Influence of pre strain on the mechanical properties of TA2 and the establishment of constitutive model
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摘要: 为研究预应变对TA2力学性能的影响，对原始材料和预应变量为10%、20%和30%的TA2进行室温拉伸试验；根据预应变对TA2力学性能的影响规律，引入预应变量对Hollomon 模型、Ludwik 模型和Swift 模型进行修正，以预测预应变TA2的力学行为。结果表明，随预应变量的增加，TA2的屈服强度显著增大、抗拉强度小幅增大，而断后伸长率、强塑积和应变硬化指数减小。预应变通过消耗塑性性能来提升TA2的强度，TA2塑性应变能密度和断裂应变能密度随预应变量的增加而明显减小。各修正模型预测结果与试验值相关性系数的平均值分别为
0.9862 、0.9994 、0.9744 ，最大预测误差为6.34%、8.33%、16.42%，其中Hollomon 模型结构精简且具有良好的预测精度，是描述预应变对TA2力学行为影响的最佳选择。Abstract: To investigate the effect of prestrain on the mechanical properties of TA2, room temperature tensile tests were conducted on the TA2 original material and specimens with the prestrains of 10%, 20%, and 30%. Based on the influence of prestrain on the mechanical properties of TA2, prestrain variables were introduced to modify the Hollomon model, Ludwik model, and Swift model to predict the mechanical behavior of prestrained TA2. The results show that with the increase of prestrain, the yield strength of TA2 increases significantly, the tensile strength slightly increases, and the elongation after fracture, strength plastic product, and strain hardening indexes decrease. Prestrain enhances the strength of TA2 by consuming plastic properties, and the plastic strain energy density and fracture strain energy density of TA2 decrease significantly with the increase of prestrain. The average correlation coefficients between the predicted results of each modified model and the experimental values are0.9862 ,0.9994 , and0.9744 , with the maximum prediction errors of 6.34%, 8.33%, and 16.42%, respectively. Among them, the Hollomon model has a simplified structure and good prediction accuracy, making it the best choice to describe the effect of prestrain on the mechanical behavior of TA2.-
Key words:
- TA2 /
- pre-strain /
- mechanical properties /
- constitutive model
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图 2 不同预应变量下的TA2应力-应变曲线
(a)工程应力应变曲线；(b)真实应力应变曲线
Figure 2. Stress-strain curves of TA2 under different prestrain variables
图 3 屈服强度、抗拉强度和断后伸长率随预应变的变化
Figure 3. The variation of yield strength, tensile strength, and elongation after fracture with prestrain
图 4 强塑积及屈强比随预应变的变化
Figure 4. The variation of strength plastic product and yield strength ratio with prestrain
图 7 Hollomon 模型参数与预应变量关联
Figure 7. Correlation between Hollomon model parameters and prestrain
(a)KH-P；(b)nH-P
图 8 Ludwik 模型参数与预应变量关联
Figure 8. Correlation between Ludwik model parameters and prestrain
(a)KL-P；(b)σS-P；(c)nL-P
图 9 Swift 模型参数与预应变量关联
Figure 9. Correlation between Swift model parameters and prestrain: (a)KS-P；(b)ε0-P；(c)nS-P
(a)KS-P；(b)ε0-P；(c)nS-P
图 10 修正的本构模型预测结果与试验数据对比
(a) Hollomon 模型；(b) Ludwik 模型；(c) Swift 模型
Figure 10. Comparison between the improved constitutive models prediction results and experimental data: (a) Hollomon model; (b) Ludwik model; (c) Swift model
表 2 各本构模型参数
Table 2. Parameters of each constitutive model
应变/% Hollomon模型 Ludwik模型 Swift模型 KH nH KL σS nL KS ε0 nS 0 556 0.27613 402.49 250.52 0.83904 495.97 0.04 0.17316 10 552 0.17515 413.49 308.75 0.81699 523.58 0.01594 0.13123 20 543 0.11325 363.73 388.45 0.79863 522.85 0.01236 0.08834 30 525 0.06853 278.48 400.09 0.74608 514.37 0.00382 0.05758 
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表 3 各修正模型预测结果的相关性系数和最大误差
Table 3. The correlation coefficients and maximum errors of the predicted results of each modified model
P=0% P=10% P=20% P=30% R δmax/% R δmax/% R δmax/% R δmax/% Hollomon 模型 0.9913 6.34 0.9870 3.89 0.9823 3.36 0.9841 2.63 Ludwik 模型 0.9996 8.25 0.9996 8.33 0.9994 8.03 0.9991 4.14 Swift 模型 0.9643 16.42 0.9788 5.80 0.9758 3.61 0.9786 6.11
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