Constitutive Model Prediction and Flow Behavior Considering Strain Response in the Thermal Processing for the TA15 Titanium Alloy

To investigate the flow stress, microstructure, and usability of TA15 titanium alloy, isothermal compression was tested at 1073–1223 K and strain rates of 10, 1, 0.1, 0.01, and 0.001 s−1, and strain of 0.9. The impact of strain and temperature on thermal deformation was investigated through the exponent-type Zener–Hollomon equation. Based on the influence of various material constants (including α, n, Q, and lnA) on the TA15 titanium alloy, the strain effect was included in the constitutive equation considering strain compensation, which is presented in this paper. The validity of the proposed constitutive equation was verified through the correlation coefficient (R) and the average absolute relative error (AARE), the values of which were 0.9929% and 6.85%, respectively. Research results demonstrated that the strain-based constitutive equation realizes consistency between the calculated flow stress and the measured stress of TA15 titanium alloy at high temperatures.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.811.152 ◽

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.

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

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.233.339 ◽

2012 ◽

Vol 233 ◽

pp. 339-342 ◽

Cited By ~ 1

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.

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

High Temperature Materials and Processes ◽

10.1515/htmp-2016-0123 ◽

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.

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Establishment of the High Temperature Constitutive Relationship of the Haynes 230 Ni-Based Superalloy

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.385.397 ◽

2018 ◽

Vol 385 ◽

pp. 397-402

Author(s):

Xiu Quan Cheng ◽

Ning Yuan Zhu ◽

Qin Xiang Xia ◽

Gang Feng Xiao

Keyword(s):

High Temperature ◽

Constitutive Equation ◽

Flow Behavior ◽

Constitutive Relationship ◽

Forming Process ◽

Haynes 230 ◽

Absolute Relative Error ◽

Average Absolute Relative Error ◽

Wide Range ◽

Physically Based

The high temperature flow behavior of materials is an important basis to study their formability and to determine reasonable forming process parameters. In this work, the high temperature plane strain compression (HTPSC) tests were employed to reveal the high temperature flow behavior of Haynes 230 Ni-based superalloy under the wide range of temperatures (950°C-1200°C) and strain rates (0.01/s-10/s). The stress-strain data from the tests were applied to model the strain-compensated Arrhenius physically-based constitutive equation and considering the dynamic recovery (DRV) and dynamic recrystallization (DRX) phenomenological constitutive equation. The comparison indicated that the predictions of the two modeled constitutive equations are in good agreement with the experimental data. The prediction of the flow behavior of Haynes 230 Ni-based superalloy of strain-compensated Arrhenius constitutive equation is more accurately (average absolute relative error (AARE) is 2.84%) than that of considering DRV and DRX constitutive equation (AARE is 7.57%).

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Hot Compressive Behavior and Constitutive Equation of Ti-Al-Nb-Zr-Mo-Cr Alloy

Materials Science Forum ◽

10.4028/www.scientific.net/msf.993.230 ◽

2020 ◽

Vol 993 ◽

pp. 230-236

Author(s):

Li Wei Zhu ◽

Yun Peng Xin ◽

Xin Nan Wang ◽

Zhi Shou Zhu

Keyword(s):

Activation Energy ◽

Titanium Alloy ◽

Flow Stress ◽

Constitutive Equation ◽

Deformation Behavior ◽

Flow Behavior ◽

True Stress ◽

Compressive Behavior ◽

Hot Deformation Behavior ◽

Peak Value

The hot deformation behavior of Ti-Al-Nb-Zr-Mo-Cr titanium alloy was studied by hot compressive method in this paper, and the flow stress constitutive equation and activation energy also calculated. The results show that the flow stress increased with deformation temperature dropping and strain rate increasing. The flow behavior of the sample hot-deformaed exhibited a peak value of stress in the α+β field, whereas, the true stress attained a steady state in the β field. According to the stress-strain curves of the alloy and its stress characteristics, the Arrhenius constitutive equation was obtained. The average activation energy was about 654.228 KJ/mol in the α+β field, and about 272.196 KJ/mol in the β field, respectively.

