Strain-compensated Arrhenius Model Research Articles

Hot deformation behavior and microstructure evolution of TC11 dual-phase titanium alloy

Thermomechanical processing is one of the major steps in the fabrication of structural components used in various engineering applications. The thermomechanical coupling effect of temperature and strain rate has a significant impact on the stress-strain thermal deformation behavior of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si (TC11) alloy. Here, the hot deformation behavior of TC11 dual-phase alloy has been comprehensively investigated by the hot compression tests with deformation temperatures ranging from 870 °C to 960 °C and strain rates of 0.01 s−1 to 1 s−1. Based on the flow stress curves and Arrhenius-type constitutive equation, a strain compensated Arrhenius model for TC11 alloy was successfully developed, achieving rapid and accurate prediction of high-temperature flow stress. By studying the deformed microstructure characteristics of materials under various deformation conditions, the role of deformation temperatures and strain rates was fully discussed in microstructure evolution, including the primary α phase (αp) and lamellar (αs). The thin-long lamellar shape αs can be obtained at a higher strain rate and deformation temperature. The predominance of single-peaked stress features in most flow curves, along with EBSD characterization results, indicates that continuous dynamic recrystallization (DRX) is the primary softening mechanism under different deformation conditions. This work supports the rapid prediction of flow stress and the relationship between process parameters and microstructural evolution to expedite the design optimization of plastic deformation process parameters and the development of advanced TC11 titanium alloy with targeted microstructures.

BPANN modified constitutive descriptions for flow behavior and softening mechanism in the α+β phase region of Ti-55511 alloy with equiaxed microstructure

The deformation behavior of Ti-55511 alloy was investigated by hot compression tests conducted at deformation temperatures of 993∼1113 K and strain rates of 0.001–1 s−1. To eliminate the effects of friction and adiabatic temperature rise on the flow stresses, the flow curves were corrected. Subsequently, a strain compensated Arrhenius (SCA) model was developed and further modified using the back propagation artificial neural network (BPANN) method. The modified model exhibits significant improvements compared to the SCA model. The average absolute relative error (AARE) decreases from 4.895 % to 0.756 %, while the relative error (δ) range decreases from −14.75 %–17.99 % to −4.78 %–8.01 %. Moreover, cross-validation also confirms the modified model has higher generalization ability and prediction accuracy than the SCA model. Microstructural characterization reveals dynamic recrystallization (DRX) of the α phase and dynamic recovery (DRV) of the β phase are the main mechanisms responsible for softening, and their volume fractions increase with decreasing strain rate and increasing deformation temperature. The equiaxed α phase undergoes elongation first, followed by gradual migration and transformation of grain boundaries. Finally, the β phase wedges into the α phase until the α phase separates. The continuous dynamic recrystallization (CDRX) of β phase accompanies its DRV, which is mainly characterised by progressive sub-grain rotation. The α grains aggregated by dislocations promote CDRX of the β phase.

Hot Deformation Behavior and Microstructural Evolution of the As-rolled 7050Al Alloy

The hot deformation behavior of the as-rolled 7050 aluminum alloy was investigated using isothermal hot compression experiments with temperatures ranging from 300 to 460 °C and strain rates ranging from 0.001 to 1 s−1, up to a total strain of 1.1. A strain-compensated Arrhenius (SCA) model was established based on the experimental flow stress data. The predictive accuracy of the model was numerically evaluated using the Correlation Coefficients (R) and the Average Absolute Relative Error (AARE). Electron backscatter diffraction (EBSD) was used to characterize the effects of strain rate and compressive temperature on the microstructure evolution and recrystallization behavior. The results indicated that the geometric dynamic recrystallization (GDRX) occurred at high strain rates or low temperatures, while continuous dynamic recrystallization (CDRX) became the dominant recrystallization mechanism with increasing deformation temperature and decreasing strain rate. The work hardening effect was enhanced during the later stage of deformation, and discontinuous dynamic recrystallization (DDRX) became the main recrystallization mechanism.

