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

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.

Download Full-text

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

Materials ◽

10.3390/ma13153424 ◽

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.

Download Full-text

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.

Download Full-text

Phenomenological Models to Predict the Flow Stress up to the Peak of as-Extruded 7050 Aluminum Alloy

High Temperature Materials and Processes ◽

10.1515/htmp-2016-0094 ◽

2017 ◽

Vol 36 (10) ◽

pp. 1025-1033

Author(s):

Yu-Feng Xia ◽

Jia Zhao ◽

Lai Jiang ◽

Shuai Long ◽

Tian-yu Wang

Keyword(s):

Aluminum Alloy ◽

Flow Stress ◽

Phenomenological Models ◽

Linear Model ◽

Nonlinear Model ◽

Peak Stress ◽

Compression Tests ◽

Absolute Relative Error ◽

Average Absolute Relative Error ◽

7050 Aluminum Alloy

AbstractIn order to improve the understanding of the hot flow behaviors of as-extruded 7050 aluminum alloy, a series of isothermal compression tests with a fixed height reduction of 60 % were performed at the temperatures of 573 K, 623 K, 673 K and 723 K, and the strain rates of 0.01 s−1, 0.1 s−1, 1 s−1 and 10 s−1 on a Gleeble-1500 thermo-mechanical simulator. Based on both nonlinear and linear estimations of work hardening rate versus strain curves, two phenomenological models have been developed to predict the flow stress values under different hot forming conditions up to the peak stress. The suitability levels of these two models were evaluated by comparing both the correlation coefficient (R) and the average absolute relative error (AARE). R-value and AARE-value for the linear phenomenological model are 0.9995 and 2.18 %, respectively, while the R-value and AARE-value for the nonlinear model are 0.9901 and 10.60 %, respectively. The results showed that the predictions of these two models were in good agreement with the experimental data for 7050 aluminum alloy. Fewer materials constants were involved in the linear model, and the predicting ability of the linear model is stronger than the nonlinear model.

Download Full-text

Constitutive Equations for 6061 Aluminum Alloy at Elevated Temperature

Materials Science Forum ◽

10.4028/www.scientific.net/msf.898.387 ◽

2017 ◽

Vol 898 ◽

pp. 387-391

Author(s):

Zhi Shen

Keyword(s):

Aluminum Alloy ◽

Flow Stress ◽

Constitutive Equations ◽

Type Equation ◽

High Temperature Deformation ◽

Temperature Deformation ◽

Compression Tests ◽

Stress Strain ◽

6061 Aluminum Alloy ◽

Gleeble 3500

Isothermal compression tests were conducted on 6061 aluminum alloy using a Gleeble-3500 thermal simulator under constant strain rates and at deformation temperatures ranging from 623 to 773K, up to a 60% height reduction of the sample. The high temperature deformation behavior of 6061 aluminum alloy was characterized based on an analysis of the stress-strain curves. A set of constitutive equations for 6061 aluminum alloy were proposed by employing an Arrhenius-type equation. Material constants, A, n and activation energy Q were found to be functions of strain. The equations revealed the dependence of flow stress on strain, strain rate and temperature. In order to evaluate the accuracy of the deformation constitutive equations, the mean errors of flow stress between the experimental data and predicted results were plotted. The results showed that the predicted data agreed well with the experimental stress-strain curves.

Download Full-text

Constitutive Modeling of the Flow Stress Behavior for the Hot Deformation of Cu-15Ni-8Sn Alloys

Frontiers in Materials ◽

10.3389/fmats.2020.577867 ◽

2020 ◽

Vol 7 ◽

Author(s):

Dongxin Niu ◽

Chao Zhao ◽

Daoxi Li ◽

Zhi Wang ◽

Zongqiang Luo ◽

...

Keyword(s):

Flow Stress ◽

Relative Error ◽

Hot Deformation ◽

Hot Extrusion ◽

Compression Tests ◽

Arrhenius Model ◽

Stress Behavior ◽

Flow Stress Behavior ◽

Average Absolute Relative Error ◽

Jc Model

Three constitutive models, strain-compensated Arrhenius model, modified Johnson–Cook (JC) model, and modified Zerilli–Armstrong (ZA) model, were established for the hot-deformed Cu-15Ni-8Sn alloy based on hot compression tests. By introducing average absolute relative error (AARE), correlation coefficient (R), and relative error, the prediction accuracy of these three models was assessed. The results indicate that strain-compensated Arrhenius model has the highest accuracy at describing the flow stress behavior of the studied alloy, followed by modified JC model and modified ZA model. Moreover, the strain-compensated Arrhenius model established in this work has a great practicability in the hot-extrusion simulation of Cu-15Ni-8Sn alloys. This article provides a theoretical basis for optimizing hot deformation parameters in industrial production of the Cu-15Ni-8Sn alloys.

