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.

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