不同变形条件下锰铜合金的应力松弛特性及数值仿真

doi:10.16180/j.cnki.issn1007-7820.2024.08.007

摘要/Abstract

摘要：

计算机运算能力的提升为有限元仿真分析提供支撑,可更高效地求解较复杂的结构及非线性问题。文中基于有限元仿真分析技术,针对锰铜合金复杂的力学特性进行仿真计算,分别采用Prony级数本构模型和并联流变本构模型对锰铜合金进行不同变形条件下的应力松弛实验仿真。通过提取应力松弛实验数据将其转化为相应模型参数并进行有限元仿真计算,获得可准确描述锰铜合金非线性力学特性的仿真模型参数。通过对比仿真和实验结果可知,并联流变模型能够更加准确地表征锰铜合金的应力松弛行为,在不同初始应变条件下,仿真结果和相应工况下的实验结果相对误差小于1%。并联流变模型比Prony级数模型更适用于锰铜合金在复杂工况下的仿真计算。

关键词: 锰铜合金, 黏弹性, 非线性, 并联流变模型, Prony级数, 有限元, 应力松弛, 仿真

Abstract:

The improvement of computing power provides a support for finite element simulation analysis, which can solve more complex structures and nonlinear problems more efficiently. In this study, based on the finite element simulation analysis technology, the complex mechanical properties of Mn-Cu alloy are simulated. Prony series constitutive model and parallel rheological constitutive model are respectively adopted to simulate the stress relaxation test of Mn-Cu alloy under different deformation conditions. The stress relaxation experimental data are extracted and converted into the corresponding model parameters and the finite element simulation calculation is carried out. The simulation model parameters which can accurately describe the nonlinear mechanical properties of Mn-Cu alloy are obtained. By comparing the simulation and experimental results, it is concluded that the parallel rheological framework can more accurately characterize the stress relaxation behavior of Mn-Cu alloy. Under different initial strain conditions, the relative error of the simulation results and the test results under corresponding working conditions is less than 1%. Compared with Prony series constitutive model, parallel rheological framework is more suitable for the simulation of Mn-Cu alloy under complex working conditions.

Key words: Mn-Cu alloy, viscoelasticity, nonlinearity, parallel rheological framework, Prony series, finite element, stress relaxation, simulation

中图分类号:

TP391.9

熊亚军, 刘艳, 袁贤浦. 不同变形条件下锰铜合金的应力松弛特性及数值仿真[J]. 电子科技, 2024, 37(8): 47-53.

XIONG Yajun, LIU Yan, YUAN Xianpu. Stress Relaxation Characteristics and Numerical Simulation of Mn-Cu Alloy under Different Deformation Conditions[J]. Electronic Science and Technology, 2024, 37(8): 47-53.