Download Full-text

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.

Download Full-text

An Improved CO2-Crude Oil Minimum Miscibility Pressure Correlation

Journal of Chemistry ◽

10.1155/2015/175940 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 9

Author(s):

Hao Zhang ◽

Dali Hou ◽

Kai Li

Keyword(s):

Experimental Data ◽

Crude Oil ◽

Relative Error ◽

Oil And Gas ◽

Empirical Correlation ◽

Volatile Components ◽

Absolute Relative Error ◽

Minimum Miscibility Pressure ◽

New Correlation ◽

Average Absolute Relative Error

Minimum miscibility pressure (MMP), which plays an important role in miscible flooding, is a key parameter in determining whether crude oil and gas are completely miscible. On the basis of 210 groups of CO2-crude oil system minimum miscibility pressure data, an improved CO2-crude oil system minimum miscibility pressure correlation was built by modified conjugate gradient method and global optimizing method. The new correlation is a uniform empirical correlation to calculate the MMP for both thin oil and heavy oil and is expressed as a function of reservoir temperature, C7+molecular weight of crude oil, and mole fractions of volatile components (CH4and N2) and intermediate components (CO2, H2S, and C2~C6) of crude oil. Compared to the eleven most popular and relatively high-accuracy CO2-oil system MMP correlations in the previous literature by other nine groups of CO2-oil MMP experimental data, which have not been used to develop the new correlation, it is found that the new empirical correlation provides the best reproduction of the nine groups of CO2-oil MMP experimental data with a percentage average absolute relative error (%AARE) of 8% and a percentage maximum absolute relative error (%MARE) of 21%, respectively.

Download Full-text

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.

Download Full-text

A Comparative Study on Johnson–Cook, Modified Johnson–Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict Hot Deformation Behavior of TA2

High Temperature Materials and Processes ◽

10.1515/htmp-2019-0026 ◽

2019 ◽

Vol 38 (2019) ◽

pp. 699-714 ◽

Cited By ~ 2

Author(s):

Bing Zhang ◽

Xiaodi Shang ◽

Su Yao ◽

Qiuyu Wang ◽

Zhijuan Zhang ◽

...

Keyword(s):

Deformation Behavior ◽

Flow Behavior ◽

True Strain ◽

Constitutive Models ◽

Type Model ◽

Compression Tests ◽

Absolute Relative Error ◽

Average Absolute Relative Error ◽

Wide Range ◽

Jc Model

AbstractThe true strain data and true stress data are obtained from the isothermal compression tests under a wide range of strain rates (0.1–20 s−1) and temperatures (933–1,133 K) over the Gleeble-3500 thermomechanical simulator. The data are employed to generate the constitutive equations according to four constitutive models, respectively, the strain-compensated Arrhenius-type model, the modified Zerilli–Armstrong (ZA) model, the modified Johnson–Cook (JC) model and the JC model. In the meanwhile, a comparative research was made over the capacities of these four models and hence to represent the elevated temperature flow behavior of TA2. Besides, a comparison of the accuracy of the predictions of average absolute relative error, correlation coefficient (R) and the deformation behavior was made to test the sustainability level of these four models. It is shown from these results that the JC model is not suitable for the description of flow behavior of TA2 alloy in α+β phase domain, while the predicted values of modified JC model, modified ZA model and the strain-compensated Arrhenius-type model could be consistent well with the experimental values except under some deformation conditions. Moreover, the strain-compensated Arrhenius-type model can be also used to track the deformation behavior more precisely in comparison with other models.

Download Full-text

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

Materials ◽

10.3390/ma11101985 ◽

2018 ◽

Vol 11 (10) ◽

pp. 1985 ◽

Cited By ~ 4

Author(s):

Jiang Li ◽

Fuguo Li ◽

Jun Cai

Keyword(s):

Titanium Alloy ◽

Flow Stress ◽

Constitutive Equation ◽

Flow Behavior ◽

Strain Effect ◽

Absolute Relative Error ◽

Average Absolute Relative Error ◽

Ta15 Titanium Alloy ◽

Measured Stress ◽

The Impact

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.

Download Full-text