scholarly journals Constitutive Equations for Describing the Hot Compressed Behavior of TC4–DT Titanium Alloy

Materials ◽  
2020 ◽  
Vol 13 (15) ◽  
pp. 3424
Author(s):  
Haoran Wang ◽  
Chunge Wang ◽  
Muyu Li ◽  
Rui Ma ◽  
Jun Zhao
Keyword(s):  
Titanium Alloy ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Relative Error ◽  
Constitutive Equations ◽  
Type Equation ◽  
Original Strain ◽  
Strain Rates ◽  
Compression Tests ◽  
Average Absolute Relative Error

Isothermal hot compression tests of TC4–DT titanium alloy were performed under temperatures of 1203–1293 K and strain rates of 0.001–10 s−1. The purpose of this study is to develop a new high-precision modified constitutive model that can describe the deformation behavior of TC4–DT titanium alloy. Both the modified strain-compensated Arrhenius-type equation and the modified Hensel–Spittel equation were established by revising the strain rate. The parameters in the above two modified constitutive equation were solved by combining regression analysis with iterative methods, which was used instead on the traditional linear regression methods. In addition, both the original strain-compensated Arrhenius-type equation and Hensel–Spittel equation were established to compare with the new modified constitutive equations. A comparison of the predicted values based on the four constitutive equations was performed via relative error, average absolute relative error (AARE) and the correlation coefficient (R). These results show the modified Arrhenius-type equation and the modified Hensel–Spittel equation is more accurate and efficient with a similar prediction accuracy. The AARE-value of the two modified constitutive equation is relatively low under various strain rates and their fluctuation is small as the strain rate changes.

scholarly journals Constitutive Equations for Describing the Warm and Hot Deformation Behavior of 20Cr2Ni4A Alloy Steel

Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1169
Author(s):  
Haoran Wang ◽  
Wei Wang ◽  
Ruixue Zhai ◽  
Rui Ma ◽  
Jun Zhao ◽  
...  
Keyword(s):  
Flow Stress ◽  
Alloy Steel ◽  
Relative Error ◽  
Constitutive Equations ◽  
Type Equation ◽  
Coefficient Of Determination ◽  
Original Strain ◽  
Compression Tests ◽  
Absolute Relative Error ◽  
Average Absolute Relative Error

Isothermal hot compression tests of 20Cr2Ni4A alloy steel were performed under temperatures of 973–1273 K and strain rates of 0.001–1 s−1. The behavior of the flow stress of 20Cr2Ni4A alloy steel at warm and hot temperatures is complicated because of the influence of the work hardening, the dynamic recovery, and the dynamic recrystallization. Four constitutive equations were used to predict the flow stress of 20Cr2Ni4A alloy steel, including the original strain-compensated Arrhenius-type (osA-type) equation, the new modified strain-compensated Arrhenius-type (msA-type) equation, the original Hensel–Spittel (oHS) equation and the modified Hensel–Spittel (mHS) equation. The msA-type and mHS are developed by revising the deformation temperatures, which can improve prediction accuracy. In addition, we propose a new method of solving the parameters by combining a linear search with multiple linear regression. The new solving method is used to establish the two modified constitutive equations instead of the traditional regression analysis. A comparison of the predicted values based on the four constitutive equations was performed via relative error, average absolute relative error (AARE) and the coefficient of determination (R2). These results show the msA-type and mHS equations are more accurate and efficient in terms of predicting the flow stress of the 20Cr2Ni4A steel at elevated temperature.

scholarly journals High-Temperature Flow Behaviour and Constitutive Equations for a TC17 Titanium Alloy

2019 ◽  
Vol 38 (2019) ◽  
pp. 168-177 ◽  
Author(s):  
Liu Shi-feng ◽  
Shi Jia-min ◽  
Yang Xiao-kang ◽  
Cai Jun ◽  
Wang Qing-juan
Keyword(s):  
Titanium Alloy ◽  
High Temperature ◽  
Constitutive Equation ◽  
Constitutive Equations ◽  
Deformation Behaviour ◽  
High Temperature Deformation ◽  
Temperature Deformation ◽  
Compression Tests ◽  
Average Absolute Relative Error ◽  
Wide Range