图/表 10

图1

图2

图3

图4

图5

图6

表1

表2

表3

图7

参考文献 20

[1]	杨云辉, 徐连江. 面向高精度机械加工的有限元分析技术研究综述[J]. 电子科技, 2022, 35(11):98-103.
	Yang Yunhui, Xu Lianjiang. Summary of finite element analysis technology for high precision machining[J]. Electronic Science and Technology, 2022, 35(11):98-103.
[2]	汪中厚, 赵超凡. 基于接触有限元的斜齿轮传动误差仿真与修形[J]. 电子科技, 2017, 30(12):59-61,66.
	Wang Zhonghou, Zhao Chaofan. Study of helical gear transmission error simulation and modification by using contact finite element analysis method[J]. Electronic Science and Technology, 2017, 30(12):59-61,66.
[3]	林磊, 徐德城, 陈志林, 等. 锰铜阻尼合金在管道壳壁振动缓解中的应用[J]. 噪声与振动控制, 2021, 41(4):221-227. doi: 10.3969/j.issn.1006-1355.2021.04.034
	Lin Lei, Xu Decheng, Chen Zhilin, et al. Application of Mn-Cu damping alloy in pipe shell-wall vibration mitigation[J]. Noise and Vibration Control, 2021, 41(4):221-227. doi: 10.3969/j.issn.1006-1355.2021.04.034
[4]	朱锐, 杨雨迎, 毛保全, 等. 锰铜基阻尼合金广义分数阶M-axwell本构模型[J]. 兵工学报, 2021, 42(6):1290-1302.
	Zhu Rui, Yang Yuying, Mao Baoquan, et al. Generalized fractional Maxwell constitutive model of Mn-Cu damping alloy[J]. Acta Armamentarii, 2021, 42(6):1290-1302.
[5]	朱锐, 毛保全, 赵俊严, 等. 机枪遥控武器站锰铜基阻尼合金缓冲器非线性有限元分析及试验[J]. 北京理工大学学报, 2022, 42(9):935-946.
	Zhu Rui, Mao Baoquan, Zhao Junyan, et al. The nonlinear finite element analysis and experiment of Mn-Cu damping alloy buffer for remote control weapon station[J]. Transactions of Beijing Institute of Technology, 2022, 42(9):935-946.
[6]	Stachurski Z H. Mechanical behavior of materials[J]. Materials Today, 2009, 12(3):44-49.
[7]	朱智, 张立文, 顾森东. Hastelloy C-276合金应力松弛试验及蠕变本构方程[J]. 中国有色金属学报, 2012, 22(4):1063-1067.
	Zhu Zhi, Zhang Liwen, Gu Sendong. Stress relaxation test of Hastelloy C-276 alloy and its creep constitutive equation[J]. The Chinese Journal of Nonferrous Metals, 2012, 22(4):1063-1067.
[8]	朱智, 张立文, 宋冠宇, 等. Hastelloy C-276合金应力松弛行为的研究[J]. 稀有金属材料与工程, 2012, 41(4):697-700.
	Zhu Zhi, Zhang Liwen, Song Guanyu, et al. Study on stress relaxation behavior of Hastelloy C-276 alloy[J]. Rare Metal Materials and Engineering, 2012, 41(4):697-700.
[9]	毕静, 崔学习, 张艳苓, 等. Ti-6Al-4V钛合金薄板应力松弛行为研究[J]. 机械工程学报, 2019, 55(18):43-52,62. doi: 10.3901/JME.2019.18.043
	Bi Jing, Cui Xuexi, Zhang Yanling, et al. Investigations on stress relaxation behavior of Ti-6Al-4V titanium alloy sheet[J]. Journal of Mechanical Engineering, 2019, 55(18):43-52,62. doi: 10.3901/JME.2019.18.043
[10]	郝江江. Mn-Cu合金阻尼特性和减振特性分析[D]. 成都: 西南交通大学, 2017:16-17.
	Hao Jiangjiang. Study on damping performance and vibration behavior of Mn-Cu alloy[D]. Chengdu: Southwest Jiaotong University, 2017:16-17.
[11]	郝顺平. 高锰阻尼合金的制备及性能研究[D]. 镇江: 江苏大学, 2018:32-33.
	Hao Shunping. Study on preparation and properties of high manganese damping alloy[D]. Zhenjiang: Jiangsu University, 2018:32-33.
[12]	Wei L, Li Q, Zhang X, et al. Remarkable improvement indamping capacity of M2052 alloy by stepcooling treatment[J]. Materials Research Express, 2021, 8(1):16526-16533.
[13]	佘彩凤. 金属变形滞后回弹的本构模型UMAT二次开发及有限元分析[D]. 北京: 北京理工大学, 2015:11-15.
	She Caifeng. UMAT secondary development of constitutive equation and finite element analysis for metallic time-dependent springback after deformation[D]. Beijing: Beijing Institute of Technology, 2015:11-15.
[14]	周梦雨, 李凡珠, 杨海波, 等. 基于非线性黏弹性本构模型的轮胎滚动和生热[J]. 高分子材料科学与工程, 2020, 36(3):73-78.
	Zhou Mengyu, Li Fanzhu, Yang Haibo, et al. Tire rolling and heat generation based on nonlinear viscoelastic model ofparallel rheological framework[J]. Polymer Materials Science and Engineering, 2020, 36(3):73-78.
[15]	周梦雨, 李凡珠, 杨海波, 等. 橡胶材料的非线性黏弹性本构方程[J]. 高分子材料科学与工程, 2020, 36(3):79-84.
	Zhou Mengyu, Li Fanzhu, Yang Haibo, et al. A nonlinear viscoelastic constitutive equation based on parallel rheological framework for rubber materials[J]. Polymer Materials Science and Engineering, 2020, 36(3):79-84.
[16]	中国钢铁工业协会. GB/T 10120-2013.金属材料拉伸应力松弛试验方法[S]. 北京: 中国标准出版社, 2013.
	China Iron and Steel Association. GB/T 10120-2013.Test method for tensile stress relaxation of metallic materials[S]. Beijing: China Standards Press, 2013.
[17]	杨啸. 丙烯基弹性体力学松弛行为和结构演化[D]. 合肥: 中国科学技术大学, 2021:36-37.
	Yang Xiao. Strain dependent evolution of structure and stress in propylene-based elastomer during stressr-elaxation[D]. Hefei: University of Science and Technology of China, 2021:36-37.
[18]	荣继纲, 黄友剑, 卜继玲, 等. 隔振橡胶材料基于简单应变模式的蠕变特性研究[J]. 橡胶工业, 2022, 69(7):506-511.
	Rong Jigang, Huang Youjian, Bu Jiling, et al. Research on creep characteristics of damping rubber materials on simple strain mode[J]. China Rubber Industry, 2022, 69(7):506-511.
[19]	Karim M, Zhang Z, Zhu Y. Prediction of nonlinear viscoelastic recovery of thermoplastic polymers using abaqus parallel rheological framework model[C]. Santa Clara: Simulia User Meeting, 2016:6-7.
[20]	徐一航, 李道奎, 周仕明, 等. 基于并行流变框架HTPB推进剂本构模型研究[J]. 推进技术, 2022, 43(9):403-410.
	Xu Yihang, Li Daokui, Zhou Shiming, et al. HTPB propellant constitutive model based on parallel rheological framework[J]. Journal of Propulsion Technology, 2022, 43(9):403-410.

n	G(n)	τ_n
1	0.122 600	0.000 108 7
2	0.069 000	0.071 570 0
3	0.011 600	0.270 500 0
4	0.008 066	2.141 000 0
5	0.008 638	38.260 000 0

阶数(i)	μ(i)	α(i)	D(i)
1	-3.095×10⁸	8.786	4.7×10^-5
2	1.557×10⁸	17.680	0
3	3.035×10⁸	-9.593	0
4	-1.497×10⁸	-19.230	0

阶数(i)	S(i)	A(i)	n(i)	m(i)
1	0.070 5	0.000 008 641	1.018	-0.367 1
2	0.080 7	0.000 067 250	9.838	-0.366 7
3	0.249 0	3.632 000 000	1.406	-0.110 9
4	0.012 0	43.570 000 000	3.820	-0.303 5
5	0.187 7	750.000 000 000	8.414	-0.229 6