Flow stress prediction of Hastelloy C-276 alloy using modified Zerilli−Armstrong,Johnson−Cook and Arrhenius-type constitutive models

To better understand the hot deformation behaviors of Hastelloy C-276 alloy under elevated temperatures, hot tensile tests were carried out in the temperature range of 1223−1423 K and the strain rate range of 0.01−10 s⁻¹, respectively. Based on the modified Zerilli−Armstrong, modified Johnson-Cook, and strain-compensated Arrhenius-type models, three constitutive equations were established to describe the high-temperature flow stress of this alloy. Meanwhile, the predictability of the obtained models was evaluated by the calculation of correlation coefficients (r) and absolute errors (Δ), where the values of r for the modified Zerilli−Armstrong, Johnson−Cook, and Arrhenius-type constitutive models were computed to be 0.935, 0.968 and 0.984, and the values of Δ were calculated to be 13.4%, 10.5% and 6.7%, respectively. Moreover, the experimental and predicted flow stresses were compared in the strain range of 0.1−0.5, the results further indicated that the obtained modified Arrhenius-type model possessed better predictability on hot flow behavior of Hastelloy C-276.     

Prediction on hot deformation behavior of spray-formed 7055 aluminum alloy via phenomenological models

Hot compression tests in the temperature range of 340–450 °C and strain rate range of 0.001–1 s^?1 of spray-formed 7055 aluminum alloy were carried out to study its hot deformation behavior. Three phenomenological models including Johnson–Cook, modified Fields–Backofen and Arrhenius-type were introduced to predict the flow stresses during the compression process. And then, a comparative predictability of the phenomenological models was estimated in terms of the relative errors, correlation coefficient (R), and average absolute relative error (AARE). The results indicate that Johnson–Cook model and modified Fields–Backofen model cannot well predict the hot deformation behavior due to the large deviation in the process of line regression fitting. Arrhenius-type model obtains the best fit through combining the effect of strain rate and temperature.     

Modeling Constitutive Relationship of Cu-0.4 Mg Alloy During Hot Deformation

For predicting the high-temperature deformation behavior in a Cu-0.4 Mg alloy, the true stress-strain data from isothermal hot compression tests on a Gleeble-1500 thermo-mechanical simulator, in a wide range of temperatures (500, 600, 700, 750, and 800 °C) and strain rates (0.005, 0.01, 0.1, 1, 5, and 10 s^?1), were employed to develop the Arrhenius-type constitutive model and the artificial neural network (ANN) constitutive model. Furthermore, prediction ability of the two models for high-temperature deformation behavior was evaluated. Correlation coefficients (R) between the experimental and predicted flow stress for the Arrhenius-type constitutive model and the ANN constitutive model are 0.9860 and 0.9998, respectively, and average absolute relative errors between the experimental and predicted flow stress for these two models are 5.3967% and 0.7401%, respectively. Results show that the ANN constitutive model can accurately predict the high-temperature deformation behavior over a wider range of temperatures and strain rates, while for the Arrhenius-type constitutive model there is greater divergence in the regime of high strain rates and low temperatures.     

AA7075高强铝合金热冲压流变行为本构模型对比研究

在热冲压过程中,AA7075高强铝合金板料经充分固溶后移入室温模具进行冲压成形并淬火。为表征AA7075铝合金在热冲压工艺中的变形行为,在温度200~480℃、应变速率0.01~10s-1范围内进行了高温拉伸试验。基于Arrhenius类型本构模型、Johnson-Cook模型以及Zerilli-Armstrong模型提出了多种修正本构模型,并应用实验所获流变曲线进行了拟合。提出的修正模型通过将模型参数表示为应变、应变速率及温度相关的多项式函数耦合了应变、应变速率及温度对流变应力的影响,并通过均方误差(MSE)以及相关系数R值对模型流变应力预测准确性进行了评价。结果表明,修正的Johnson-Cook模型能够更加准确的预测AA7075高温流变行为。     