Studies on flow stress behaviour prediction of AZ31B alloy: Microstructural evolution and fracture mechanism

The hot tensile flow behaviour of the AZ31B alloy is investigated at various varying deformation temperatures (200–350 °C) and strain rates (0.1s−1, 0.01s−1, and 0.001s−1). The deformation condition significantly influenced the mechanical properties and microstructural evolution. Observation from the tensile tests indicated a strong dependence of flow stress on deformation temperature and strain rates. At a constant strain rate, flow stress decreased as the temperature increased, while at a constant deformation temperature, flow stress decreased with decreasing strain rates. The strain rate sensitivity varies from 0.01 to 0.25, suggesting a diffusion-controlled dislocation climb mechanism. Dynamic recrystallization (DRX) initiation was observed at 250 °C and a strain rate of 0.001s−1, characterized by the formation of necklace-type grains with low pole intensity. Predominantly, the DRX softening mechanism, including continuous dynamic recrystallization (CDRX) and discontinuous dynamic recrystallization (DDRX), was observed at 350 °C and 300 °C for a strain rate of 0.001s−1. Fracture morphology analysis of the tested samples indicated a micro-void coalescence mechanism. Equiaxed dimples were found at 350 °C and a strain rate of 0.001s−1, while oval-shaped dimples were observed at 300 °C and 0.1s−1. A strain-compensated Arrhenius model was incorporated to estimate the flow stress prediction for hardening and softening regions. Statistical parameters such as the average absolute relative error (AARE = 13.50) and coefficient of determination (R = 0.97) were calculated. Good agreement between experimental and prediction stresses was achieved at a 0.001s−1 strain rate for all deformation temperatures.

Investigating the effects of deformation-induced densification on the constitutive behavior and corrosion resistance of Al–Zn–Mg powder metallurgy alloy during hot deformation

The electrochemical behavior is most strongly influenced by deformation, which may either accelerate or decelerate failure during service. Therefore, in the present study, the Al–5.6Zn–2Mg alloy fabricated by powder metallurgy was subjected to hot deformation at various temperatures (300–500 °C) and strain rates (0.5–0.005 s−1) on a hydraulic press, and then, the effect of deformation-induced densification on corrosion behavior was studied using electrochemical corrosion tests. Flow stress is mathematically modeled using the strain-compensated Arrhenius model. The model developed was reliable to predict, with an average absolute relative error (AARE) of 3.16% and an R2 value of 0.98. The potentiodynamic polarization results showed that as the degree of porosity in a sintered sample is reduced, there was a decrease in the corrosion current density and an increase in the pitting potential. Al–5.6Zn–2Mg corrosion resistance significantly improved with deformation temperature, whereas strain rates decrease it, due to a decrease in pore content. Icorr of 2.4982 µA/cm2 and Epit of 0.876 V have been found for the highly deformed preforms under 500 °C and 0.005 s−1 strain rate condition. EIS results showed a high contact resistance of 2659 Ohm·cm2 and high hardness value of 113.12 Hv for the preform deformed under 500 °C and 0.005 s−1 strain rate. The reduction in porosity, decrease in active surface area after the deformation process, densification behavior, and hardness are all related to the electrochemical behavior. Pitting corrosion was observed in deformed preforms as a corrosion mechanism; the dynamic recovery feature is observed from the flow behavior.

Hot Deformation Behavior and Processing Maps of Pure Copper during Isothermal Compression.

In this study, pure copper's hot deformation behavior was studied through isothermal compression tests at deformation temperatures of 350~750 °C with strain rates of 0.01~5 s-1 on a Gleeble-3500 isothermal simulator. Metallographic observation and microhardness measurement were carried out of the hot compressed specimens. By analyzing the true stress-strain curves of pure copper under various deformation conditions during the hot deformation process, the constitutive equation was established based on the strain-compensated Arrhenius model. On the basis of the dynamic material model proposed by Prasad, the hot-processing maps were acquired under different strains. Meanwhile, the effect of deformation temperature and strain rate on the microstructure characteristics was studied by observing the hot-compressed microstructure. The results demonstrate that the flow stress of pure copper has positive strain rate sensitivity and negative temperature correlation. The average hardness value of pure copper has no obvious change trend with the strain rate. The flow stress can be predicted with excellent accuracy via the Arrhenius model based on strain compensation. The suitable deforming process parameters for pure copper were determined to be at a deformation temperature range of 700~750 °C and strain rate range of 0.1~1 s-1.

