Cluster Analysis of Correlation Between Rubber Carbon Black Filling and Yeoh Model Parameters

doi:10.19894/j.issn.1000-0518.200323

Chinese Journal of Applied Chemistry ›› 2021, Vol. 38 ›› Issue (6): 675-684.DOI: 10.19894/j.issn.1000-0518.200323

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Cluster Analysis of Correlation Between Rubber Carbon Black Filling and Yeoh Model Parameters

DU Kang^1,2, ZHOU Heng-Wei¹, DING Ming-Ming^1,2*, YE Feng^2*, SHI Tong-Fei^1,2

¹Xinjiang Laboratory of Phase Transitions and Microstructures in Condensed Matter Physics, College of Physical Science and Technology, Yili Normal University, Yining 835000, China
²State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun 130022, China

Received:2020-10-29 Revised:2021-01-07 Published:2021-06-01 Online:2021-08-01

Abstract

Abstract: In order to explore the correlation between carbon black filling amount and Yeoh model parameters, this paper proposes a classification method of different filling amounts by cluster analysis. Based on the three-parameter Yeoh model, the uniaxial tensile stress-strain curves of carbon black filled rubbers are fitted, and three parameters C₁₀, C₂₀ and C₃₀ are obtained. The cluster method is used to classify the parameters unsupervised, and the number of clusters is set at 3~8 to explore the influence of different categories on the results. The results show that the accuracy of all categories is above 60%, and the filling fraction is the most uniform when clustering into five categories, and the accuracy rate is up to 84%. The feasibility of using cluster analysis to classify different carbon black filling amounts is verified, and the parameters of the constitutive model can be predicted and the corresponding stress-strain curve can be obtained when the carbon black content is fixed.

Key words: Carbon black-extended rubber, Superelasticity, Constitutive model, Cluster analysis

CLC Number:

O631

DU Kang, ZHOU Heng-Wei, DING Ming-Ming, YE Feng, SHI Tong-Fei. Cluster Analysis of Correlation Between Rubber Carbon Black Filling and Yeoh Model Parameters[J]. Chinese Journal of Applied Chemistry, 2021, 38(6): 675-684.

