Constitutive modeling of high-temperature flow behavior of Fe-27Mn-10Al-1.0C lightweight steel based on the fields-backofen model
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摘要: 为表征Fe-27Mn-10Al-1.0C轻质钢的高温流动行为，在850～
1050 ℃、0.01～10 s−1的试验条件下，使用Gleeble-3800热模拟试验设备对其进行了高温压缩试验。基于Fields-Backofen(FB)模型，依据试验数据进行了本构建模研究，通过引入温度软化项，并考虑应变效应及应变、应变速率和温度间的耦合效应对模型参数的影响，成功建立了修正M-FB模型。采用统计参数相关系数R、平均绝对误差AARE和相对误差RE，对M-FB模型预测精度进行验证。研究结果表明，Fe-27Mn-10Al-1.0C轻质钢对应变、应变速率和变形温度显著敏感，M-FB模型预测数据与试验数据相关性高度一致，能可靠应用于预测其高温流动行为。-
关键词:
- Fe-27Mn-10Al-1.0C轻质钢 /
- FB模型 /
- 高温流动行为
Abstract: To characterize the high-temperature flow behavior of Fe-27Mn-10Al-1.0C lightweight steel, high-temperature compression tests were performed using a Gleeble-3800 thermal simulation testing system under experimental conditions of 850-1050 ℃ and 0.01-10 s−1. Based on the Fields-Backofen (FB) model, a constitutive modeling study was conducted using the experimental data. By introducing a temperature softening term and accounting for the strain effects as well as the coupling effects of strain, strain rate, and temperature on model parameters, a modified M-FB model was successfully established. The prediction accuracy of the M-FB model was validated using statistical parameters, including the correlation coefficient (R), average absolute relative error (AARE), and relative error (RE). The research results indicate that Fe-27Mn-10Al-1.0C lightweight steel is significantly sensitive to strain, strain rate, and deformation temperature. The predicted data of the M-FB model are highly consistent with the experimental data, and it can be reliably applied to predict its high-temperature flow behavior. -
图 1 不同应变速率下的应力-应变曲线
Figure 1. Stress–strain curves at different strain rates
(a)0.01 s−1；(b)0.1 s−1；(c)1 s−1；(d)10 s−1
图 2 不同温度下n与$ \ln \dot{\varepsilon } $的关系
Figure 2. Relationship between n and $ \ln \dot{\varepsilon } $
图 5 不同温度下K与$ \ln \dot{\varepsilon } $的关系
Figure 5. Relationship between K and $ \ln \dot{\varepsilon } $
图 7 原FB模型预测值与试验值对比
Figure 7. Comparison of predicted values from the original FB model with experimental values
(a)0.01 s−1；(b)10 s−1
图 8 $ \dot{\varepsilon } $=0.01 s–1、$ T $=850 ℃时，试验应力与应变的变化关系
Figure 8. Relationship between experimental stress and strain at 0.01 s–1 and 850 ℃
图 10 m与$ \ln \dot{\varepsilon } $的变化关系
Figure 10. Relationship between m and$ \ln \dot{\varepsilon } $
图 11 m与$ \varepsilon $、$ \ln \dot{\varepsilon } $的拟合关系
Figure 11. Fitting relationship between m and$ \varepsilon $、$ \ln \dot{\varepsilon } $
图 12 不同温度下E与$ \varepsilon $的变化关系
Figure 12. Relationship between E and $ \varepsilon $ under different temperatures
(a)950 ℃；(b)1 050 ℃
图 13 不同温度下E与$ \ln \dot{\varepsilon } $的变化关系
Figure 13. Relationship between E and $ \ln \dot{\varepsilon } $ under different temperatures
(a)950 ℃；(b)1050 ℃
图 14 不同应变速率下E与T的变化关系
Figure 14. Relationship between E and T under different strain rates
(a)0.1 s–1；(b)10 s–1
图 15 测试钢在不同应变速率下的试验数据与M-FB模型预测数据对比
Figure 15. Experimental data compared to predicted data by M-FB model for the tested steel at different strain rates
(a)0.01 s−1；(b)0.1 s−1；(c)1 s−1；(d)10 s−1
图 16 四种应变速率下M-FB模型相关性
Figure 16. Correlation of the M-FB model at four strain rates
(a)0.01 s−1；(b)0.1 s−1；(c)1 s−1；(d)10 s−1
表 1 试验钢的化学成分
Table 1. Chemical composition of the experimental steel
% Mn Al C Si P S Fe 26.86 10.01 1.05 0.014 0.01 0.012 Bal. 
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表 2 不同条件下的m值
Table 2. m values under different conditions
$ \varepsilon $ m 850 ℃ 900 ℃ 950 ℃ 1000 ℃1050 ℃0.1 0.09075 0.10677 0.13461 0.1408 0.18703 0.3 0.11858 0.1241 0.14571 0.15429 0.17143 0.5 0.13463 0.13953 0.15117 0.16135 0.18163 0.7 0.13623 0.14354 0.14318 0.15960 0.17274 0.9 0.11372 0.11662 0.12068 0.1349 0.16598
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表 3 不同测试条件下M-FB模型预测的相对误差的最小、最大值及平均绝对误差
Table 3. Minimum and maximum of relative error and average absolute error predicted by M-FB model under different test conditions
% T/℃ $ \dot{\varepsilon } $=0.01 s−1 $ \dot{\varepsilon } $=0.1 s−1 $ \dot{\varepsilon } $=1 s−1 $ \dot{\varepsilon } $=10 s−1 ARRE REmin REmax ARRE REmin REmax ARRE REmin REmax ARRE REmin REmax 850 0.47 −1.34 −1.15 0.70 −0.42 1.28 2.06 −9.48 5.56 2.34 −2.36 6.01 900 2.82 −4.69 5.37 2.02 −7.07 5.33 2.32 −5.46 5.25 2.35 −3.78 7.36 950 2.36 −6.97 0.45 3.93 −11.41 7.85 3.09 −7.05 5.46 3.78 −6.26 9.65 1 000 2.97 −1.43 6.78 6.09 −12.56 −0.19 3.85 −4.75 7.25 2.71 −4.01 7.08 1 050 5.56 −8.80 −1.95 4.25 −9.19 5.94 5.45 −5.61 10.05 6.73 −13.40 −0.10
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