Hot deformation and constitutive model of as-cast Ni–Cr–Co nickel-base alloy

Abstract Nickel-based superalloys are widely used in thermal power, nuclear power, aerospace and other fields due to their excellent properties. Since the deformation resistance of Ni–Cr–Co superalloy is large and the forming range is narrow, the hot deformation behavior of Ni–Cr–Co superalloy was studied by hot compression experiments on a Gleeble-3800 under different deformation conditions (deformation temperature: 950–1200 °C, strain rate: 0.01–10 s−1, and deformation: 60 %). The modified Johnson–Cook, modified Zerilli–Armstrong and strain compensated Arrhenius models were constructed based on the stress–strain curves corrected for friction and temperature. The correlation coefficient (R) and average absolute relative error (AARE) were compared to verify the accuracy of the model. The results showed that the strain compensated Arrhenius model had high accuracy, the modified Zerilli–Armstrong had high accuracy in predicting the flow behavior above 1100 °C, while the modified Johnson cook had high accuracy only under the reference conditions. Electron back-scattered diffraction analysis showed that high-angle grain boundaries formed when the low-angle grain boundaries piled up to a certain extent, which is beneficial for refining the as-cast microstructure, and the increase in strain rate was beneficial for refining the microstructure and promoting the occurrence of recrystallization.

A Comparative Study of Three Constitutive Models concerning Thermo-Mechanical Behavior of Q345 Steel during Hot Deformation

The Gleeble-3800 thermal simulator was used to perform hot compression experiments on Q345 steel at a temperature of 1123~1373 K, a strain rate of 0.01~10 s−1, and 60% deformation. Analysis of the flow curves of Q345 steel revealed that flow stress decreases with the increase of deformation temperature and decrease of strain rate. According to the stress–strain curve of Q345 steel, three constitutive models of Johnson–Cook, Modified Johnson–Cook and strain-compensated Arrhenius were established. By comparison, it was found that the strain-compensated Arrhenius model has higher accuracy, and its correlation coefficient and average relative error are 0.995 and 4.93%, respectively. In addition, the thermal processing map of Q345 steel was established, and the optimal processing range was temperature 1253–1373 K, strain rate 0.5–10 s−1.

Comparison of Modified Johnson–Cook Model and Strain–Compensated Arrhenius Constitutive Model for 5CrNiMoV Steel during Compression around Austenitic Temperature

Isothermal compression behaviors of 5CrNiMoV steel were studied at temperatures of 870, 800, 750, and 700 °C, with strain rates of 0.001, 0.005, 0.01, 0.05, and 0.1 s−1, the compression temperatures 870 and 800 °C are above Ac3, as well as 750 and 700 °C below Ac3 temperature. The Modified Johnson–Cook (MJC) model and the Strain–Compensated Arrhenius (SCA) model were employed to demonstrate the relationship between the flow stress and the compression parameters. The correlation coefficient (R) and average absolute relative error (AARE) between the calculational and experimental flow stress were used to evaluate the accuracy of the two models. The results show that the effect of dynamic softening on flow stress is much more significant at higher temperatures and lower strain rates, while this effect is not obvious when the strain rate exceeds 0.005 s−1 with the temperature below Ac3. The MJC model has a good accuracy close to the reference conditions (0.001 s−1 and 700 °C), and it is suitable to predict the plastic behavior when the flow stress is lower than 200 Mpa. The unbiased AARE values were 6.82 and 5.71 for MJC model and SCA model, respectively, which implied the SCA model has a higher accuracy than the MJC model. The SCA model was believed to be capable of being used to illustrate the thermomechanical behavior of 5CrNiMoV tool steel in a wide range of plastic deformation conditions.

