体动力学建模与行走性能仿真分析[J]. 机械工程学报,2015,51(6):173-180. ZHANG T, DAI Y, LIU S J, et al. Multi-body dynamic modeling and mobility simulation analysis of deep ocean tracked miner[J]. Journal of Mechanical Engineering, 2015,51(6):173-180.（in Chinese）
[20]	PENG X Q, GUO Z Y, MORAN B. An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus[J]. Journal of Applied Mechanics, 2006,73(5):815-824.
[21]	钱胜, 陆益民, 杨咸启,等. 橡胶材料超弹性本构模型选取及参数确定概述[J]. 橡胶科技, 2018,16(5):5-10.QIAN S, LU Y M, YANG X Q, et al. Overview of selection and parameter determination for hyperelastic constitutive model of rubber material[J]. Rubber Science and Technology, 2018,16(5): 5-10.（in Chinese）
[22]	HOSSAIN M, STENMANN P. More hyperelastic models for rubber-like materials: consistent tangent operators and comparative study[J].Journal of the Mechanical Behavior of Materials, 2013,22(1/2):27-50.
[23]	胡虹玲, 龚友坤, 彭雄奇, 等.考虑拉剪耦合的二维编织物各向异性超弹性本构模型[J].复合材料学报, 2017,34(6):1388-1393.HU H L, GONG Y K, PENG X Q, et al. An anisotropic hyperelastic constitutive model considering shear-tension coupling for 2-dimensional woven fabrics[J]. Acta Materiae Compositae Sinica, 2017,34(6):1388-1393.（in Chinese）
[24]	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[J]. 应用数学和力学, 2014,35(5):471-477.SUN S L, MAO J L, PENG X Q. An anisotropic hyperelastic constitutive model with fibre bending stiffness for cord-rubber composites[J]. Applied Mathematics and Mechanics, 2014,35(5): 471-477.（in Chinese）
[25]	ISHIKAWA S, TOKUDA A, KOTERA H. Numerical simulation for fibre reinforced rubber[J]. Transactions of the Japan Society of Mechanical Engineers Series A, 2008,74: 543-549.
[26]	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[J]. 计算力学学报, 2016,33(2): 231-237.DONG J P, ZHANG Z Q. Establishment and application of short fiber reinforced rubber constitutive model based on transversely isotropic hyperelastic theory[J]. Chinese Journal of Computational Mechanics, 2016,33(2):231-237.（in Chinese）
[27]	李庆扬, 王能超, 易大义. 数值分析[M]. 北京: 清华大学出版社, 2001.LI Q Y, WANG N C, YI D Y. Numerical analysis[M]. Beijing: Tsinghua University Press, 2001.（in Chinese）
[28]	赵江, 周锐. 基于粒子群优化的再入可达区计算方法研究[J]. 兵工学报, 2015,36(9):1680-1687.ZHAO J, ZHOU R. Landing footprint computation based on particle swarm optimization[J]. Acta Armamentarii, 2015,36(9):1680-1687.（in Chinese）

[1]	LIU Qiang, CHEN Pengwan, SU Jianjun, LI Zhirong, ZHANG Yulei. Tensile Mechanical Properties and Constitutive Model of SiC/polyurea Nanocomposites [J]. Acta Armamentarii, 2021, 42(6): 1238-1249.
[2]	LI Dongwei， MIAO Feichao， ZHANG Xiangrong， XIONG Guosong， ZHOU Lin， ZHAO Shuangshuang. Dynamic Mechanical Properties of an Insensitive DNAN-based Melt-cast Explosive [J]. Acta Armamentarii, 2021, 42(11): 2344-2349.
[3]	YUAN Ye, WANG Liyan, CAO Zhanwei, NIE Chunsheng, NIE Liang, MA Haojun. Experimental Research on the Influence of Ablation Product of Carbon Fiber Reinforced Composite Material on the PlasmaFlow Field Characteristics [J]. Acta Armamentarii, 2020, 41(2): 298-304.
[4]	JI Shiming， QIU Wenbin， ZENG Xi， XI Fengfei， QIU Lei， ZHENG Qianqian， SHI Meng. Analysis of Micromechanical Characteristics of Softness Consolidation Abrasives [J]. Acta Armamentarii, 2019, 40(5): 1068-1076.
[5]	FU Shi-zhong， YANG Guo-lai. A Nonlinear Combined Hardening Model for Residual Stress Analysis of Autofretted Thick-walled Cylinder [J]. Acta Armamentarii, 2018, 39(7): 1277-1283.
[6]	WANG Hong-li, XU Jin-sheng, LIU Zong-kui, TONG Xin, ZHOU Chang-sheng. Research on the Viscoelasticity-viscoplasticity-viscodamage Constitutive Model of Composite Modified Double Base Propellant [J]. Acta Armamentarii, 2018, 39(7): 1308-1315.
[7]	LI Jun-bao, LI Wei-bing, CHENG Wei, WANG Xiao-ming, LI Wen-bin, HONG Xiao-wen. Mechanical Properties and Constitutive Model of Aluminum Powder/Rubber Composites [J]. Acta Armamentarii, 2018, 39(6): 1186-1194.
[8]	LI Dian, HOU Hai-liang, ZHU Xi, CHEN Chang-hai, LI Mao. Study of the Failure Mechanism of Fiber Reinforced Composite Laminates Subjected to Fragment Cluster Penetration and theEquivalent Method for Armor Piercing Ability of Fragment Cluster [J]. Acta Armamentarii, 2018, 39(4): 707-716.
[9]	LI Lin, BAI Bin-sheng, CHENG Ying, MEI Zhi-yong. Research on Nonlinear Analysis Method of a New Flexible Pavement [J]. Acta Armamentarii, 2018, 39(4): 810-815.
[10]	GAO Hua， XIONG Chao， YIN Jun-hui. Experimental and Constitutive Model on Dynamic Compressive Mechanical Properties of Aluminum Foams under RepeatedImpacts [J]. Acta Armamentarii, 2018, 39(12): 2410-2419.
[11]	GAO Yu-bo, ZHANG Wei, LI Da-cheng, YI Chen-hong, TANG Tie-gang. Reversion Analysis of Ceramic Damage Based on Back Propagation Neural Network [J]. Acta Armamentarii, 2018, 39(1): 146-152.
[12]	HE Cheng-long, YANG Jun. Research on Dynamic Response of Rock under Blast Loading and Active Confining Pressure [J]. Acta Armamentarii, 2017, 38(12): 2395-2405.
[13]	YANG Xiao-hong, XU Jin-sheng, SUN Jun-li, HU Shao-qing, ZHOU Chang-sheng. Research on Visco-hyperelastic Constitutive Model of EPDM [J]. Acta Armamentarii, 2014, 35(8): 1205-1209.
[14]	HU Shao-qing， JYU Yu-tao， CHANG Wu-jun， ZHOU Chang-sheng. A Visco-hyperelastic Constitutive Behaviour of NEPE Propellant [J]. Acta Armamentarii, 2013, 34(2): 168-173.
[15]	Li YingLei **, Hu Shisheng, Wei Zhigang,Shi Honggang ,Feng Hongwei *. Dynamic Behavior of Tungsten Alloy Forged with Large Deformation [J]. Acta Armamentarii, 2003, 24(3): 378-380.