References

[1] 丁芳, 张欢, 丁明明, 等. 聚合物弹性体材料应力-应变关系的理论研究[J]. 高分子学报, 2019, 50(12): 1357-1366.
DING F, ZHANG H, DING M M, et al. Theoretical models for stress-strain curves of elastomer materials[J]. Acta Polym Sin, 2019, 50(12): 1357-1366.
[2] 裴雨飞. 金砖国家橡胶工业发展现状—巴西篇[J]. 中国橡胶, 2019, 35(2): 28-31.
PEI Y F. The development status of the rubber industry in the BRICS countries-Brazil [J]. China Rubber, 2019, 35(2): 28-31.
[3] OGDEN O H. Non-linear elastic deformations[J]. Anal Bound Elem, 1984, 1(2): 119.
[4] BOYCE M C, ARRUDA E M. Constitutive models of rubber elasticity: a review[J]. Rubber Chem Technol, 2012, 73(3): 504-523.
[5] 贺梦达. 某款橡胶阻尼式扭转减振器结构设计与优化[D].厦门: 厦门理工学院, 2017.
HE M D. Structural design and optimization of a rubber-type torsional vibration damper[D]. Xiamen: Xiamen University of Technology, 2017.
[6] 李晓芳, 杨晓翔. 橡胶材料的超弹性本构模型[J]. 弹性体, 2005, 1: 50-58.
LI X F, YANG X X. A review of elastic constitutive model for rubber materials[J]. Elastomerics, 2005, 1: 50-58.
[7] JHA V, HON A A. THOMAS A G, et al. Modeling of the effect of rigid fillers on the stiffness of rubbers[J]. Appl Polym Sci, 2008, 107(4): 2572-2577.
[8] FLORY P J, REHNER J. Statistical mechanics of cross-linked polymernetworks II. swelling[J]. J Chem Phys, 1943, 11: 512-520.
[9] AMIN A F, ALAM M S, OKUI Y. An improvedhyperelasticity relation in modeling viscoelasticity response of natural and high damping rubbers in compression: experiments, parameter identification and numerical verification[J]. Mech Mater, 2002, 34(2): 75-95.
[10] BROWN B R P. Physical testing of rubber[M]. London: Elsevier Applied Science Publishers, 1986.
[11] OGDEN R W. Large deformation isotropic elasticity:on the correlation of theory and experiment for compressible rubberlike solids[J]. Proc Royal Soc A, 1972, 96(328): 567-583.
[12] 于海富. 橡胶材料本构方程的研究[D]. 北京: 北京化工大学, 2017.
YU H F. The research of visco-hyperelastic constitutive model for rubber materials[D]. Beijing: Beijing University of Chemical Technology, 2017.
[13] 李庆, 杨晓翔. N330炭黑增强天然橡胶材料力学性能的实验研究[J]. 实验力学, 2014, 29(1): 42-50.
LI Q, YANG X X. Experimental study of mechanical properties of N330 carbon black reinforced natural rubber[J]. Exp Mech, 2014, 29(1): 42-50.
[14] 胡小玲. 炭黑填充橡胶黏超弹性力学行为的宏细观研究[D]. 湘潭: 湘潭大学, 2013.
HU X L. Micro- and macro-viscohyperelastic behavior of carbon black filled rubbers[D]. Xiangtan: Xiangtan University, 2013.
[15] 明杰婷. 橡胶材料粘弹性本构模型的研究及其在胎面橡胶块上的应用[D]. 长春: 吉林大学, 2016.
MING J T. The Research of viscoelastic constitutive model for rubber material and its application in tread block of tires[D]. Changchun: Jilin University, 2016.
[16] RIVLIN R S. Large elastic deformation of isotropic materials IV, further development of general theory[J]. Philos Trans Royal Soc A, 1948, 241(835): 379-397.
[17] ELTAYEB N S M, NASIR R M. Effect of soft carbon black ontribology of deproteinised and polyisoprene rubbers[J]. Wear, 2007, 262(3/4): 350-361.
[18] YEOH O H. Some forms of the strain energy function for rubber[J]. Rubber Chem Technol, 2012, 66(5): 754-771.
[19] GREGORY M J. The stress/strainbehaviour of filled rubbers at moderate strains[J]. Plast Rubber Compos Process Appl, 1979, 4: 184-188.
[20] KAWABATA S. Strain energy density functions of rubber vulcanizates from biaxial extension[J]. Adv Polym Sci, 1977, 24: 90-124.
[21] YAMASHITA Y, KAWABATA S. Approximated form of the strain energy-density function of carbon-black filled rubbers for industrial applications[J]. J Soc Rubber Ind Jpn, 1992, 65(9): 517-528.
[22] YEOH O H. Characterization of elastic properties of carbon-black-filled rubbe rvulcanizates[J]. Rubber Chem Technol, 2012, 63(5): 792-805.
[23] 杨晓红, 周长省, 常武军, 等. 丁羟包覆层力学特性及本构模型研究[J]. 弹道学报, 2014, 26(4): 94-97.
YANG X H, ZHOU C S, CHANG W J, et al. Research on mechanical properties and constitutive model of HTPB rubber inhibitor[J]. J Ballist, 2014, 26(4): 94-97.