A modified Arrhenius constitutive model of 2219-O aluminum alloy based on hot compression with simulation verification

A precise constitutive equation is essential to accurately describe the flow behavior of aluminum alloy in numerical simulation of hot-forming process. In this study, the hot compression tests were conducted by Gleeble-3500 thermal-mechanical simulator, and flow stress data of 2219-O aluminum alloy at temperature of 523–763 K and strain rate of 0.01–25 s−1 were obtained. Based on the corrections of the original flow stresses data with the consideration of interfacial friction and specimen temperature variation, Arrhenius constitutive models with four different forms were established and their prediction accuracy was evaluated. Although the strain compensated Arrhenius model can achieve the highest accuracy, its expression is very complex. Hence, a newly modified constitutive model of 2219-O Al alloy with a simpler function structure was proposed to accurately predict the evolution behavior of flow stress with strain effect included. In order to compare the calculation of the founded model with the other models, a finite element model of the hot compression process by integrating with the aforementioned equations was established. The simulated flow stress evolution based on both newly modified model and strain compensated model showed an excellent agreement with the experimental data. The newly founded constitutive model of 2219-O Al alloy show its advantages in applications because of its structural simplicity.

Comparison of Constitutive Models and Microstructure Evolution of GW103K Magnesium Alloy during Hot Deformation.

The characteristics of constitutive behavior and microstructure evolution of GW103K magnesium alloy were investigated via hot compression tests at a strain rate of 0.001–1 s−1 and a temperature of 623–773 K. The rheological stress of GW103K alloy decreased with increasing temperature or decreasing strain rate during hot deformation. Three models including the Johnson Cook (JC) model, the strain-compensated Arrhenius (SCA) model and back-propagation neural networks (BPNN) were applied to describe the constitutive relationships. Subsequently, the predictability and precision of the models were compared by evaluating the correlation coefficient (R), root mean square errors (RMSE), and relative errors (RE). Compared with the JC and SCA models, the BPNN model was more efficient and had higher prediction accuracy in describing flow stress behavior. Furthermore, EBSD maps confirmed that magnesium alloy easily causes dynamic recrystallization (DRX) during hot deformation. The volume fraction and size of DRX grains increased with decreasing strain rate and/or increasing temperature.

Flow behavior and microstructure evolution of Al-3.65Cu-0.98Li (wt%) alloy during hot deformation

The phenomenological constitutive model, processing map and microstructure evolution of Al-3.65Cu-0.98Li (wt%) alloy were studied by means of isothermal compression tests conducted on a Gleeble-3500 isothermal simulator in the temperature range of 350 °C−500 °C and strain rate range of 0.01 s−1–10 s−1 and EBSD. The strain compensated Arrhenius model describes the flow curves accurately with a relative error of 0.9898 and an average absolute relative error of 4.70%. The plastic capability was characterized by strain rate sensitivity index, and it has the positive relation with temperature and negative relation with strain rate. The processing map was constructed, the instable deformation window and optimal hot working window of this alloy was identified to be 350 ∼ 455 °C & 0.37 ∼ 10s−1 and 440 ∼ 500 °C & 0.01 ∼ 0.368s−1, respectively. Moreover, the dynamic recrystallization occurs more violently at lower strain rate, and most portion were transformed into substructure with increasing strain rate, which was nearly vanished at the strain rate of 10 s−1. The geometric necessary dislocation distributions under different temperatures and strain rates were analyzed. More uniform distributed dislocation cell structures were observed at high temperature with low strain rate conditions and intensive dislocation and more pileups occurs at the contrary conditions.

Prediction of Flow Stress of Annealed 7075 Al Alloy in Hot Deformation Using Strain-Compensated Arrhenius and Neural Network Models.

