未硫化橡胶黏弹塑性本构模型及有限元实现

doi:10.16183/j.cnki.jsjtu.2022.022

上海交通大学学报 ›› 2023, Vol. 57 ›› Issue (8): 1086-1095.doi: 10.16183/j.cnki.jsjtu.2022.022

所属专题：《上海交通大学学报》2023年“材料科学与工程”专题

未硫化橡胶黏弹塑性本构模型及有限元实现

王银龙¹^,², 李钊³, 李子然¹^,²(), 汪洋¹^,²

1.中国科学技术大学近代力学系,合肥 230027
2.中国科学技术大学中国科学院材料力学行为和设计重点实验室,合肥 230027
3.武汉第二船舶设计研究所, 武汉 430205

收稿日期:2022-01-24 修回日期:2022-04-07 接受日期:2022-05-05 出版日期:2023-08-28 发布日期:2023-08-31
通讯作者: 李子然,副教授;E-mail: lzr@ustc.edu.cn.
作者简介:王银龙(1995-),博士生,从事橡胶、轮胎力学研究.
基金资助:
国家自然科学基金资助项目(11902229);中国科学院战略性先导科技专项(C类)(XDC06030200)

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

WANG Yinlong¹^,², LI Zhao³, LI Ziran¹^,²(), WANG Yang¹^,²

1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
2. CAS Key Laboratory of Mechanical Behavior and Design of Materials, University of Science and Technology of China, Hefei 230027, China
3. Wuhan Second Ship Design and Research Institute, Wuhan 430205, China

Received:2022-01-24 Revised:2022-04-07 Accepted:2022-05-05 Online:2023-08-28 Published:2023-08-31

摘要/Abstract

摘要：

为了探究未硫化橡胶的拉伸力学性能,开展了未硫化橡胶不同应变率下的单向拉伸及循环加卸载实验.结果表明,未硫化橡胶具有较为复杂的非线性黏弹塑性力学行为,随着应变率增加,应力水平明显上升,迟滞效应增加,残余应变降低,应力软化增强.为了表征其力学响应,提出了一个三网络(TN)黏弹塑性本构模型,该模型由一个基于八链模型的超弹性网络和两个基于Bergstr?m-Boyce流动模型的非线性黏塑性网络构成,同时考虑了材料的Mullins损伤软化等变形特征,能够较好地表征未硫化橡胶的非线性力学行为.最后,依托于Abaqus有限元软件,完成了本构模型材料子程序的开发,对未硫化橡胶多段松弛加卸载和轮胎胎面胶压入模具过程开展了数值仿真,验证了TN模型的数值有效性以及在复杂变形模式下的数值稳定性.

关键词: 未硫化橡胶, 拉伸实验, 本构模型, 黏弹塑性, 有限元实现

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

中图分类号:

TQ330.1
O39

王银龙, 李钊, 李子然, 汪洋. 未硫化橡胶黏弹塑性本构模型及有限元实现[J]. 上海交通大学学报, 2023, 57(8): 1086-1095.

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.

图/表 10

图1

图2

图3

图4

表1

三网络模型拟合参数

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	—

表1

图5

图6

图7

图8

图9

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未硫化橡胶黏弹塑性本构模型及有限元实现

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

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