AbstractIn this study, the high-temperature deformation behaviour of a TC17 titanium alloy was investigated by isothermal hot compression tests in a wide range of temperatures (973–1223 K) and strain rates (0.001–10 s−1). Then, the constitutive equations of different phase regimes (α + β and single β phases) were developed on the basis of experimental stress-strain data. The influence of the strain has been incorporated in the constitutive equation by considering its effect on different material constants for the TC17 titanium alloy. Furthermore, the predictability of the developed constitutive equation was verified by the correlation coefficient and average absolute relative error. The results indicated that the obtained constitutive equations could predict the high-temperature flow stress of a TC17 titanium alloy with good correlation and generalization.

Constitutive Analysis to Predict Elevated Temperature Flow Behavior of TC21 Titanium Alloy

2013 ◽  
Vol 811 ◽  
pp. 152-156
Author(s):  
Li Bin Jia ◽  
Lin Li ◽  
Yi Ru
Keyword(s):  
Titanium Alloy ◽  
Constitutive Equation ◽  
Flow Behavior ◽  
Strain Rates ◽  
Hot Workability ◽  
Compression Tests ◽  
Absolute Relative Error ◽  
Constitutive Analysis ◽  
Hyperbolic Sine ◽  
Average Absolute Relative Error

In order to study the hot workability of TC21 titanium alloy, isothermal hot compression tests were conducted in the temperatures range of 1123~1203K and strain rates range of 0.01~10s-1. The influence of strain was incorporated in hyperbolic sine constitutive equation by considering the effect of strain on material constants. Correlation coefficient (R) and average absolute relative error (AARE) were introduced to verify the validity of the developed hyperbolic sine constitutive equation. The values of R and AARE were determined to be 0.9891 and 7.753% respectively, which indicated that the developed hyperbolic sine constitutive equation considering strain compensation could precisely predict the flow behavior of TC21 titanium alloy throughout the entire range of temperatures and strain rates.

scholarly journals Application of the Strain Compensation Model and Processing Maps for Description of Hot Deformation Behavior of Metastable β Titanium Alloy

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 2021
Author(s):  
Oleksandr Lypchanskyi ◽  
Tomasz Śleboda ◽  
Aneta Łukaszek-Sołek ◽  
Krystian Zyguła ◽  
Marek Wojtaszek
Keyword(s):  
Titanium Alloy ◽  
Strain Rate ◽  
Flow Behavior ◽  
Microstructural Analysis ◽  
Calculated Data ◽  
Processing Temperature ◽  
Processing Maps ◽  
Compression Tests ◽  
Strain And Strain Rate ◽  
Average Absolute Relative Error

The flow behavior of metastable β titanium alloy was investigated basing on isothermal hot compression tests performed on Gleeble 3800 thermomechanical simulator at near and above β transus temperatures. The flow stress curves were obtained for deformation temperature range of 800–1100 °C and strain rate range of 0.01–100 s−1. The strain compensated constitutive model was developed using the Arrhenius-type equation. The high correlation coefficient (R) as well as low average absolute relative error (AARE) between the experimental and the calculated data confirmed a high accuracy of the developed model. The dynamic material modeling in combination with the Prasad stability criterion made it possible to generate processing maps for the investigated processing temperature, strain and strain rate ranges. The high material flow stability under investigated deformation conditions was revealed. The microstructural analysis provided additional information regarding the flow behavior and predominant deformation mechanism. It was found that dynamic recovery (DRV) was the main mechanism operating during the deformation of the investigated β titanium alloy.