Hot compression experiments of annealed 7075 Al alloy were performed on TA DIL805D at different temperatures (733, 693, 653, 613 and 573 K) with different strain rates (1.0, 0.1, 0.01 and 0.001 s−1.) Based on experimental data, the strain-compensated Arrhenius model (SCAM) and the back-propagation artificial neural network model (BP-ANN) were constructed for the prediction of the flow stress. The predictive power of the two models was estimated by residual analysis, correlation coefficient (R) and average absolute relative error (AARE). The results reveal that the deformation parameters including strain, strain rate, and temperature have a significant effect on the flow stress of the alloy. Compared with the SCAM model, the flow stress predicted by the BP-ANN model is in better agreement with experimental values. For the BP-ANN model, the maximum residual is only 1 MPa, while it is as high as 8 MPa for the SCAM model. The R and AARE for the SCAM model are 0.9967 and 3.26%, while their values for the BP-ANN model are 0.99998 and 0.18%, respectively. All these reflect that the BP-ANN model has more accurate prediction ability than the SCAM model, which can be applied to predict the flow stress of the alloy under high temperature deformation.

The Comprehensive Study on the Classical Constitutive Models in Predicting the Hot Deformation Behavior of Al5083-SiC Metal Matrix Composite

The main goal of this research is to study the hot deformation process of metal-matrix composites and investigate the possibility of using classical constitutive models to calculate the flow stress of such composites during the hot deformation process. A 5083 aluminum-based metal composite reinforced with 9 wt.% of 37 micron SiC particles, and made by stir-casting method, was used for the study. Standard and improved Johnson-Cook model, Arrhenius and Zerilli-Armstrong models in the temperature range of 673-823 K, and strain rates of 0.001-1 s-1 were extracted and their accuracy was studied. Based on the results, classical models used to predict the hot deformation behavior of metal alloys can also be used to predict the behavior of aluminum-matrix composites with reasonable accuracy depending on the type of model. The hot deformation activation energy Q for the composite based on the hyperbolic-sine law Arrhenius equation, is 265.5 kJ/mol. The strain-compensated Arrhenius model was the best model to predict the behavior of the composite with the error less than 7% and can reasonably predict the trend of changing the flow stress even at high temperatures with the correlation factor of 0.989.

Comparison of flow behaviors of near beta Ti-55511 alloy during hot compression based on SCA and BPANN models

The flow behavior of Ti-55511 alloy was studied by hot compression tests at temperatures of 973−1123 K and strain rates of 0.01−10 s−1. Strain-compensated Arrhenius (SCA) and back-propagation artificial neural network (BPANN) methods were selected to model the constitutive relationship, and the models were further evaluated by statistical analysis and cross-validation. The stress−strain data extended by two models were implanted into finite element to simulate hot compression test. The results indicate that the flow stress is sensitive to deformation temperature and strain rate, and increases with increasing strain rate and decreasing temperature. Both the SCA model fitted by quintic polynomial and the BPANN model with 12 neurons can describe the flow behaviors, but the fitting accuracy of BPANN is higher than that of SCA. Sixteen cross-validation tests also confirm that the BPANN model has high prediction accuracy. Both models are effective and feasible in simulation, but BPANN model is superior in accuracy.

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

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.

Phenomenological Constitutive Models for Hot Deformation Behavior of Ti6Al4V Alloy Manufactured by Directed Energy Deposition Laser

This work focuses on the hot deformation behavior and constitutive models of Ti6Al4V alloy manufactured by directed energy deposition laser (DEDL). The hot compression tests of DEDL Ti6Al4V alloy at deformation temperature of 700–950 °C and strain rate range of 0.001–1 s−1 were carried out. Three phenomenological models including modified Johnson–Cook model, modified Fields–Backofen model, and strain-compensated Arrhenius model were introduced to predict the flow stresses during uniaxial compression. The predictability of the three models is evaluated according to correlation coefficient, average absolute relative error, and average root mean square error. Traditional linear regression method (TLRM) and nonlinear regression analysis (NRA) were used to solve the constants of modified Johnson–Cook model and strain-compensated Arrhenius model, NRA was used to solve the constants of modified Fields–Backofen model. Compared with the TLRM, the NRA improves the accuracy of modified Johnson-Cook model, while has limited effect on that of strain-compensated Arrhenius model. The accuracy of modified Fields–Backofen model and strain-compensated Arrhenius model is higher than that of modified Johnson–Cook model.

