锰铜基阻尼合金广义分数阶Maxwell本构模型

doi:10.3969/j.issn.1000-1093.2021.06.020

摘要/Abstract

摘要： 针对锰铜基阻尼合金简化为线弹性材料、与实际非线性本构关系不符的问题，以M2052锰铜基阻尼合金为研究对象，结合锰铜基阻尼合金高阻尼特性机理，提出一种基于广义分数阶Maxwell模型的三参数本构方程。通过常应变率单轴循环拉伸试验分析验证本构模型的准确性，采用均值系数法拓宽本构模型的实用性，并研究广义分数阶Maxwell模型的拟合性能。结果表明：锰铜基阻尼合金的本构关系具有很强的非线性，应力-应变曲线呈梭型，滞回面积随着最大应变幅值增大而增大；广义分数阶Maxwell模型可以较好地描述M2052阻尼合金应力-应变曲线的非线性和滞回特性，试验拟合均方差在0.468 4~2.651 0之间，确定系数均大于0.992 9；广义分数阶Maxwell模型具有较强的适用性，模型各参数可通过应变幅值拟合确定，不用进行特定试验，较其他黏弹性模型可更好地模拟阻尼合金的非线性特性。

关键词: 锰铜基阻尼合金, 本构关系, 广义分数阶Maxwell模型, 非线性

Abstract: A three-parameter constitutive equation based on the generalized fractional Maxwell model for Mn-Cu damping alloy is proposed. The accuracy of the constitutive model is analyzed and verified by uniaxial cyclic tensile test with constant strain rate. The applicability of the constitutive model is broadened by the mean coefficient method, and the fitting performance of the generalized fractional Maxwell model is studied. The results show that the constitutive relation of the Mn-Cu-based damping alloy has a strong nonlinearity. Its stress-strain curve is like a shuttle, and its hysteresis area increases with the increase in the maximum strain amplitude. The generalized fractal Maxwell model can well describe the nonlinear and hysteresis characteristics of the stress-strain curve of M2052 damping alloy. The mean square deviation of the fitting is between 0.468 4 and 2.651 0, and the coefficients of determination are all greater than 0.992 9. Each parameter of the proposed constitutive model can be determined by strain amplitude without a specific test. The constitutive model can better simulate the nonlinear characteristics of damping alloy compared to viscoelastic models.

Key words: Mn-Cudampingalloy, constructivemodel, generalizedfractionalMaxwellmedol, nonlinea-rity

中图分类号:

TB301.1

朱锐，杨雨迎，毛保全，韩小平，王之千，赵其进. 锰铜基阻尼合金广义分数阶Maxwell本构模型[J]. 兵工学报, 2021, 42(6): 1290-1302.

ZHU Rui, YANG Yuying, MAO Baoquan, HAN Xiaoping, WANG Zhiqian, ZHAO Qijin. Generalized Fractional Maxwell Constitutive Model for Mn-Cu Damping Alloy[J]. Acta Armamentarii, 2021, 42(6): 1290-1302.