Hot working of SP-700 titanium alloy with lamellar α + β starting structure using a processing map

2020 ◽  
Vol 111 (4) ◽  
pp. 297-306
Author(s):  
Amir Hosein Sheikhali ◽  
Maryam Morakkabati
Keyword(s):  
Titanium Alloy ◽  
Strain Rate ◽  
Hot Deformation ◽  
Processing Map ◽  
Microstructural Analysis ◽  
Shear Bands ◽  
Alpha Phase ◽  
Strain Rates ◽  
Compression Tests ◽  
Temperature Range

Abstract In this study, hot deformation behavior of SP-700 titanium alloy was investigated by hot compression tests in the temperature range of 700-9508C and at strain rates of 0.001, 0.1, and 1 s-1. Final mechanical properties of the alloy (hot compressed at different strain rates and temperatures) were investigated using a shear punch testing method at room temperature. The flow curves of the alloy indicated that the yield point phenomenon occurs in the temperature range of 800- 9508C and strain rates of 0.1 and 1 s-1. The microstructural analysis showed that dynamic globularization of the lamellar α phase starts at 7008C and completes at 8008C. The alpha phase was completely eliminated from b matrix due to deformation- induced transformation at 8508C. The microstructure of specimens compressed at 8508C and strain rates of 0.001 and 0.1 s-1showed the serration of beta grain boundaries, whereas partial dynamic recrystallization caused a necklace structure by increasing strain rate up to 1 s-1. The specimen deformed at 7008C and strain rate of 1 s-1was located in the instability region and localized shear bands formed due to the low thermal conductivity of the alloy. The processing map of the alloy exhibited a peak efficiency domain of 54% in the temperature range of 780-8108C and strain rates of 0.001- 0.008 s-1. The hot deformation activation energy of the alloy in the α/β region (305.5 kJ mol-1) was higher than that in the single-phase β region (165.2 kJ mol-1) due to the dynamic globularization of the lamellar a phase.

Prediction of High Temperature Flow Stress for AISI 4120 Steel during Hot Compression

2012 ◽  
Vol 233 ◽  
pp. 339-342 ◽  
Author(s):  
Ming Ping Zou ◽  
Wu Jiao Xu ◽  
Peng Cheng Wang
Keyword(s):  
High Temperature ◽  
Flow Stress ◽  
Constitutive Equation ◽  
Constitutive Equations ◽  
Good Prediction ◽  
Compression Tests ◽  
Absolute Relative Error ◽  
Constitutive Analysis ◽  
Average Absolute Relative Error ◽  
Deformation Behaviors

To investigate the hot deformation behaviors of AISI 4120 steel, isothermal compression tests were conducted using Gleeble-1500 thermal-mechanical simulator in the temperature range of 1073-1373K with the strain rate of 0.01-10s-1. The hyperbolic sine law in Arrhenius type is used in the constitutive modeling for AISI 4120. The influence of strain is incorporated in constitutive analysis by considering the effect of strain on material constants α, n, Q and ln A. The flow stress values predicted by the developed constitutive equations show a good agreement with experimental results, which reveals that the developed constitutive equations could give an accurate and precise prediction for the high temperature flow behaviors of AISI 4120 steel. The predictability of developed constitutive equation was further quantified in terms of correlation coefficient (R) and average absolute relative error (AARE). The R and AARE were found to be 0.9847 and 8.0372% respectively, which reflects the good prediction capabilities of the developed constitutive equation.

A Modified Double Multiple Nonlinear Regression Constitutive Equation for Modeling and Prediction of High Temperature Flow Behavior of BFe10-1-2 Alloy

2018 ◽  
Vol 37 (1) ◽  
pp. 75-87
Author(s):  
Jun Cai ◽  
Kuaishe Wang ◽  
Jiamin Shi ◽  
Wen Wang ◽  
Yingying Liu
Keyword(s):  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Nonlinear Regression ◽  
Flow Behavior ◽  
Strain Rate Range ◽  
Compression Tests ◽  
Constitutive Analysis ◽  
Average Absolute Relative Error ◽  
Wide Range

AbstractConstitutive analysis for hot working of BFe10-1-2 alloy was carried out by using experimental stress–strain data from isothermal hot compression tests, in a wide range of temperature of 1,023~1,273 K, and strain rate range of 0.001~10 s–1. A constitutive equation based on modified double multiple nonlinear regression was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data calculated from the developed equation was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. Subsequently, a comparative study was made on the capability of strain-compensated Arrhenius-type constitutive model. The results showed that the developed constitutive equation based on modified double multiple nonlinear regression could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Constitutive Equation of Mg-13Al-3Ca-3Zn-1Nd-0.2Mn Magnesium Alloy

