A Visco-Elastoplastic Constitutive Model of Uncured Rubber and Its Finite Element Implementation

doi:10.16183/j.cnki.jsjtu.2022.022

Abstract

Abstract:

In order to investigate the mechanical properties of uncured rubber, uniaxial and cyclic tensile experiments are conducted on uncured rubber at different strain rates. From the experimental results, the rate-dependent nonlinear mechanical behaviors of uncured rubber can be clearly observed. With strain rate increasing, the stress level, hysteresis and Mullins effect get enhanced, and the residual strain decreases. To characterize the nonlinear visco-elastoplastic mechanical behaviors of uncured rubber, a three-network (TN) constitutive model that contains a hyperelastic network and two nonlinear viscoplastic networks is proposed. The eight-chain model is used to characterize the hyperelastic behavior while the Bergstr?m-Boyce flow model is applied in the viscoplastic networks to capture the nonlinear viscous flow. The proposed constitutive model is implanted into the finite element software Abaqus with which, the multistep tensile relaxation test is simulated. The simulation result is satisfactorily consistent with experimental results, which verifies the effectiveness of the TN model. Finally, the simplified molding process of a tire tread is simulated, which further verifies the stability of the TN model.

Key words: uncured rubber, tensile experiments, constitutive model, viscoelasticity, finite element implementation

CLC Number:

TQ330.1
O39

WANG Yinlong, LI Zhao, LI Ziran, WANG Yang. A Visco-Elastoplastic Constitutive Model of Uncured Rubber and Its Finite Element Implementation[J]. Journal of Shanghai Jiao Tong University, 2023, 57(8): 1086-1095.

Figures/Tables 10

Fig.1

Fig.2

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Tab.1

Ultimate optimization parameters of NT model

参数名称	参数符号	参数值	参数取值区间
切变模量	G_0B, G_0C /MPa	1.562 2, 0.403 87	>0
链段密度	N_B, N_C	9.610 1	(1, 10)
体积模量	K/MPa	180.656	>0
流动阻力	$τ^B$ , $τ^C$ /MPa	1.311 8, 5.810 4	>0
流动指数	m_B, m_C	2.340 1, 5.610 7	(1, 20)
B、C网络模量缩放因子	α, h	1.254 2, 2.681 4	(1, 10)
A网络模量因子	C₄, C₅, C₆	0.367 4, 17.185 9, 2.292 1	—
A网络模量因子	C₇, C₈, C₉	1.048 1, 0.354 1,-0.052 4	—