Strain-Compensated Arrhenius-Type Constitutive Model for Flow Behavior of Al-12Zn-2.4Mg-1.2Cu Alloy

在Gleeble-3500热模拟试验机上进行了挤压态Al-12Zn-2.4Mg-1.2Cu合金的等温压缩试验,获得了温度523~723 K、真应变0.1~0.6和应变速率0.001, 0.01, 0.1和1 s-1下的应力应变试验数据。基于Arrhenius本构模型,采用了含有Zener-Holloman参数的幂指数方程来描述温度和应变速率对流变行为的影响。采用线性回归分析的方法,研究了不同温度和应变速率下,材料常数随应变的变化规律。结果表明：除加工硬化率n外,其他材料常数Q,α,β和lnA3的数值均随着应变数值的增大而呈现出增大趋势;同时拟合出不同试验条件下不同材料常数的应变补偿方程,并借助于调整判定系数进行了应变补偿材料常数方程的拟合优度分析,在此基础上建立了试验合金的应变补偿本构模型。通过对比,分析了不同试验条件下的真实应力-应变曲线和建立模型的预测应力-应变曲线,并以相关系数R和平均绝对误差（AARE）为评价因子研究了考虑应变补偿Arrhenius本构模型的可靠性和适宜性,预测结果与试验结果相比较的R和AARE数值分别为0.995 82和6.66%,表明该模型精度高,可靠性好。     

Simulation of low proportion of dynamic recrystallization in 7055 aluminum alloy

The hot deformation and dynamic recrystallization (DRX) behaviors of 7055 aluminum alloy were studied at temperatures of 390−470 °C and strain rates of 0.01−1 s⁻¹. A low DRX fraction between 1% and 13% was observed by using EBSD technique. A modified JMAK-type DRX model was proposed for such low DRX fraction problems. The model was used together with commercial FEM software DEFORM-3D to simulate the hot compression of 7055 aluminum alloy. There was a good agreement between experimental and predicted DRX fractions and grain size with an average absolute relative error (AARE) of 13.7% and 6.3%, respectively. In order to further verify the validity of the proposed model, the model was also used to simulate DRX in industrial hot rolling of 7055 aluminum alloys. The results showed that the distribution of DRX fraction was inhomogeneous, and agreed with experimental observations.     

Hot working behavior of near alpha titanium alloy analyzed by mechanical testing and processing map

The hot deformation characteristics of the Ti−5.7Al−2.1Sn−3.9Zr−2Mo−0.1Si (Ti-6242S) alloy with an acicular starting microstructure were analyzed using processing map. The uniaxial hot compression tests were performed at temperatures ranging from 850 to 1000 °C and at strain rates of 0.001−1 s⁻¹. The developed processing map was used to determine the safe and unsafe deformation conditions of the alloy in association with the microstructural evolution by SEM and OM. It was recognized that the flow stress revealed differences in flow softening behavior by deformation at 1000 °C compared to the lower deformation temperatures, which was attributed to microstructural changes. The processing map developed for typical strain of 0.7 in two-phase field exhibited high efficiency value of power dissipation of about 55% at 950 °C and 0.001 s⁻¹, basically due to extensive globularization. An increase in strain rate and a decrease in temperature resulted in a decrease in globularization of α lamellae, while α lamellar kinking increased. Eventually, the instability domain of flow behavior was identified in the temperature range of 850−900 °C and at the strain rate higher than 0.01 s⁻¹ reflecting the flow localization and adiabatic shear banding. By considering the power efficiency domains and the microstructural observations, the deformation in the temperature range of 950−1000 °C and strain rate range of 0.001−0.01 s⁻¹ was desirable leading to high efficiencies. It was realized that (950 °C, 0.001 s⁻¹) was the optimum deformation condition for the alloy.     

