基于物理及元建模法的TB15钛合金本构模型研究

采用Gleeble-3800热模拟机对TB15钛合金进行等温恒应变速率热压缩试验，研究其在变形温度为810～930℃、应变速率为0.001～10s-1和高度压下量为60%条件下的热变形行为；建立了物理、支持向量回归(SVR)和响应面三种本构关系模型来预测TB15钛合金的流动应力，同时对比了三种本构模型的预测精度。结果表明:TB15钛合金的流动应力随应变速率的降低和变形温度的升高而减小，峰值应力的变化对应变速率的敏感性更高；物理本构模型、SVR本构模型和响应面本构模型相关系数R均大于0.98，但是响应面本构模型的R值达到了0.993，而且响应面本构模型的相对误差在±5%范围内的预测值频率达到了67.9%，大于物理本构模型的58.6%。同时经过方差分析得到所构建的响应面本构模型的显著性检验值P<0.0001，表明响应面本构模型预测的流动应力与变形温度、应变速率和应变之间的回归关系显著，比物理本构模型和SVR本构模型有更高的精度，能够更好的预测TB15钛合金的流动应力。

Constitutive model of TB15 titanium alloy based on physics and meta-modeling

The Gleeble-3800 thermal simulator was used to conduct isothermal constant strain rate thermal compression tests on TB15 titanium alloy to study its thermal deformation behavior at deformation temperatures of 810-930°C, strain rates of 0.001-10s-1 and height depression of 60%; three constitutive relationship models, physical, support vector regression (SVR) and response surface, were developed to predict the flow stresses of TB15 titanium alloy were predicted by three physical, support vector regression (SVR) and response surface constitutive models, and the prediction accuracy of the three constitutive models was compared. The results show that the flow stress of TB15 titanium alloy decreases with decreasing strain rate and increasing deformation temperature, and the change of peak stress is more sensitive to the strain rate; the correlation coefficient R of physical, SVR and response surface constitutive models are all greater than 0.98, but the R value of response surface constitutive model reaches 0.993, and the frequency of the relative error of the response surface constitutive models ±5% of the predicted value reached 67.9%, which was greater than that of the physical constitutive models at58.6%. The significance test value P<0.0001 of the constructed response surface constitutive model was also obtained by ANOVA, indicating that the regression relationship between the flow stress predicted by the response surface constitutive model and the deformation temperature, strain rate and strain was significant and had higher accuracy than the physical constitutive model and SVR constitutive model, which could better predict the flow stress of TB15 titanium alloy.