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

High Temperature Materials and Processes ◽

10.1515/htmp-2018-0060 ◽

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.

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

Materials ◽

10.3390/ma14082021 ◽

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.

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Hot Deformation Behavior and Processing Maps of a New Ti-6Al-2Nb-2Zr-0.4B Titanium Alloy

Materials ◽

10.3390/ma14092456 ◽

2021 ◽

Vol 14 (9) ◽

pp. 2456

Author(s):

Zhijun Yang ◽

Weixin Yu ◽

Shaoting Lang ◽

Junyi Wei ◽

Guanglong Wang ◽

...

Keyword(s):

Titanium Alloy ◽

Flow Stress ◽

Constitutive Equation ◽

Deformation Mechanism ◽

Power Dissipation ◽

Hot Deformation ◽

Dissipation Rate ◽

Dynamic Recovery ◽

Processing Maps ◽

Temperature Range

The hot deformation behaviors of a new Ti-6Al-2Nb-2Zr-0.4B titanium alloy in the strain rate range 0.01–10.0 s−1 and temperature range 850–1060 °C were evaluated using hot compressing testing on a Gleeble-3800 simulator at 60% of deformation degree. The flow stress characteristics of the alloy were analyzed according to the true stress–strain curve. The constitutive equation was established to describe the change of deformation temperature and flow stress with strain rate. The thermal deformation activation energy Q was equal to 551.7 kJ/mol. The constitutive equation was ε ˙=e54.41[sinh (0.01σ)]2.35exp(−551.7/RT). On the basis of the dynamic material model and the instability criterion, the processing maps were established at the strain of 0.5. The experimental results revealed that in the (α + β) region deformation, the power dissipation rate reached 53% in the range of 0.01–0.05 s−1 and temperature range of 920–980 °C, and the deformation mechanism was dynamic recovery. In the β region deformation, the power dissipation rate reached 48% in the range of 0.01–0.1 s−1 and temperature range of 1010–1040 °C, and the deformation mechanism involved dynamic recovery and dynamic recrystallization.

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Elasto-thermoviscoplastic finite element analyses of cold upsetting and forging processes of S25C steel with dynamic strain aging considered

Journal of Physics Conference Series ◽

10.1088/1742-6596/2047/1/012001 ◽

2021 ◽

Vol 2047 (1) ◽

pp. 012001

Author(s):

S M Ji ◽

M K Razali ◽

K H Lee ◽

W J Chung ◽

M S Joun

Keyword(s):

Finite Element ◽

Flow Stress ◽

Dynamic Strain Aging ◽

Strain Aging ◽

Large Strain ◽

Flow Behavior ◽

Cold Forging ◽

Dynamic Strain ◽

Strain Effect ◽

Strain And Strain Rate

Abstract A practical methodology is presented to characterize the thermoviscoplastic flow stress at larger strain over the temperature range of cold metal forming using tensile and compression tests. Its importance is emphasized for non-isothermal finite element (FE) analysis of automatic multi-stage cold forging (AMSCF) process where maximum strain and strain rate exceed around 3.0 and 200/s, respectively. The experimental compressive flow stress is first characterized using traditional bilinear C-m model with high accuracy. It is employed for describing the closed-form function model to extrapolate the experimental flow stress over the experimentally uncovered ranges of state variables. The strain effect on the flow stress is then improved using the experimental tensile flow stress accurately calculated at large strain and room temperature. A complicated flow behavior of S25C characterized by its dynamic strain aging features is expressed by the presented methodology, which is utilized to analyze the test upsetting and AMSCF processes by the elasto-thermoviscoplastic finite element method for revealing the effects of flow stresses on the process.

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

High Temperature Materials and Processes ◽

10.1515/htmp-2017-0145 ◽

2019 ◽

Vol 38 (2019) ◽

pp. 168-177 ◽

Cited By ~ 1

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.

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