DEFORMATION BEHAVIOR OF AA6063 ALUMINIUM ALLOY AFTER REMOVING FRICTION EFFECT UNDER HOT WORKING CONDITIONS

The hot deformation behavior of AA6063 aluminium alloy has been investigated by means of compression tests at temperatures between 400 and 520℃, and strain rates ranging from 2.5 to 10 s^-1. Owing to the barreling, the theoretical model on the basis of Hills general method is used to calculate the flow stress of a cylindrical specimen under uniaxial simple compression so as to consider the friction effect at the die-specimen interface. A method of evaluating the friction coefficient by combining compression tests with the finite element method is presented. The real flow behavior of AA6063 aluminium alloy can be described with sinh-Arrhenius equation. The hot deformation activation energy Q derived from the corrected stress and strain data is 232. 350 kJ/mol.     

The Strain-Compensated Constitutive Equation for High Temperature Flow Behavior of an Al-Zn-Mg-Cu Alloy

In order to study flow stress behavior for hot working of a typical Al-Zn-Mg-Cu alloy, experimental stress-strain data obtained from isothermal hot compression tests at strain rates of 0.004, 0.04, and 0.4 s^?1 and deformation temperatures of 400, 450, 500, and 520 °C were used to develop the constitutive equation. The peak stress decreased with increasing deformation temperature and decreasing strain rate. The effects of temperature and strain rate on deformation behavior were represented by Zener-Hollomon parameter in an exponent-type equation. Employing an Arrhenius-type constitutive equation, the influence of strain has been incorporated by considering the related material constants as functions of strain. The accuracy of the developed constitutive equations has been evaluated using standard statistical parameters such as correlation coefficient and average absolute relative error. The results indicate that the proposed strain-dependent constitutive equation gives an accurate and precise estimate of the flow stress in the relevant temperature range.     

ARTIFICIAL NEURAL NETWORK MODEL OF CONSTTTUTIVE RELATIONSHIP FOR 2A70 ALUMINUM ALLOY

The hot deformation behavior of 2A70 aluminum alloy was investigated by means of isothermal compression tests performed on a Gleeble-1500 thermal simulator over a wide range of temperatures 360-480℃ with strain rates of 0.01-1s-1 and the largest deformation of 60%, and the true stress of the material was obtained under the above-mentioned conditions. The experimental results shows that 2A70 aluminum alloy is a kind of aluminum alloy with the property of dynamic recovery; its flow stress declines with the increase of temperature, while its flow stress increases with the increase of strain rates. On the basis of experiments, the constitutive relationship of the 2A70 aluminum alloy was constructed using a BP artificial neural network. Comparison of the predicted values with the experimental data shows that the relative error of the trained model is less than ±3% for the sampled data while it is less than ±6% for the non- sampled data. It is evident that the model constructed by BP ANN can accurately predict the flow stress of the 2A70 alloy.     

An Application of ANFIS to Predict the Hot Flow Behavior of 6063 Aluminum Alloy

In order to determine the optimum hot-forming processing parameters for 6063 aluminum alloy, the compressive deformation behavior of 6063 aluminum alloy was investigated at the temperatures from 300 to 500?°C and strain rates from 0.5 to 50?s^?1 on a Gleeble-1500 Thermal Simulator. Based on the compression experimental data, a novel adaptive network-based fuzzy inference system (ANFIS) model is developed to predict the flow behavior of 6063 aluminum alloy. In the ANFIS system, the inputs of the ANFIS are the strain, the strain rate and the temperature, whereas the flow stress is the output. The effects of strain, strain rate, and temperature on the flow behavior of 6063 aluminum alloy have been studied by comparing the experimental and the predicted results using the developed ANFIS model. The results show that predicted values using the developed model are in good agreement with the experimental data, which demonstrates the reliability of the developed ANFIS model.     