参考文献

［1］ MIELCZAREK A, RIEHEMANN W, VOGELGESANG S, et al. Amplitude dependent internal friction of CuAlMn shape memory alloys［J］. Key Engineering Materials, 2006, 319:45-52.
［2］ SAKAGUCHI T, YIN F. Holding temperature dependent variation of damping capacity in a MnCuNiFe damping alloy［J］. Scripta Materialia, 2006, 54(2): 241-246.
［3］卢凤双, 芮永岭, 田宇鹏, 等. M2052高阻尼合金的研究及应用［J］. 金属功能材料, 2013,20(4):43-48.
LU F S, RUI Y L,TIAN Y P, et al. Research and application of M2052 high damping alloys ［J］. Metallic Functional Materials，2013, 20(4)： 43-48. (in Chinese)
［4］谢晋武, 刘文博, 李宁, 等. 枝晶偏析对MnCu合金阻尼性能的影响［J］. 功能材料, 2015, 46(13):13087-13090,13094.
XIE J W, LIU W B, LI N, et al. Effect of dendritic segregation on the damping property of MnCu alloy ［J］. Journal of Functional Materials, 2015, 46(13): 13087-13090,13094. (in Chinese)
［5］邓华铭, 钟志源, 张骥华, 等. γ Mn基合金反铁磁畸变与高阻尼孪晶的形成［J］. 上海交通大学学报, 2002, 36(1):28-31.
DENG H M, ZHONG Z Y, ZHANG J H, et al. Antiferromagnetic distortion and formation of high damping twins in γ Mn-based alloys ［J］. Journal of Shanghai Jiao Tong University, 2002, 36(1): 28-31. (in Chinese)
［6］鞆田顕章.Mn基合金の内部摩擦を考慮した振動シミュレータの検討［J］.福岡工業大学総合研究機構研究所所報,2018,12:13-17.
AKINORI T. Study on the vibration simulator considering internal friction in manganese-base alloys［J］.Journal of the Comprehensive Research Organization of Fukuoka Institute of Technology, 2018, 12:13-17.(in Japanese)
［7］凌闯. 热处理和变形对锰铜合金微观组织和阻尼性能的影响［D］.重庆：重庆大学, 2011.
LIN C. Effects of heat treatment and deformation on microstructure and damping capacity of Mn-Cu alloy ［D］. Chongqing：Chongqing University, 2011. (in Chinese)
［8］ TIAN Q C, YIN F X,SAKAGUCHI T, et al. Internal friction behavior of the reverse martensitic transformation in deformed Mn-Cu alloy ［J］. Materials Science and Engineering:A, 2006, 438/439/440： 374-378.
［9］陆文龙,姜银方.热处理对挤压态Mn-Cu阻尼合金性能的影响［J］.特种铸造及有色合金,2002(6):10-11.
LU W L, JIANG Y F. Effect of heat treatment on the damping properties of the extruded Mn-Cu damping alloy［J］. Special Cas-ting & Nonferrous Alloys，2002(6):10-11. (in Chinese)
［10］刘宏昭,原大宁,李冬平, 等. 结构阻尼时域本构模型及其应用［J］. 计算力学学报, 2004, 21(3):303-307.
LIU H Z, YUAN D N, LI D P, et al. Structural damping time domain constitution and its application ［J］. Chinese Journal of Computational Mechanics，2004, 21(3)：303-307. (in Chinese)
［11］王国庆,刘宏昭,何长安. 锌基阻尼合金在含间隙机构振动控制中的应用［J］. 中国机械工程, 2005,16(11)：993-995.
WANG G Q, LIU H Z, HE C A. Application of Zn-27Al-1Cu damping alloy in vibration control of mechanism with clearance joints ［J］. China Mechanical Engineering，2005, 16(11)：993- 995. (in Chinese)
［12］孙亚坤. 阻尼合金齿轮减速器动力学仿真及减振实验研究［D］.重庆：重庆大学,2018.
SUN Y K. Study on dynamic simulation and vibration reduction experiment of damping alloy gear reducer ［D］. Chongqing：Chongqing University, 2018. (in Chinese)
［13］方常青. 基于分数阶导数的热致非晶态形状记忆聚合物本构研究［D］.南京：南京航空航天大学,2018.
FANG C Q. Research on fractional derivative based constitutive models of thermally activated amorphous shape memory polymers ［D］.Nanjing： Nanjing University of Aeronautics and Astronautics, 2018. (in Chinese)
［14］李春蕊. 基于分数阶微积分理论的粘弹性流体流动与传热研究［D］.北京：北京科技大学,2015.
LI C R. Study on the flow and heat transfer of viscoelastic fluid based on the theory of fractional calculus ［D］. Beijing：University of Science and Technology Beijing,2015. (in Chinese)
［15］潘文潇,谭文长.广义Maxwell黏弹性流体在两平板间的非定常流动［J］.力学与实践,2003,25(1):19-22.
PAN W X, TAN W C.An unsteady flow of a viscoelastic fluid with the fractional Maxwell model between two parallel plates ［J］. Mechanics in Engineering，2003,25(1): 19-22. (in Chinese)
［16］孙海忠. 高分子材料的分数导数型本构关系及其应用［D］. 广州：暨南大学, 2006.
SUN H Z. Fractional derivative constitutive relationship of polymer materials and its application ［D］. Guangzhou：Jinan University, 2006. (in Chinese)
［17］ FRIEDRICH C. Relaxation and retardation functions of the Maxwell model with fractional derivatives［J］. Rheologica Acta, 1991, 30(2): 151-158.
［18］许福, 李科锋, 邓旭辉, 等. 基于分数阶微分流变模型的非晶合金黏弹性行为及流变本构参数研究［J］. 物理学报, 2015, 65(4): 046101.
XU F, LI K F, DENG X H, et al. Research on viscoelastic behavior and rheological constitutive parameters of metallic glasses based on fractional-differential rheological model ［J］. Acta Physica Sinica，2016, 65(4):046101. (in Chinese)
［19］肖有才. PBX 炸药的动态力学性能及冲击损伤行为研究［D］. 哈尔滨：哈尔滨工业大学, 2016.
XIAO Y C. Study of dynamic mechanical property and impact damage behavior of PBX ［D］. Harbin：Harbin Institute of Technology, 2016. (in Chinese)
［20］黄克智, 黄永刚. 固体本构关系［M］. 北京：清华大学出版社, 1999.
HUANG K Z, HUANG Y G. The constitutive relation of solid ［M］. Beijing：Tsinghua University Press，1999. (in Chinese)
［21］方建敏.橡胶材料的分数导数型本构模型研究及动力学应用［D］. 南京：南京航空航天大学,2012.
FANG J M. Research on the fractional derivative constitutive model of the rubber isolator and its dynamic application［D］. Nanjing：Nanjing University of Aeronautics and Astronautics, 2012. (in Chinese)
［22］ DING X, ZHANG G Q, ZHAO B, et al. Unexpected viscoelastic deformation of tight sandstone: insights and predictions from the fractional Maxwell model［J］. Scientific Reports,2017, 7(1): 11336. (in Chinese)
［23］ CARRERA Y, AVILA-DE LA ROSA G, VERNON-CARTER E J, et al. A fractional-order Maxwell model for non-Newtonian fluids ［J］. Physica A: Statistical Mechanics and Its Applications, 2017,482：276-285.
［24］卢凤双，张建福.高锰基阻尼合金材料主要性能测试报告［R］.北京：钢铁研究总院，2017.
LU F S, ZHANG J F.The test report of high manganese base damping alloy［R］. Beijing：Central Iron & Steel Research Institute, 2017. (in Chinese)
［25］ YIN F X. Damping behavior characterization of the M2052 alloy aimed for practical application［J］. Acta Metallurgica Sinica, 2003, 39(11):1139-1144.
［26］ STANKIEWICZ A. Fractional Maxwell model of viscoelastic biological materials［J］. BIO Web of Conferences，2018, 10：02032.

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