Prediction of high temperature rheological behavior of TC4 titanium alloy based on Z-A constitutive model
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摘要: 在描述材料承受不同变形条件下的响应行为及其热成形工艺过程优化方面，本构模型具有重要意义。因此，为了获得准确描述TC4钛合金高温流变行为的物理本构模型，利用Gleeble-
3800 热模拟试验机，在不同温度（550 ～950 ℃）下、不同应变速率（0.01、0.1、1 s−1）下完成了等温压缩试验。依据试验数据，对改进的Z-A本构模型参数进行了标定，并对其有效性进行了分析。基于分析结果，建立了一种优化的Z-A本构模型，借助相关性系数R，平均相对误差值AARE和均方根误差RSME三种统计参数，探讨了该模型的可预测性。结果表明优化的Z-A本构模型能够准确地预测该材料的高温流变行为，其模型的R、AARE和RSME分别为0.9994 ，1.62%和1.3248 。Abstract: The constitutive model plays an important role in describing the response behavior of materials under different deformation conditions and in optimizing the hot forming process. Therefore, in order to obtain the physical constitutive model for accurately describing the high temperature rheological behavior of TC4 titanium alloy, the isothermal compression experiments were performed under different temperatures (500~900 ℃) and different strain rates (0.01, 0.1, 1 s−1) by using the Gleeble-3800 thermal simulator. According to the experimental data, the parameters of modified Z-A constitutive model are calibrated, and its effectivity is analyzed. Based on the analysis results, an optimized Z-A constitutive model was established, and the predictability of the model was discussed with the help of correlation coefficient R, mean absolute relative error value AARE and root mean square error RSME. The results indicate that the optimized Z-A constitutive model can accurately predict the high-temperature rheological behavior of the material. The R, AARE and RSME of the model are0.9992 , 1.63% and1.3252 , respectively. -
图 1 不同条件下TC4钛合金的应力-应变曲线
Figure 1. Stress-strain curves of TC4 titanium alloy under different conditions
图 2 参数相关性拟合结果
(a) $ \ln \sigma $与$ {T^*} $的相关性；(b) $ \ln(\text{e}^{\text{I}_1}-\mathit{\text{C}}_1) $与$ \ln \varepsilon $的相关性；(c)I2与ε的相关性；(d) $ \ln \sigma $与$ \ln {\dot \varepsilon ^ * } $的相关性；(e)$ {{{I}}_3} $与$ {T^*} $的相关性
Figure 2. Fitting results of parameters correlation
图 3 不同温度下改进的Z-A模型预测值与试验值的对比
Figure 3. Comparison between the experimental and predicted values of the modified Z-A model under different temperatures
图 4 优化后的拟合关系
（a） I3随ε的变化关系；(b) $ {{\text{e}}^{{{{I}}_1}}} $与ε的拟合关系 ；(c) I2与ε的拟合关系
Figure 4. Optimized fitting results
图 5 不同温度下的试验值与优化的Z-A本构模型预测值间的对比
Figure 5. Comparison between the experimental and predicted values of the optimized Z-A model under different temperatures
图 6 优化的Z-A模型的预测值与试验值间的相关性
Figure 6. Correlation between the experimental and predicted values of the optimized Z-A model
表 1 TC4钛合金化学成分
Table 1. Chemical composition of TC4 titanium alloy
% Al V Fe C N H O Ti 6.5 4.2 0.28 0.08 0.04 0.012 0.18 Bal. 
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表 2 不同应变处C5、 C6的值
Table 2. Values of C5 and C6 at different strains
ε C5 C6 0.1 0.01507 0.000497 0.2 0.01701 0.000524 0.3 0.01765 0.000530 0.4 0.01642 0.000556 0.5 0.01763 0.000583 0.6 0.01843 0.000545 0.7 0.01781 0.000564 0.8 0.01896 0.000596
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表 3 改进的Z-A本构模型参数
Table 3. Parameters of the modified Z-A constitutive model
C1 C2 C3 C4 C5 C6 n 538 175.98169 − 0.00539 − 0.00164 0.01781 0.000564 0.45742
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表 4 参数d0～d5的数值
Table 4. Values of d0～d5 parameters
d0 d1 d2 d3 d4 d5 0.015377 0.006469 − 0.008046 0.007020 0.000501 0.000075
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表 5 优化的Z-A模型相关性系数（R）平均相对误差（AARE）及均方根误差（RMSE）
Table 5. Correlation coefficient and average relative error of the optimized Z-A model
本构模型 相关性系数（R） 平均相对误差（AARE）/% 均方根误差（RMSE） OZ-A 0.9994 1.62 1.3248
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