Constitutive analysis of 6013 aluminum alloy in hot plane strain compression process considering deformation heating integrated with heat transfer

Hot plane strain compression tests of 6013 aluminum alloy were conducted at temperatures ranging from 613 to 773 K and strain rates ranging from 10^-3 to 10 s^-1. A novel model is developed to describe the temperature rise considering deformation heating integrated with heat transfer in tests. The experimental flow stress data are corrected by the proposed novel model. Based on the corrected flow stress, the modified power function constitutive model is developed considering the coupled effects of deformation temperature and strain rate on flow stress. Meanwhile, another two widely used models, temperature-compensated power function and straincompensated hyperbolic sine constitutive model, are also established for the studied 6013 aluminum alloy. Finally, the three constitutive models are compared from the aspects of accuracy, stability and efficiency. It is found that the experimental flow stress is significantly affected by the temperature rise. Furthermore, the influence of heat transfer on temperature rise cannot be ignored. When the constitutive model is established, the coupled effects of deformation temperature and strain rate on flow stress should be considered. The modified power function constitutive model is the best one in describing the flow behavior among the three models.     

Incoloy825合金热变形过程中的本构模型和特殊晶界演变

采用原始JC模型、修正JC模型和应变补偿Arrhenius方程，描述了Incoloy825合金在不同温度（950～1150 °C）和应变速率（1~10 s^-1）下经摩擦和温升修正后的应力-应变曲线。结果表明，修正后曲线具有明显的动态再结晶特征。与原始JC模型和修正的JC模型相比，Arrhenius应变补偿模型更适合于描述Incoloy825合金热变形过程中的应力应变行为。温度和应变速率对特殊晶界的演变有显著影响。特殊晶界长度分数与动态再结晶分数呈正相关。与冷轧后退火处理工艺相比，热变形工艺调控的特殊晶界长度分数较低，热变形工艺不适合用来调整特殊晶界分数，其原因是在热变形过程中动态再结晶的大量形核造成较小的晶粒团簇。     

轧制态6082-T6铝合金的热压缩力学行为及微观组织分析

采用热模拟试验机对轧制态6082-T6铝合金进行热压缩试验,分析了合金在变形温度100~400 ℃,应变速率0.01 s^-1条件下的流变应力,对不同温度热变形的微观组织进行了表征。结果表明,轧制态6082铝合金的力学性能受变形温度和轧制方向的影响。变形过程中应力呈现负的温度敏感性,即随着变形温度升高,应力不断下降。合金表现出明显的力学性能各向异性,压缩强度在与轧制方向呈0°和90°较高,45°方向强度较低。经过热压缩变形后,与轧向呈不同方向的6082-T6铝合金的晶粒组织均沿着剪切力方向发生扭曲,同时,变形温度对晶粒组织的演变影响不大。随着变形温度的升高,合金基体内的位错密度明显下降,析出相发生粗化。     

Mg-3Sn-1Mn-1La镁合金热压缩组织演变与应变修正本构方程

通过对铸态Mg-3Sn-1Mn-1La合金在变形温度为200~450℃、应变速率为0.001~1.0s^-1条件下进行热压缩实验,研究了其热变形行为和微观组织变化规律。结果表明:随着变形温度的降低和应变速率的升高,流变应力明显增大而再结晶晶粒尺寸减小。在变形温度较低的条件下,连续动态再结晶是主要的再结晶机制。然而,当变形温度升高时,非连续动态再结晶机制占主导。分析和修正了摩擦和变形热对流变应力的影响。结果表明,与摩擦相比变形热对流变应力的影响更加明显,且随着应变速率的增加和变形温度的降低,变形热对流变应力的影响更加明显。在实验数据的基础上建立了应变修正的本构方程。通过对实验值与预测值的对比发现,所建立的本构方程能够准确地描述实验合金的热变形行为。     

Flow behavior of Al–6.2Zn–0.70Mg–0.30Mn–0.17Zr alloy during hot compressive deformation based on Arrhenius and ANN models

