Predicting the mechanical properties and composition optimization of a burn-resistant titanium alloy for aero-engines
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摘要: 采用支持向量机算法，在实验数据的基础上，建立航空发动机阻燃钛合金的合金化元素与力学性能关系模型，分析合金化元素对力学性能的影响规律。模型的输入参数为V、Al、Si和C元素，输出参数为室温拉伸性能（抗拉强度、屈服强度、延伸率和断面收缩率）。结果表明：各个力学性能支持向量机模型的线性相关系数均在0.975以上，具有较高的预测能力；各个力学性能测试样本实验值与模型预测值的绝对百分误差均在5%以内，具有良好的泛化能力，能够有效地反映出阻燃钛合金的合金化元素与力学性能之间的定量关系，进而实现对该合金的成分优化。对于Ti−35V−15Cr阻燃钛合金，可以通过加入质量分数为0～0.1%的Si元素和质量分数为0.05%～0.125%的C元素，并减少质量分数为2%～5%的V元素，来提高力学性能；对于Ti−25V−15Cr阻燃钛合金，可以通过加入质量分数为1.5%～1.8%的Al元素和质量分数为0.15%～0.2%的C元素，来提高力学性能。Abstract: Lightweight high-temperature titanium alloys are a key material for aero-engines. With the increasing use of new titanium alloys in aero-engines, titanium fire has become a typical catastrophic fault that plagues material design and selection. A burn-resistant titanium alloy is a special material developed to deal with the problem of titanium fire. Its application in aero-engines has become one of the key technologies for the prevention and control of titanium fire. Therefore, explaining the influence of the alloying elements of burn-resistant titanium alloys on mechanical properties is important to provide an important theoretical basis for the design and application of these alloys. Based on the experimental data, the relationship model between the alloying elements and mechanical properties of a burn-resistant titanium alloy was established using a support vector machine algorithm, and the effect of the alloying elements on the mechanical properties was analyzed. The input parameters of the model were V, Al, Si, and C elements, and the output parameters were the room temperature tensile properties (tensile strength, yield strength, elongation, and the reduction of area). Results show that the linear correlation coefficient of each mechanical property of the SVM model is above 0.975, which signifies good prediction ability. The absolute percentage error between the predicted and experimental values of each mechanical property test sample is within 5%, indicating good generalization ability and an effective reflection of the quantitative relationship between the alloying elements and mechanical properties of the burn-resistant titanium alloy for optimizing the composition of the alloy. The mechanical properties of the Ti–35V–15Cr alloy can be improved by adding 0–0.1% Si element and 0.05%–0.125% C element and reducing 2%–5% V element. Meanwhile, the mechanical properties of the Ti–25V–15Cr alloy can be improved by adding 1.5%–1.8% Al element and 0.15%–0.2% C element.
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图 1 力学性能实验值与模型预测值的线性相关性分析.(a)抗拉强度; (b)屈服强度; (c)伸长率; (d)断面收缩率
Figure 1. Linear correlation analysis between the experimental and predicted values using SVM: (a) tensile strength; (b) yield strength; (c) elongation; (d) reduction of area
图 2 V元素含量对Ti−V−Cr系阻燃钛合金力学性能的影响.(a)强度; (b)塑性
Figure 2. Influence of the V element content on the mechanical properties of the Ti−V−Cr burn-resistant titanium alloy: (a) strength；(b) ductility
图 3 Al元素含量对Ti−V−Cr系阻燃钛合金力学性能的影响。（a）强度；（b）塑性
Figure 3. Influence of the Al element content on the properties of the Ti−V−Cr burn-resistant titanium alloy: (a) strength; (b) ductility
图 4 Si元素含量对Ti−V−Cr系阻燃钛合金力学性能的影响。（a）强度；（b）塑性
Figure 4. Influence of the Si element content on the properties of the Ti−V−Cr burn-resistant titanium alloy: (a) strength; (b) ductility
图 5 C元素含量对Ti−V−Cr系阻燃钛合金力学性能的影响。（a）强度；（b）塑性
Figure 5. Influence of the C element content on the properties of the Ti−V−Cr burn-resistant titanium alloy: (a) strength; (b) ductility
表 1 Ti−V−Cr系阻燃钛合金实验值与支持向量机模型预测值的误差比较
Table 1. Error comparison of the mechanical properties of the experimental data with the predicted values using SVM
Sample Mass fraction/% Comparison Mechanical properties V Al Si C Tensile strength/MPa Yield strength/MPa Elongation/% Reduction of area/% 1 35.00 0 0 0 Experimental 1042 1028 10.0 15.0 Predicted 1042.10 1028.10 10.10 15.10 Absolute error/% 0.01 0.01 1.00 0.67 2 35.00 0 0.25 0 Experimental 1060 1032 15.1 19.5 Predicted 1059.90 1031.90 15.00 19.40 Absolute error/% 0.01 0.01 0.66 0.52 3 35.00 0 0.50 0 Experimental 1111 1080 7.3 11.0 Predicted 1110.90 1079.90 7.40 11.10 Absolute error/% 0.01 0.01 1.37 0.91 4 35.00 0 0 0.08 Experimental 1071 1005 18.4 33.0 Predicted 1060.60 997.32 18.30 32.90 Absolute error% 0.97 0.76 0.55 0.30 5 35.00 0 0.50 0.08 Experimental 1065 1005 19.0 33.5 Predicted 1065.10 1005.10 18.90 33.40 Absolute error/% 0.01 0.01 0.52 0.30 6 35.00 0 0 0.15 Experimental 1034 952 21.0 38.1 Predicted 1034.10 952.10 21.10 38.20 Absolute error/% 0.01 0.01 0.47 0.26 7* 25.50 2.60 0 0.27 Experimental 1070 1050 16.0 22.5 Predicted 1069.90 1049.90 14.66 23.11 Absolute error/% 0.01 0.01 8.39 2.70 8* 20.00 0 0.20 0 Experimental 960 933 24.5 46.0 Predicted 960.10 933.10 24.40 45.90 Absolute error/% 0.01 0.01 0.41 0.22 9* 30.00 0 0.20 0 Experimental 1025 973 20.0 38.5 Predicted 1024.90 973.10 19.90 32.84 Absolute error/% 0.01 0.01 0.50 14.70 10 35.00 0 0.30 0.10 Experimental 1025 964 17.2 33.0 Predicted 1024.90 963.90 17.30 33.10 Absolute error/% 0.01 0.01 0.58 0.30 11 35.20 0 0.17 0.07 Experimental 1026 963 16.5 29.4 Predicted 1026.10 970.16 16.60 29.50 Absolute error/% 0.01 0.74 0.61 0.34 12** 25.20 0 0.21 0 Experimental 969 942 18.5 30.4 Predicted 986.21 936.34 19.18 31.78 Absolute error/% 1.78 0.60 3.68 4.54 Note: **are test sets and the rest are training sets;* is the data from references [12,16]. 
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参考文献
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