[24] CHEN H L, CHUANG K T, CHEN M S. Ondata labeling for clustering categorical data[J]. IEEE Trans Knowl Data Eng, 2008, 20(11): 1458-1472.
[25] 杨俊闯, 赵超. K-Means聚类算法研究综述[J]. 计算机工程与应用, 2019, 55(23): 7-14.
YANG J C, ZHAO C. Survey on K-means clustering algorithm[J]. Comput Eng Appl, 2019, 55(23): 7-14.
[26] HUANG X, YE Y, ZHANG H. Extensions of kmeans-type algorithms: a new clustering framework by integrating intracluster compactness and intercluster separation[J]. IEEE Trans Neural Networks Learn Sys, 2014, 25(8): 1433-1446.
[27] RALAMBONDRAINY H. A conceptual version of the K-means algorithm[J]. Pattern Recognit Lett, 1995, 16(11): 1147-1157.
[28] SIM K, GOPALKRISHNAN V, ZIMEK A, et al. A survey on enhanced subspace clustering[J]. Data Min Knowl Discovery, 2013, 26(2): 332-397.
[29] 杨成鹏, 矫桂琼, 王波. 2D-C/SIC复合材料的单轴拉伸力学行为及其强度[J]. 力学学报, 2011,43(2): 330-337.
YANG C P, JIAO G Q, WANG B.Uniaxial tensile stress-strain behavior and strength of plain woven C/SIC composite[J]. Chinese J Theor Appl Mech, 2011, 43(2): 330-337.
[30] 王晓明, 郑东, 吴荣兴, 等. 类橡胶材料变形直到破坏的显式本构模型[J]. 力学季刊, 2019, 40(2):34-46.
WANG X M, ZHENG D, WU R X, et al. Explicit constitutive model of rubber-like materials up to failure[J]. Chinese Q Mech, 2019, 40(2): 252-264.
[31] TANG J, TUNG M A, LELIEVRE J, et al. Stress-strain relationships for gellan gels in tension, compression and torsion[J]. J Food Eng, 1997, 31(4): 511-529.
[32] 段晓畅, 孙杰, 刘迎彬, 等. 基于SVM算法的TATB基PBX单轴准静态应力应变关系[J]. 含能材料, 2019, 27(5): 64-70.
DUAN X C, SUN J, LIU Y B, et al.Uniaxial quasi-static stress-strain relationship of TATB-based PBX based on SVM algorithm[J]. J Energ Mater, 2019, 27(5): 410-416.
[33] HAMED G R, PARK B H. The mechanism of carbon black reinforcement of SBR and NR vulcanizates[J]. Rubber Chem Technol, 1999, 72(5): 946-959.
[34] XU Z, JERRAMS S, GUO H,et al. Influence of graphene oxide and carbon nanotubes on the fatigue properties of silica/styrene-butadiene rubber composites under uniaxial and multiaxial cyclic loading[J]. Int J Fatigue, 2020, 131: 105388.
[35] 胡小玲, 刘秀, 李明, 等. 炭黑填充橡胶超弹性力学性能的三维有限元模拟[J]. 固体力学学报, 2013(S1): 117-121.
HU X L, LIU X, LI M, et al. 3D finite element modeling of thehyperelastic mechanical behavior of CB-filled rubber[J]. Acta Mech Solid Sin, 2013(S1): 117-121.
[36] MDARHRI A, BROSSEAU C, CARMONA F. Microwave dielectric properties of carbon black filled polymers under uniaxial tension[J]. J Appl Phys, 2007, 101(8): 21-248.
[37] ZHANG H, SCHOLZ A K, DE C J, et al. Nanocavitation in carbon black filled styrene-butadiene rubber under tension detected by real time small angle X-ray scattering[J]. Macromolecules, 2012, 45(3): 1529-1543.
[38] REY L D. New phenomenological behavior laws for rubbers and thermoplastic elastomers[J]. Eur J Mech A-Solid, 1999, 18(6): 1027-1043.
[39] KAWABATA S, MATSUDA M, TEI K,et al. Experimental survey of the strain energy density function of isoprene rubber vulcanizate[J]. Macromolecules, 1981, 14(1): 154-162.
[40] STARKOVA O, ANISKEVICH A. Poisson's ratio and the incompressibility relation for various strain measures with the example of asilica-filled SBR rubber in uniaxial tension tests[J]. Polym Test, 2010, 29(3): 310-318.
[41] ALIMARDANI M, RAZZAGHI-KASHANI M, KARIMI R, et al. Contribution of mechanical engagement and energetic interaction in reinforcement of SBR-silane-treated silica composites[J]. Rubber Chem Technol, 2016, 89(2): 292-305.
[42] FUJIKAWA M, MAEDA N, YAMABE J,et al. Performance evaluation of hyperelastic models for carbon-black-filled SBR vulcanizates[J]. Rubber Chem Technol, 2016, 89(2): 292-305.
[43] TUICHIEV S, TABAROV S K, GINZBURG B M. Effect of C₆₀ fullerene additions on the mechanical properties of a polybutadiene-styrene raw rubber[J]. Tech Phys, 2008, 53(7): 956-958.

Cluster Analysis of Correlation Between Rubber Carbon Black Filling and Yeoh Model Parameters

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