The hot deformation behavior of Al–6.2Zn–0.70Mg–0.30Mn–0.17Zr alloy was investigated by isothermal compression test on a Gleeble–3500 machine in the deformation temperature range between 623 and 773 K and the strain rate range between 0.01 and 20 s^?1. The results show that the flow stress decreases with decreasing strain rate and increasing deformation temperature. Based on the experimental results, Arrhenius constitutive equations and artificial neural network (ANN) model were established to investigate the flow behavior of the alloy. The calculated results show that the influence of strain on material constants can be represented by a 6th-order polynomial function. The ANN model with 16 neurons in hidden layer possesses perfect performance prediction of the flow stress. The predictabilities of the two established models are different. The errors of results calculated by ANN model were more centralized and the mean absolute error corresponding to Arrhenius constitutive equations and ANN model are 3.49% and 1.03%, respectively. In predicting the flow stress of experimental aluminum alloy, the ANN model has a better predictability and greater efficiency than Arrhenius constitutive equations.     

Constitutive Analysis to Predict High-Temperature Flow Stress in 2099 Al-Li Alloy

采用高温等温压缩试验并利用修正后的流变曲线,研究了2099 Al-Li合金在变形温度为300~500℃,应变速率为0.001~10 s-1,变形量(真应变)为0.7条件下的流变行为。结果表明:可用包含Z参数的双曲正弦形式来表征变形温度和应变速率对2099 Al-Li合金热变形行为的影响;将应变作为影响因素,求解了不同应变量下的材料常数,并构建了考虑应变的本构模型;统计分析结果表明,除了在变形温度为300℃,应变速率为10 s-1之外,该模型能够很好的预测2099 Al-Li合金高温流变行为。     

Hot deformation behavior of rare earth magnesium alloy without pre-homogenization treatment

The behavior and structure evolvement of as-cast Mg-Gd-Y-Nd-Zr magnesium alloy during the hot deformation process were discussed.The flow stress behavior of magnesium alloy over the strain rate range of 0.002-1 s~(-1) and the temperature range of 573-723 K was researched on Gleeble-1500D hot simulator under the maximum deformation degree of 60%.The experimental results show that the relationship between stress and strain is obviously affected by the strain rate and deformation temperature.The important s...     

铸态GH4169合金热变形行为及三种本构模型对比

在Gleeble-1500热力模拟机上对铸态GH4169合金进行热压缩试验,变形参数为:温度(1193～1373K)、应变速率(0.01～10s~(-1))、变形量50%。通过分析真应力真应变曲线,研究铸态GH4169合金的热变形行为;对比分析了Johnson-Cook(JC)、修正的Johnson-Cook(MJC)和应变补偿Arrhenius3种本构模型的相关系数(R)和平均相对误差(AARE)。结果表明:铸态GH4169合金的流变应力随变形温度的升高和应变速率的降低而减小。JC模型、MJC模型和应变补偿的Arrhenius本构模型的相关系数(R)分别为0.891、0.956和0.961,AARE依次为29.02%、11.16%和9.31%。因此,应变补偿的Arrhenius模型能够更为精确地描述铸态GH4169的热变形行为。     

GH79合金高温变形行为及变形机理研究

利用Gleeble-3800热压缩模拟试验机,对GH79合金高温热变形行为及变形机理进行了系统的研究。以高温压缩实验为基础,以高温压缩过程的力学行为特征及微观组织演变规律为主线,获得了该合金在不同应变速率、不同变形温度下的应变速率敏感性指数m值、变形激活能Q值、晶粒指数p值的变化规律。分别构建了不同失稳判据下的动态DMM热加工图及包含位错数量的变形机理图。应用热加工图理论分析了该合金的适合成形加工区和流变失稳区,运用变形机理图预测了该合金高温变形过程基于柏氏矢量补偿的晶粒尺寸、模量补偿的流变应力下的位错演变规律及高温变形机理。