Kinetic analysis and strain-compensated constitutive models of Ti-42.9Al-4.6Nb–2Cr during isothermal compression

The hot deformation behavior of Ti-42.9Al-4.6Nb–2Cr (at. %) was investigated by isothermal compression tests at the deformation temperature range of 1373–1573 K, strain rate range of 0.001–1.0 s−1, up to the strain of 0.69. The flow stress test results of Ti-42.9Al-4.6Nb–2Cr showed negative temperature and positive strain rate sensitivity. Besides, strain had a great effect on the hot deformation behavior of Ti-42.9Al-4.6Nb–2Cr. Kinetic analysis was adopted to assess the hot workability of Ti-42.9Al-4.6Nb–2Cr via apparent activation energy (Q) of hot deformation, strain-rate sensitivity index (m) and strain hardening index (n). The Q value varied from 607.1 ± 0.7 kJ·mol−1 to 512.6 ± 10.8 kJ mol−1 with the increasing of strain from 0.1 to 0.6. The effect of strain on the Q value at the deformation temperatures below 1473 K was mainly related to dynamic recrystallization of γ phase and kinking of γ lamellae, while the Q value at the deformation temperature above 1473 K might be linked to γ→α phase transformation and DRV of α phase. Based on the kinetic analysis, strain-compensated Arrhenius model and Hensel-Spittel model were successfully established to predict the hot workability (flow stress). Average absolute relative errors of established strain-compensated Arrhenius model and Hensel-Spittel model were 7.52% and 11.95%, respectively. Moreover, both established constitutive models can be extrapolated for predicting the flow stress of Ti-42.9Al-4.6Nb–2Cr to larger strain levels.

A comparative study at the flow behavior description of 2A14 alloy using BP-ANN and strain compensated Arrhenius model

In this work, a back-propagation artificial neural network (BP-ANN) and Arrhenius constitutive model were used to predict the stress-strain curves of 2A14 aluminum alloy based on the results of isothermal compression tests conducted at the temperature of 648 K–723 K and the strain rate of 0.01 −10 A series of statistical analyses were introduced to compare the accuracy of predictions of the two models. The average absolute relative error (AARE) , correlation coefficient (R) , relative error and standard deviation were 0.4338%, 0.9997, 0.2384, 0.0242 by BP-ANN model and 3.06%, 0.9941, 1.7993, 2.6610 by Arrhenius constitutive model, respectively, which indicates that the trained BP-ANN model is more precise than the Arrhenius constitutive model. Then the finite element simulations were conducted under the same deformation conditions on the basis of the pure experimental results and pure BP-ANN predicted results. As a result, the stroke load curve and the distributions of the effective strain are similar, which further proves that the BP-ANN model have a good capability to predict the flow behavior of 2A14 alloy.

Research on several constitutive models to predict the flow behaviour of GCr15 continuous casting bloom with heavy reduction

In this work, the modified Johnson-Cook (J-C) model was developed. The predictive abilities of the JC model, new modified JC model, modified Zerilli-Armstrong (ZA) model, and strain-compensated Arrhenius model of the flow behaviour of GCr15 continuous casting bloom with heavy reduction (HR) were compared. The deformation mechanism was explored. Experimental stress-strain data from single-pass thermo-simulation compression experiments over a wide range of temperatures (1023–1573 K), strains (0.05–0.7) and strain rates (0.001–0.1 s−1) were applied to deduce the material parameters of these constitutive models. The applicability of the models was analysed by calculating the correlation coefficient; the average relative error (AARE) of the model; and the number of model parameters, which represents the computation time of each model. The experimental results showed that the new modified JC model was more suitable for describing the flow behaviour of GCr15 continuous casting bloom with HR because of its convenient calculation and better accuracy.