2014 ◽  
Vol 968 ◽  
pp. 3-6
Author(s):  
Wei Chen ◽  
Gang Chen ◽  
Jing Zhai ◽  
Li Ma
Keyword(s):  
Activation Energy ◽  
Magnesium Alloy ◽  
Constitutive Equation ◽  
Temperature Regime ◽  
Constitutive Equations ◽  
Flow Behavior ◽  
Strain Rates ◽  
Compression Tests ◽  
Related Material ◽  
Base Analysis

The constitutive equations may properly describe the flow behavior of the materials. In the present study, the constitutive equation of Mg-13Al-3Ca-3Zn-1Nd-0.2Mn alloy were investigated using hot compression tests at the temperatures range of 200, 250, 300, 350 and 400°Cwith the constant strain rates of 0.001, 0.01, 0.1, 1 and 10s-1.The hot working constitutive base analysis has been conducted on the experimental alloy. The related material constants n, α and β, as well as the activation energy Q for each temperature regime have been determined. At last, the constitutive equations is given.

Flow and Densification Behaviors of Sintered P/F-10C50 Steel under Hot Compression

2016 ◽  
Vol 849 ◽  
pp. 811-818
Author(s):  
Biao Guo ◽  
Chang Chun Ge ◽  
Yi Xu ◽  
Qiu Yan Lu ◽  
Sui Cai Zhang
Keyword(s):  
Constitutive Equation ◽  
Strain Rate ◽  
Hot Deformation ◽  
Deformation Temperature ◽  
Hot Compression ◽  
Compression Tests ◽  
Sintered Steel ◽  
Absolute Relative Error ◽  
Average Absolute Relative Error ◽  
Deformation Behaviors

The hot deformation and densification behaviors of sintered P/F-10C50 steel were investigated by hot compression tests on Gleeble-1500 thermal mechanical simulator at the temperature ranging from 900 °C to 1000 °C and the strain rate ranging from 0.1 s-1 to 10 s-1. The flow and densification characteristics of the tested specimens at different deformation temperatures and strain rates were studied. The flow stress of the sintered steel persistently increases until the end of the test as the result of matrix and geometric work hardening. The higher deformation temperature and strain rate are conductive to the healing of the pores and promote the densification of the sintered steel, while the higher deformation temperature and lower strain rate impede the densification. The constitutive equation of the sintered steel is established by the means of stepwise regression. The flow stresses predicted by the established constitutive equation are in good agreement with the experimental values, and the correlation coefficient (R) and the average absolute relative error (AARE) are 0.9931 and 3.52%, respectively. These results demonstrate the hot deformation behaviors of the sintered P/F-10C50 steel are excellently predicted by the established constitutive equation.

scholarly journals A Constitutive Equation for Predicting Elevated Temperature Flow Behavior of BFe10-1-2 Cupronickel Alloy through Double Multiple Nonlinear Regression

2019 ◽  
Vol 38 (2019) ◽  
pp. 461-475
Author(s):  
Jun Cai ◽  
Meng Wang ◽  
Jiamin Shi ◽  
Kuaishe Wang ◽  
Wen Wang
Keyword(s):  
Elevated Temperature ◽  
Flow Stress ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Nonlinear Regression ◽  
Flow Behavior ◽  
Strain Rate Range ◽  
Compression Tests ◽  
Constitutive Analysis ◽  
Average Absolute Relative Error

AbstractConstitutive analysis for elevated temperature flow behavior of BFe10-1-2 alloy was carried out by using experimental stress–strain data from isothermal hot compression tests on a Gleeble-3800 thermo-mechanical simulator, in a wide of temperature range of 1,023–1,273 K, and strain rate range of 0.001–10 s−1. A constitutive equation based on double multiple nonlinear regression (DMNR) was proposed considering the independent effects of strain, strain rate, temperature and their interrelation. The predicted flow stress data obtained from the developed equation based on DMNR was compared with the experimental data. Correlation coefficient (R), average absolute relative error (AARE) and relative errors were introduced to verify the validity of the developed constitutive equation. The results showed that the developed constitutive equation based on DMNR could predict flow stress of BFe10-1-2 alloy with good correlation and generalization.

Sign in / Sign up

Export Citation Format

Share Document