基于应变补偿和PSO-BP神经网络的Ti-2.7Cu合金本构关系
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摘要
采用Gleeble-3500型热模拟试验机对Ti-2.7Cu合金进行等温恒应变速率压缩实验,研究其在变形温度740～890℃,应变速率0.001～10s~(-1)范围内的热变形行为;并在Arrhenius型双曲正弦函数方程基础上引入应变量构建了基于应变补偿的本构模型,同时构建了基于PSO-BP神经网络的本构关系模型。结果表明:合金的流变应力对变形温度和应变速率较为敏感,变形温度升高和应变速率减小都会使流变应力降低;在高温和低应变速率条件下,流变曲线大多呈现稳态流动特征。经过误差计算得出,基于应变补偿的本构模型,预测值偏差在15%以内的数据点占85.28%;采用PSO-BP神经网络建立的本构模型,预测值偏差在15%以内的数据点占96.67%,PSO-BP神经网络模型具有更高的精度,能准确预测Ti-2.7Cu合金的高温流变应力。
The isothermal compression tests of Ti-2.7Cu alloy were tested to study the hot deformation behavior in temperature range of 740-890℃ and strain rate range of 0.001-10 s~(-1) on a Gleeble-3500 thermomechanical simulator. Constitutive model based on strain compensation was established by the Arrhenius hyperbolic sine function equation, and set up a constitutive equation for PSO-BP neural network. The results show that the flow stress is more sensitive to deformation temperature and strain rate, the flow stress is decreased with the increase of deformation temperature and decrease of strain rate; the flow stress curves present stable states in high temperature and low strain rate. For a constitutive equation based on strain compensation, the data points with the predicted error less than 15% account for 85.28% of all test data by error calculation; and for the constitutive equation based on PSO-BP neural network, the data points with the predicted error less than 15% account for 96.67% of all test data. PSO-BP neural network model has higher accuracy, it can better predict the flow stress of Ti-2.7Cu at elevated temperature.
The isothermal compression tests of Ti-2.7Cu alloy were tested to study the hot deformation behavior in temperature range of 740-890℃ and strain rate range of 0.001-10 s~(-1) on a Gleeble-3500 thermomechanical simulator. Constitutive model based on strain compensation was established by the Arrhenius hyperbolic sine function equation, and set up a constitutive equation for PSO-BP neural network. The results show that the flow stress is more sensitive to deformation temperature and strain rate, the flow stress is decreased with the increase of deformation temperature and decrease of strain rate; the flow stress curves present stable states in high temperature and low strain rate. For a constitutive equation based on strain compensation, the data points with the predicted error less than 15% account for 85.28% of all test data by error calculation; and for the constitutive equation based on PSO-BP neural network, the data points with the predicted error less than 15% account for 96.67% of all test data. PSO-BP neural network model has higher accuracy, it can better predict the flow stress of Ti-2.7Cu at elevated temperature.
引文
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[2] CUI W F, JIN Z, GUO A H, et al. High temperature deforma-tion behaviors for α+β type biomedical titanium alloy Ti-6Al-7Nb[J]. Materials Science and Engineering: A, 2009, 499(1/2):252-256.
[3] 于振涛,余森,程军,等. 新型医用钛合金材料的研发和应用现状[J]. 金属学报, 2017, 53(10):1238-1264. YU Z T, YU S, CHENG J, et al. Development and application of novel biomedical titanium alloy materials[J].Acta Metallurgica Sinica,2017, 53(10):1238-1264.
[4] TAKAHASHI M, KIKUCHI M, TAKADA Y, et al. Mechan-ical properties and microstructures of dental cast Ti-Ag and Ti-Cu alloys[J]. Dental Materials Journal, 2002, 21(3):270.
[5] 刘延辉,姚泽坤,宁永权,等. 生物医用TC20钛合金高温变形行为及本构关系[J]. 材料工程, 2014(7):16-21. LIU Y H, YAO Z K, NING Y Q, et al. Hot deformation behavior and constitutive relationship of biomedical TC20 alloy[J]. Journal of Materials Engineering, 2014(7):16-21.
[6] 蔡志伟,陈拂晓,郭俊卿. AZ41M镁合金热变形行为及本构方程[J]. 材料热处理学报, 2015, 36(11):65-71. CAI Z W, CHEN F X, GUO J Q. Hot deformation behavior and constitutive equation of AZ41M magnesium alloy[J]. Trans-actions of Materials and Heat Treatment, 2015, 36(11):65-71.
[7] 刘雪峰,马胜军,刘锦平,等. Cu-12%A1合金高温压缩变形过程本构关系的BP神经网络模型[J]. 材料工程, 2009(1):10-14. LIU X F, MA S J, LIU J P, et al. BP neural networks models for constitutive relationship during high temperature deformation process of Cu-12%Al alloy[J]. Journal of Materials Engineering, 2009(1):10-14.
[8] 孙宇,曾卫东,赵永庆,等. 基于BP神经网络Ti600合金本构关系模型的建立[J]. 稀有金属材料与工程, 2011, 40(2):220-224. SUN Y, ZENG W D, ZHAO Y Q, et al. Modeling of constitu-tive relationship of Ti600 alloy using BP artificial neural network[J]. Rare Metal Materials and Engineering, 2011,40(2):220-224.
[9] 张德丰. MATLAB神经网络仿真与应用[M]. 北京:电子工业出版社, 2009. ZHANG D F. MATLAB neural network simulation and appli-cation [M]. Beijing: Electronic Industry Press, 2009.
[10] 赵振江. 基于PSO-BP神经网络的网络流量预测与研究[J]. 计算机应用与软件, 2009, 26(1):218-221. ZHAO Z J. Prediction and research on network traffic based on PSO-BP neural network[J]. Computer Application and Soft-ware, 2009, 26(1):218-221.
[11] 姚彭彭,李萍,李成铭,等. TA15钛合金β热变形行为及显微组织[J]. 稀有金属, 2015, 39(11):967-974. YAO P P, LI P, LI C M, et al. Hot deformation behavior and microstructure of TA15 titanium alloy in β field[J]. Chinese Journal of Rare Metals, 2015, 39(11):967-974.
[12] 尹雪雁,于建民,张治民,等. Mg-13Gd-4Y-2Zn-0.5Zr合金的高温热压缩变形[J]. 特种铸造及有色合金, 2016, 36(10):1117-1120. YI X Y, YU J M, ZHANG Z M, et al. Hot compression deformation behavior of Mg-13Gd-4Y-2Zn-0.5Zr magnesium alloy[J]. Special-cast and Non-ferrous Alloys, 2016, 36(10):1117-1120.
[13] KOTKUNDE N, DEOLE A D, GUPTA A K, et al. Comp-arative study of constitutive modeling for Ti-6Al-4V alloy at low strain rates and elevated temperatures[J]. Materials and Design, 2014, 55(6):999-1005.
[14] 罗子健,杨旗. 考虑变形热效应的本构关系建立方法[J]. 中国有色金属学报, 2000, 10(6):804-808. LUO Z J, YANG Q. New method to establish constitutive relationship considering effect of deformation heating[J]. The Chinese Journal of Nonferrous Metals, 2000, 10(6):804-808.
[15] XIAO Y H, GUO C, GUO X Y. Constitutive modeling of hot deformation behavior of H62 brass[J]. Materials Science and Engineering A, 2011, 528(21):6510-6518.
[16] LIN Y C, CHEN M S, ZHONG J. Constitutive modeling for elevated temperature flow behavior of 42CrMo steel[J]. Computational Materials Science, 2008, 42(3):470-477.