Tab.1

Fig.5

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Fig.9

References 32

[1]	MARK J E, ERMAN B, ROLAND C M, et al. The science and technology of rubber[M]. 4th ed. Waltham: Academic Press, 2013: 337-340.
[2]	董义军. 农业子午线轮胎成型胎坯质量缺陷原因分析与解决措施[J]. 轮胎工业, 2021, 41(5): 327-330.
	DONG Yijun. Cause analysis and solutions of green tire quality defects of agricultural radial tire[J]. Tire Industry, 2021, 41(5): 327-330.
[3]	ANDRZEJ W, MICHAL O, SEWERYN K, et al. Characteristics and investigation of selected manufacturing defects of passenger car tires[J]. Transportation Research Procedia, 2019, 40: 119-126. doi: 10.1016/j.trpro.2019.07.020 URL
[4]	KALISKE M, ZOPF C, BRÜGGEMANN C. Experimental characterization and constitutive modeling of the mechanical properties of uncured rubber[J]. Rubber Chemistry and Technology, 2010, 83(1): 1-15. doi: 10.5254/1.3548264 URL
[5]	FENG X J, WEI Y T, LI Z C, et al. Research on nonlinear viscoelastic constitutive model for uncured rubber[J]. Engineering Mechanics, 2016, 33: 212-219.
[6]	DAL H, ZOPF C, KALISKE M. Micro-sphere based viscoplastic constitutive model for uncured green rubber[J]. International Journal of Solids and Structures, 2018, 132-133: 201-217.
[7]	ZOPF C, KALISKE M. Numerical characterisation of uncured elastomers by a neural network based approach[J]. Computers & Structures, 2017, 182: 504-525. doi: 10.1016/j.compstruc.2016.12.012 URL
[8]	ZOPF C, HOQUE S E, KALISKE M. Comparison of approaches to model viscoelasticity based on fractional time derivatives[J]. Computational Materials Science, 2015, 98: 287-296. doi: 10.1016/j.commatsci.2014.11.012 URL
[9]	CHEN L, ZHOU W, ZHOU H, et al. Radial tire construction design method based on finite element simulation[J]. Journal of Donghua University, 2017, 34(03): 150-157.
[10]	王国林, 周伟, 周海超, 等. 子午线轮胎二次法成型过程仿真[J]. 机械设计与制造, 2017(7): 179-182.
	WANG Guolin, ZHOU Wei, ZHOU Haichao, et al. Simulation of the radial tire second-stage building process[J]. Machinery Design & Manufacture, 2017(7): 179-182.
[11]	ZHOU H, WANG G, WANG Y. Wide-base tire-building process and design optimization using finite element analysis[J]. Tire Science and Technology, 2018, 46(4): 242-259. doi: 10.2346/tire.18.460405 URL
[12]	KIM S, BERGER T, KALISKE M. Strain rate-dependent behavior of uncured rubber: Experimental investigation and constitutive modeling[DB/OL]. (2022-01-04)[2022-04-05]. https//doi.org/10.5254/rct.21.78981. doi: https//doi.org/10.5254/rct.21.78981
[13]	LI Z, WANG Y, LI X, et al. Experimental investigation and constitutive modeling of uncured carbon black filled rubber at different strain rates[J]. Polymer Testing, 2019, 75: 117-126. doi: 10.1016/j.polymertesting.2019.02.005 URL
[14]	WANG Y, LI Z, LI X, et al. Effect of the temperature and strain rate on the tension response of uncured rubber: Experiments and modeling[J]. Mechanics of Materials, 2020, 148: 103480. doi: 10.1016/j.mechmat.2020.103480 URL
[15]	GUO L, WANG Y. High-rate tensile behavior of silicone rubber at various temperatures[J]. Rubber Chemistry and Technology, 2020, 93(1): 183-194. doi: 10.5254/rct.19.81562 URL
[16]	魏明杰, 王银龙, 刘敏, 等. 温度影响下炭黑增强橡胶复合材料的循环拉伸力学行为[J]. 实验力学, 2020, 35(6): 1030-1040.
	WEI Mingjie, WANG Yinlong, LIU Min, et al. Temperature effect on the mechanical behavior of carbon black reinforced rubber composites under cyclic tensile loadings[J]. Journal of Experimental Mechanics, 2020, 35(6): 1030-1040.
[17]	GUO Q, ZAÏRI F, GUO X. A thermo-viscoelastic-damage constitutive model for cyclically loaded rubbers. Part I: Model formulation and numerical examples[J]. International Journal of Plasticity, 2018, 101: 106-124. doi: 10.1016/j.ijplas.2017.10.011 URL
[18]	BERGSTRÖM J S. Mechanics of solid polymers: Theory and computational modeling[M]. Norwich: William Andrew Publishing, 2015: 141-150.
[19]	JARRAH H R, ZOLFAGHARIAN A, HEDAYATI R, et al. Nonlinear finite element modelling of thermo-visco-plastic styrene and polyurethane shape memory polymer foams[J]. Actuators, 2021, 10(3): 46. doi: 10.3390/act10030046 URL
[20]	BOYCE M C, WEBER G G, PARKS D M. On the kinematics of finite strain plasticity[J]. Journal of the Mechanics and Physics of Solids, 1989, 37(5): 647-665. doi: 10.1016/0022-5096(89)90033-1 URL
[21]	CARROLL M M. Molecular chain networks and strain energy functions in rubber elasticity[J]. Philosophical Transactions of the Royal Society A, 2019, 377(2144): 20180067.
[22]	MELLY S K, LIU L, LIU Y, et al. A review on material models for isotropic hyperelasticity[J]. International Journal of Mechanical System Dynamics, 2021, 1(1): 71-88. doi: 10.1002/msd2.v1.1 URL
[23]	XIANG Y, ZHONG D, RUDYKH S, et al. A review of physically based and thermodynamically based constitutive models for soft materials[J]. Journal of Applied Mechanics, 2020, 87(11): 110801. doi: 10.1115/1.4047776 URL
[24]	GILLES M, ERWAN V. Comparison of hyperelastic models for rubber-like materials[J]. Rubber Chemistry and Technology, 2006, 79(5): 835-858. doi: 10.5254/1.3547969 URL
[25]	ARRUDA E M, BOYCE M C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials[J]. Journal of the Mechanics and Physics of Solids, 1993, 41(2): 389-412. doi: 10.1016/0022-5096(93)90013-6 URL
[26]	MARCKMANN G, VERRON E, GORENT L, et al. A theory of network alteration for the Mullins effect[J]. Journal of the Mechanics and Physics of Solids, 2002, 50(9): 2011-2028. doi: 10.1016/S0022-5096(01)00136-3 URL
[27]	KHAJEHSAEID H. Development of a network alteration theory for the Mullins-softening of filled elastomers based on the morphology of filler-chain interactions[J]. International Journal of Solids and Structures, 2016, 80: 158-167. doi: 10.1016/j.ijsolstr.2015.10.032 URL
[28]	VYAZOVKIN S, SBIRRAZZUOLI N. Isoconversional kinetic analysis of thermally stimulated processes in polymers[J]. Macromolecular Rapid Communications, 2010, 27(18): 1515-1532. doi: 10.1002/(ISSN)1521-3927 URL
[29]	ROBERTS A P, GARBOCZI E J. Elastic properties of model random three-dimensional open-cell solids[J]. Journal of the Mechanics and Physics of Solids, 2002, 50(1): 33-55. doi: 10.1016/S0022-5096(01)00056-4 URL
[30]	BERGSTRÖM J S. A library of advanced user materials: Version 5.0.0[EB/OL]. (2018-04-17) [2022-04-05]. http//PolyUMod.com/.
[31]	DREHER M L, NAGARAJA S, BERGSTRÖM J S, et al. Development of a flow evolution network model for the stress-strain behavior of poly(L-lactide)[J]. Journal of Biomechanical Engineering, 2017, 139(9): 091002. doi: 10.1115/1.4037071 URL
[32]	TOMAS I, CISILINO A P, FRONTINI P M. Accurate, efficient and robust explicit and implicit integration schemes for the Arruda-Boyce viscoplastic model[J]. Mecnica Computacional, 2008, 14: 1003-1042.